Vector algorithms for geometrically nonlinear 3D finite element analysis
NASA Technical Reports Server (NTRS)
Whitcomb, John D.
1989-01-01
Algorithms for geometrically nonlinear finite element analysis are presented which exploit the vector processing capability of the VPS-32, which is closely related to the CYBER 205. By manipulating vectors (which are long lists of numbers) rather than individual numbers, very high processing speeds are obtained. Long vector lengths are obtained without extensive replication or reordering by storage of intermediate results in strategic patterns at all stages of the computations. Comparisons of execution times with those from programs using either scalar or other vector programming techniques indicate that the algorithms presented are quite efficient.
NASA Astrophysics Data System (ADS)
Uhrig, Matthias P.; Kim, Jin-Yeon; Jacobs, Laurence J.
2016-02-01
This research presents a 3D numerical finite element (FE) model which, previously developed, precisely simulates non-contact, air-coupled measurements of nonlinear Rayleigh wave propagation. The commercial FE-solver ABAQUS is used to perform the simulations. First, frequency dependent pressure wave attenuation is investigated numerically to reconstruct the sound pressure distribution along the active surface of the non-contact receiver. Second, constitutive law and excitation source properties are optimized to match nonlinear ultrasonic experimental data. Finally, the FE-model data are fit with analytical solutions showing a good agreement and thus, indicating the significance of the study performed.
Simulation of 3D tumor cell growth using nonlinear finite element method.
Dong, Shoubing; Yan, Yannan; Tang, Liqun; Meng, Junping; Jiang, Yi
2016-06-01
We propose a novel parallel computing framework for a nonlinear finite element method (FEM)-based cell model and apply it to simulate avascular tumor growth. We derive computation formulas to simplify the simulation and design the basic algorithms. With the increment of the proliferation generations of tumor cells, the FEM elements may become larger and more distorted. Then, we describe a remesh and refinement processing of the distorted or over large finite elements and the parallel implementation based on Message Passing Interface to improve the accuracy and efficiency of the simulation. We demonstrate the feasibility and effectiveness of the FEM model and the parallelization methods in simulations of early tumor growth. PMID:26213205
TACO3D. 3-D Finite Element Heat Transfer Code
Mason, W.E.
1992-03-04
TACO3D is a three-dimensional, finite-element program for heat transfer analysis. An extension of the two-dimensional TACO program, it can perform linear and nonlinear analyses and can be used to solve either transient or steady-state problems. The program accepts time-dependent or temperature-dependent material properties, and materials may be isotropic or orthotropic. A variety of time-dependent and temperature-dependent boundary conditions and loadings are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additional specialized features treat enclosure radiation, bulk nodes, and master/slave internal surface conditions (e.g., contact resistance). Data input via a free-field format is provided. A user subprogram feature allows for any type of functional representation of any independent variable. A profile (bandwidth) minimization option is available. The code is limited to implicit time integration for transient solutions. TACO3D has no general mesh generation capability. Rows of evenly-spaced nodes and rows of sequential elements may be generated, but the program relies on separate mesh generators for complex zoning. TACO3D does not have the ability to calculate view factors internally. Graphical representation of data in the form of time history and spatial plots is provided through links to the POSTACO and GRAPE postprocessor codes.
Whirley, R.G.; Engelmann, B.E.
1993-11-01
This report is the User Manual for the 1993 version of DYNA3D, and also serves as a User Guide. DYNA3D is a nonlinear, explicit, finite element code for analyzing the transient dynamic response of three-dimensional solids and structures. The code is fully vectorized and is available on several computer platforms. DYNA3D includes solid, shell, beam, and truss elements to allow maximum flexibility in modeling physical problems. Many material models are available to represent a wide range of material behavior, including elasticity, plasticity, composites, thermal effects, and rate dependence. In addition, DYNA3D has a sophisticated contact interface capability, including frictional sliding and single surface contact. Rigid materials provide added modeling flexibility. A material model driver with interactive graphics display is incorporated into DYNA3D to permit accurate modeling of complex material response based on experimental data. Along with the DYNA3D Example Problem Manual, this document provides the information necessary to apply DYNA3D to solve a wide range of engineering analysis problems.
Puso, M; Maker, B N; Ferencz, R M; Hallquist, J O
2000-03-24
This report provides the NIKE3D user's manual update summary for changes made from version 3.0.0 April 24, 1995 to version 3.3.6 March 24,2000. The updates are excerpted directly from the code printed output file (hence the Courier font and formatting), are presented in chronological order and delineated by NIKE3D version number. NIKE3D is a fully implicit three-dimensional finite element code for analyzing the finite strain static and dynamic response of inelastic solids, shells, and beams. Spatial discretization is achieved by the use of 8-node solid elements, 2-node truss and beam elements, and 4-node membrane and shell elements. Thirty constitutive models are available for representing a wide range of elastic, plastic, viscous, and thermally dependent material behavior. Contact-impact algorithms permit gaps, frictional sliding, and mesh discontinuities along material interfaces. Several nonlinear solution strategies are available, including Full-, Modified-, and Quasi-Newton methods. The resulting system of simultaneous linear equations is either solved iteratively by an element-by-element method, or directly by a direct factorization method.
3-D Mesh Generation Nonlinear Systems
1994-04-07
INGRID is a general-purpose, three-dimensional mesh generator developed for use with finite element, nonlinear, structural dynamics codes. INGRID generates the large and complex input data files for DYNA3D, NIKE3D, FACET, and TOPAZ3D. One of the greatest advantages of INGRID is that virtually any shape can be described without resorting to wedge elements, tetrahedrons, triangular elements or highly distorted quadrilateral or hexahedral elements. Other capabilities available are in the areas of geometry and graphics. Exact surfacemore » equations and surface intersections considerably improve the ability to deal with accurate models, and a hidden line graphics algorithm is included which is efficient on the most complicated meshes. The primary new capability is associated with the boundary conditions, loads, and material properties required by nonlinear mechanics programs. Commands have been designed for each case to minimize user effort. This is particularly important since special processing is almost always required for each load or boundary condition.« less
3-D Finite Element Heat Transfer
1992-02-01
TOPAZ3D is a three-dimensional implicit finite element computer code for heat transfer analysis. TOPAZ3D can be used to solve for the steady-state or transient temperature field on three-dimensional geometries. Material properties may be temperature-dependent and either isotropic or orthotropic. A variety of time-dependent and temperature-dependent boundary conditions can be specified including temperature, flux, convection, and radiation. By implementing the user subroutine feature, users can model chemical reaction kinetics and allow for any type of functionalmore » representation of boundary conditions and internal heat generation. TOPAZ3D can solve problems of diffuse and specular band radiation in an enclosure coupled with conduction in the material surrounding the enclosure. Additional features include thermal contact resistance across an interface, bulk fluids, phase change, and energy balances.« less
Postprocessing techniques for 3D non-linear structures
NASA Technical Reports Server (NTRS)
Gallagher, Richard S.
1987-01-01
How graphics postprocessing techniques are currently used to examine the results of 3-D nonlinear analyses, some new techniques which take advantage of recent technology, and how these results relate to both the finite element model and its geometric parent are reviewed.
High resolution 3D nonlinear integrated inversion
NASA Astrophysics Data System (ADS)
Li, Yong; Wang, Xuben; Li, Zhirong; Li, Qiong; Li, Zhengwen
2009-06-01
The high resolution 3D nonlinear integrated inversion method is based on nonlinear theory. Under layer control, the log data from several wells (or all wells) in the study area and seismic trace data adjacent to the wells are input to a network with multiple inputs and outputs and are integratedly trained to obtain an adaptive weight function of the entire study area. Integrated nonlinear mapping relationships are built and updated by the lateral and vertical geologic variations of the reservoirs. Therefore, the inversion process and its inversion results can be constrained and controlled and a stable seismic inversion section with high resolution with velocity inversion, impedance inversion, and density inversion sections, can be gained. Good geologic effects have been obtained in model computation tests and real data processing, which verified that this method has high precision, good practicality, and can be used for quantitative reservoir analysis.
Biffle, J.H.
1993-02-01
JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
A finite element solver for 3-D compressible viscous flows
NASA Technical Reports Server (NTRS)
Reddy, K. C.; Reddy, J. N.; Nayani, S.
1990-01-01
Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.
3-D Finite Element Code Postprocessor
1996-07-15
TAURUS is an interactive post-processing application supporting visualization of finite element analysis results on unstructured grids. TAURUS provides the ability to display deformed geometries and contours or fringes of a large number of derived results on meshes consisting of beam, plate, shell, and solid type finite elements. Time history plotting is also available.
3-D Finite Element Analyses of the Egan Cavern Field
Klamerus, E.W.; Ehgartner, B.L.
1999-02-01
Three-dimensional finite element analyses were performed for the two gas-filled storage caverns at the Egan field, Jennings dome, Louisiana. The effects of cavern enlargement on surface subsidence, storage loss, and cavern stability were investigated. The finite element model simulated the leaching of caverns to 6 and 8 billion cubic feet (BCF) and examined their performance at various operating conditions. Operating pressures varied from 0.15 psi/ft to 0.9 psi/ft at the bottom of the lowest cemented casing. The analysis also examined the stability of the web or pillar of salt between the caverns under differential pressure loadings. The 50-year simulations were performed using JAC3D, a three dimensional finite element analysis code for nonlinear quasistatic solids. A damage criterion based on onset of dilatancy was used to evaluate cavern instability. Dilation results from the development of microfractures in salt and, hence, potential increases in permeability onset occurs well before large scale failure. The analyses predicted stable caverns throughout the 50-year period for the range of pressures investigated. Some localized salt damage was predicted near the bottom walls of the caverns if the caverns are operated at minimum pressure for long periods of time. Volumetric cavern closures over time due to creep were moderate to excessive depending on the salt creep properties and operating pressures. However, subsidence above the cavern field was small and should pose no problem, to surface facilities.
Finite sampling corrected 3D noise with confidence intervals.
Haefner, David P; Burks, Stephen D
2015-05-20
When evaluated with a spatially uniform irradiance, an imaging sensor exhibits both spatial and temporal variations, which can be described as a three-dimensional (3D) random process considered as noise. In the 1990s, NVESD engineers developed an approximation to the 3D power spectral density for noise in imaging systems known as 3D noise. The goal was to decompose the 3D noise process into spatial and temporal components identify potential sources of origin. To characterize a sensor in terms of its 3D noise values, a finite number of samples in each of the three dimensions (two spatial, one temporal) were performed. In this correspondence, we developed the full sampling corrected 3D noise measurement and the corresponding confidence bounds. The accuracy of these methods was demonstrated through Monte Carlo simulations. Both the sampling correction as well as the confidence intervals can be applied a posteriori to the classic 3D noise calculation. The Matlab functions associated with this work can be found on the Mathworks file exchange ["Finite sampling corrected 3D noise with confidence intervals," https://www.mathworks.com/matlabcentral/fileexchange/49657-finite-sampling-corrected-3d-noise-with-confidence-intervals.]. PMID:26192530
NASA Astrophysics Data System (ADS)
Popov, Anton; Kaus, Boris
2015-04-01
This software project aims at bringing the 3D lithospheric deformation modeling to a qualitatively different level. Our code LaMEM (Lithosphere and Mantle Evolution Model) is based on the following building blocks: * Massively-parallel data-distributed implementation model based on PETSc library * Light, stable and accurate staggered-grid finite difference spatial discretization * Marker-in-Cell pedictor-corector time discretization with Runge-Kutta 4-th order * Elastic stress rotation algorithm based on the time integration of the vorticity pseudo-vector * Staircase-type internal free surface boundary condition without artificial viscosity contrast * Geodynamically relevant visco-elasto-plastic rheology * Global velocity-pressure-temperature Newton-Raphson nonlinear solver * Local nonlinear solver based on FZERO algorithm * Coupled velocity-pressure geometric multigrid preconditioner with Galerkin coarsening Staggered grid finite difference, being inherently Eulerian and rather complicated discretization method, provides no natural treatment of free surface boundary condition. The solution based on the quasi-viscous sticky-air phase introduces significant viscosity contrasts and spoils the convergence of the iterative solvers. In LaMEM we are currently implementing an approximate stair-case type of the free surface boundary condition which excludes the empty cells and restores the solver convergence. Because of the mutual dependence of the stress and strain-rate tensor components, and their different spatial locations in the grid, there is no straightforward way of implementing the nonlinear rheology. In LaMEM we have developed and implemented an efficient interpolation scheme for the second invariant of the strain-rate tensor, that solves this problem. Scalable efficient linear solvers are the key components of the successful nonlinear problem solution. In LaMEM we have a range of PETSc-based preconditioning techniques that either employ a block factorization of
Advances in 3D electromagnetic finite element modeling
Nelson, E.M.
1997-08-01
Numerous advances in electromagnetic finite element analysis (FEA) have been made in recent years. The maturity of frequency domain and eigenmode calculations, and the growth of time domain applications is briefly reviewed. A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will also be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis is also discussed.
3D unstructured mesh discontinuous finite element hydro
Prasad, M.K.; Kershaw, D.S.; Shaw, M.J.
1995-07-01
The authors present detailed features of the ICF3D hydrodynamics code used for inertial fusion simulations. This code is intended to be a state-of-the-art upgrade of the well-known fluid code, LASNEX. ICF3D employs discontinuous finite elements on a discrete unstructured mesh consisting of a variety of 3D polyhedra including tetrahedra, prisms, and hexahedra. The authors discussed details of how the ROE-averaged second-order convection was applied on the discrete elements, and how the C++ coding interface has helped to simplify implementing the many physics and numerics modules within the code package. The author emphasized the virtues of object-oriented design in large scale projects such as ICF3D.
3D Finite Element Analysis of Particle-Reinforced Aluminum
NASA Technical Reports Server (NTRS)
Shen, H.; Lissenden, C. J.
2002-01-01
Deformation in particle-reinforced aluminum has been simulated using three distinct types of finite element model: a three-dimensional repeating unit cell, a three-dimensional multi-particle model, and two-dimensional multi-particle models. The repeating unit cell model represents a fictitious periodic cubic array of particles. The 3D multi-particle (3D-MP) model represents randomly placed and oriented particles. The 2D generalized plane strain multi-particle models were obtained from planar sections through the 3D-MP model. These models were used to study the tensile macroscopic stress-strain response and the associated stress and strain distributions in an elastoplastic matrix. The results indicate that the 2D model having a particle area fraction equal to the particle representative volume fraction of the 3D models predicted the same macroscopic stress-strain response as the 3D models. However, there are fluctuations in the particle area fraction in a representative volume element. As expected, predictions from 2D models having different particle area fractions do not agree with predictions from 3D models. More importantly, it was found that the microscopic stress and strain distributions from the 2D models do not agree with those from the 3D-MP model. Specifically, the plastic strain distribution predicted by the 2D model is banded along lines inclined at 45 deg from the loading axis while the 3D model prediction is not. Additionally, the triaxial stress and maximum principal stress distributions predicted by 2D and 3D models do not agree. Thus, it appears necessary to use a multi-particle 3D model to accurately predict material responses that depend on local effects, such as strain-to-failure, fracture toughness, and fatigue life.
Finite-difference solutions of the 3-D eikonal equation
Fei, Tong; Fehler, M.C.; Hildebrand, S.T.
1995-12-31
Prestack Kirchhoff depth migration requires the computation of traveltimes from surface source and receiver locations to subsurface image locations. In 3-D problems, computational efficiency becomes important. Finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference method for computing the first arrival traveltime by solving the eikonal equation has been developed in Cartesian coordinates. The method, which is unconditionally stable and computationally efficient, can handle instabilities due to caustics and provide information about head waves. The comparison of finite-difference solutions of the acoustic wave equation with the traveltime solutions from the eikonal equation in various structure models demonstrate that the method developed here can provide correct first arrival traveltime information even in areas of complex velocity structure.
A Nonlinear Modal Aeroelastic Solver for FUN3D
NASA Technical Reports Server (NTRS)
Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.
2016-01-01
A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.
3D Finite Element Trajectory Code with Adaptive Meshing
NASA Astrophysics Data System (ADS)
Ives, Lawrence; Bui, Thuc; Vogler, William; Bauer, Andy; Shephard, Mark; Beal, Mark; Tran, Hien
2004-11-01
Beam Optics Analysis, a new, 3D charged particle program is available and in use for the design of complex, 3D electron guns and charged particle devices. The code reads files directly from most CAD and solid modeling programs, includes an intuitive Graphical User Interface (GUI), and a robust mesh generator that is fully automatic. Complex problems can be set up, and analysis initiated in minutes. The program includes a user-friendly post processor for displaying field and trajectory data using 3D plots and images. The electrostatic solver is based on the standard nodal finite element method. The magnetostatic field solver is based on the vector finite element method and is also called during the trajectory simulation process to solve for self magnetic fields. The user imports the geometry from essentially any commercial CAD program and uses the GUI to assign parameters (voltages, currents, dielectric constant) and designate emitters (including work function, emitter temperature, and number of trajectories). The the mesh is generated automatically and analysis is performed, including mesh adaptation to improve accuracy and optimize computational resources. This presentation will provide information on the basic structure of the code, its operation, and it's capabilities.
Finite element solver for 3-D compressible viscous flows
NASA Technical Reports Server (NTRS)
Reddy, K. C.; Reddy, J. N.
1986-01-01
The space shuttle main engine (SSME) has extremely complex internal flow structure. The geometry of the flow domain is three-dimensional with complicated topology. The flow is compressible, viscous, and turbulent with large gradients in flow quantities and regions of recirculations. The analysis of the flow field in SSME involves several tedious steps. One is the geometrical modeling of the particular zone of the SSME being studied. Accessing the geometry definition, digitalizing it, and developing surface interpolations suitable for an interior grid generator require considerable amount of manual labor. There are several types of grid generators available with some general-purpose finite element programs. An efficient and robust computational scheme for solving 3D Navier-Stokes equations has to be implemented. Post processing software has to be adapted to visualize and analyze the computed 3D flow field. The progress made in a project to develop software for the analysis of the flow is discussed. The technical approach to the development of the finite element scheme and the relaxation procedure are discussed. The three dimensional finite element code for the compressible Navier-Stokes equations is listed.
Higher Order Lagrange Finite Elements In M3D
J. Chen; H.R. Strauss; S.C. Jardin; W. Park; L.E. Sugiyama; G. Fu; J. Breslau
2004-12-17
The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles.
3D finite element simulations of high velocity projectile impact
NASA Astrophysics Data System (ADS)
Ožbolt, Joško; İrhan, Barış; Ruta, Daniela
2015-09-01
An explicit three-dimensional (3D) finite element (FE) code is developed for the simulation of high velocity impact and fragmentation events. The rate sensitive microplane material model, which accounts for large deformations and rate effects, is used as a constitutive law. In the code large deformation frictional contact is treated by forward incremental Lagrange multiplier method. To handle highly distorted and damaged elements the approach based on the element deletion is employed. The code is then used in 3D FE simulations of high velocity projectile impact. The results of the numerical simulations are evaluated and compared with experimental results. It is shown that it realistically predicts failure mode and exit velocities for different geometries of plain concrete slab. Moreover, the importance of some relevant parameters, such as contact friction, rate sensitivity, bulk viscosity and deletion criteria are addressed.
Beam and Truss Finite Element Verification for DYNA3D
Rathbun, H J
2007-07-16
The explicit finite element (FE) software program DYNA3D has been developed at Lawrence Livermore National Laboratory (LLNL) to simulate the dynamic behavior of structures, systems, and components. This report focuses on verification of beam and truss element formulations in DYNA3D. An efficient protocol has been developed to verify the accuracy of these structural elements by generating a set of representative problems for which closed-form quasi-static steady-state analytical reference solutions exist. To provide as complete coverage as practically achievable, problem sets are developed for each beam and truss element formulation (and their variants) in all modes of loading and physical orientation. Analyses with loading in the elastic and elastic-plastic regimes are performed. For elastic loading, the FE results are within 1% of the reference solutions for all cases. For beam element bending and torsion loading in the plastic regime, the response is heavily dependent on the numerical integration rule chosen, with higher refinement yielding greater accuracy (agreement to within 1%). Axial loading in the plastic regime produces accurate results (agreement to within 0.01%) for all integration rules and element formulations. Truss elements are also verified to provide accurate results (within 0.01%) for elastic and elastic-plastic loading. A sample problem to verify beam element response in ParaDyn, the parallel version DYNA3D, is also presented.
3D finite-difference seismic migration with parallel computers
Ober, C.C.; Gjertsen, R.; Minkoff, S.; Womble, D.E.
1998-11-01
The ability to image complex geologies such as salt domes in the Gulf of Mexico and thrusts in mountainous regions is essential for reducing the risk associated with oil exploration. Imaging these structures, however, is computationally expensive as datasets can be terabytes in size. Traditional ray-tracing migration methods cannot handle complex velocity variations commonly found near such salt structures. Instead the authors use the full 3D acoustic wave equation, discretized via a finite difference algorithm. They reduce the cost of solving the apraxial wave equation by a number of numerical techniques including the method of fractional steps and pipelining the tridiagonal solves. The imaging code, Salvo, uses both frequency parallelism (generally 90% efficient) and spatial parallelism (65% efficient). Salvo has been tested on synthetic and real data and produces clear images of the subsurface even beneath complicated salt structures.
3D finite element model for treatment of cleft lip
NASA Astrophysics Data System (ADS)
Jiao, Chun; Hong, Dongming; Lu, Hongbing; Wang, Jianqi; Lin, Qin; Liang, Zhengrong
2009-02-01
Cleft lip is a congenital facial deformity with high occurrence rate in China. Surgical procedure involving Millard or Tennison methods is usually employed for treatment of cleft lip. However, due to the elasticity of the soft tissues and the mechanical interaction between skin and maxillary, the occurrence rate of facial abnormality or dehisce is still high after the surgery, leading to multiple operations of the patient. In this study, a framework of constructing a realistic 3D finite element model (FEM) for the treatment of cleft lip has been established. It consists of two major steps. The first one is the reconstruction of a 3D geometrical model of the cleft lip from scanning CT data. The second step is the build-up of a FEM for cleft lip using the geometric model, where the material property of all the tetrahedrons was calculated from the CT densities directly using an empirical curve. The simulation results demonstrated (1) the deformation procedure of the model step-by-step when forces were applied, (2) the stress distribution inside the model, and (3) the displacement of all elements in the model. With the computer simulation, the minimal force of having the cleft be repaired is predicted, as well as whether a given force sufficient for the treatment of a specific individual. It indicates that the proposed framework could integrate the treatment planning with stress analysis based on a realistic patient model.
3-D dynamic rupture simulations by a finite volume method
NASA Astrophysics Data System (ADS)
Benjemaa, M.; Glinsky-Olivier, N.; Cruz-Atienza, V. M.; Virieux, J.
2009-07-01
Dynamic rupture of a 3-D spontaneous crack of arbitrary shape is investigated using a finite volume (FV) approach. The full domain is decomposed in tetrahedra whereas the surface, on which the rupture takes place, is discretized with triangles that are faces of tetrahedra. First of all, the elastodynamic equations are described into a pseudo-conservative form for an easy application of the FV discretization. Explicit boundary conditions are given using criteria based on the conservation of discrete energy through the crack surface. Using a stress-threshold criterion, these conditions specify fluxes through those triangles that have suffered rupture. On these broken surfaces, stress follows a linear slip-weakening law, although other friction laws can be implemented. For The Problem Version 3 of the dynamic-rupture code verification exercise conducted by the SCEC/USGS, numerical solutions on a planar fault exhibit a very high convergence rate and are in good agreement with the reference one provided by a finite difference (FD) technique. For a non-planar fault of parabolic shape, numerical solutions agree satisfactorily well with those obtained with a semi-analytical boundary integral method in terms of shear stress amplitudes, stopping phases arrival times and stress overshoots. Differences between solutions are attributed to the low-order interpolation of the FV approach, whose results are particularly sensitive to the mesh regularity (structured/unstructured). We expect this method, which is well adapted for multiprocessor parallel computing, to be competitive with others for solving large scale dynamic ruptures scenarios of seismic sources in the near future.
PRONTO3D users` instructions: A transient dynamic code for nonlinear structural analysis
Attaway, S.W.; Mello, F.J.; Heinstein, M.W.; Swegle, J.W.; Ratner, J.A.; Zadoks, R.I.
1998-06-01
This report provides an updated set of users` instructions for PRONTO3D. PRONTO3D is a three-dimensional, transient, solid dynamics code for analyzing large deformations of highly nonlinear materials subjected to extremely high strain rates. This Lagrangian finite element program uses an explicit time integration operator to integrate the equations of motion. Eight-node, uniform strain, hexahedral elements and four-node, quadrilateral, uniform strain shells are used in the finite element formulation. An adaptive time step control algorithm is used to improve stability and performance in plasticity problems. Hourglass distortions can be eliminated without disturbing the finite element solution using either the Flanagan-Belytschko hourglass control scheme or an assumed strain hourglass control scheme. All constitutive models in PRONTO3D are cast in an unrotated configuration defined using the rotation determined from the polar decomposition of the deformation gradient. A robust contact algorithm allows for the impact and interaction of deforming contact surfaces of quite general geometry. The Smooth Particle Hydrodynamics method has been embedded into PRONTO3D using the contact algorithm to couple it with the finite element method.
3D finite element simulation of TIG weld pool
NASA Astrophysics Data System (ADS)
Kong, X.; Asserin, O.; Gounand, S.; Gilles, P.; Bergheau, J. M.; Medale, M.
2012-07-01
The aim of this paper is to propose a three-dimensional weld pool model for the moving gas tungsten arc welding (GTAW) process, in order to understand the main factors that limit the weld quality and improve the productivity, especially with respect to the welding speed. Simulation is a very powerful tool to help in understanding the physical phenomena in the weld process. A 3D finite element model of heat and fluid flow in weld pool considering free surface of the pool and traveling speed has been developed for the GTAW process. Cast3M software is used to compute all the governing equations. The free surface of the weld pool is calculated by minimizing the total surface energy. The combined effects of surface tension gradient, buoyancy force, arc pressure, arc drag force to drive the fluid flow is included in our model. The deformation of the weld pool surface and the welding speed affect fluid flow, heat flow and thus temperature gradients and molten pool dimensions. Welding trials study is presented to compare our numerical results with macrograph of the molten pool.
Finite volume and finite element methods applied to 3D laminar and turbulent channel flows
Louda, Petr; Příhoda, Jaromír; Sváček, Petr; Kozel, Karel
2014-12-10
The work deals with numerical simulations of incompressible flow in channels with rectangular cross section. The rectangular cross section itself leads to development of various secondary flow patterns, where accuracy of simulation is influenced by numerical viscosity of the scheme and by turbulence modeling. In this work some developments of stabilized finite element method are presented. Its results are compared with those of an implicit finite volume method also described, in laminar and turbulent flows. It is shown that numerical viscosity can cause errors of same magnitude as different turbulence models. The finite volume method is also applied to 3D turbulent flow around backward facing step and good agreement with 3D experimental results is obtained.
3D Finite Difference Modelling of Basaltic Region
NASA Astrophysics Data System (ADS)
Engell-Sørensen, L.
2003-04-01
The main purpose of the work was to generate realistic data to be applied for testing of processing and migration tools for basaltic regions. The project is based on the three - dimensional finite difference code (FD), TIGER, made by Sintef. The FD code was optimized (parallelized) by the author, to run on parallel computers. The parallel code enables us to model large-scale realistic geological models and to apply traditional seismic and micro seismic sources. The parallel code uses multiple processors in order to manipulate subsets of large amounts of data simultaneously. The general anisotropic code uses 21 elastic coefficients. Eight independent coefficients are needed as input parameters for the general TI medium. In the FD code, the elastic wave field computation is implemented by a higher order FD solution to the elastic wave equation and the wave fields are computed on a staggered grid, shifted half a node in one or two directions. The geological model is a gridded basalt model, which covers from 24 km to 37 km of a real shot line in horizontal direction and from the water surface to the depth of 3.5 km. The 2frac {1}{2}D model has been constructed using the compound modeling software from Norsk Hydro. The vertical parameter distribution is obtained from observations in two wells. At The depth of between 1100 m to 1500 m, a basalt horizon covers the whole sub surface layers. We have shown that it is possible to simulate a line survey in realistic (3D) geological models in reasonable time by using high performance computers. The author would like to thank Norsk Hydro, Statoil, GEUS, and SINTEF for very helpful discussions and Parallab for being helpful with the new IBM, p690 Regatta system.
An efficient flexible-order model for 3D nonlinear water waves
Engsig-Karup, A.P. Bingham, H.B.; Lindberg, O.
2009-04-01
The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.
Toward high-speed 3D nonlinear soft tissue deformation simulations using Abaqus software.
Idkaidek, Ashraf; Jasiuk, Iwona
2015-12-01
We aim to achieve a fast and accurate three-dimensional (3D) simulation of a porcine liver deformation under a surgical tool pressure using the commercial finite element software Abaqus. The liver geometry is obtained using magnetic resonance imaging, and a nonlinear constitutive law is employed to capture large deformations of the tissue. Effects of implicit versus explicit analysis schemes, element type, and mesh density on computation time are studied. We find that Abaqus explicit and implicit solvers are capable of simulating nonlinear soft tissue deformations accurately using first-order tetrahedral elements in a relatively short time by optimizing the element size. This study provides new insights and guidance on accurate and relatively fast nonlinear soft tissue simulations. Such simulations can provide force feedback during robotic surgery and allow visualization of tissue deformations for surgery planning and training of surgical residents. PMID:26530842
Nonlinear, finite deformation, finite element analysis
NASA Astrophysics Data System (ADS)
Nguyen, Nhung; Waas, Anthony M.
2016-06-01
The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli ( C e ) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated
NASA Astrophysics Data System (ADS)
Krebs, Isabel; Jardin, Stephen C.; Igochine, Valentin; Guenter, Sibylle; Hoelzl, Matthias; ASDEX Upgrade Team
2014-10-01
We study sawtooth reconnection in ASDEX Upgrade tokamak plasmas by means of 3D non-linear two-fluid MHD simulations in toroidal geometry using the high-order finite element code M3D-C1. Parameters and equilibrium of the simulations are based on typical sawtoothing ASDEX Upgrade discharges. The simulation results are compared to features of the experimental observations such as the sawtooth crash time and frequency, the evolution of the safety factor profile and the 3D evolution of the temperature. 2D ECE imaging measurements during sawtooth crashes in ASDEX Upgrade indicate that the heat is transported out of the core through a narrow poloidally localized region. We investigate if incomplete sawtooth reconnection can be seen in the simulations which is suggested by soft X-ray tomography measurements in ASDEX Upgrade showing that an (m = 1, n = 1) perturbation is typically observed to survive the sawtooth crash and approximately maintain its radial position.
NASA Astrophysics Data System (ADS)
Li, Dian-Sen; Fang, Dai-Ning; Lu, Zi-Xing; Yang, Zhen-Yu; Jiang, Nan
2010-08-01
In the first part of the work, we have established a new parameterized three-dimensional (3D) finite element model (FEM) which precisely simulated the spatial configuration of the braiding yarns and considered the cross-section deformation as well as the surface contact relationship between the yarns. This paper presents a prediction of the effective elastic properties and the meso-scale mechanical response of 3D braided composites to verify the validation of the FEM. The effects of the braiding parameters on the mechanical properties are investigated in detail. By analyzing the deformation and stress nephogram of the model, a reasonable overall stress field is provided and the results well support the strength prediction. The results indicate it is convenient to predict all the elastic constants of 3D braided composites with different parameters simultaneously using the FEM. Moreover, the FEM can successfully predict the meso-scale mechanical response of 3D braided composites containing periodical structures.
NASA Astrophysics Data System (ADS)
Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong
2013-02-01
A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.
Nonlinear electrodynamics in 3D gravity with torsion
Blagojevic, M.; Cvetkovic, B.; Miskovic, O.
2009-07-15
We study exact solutions of nonlinear electrodynamics coupled to three-dimensional gravity with torsion. We show that in any static and spherically symmetric configuration, at least one component of the electromagnetic field has to vanish. In the electric sector of the theory, we construct an exact solution, characterized by the azimuthal electric field. When the electromagnetic action is modified by a topological mass term, we find two types of the self-dual solutions.
FDFD: A 3D Finite-Difference Frequency-Domain Code for Electromagnetic Induction Tomography
NASA Astrophysics Data System (ADS)
Champagne, Nathan J.; Berryman, James G.; Buettner, H. Michael
2001-07-01
A new 3D code for electromagnetic induction tomography with intended applications to environmental imaging problems has been developed. The approach consists of calculating the fields within a volume using an implicit finite-difference frequency-domain formulation. The volume is terminated by an anisotropic perfectly matched layer region that simulates an infinite domain by absorbing outgoing waves. Extensive validation of this code has been done using analytical and semianalytical results from other codes, and some of those results are presented in this paper. The new code is written in Fortran 90 and is designed to be easily parallelized. Finally, an adjoint field method of data inversion, developed in parallel for solving the fully nonlinear inverse problem for electrical conductivity imaging (e.g., for mapping underground conducting plumes), uses this code to provide solvers for both forward and adjoint fields. Results obtained from this inversion method for high-contrast media are encouraging and provide a significant improvement over those obtained from linearized inversion methods.
A 3D, finite element model for baroclinic circulation on the Vancouver Island continental shelf
Walters, R.A.; Foreman, M.G.G.
1992-01-01
This paper describes the development and application of a 3-dimensional model of the barotropic and baroclinic circulation on the continental shelf west of Vancouver Island, Canada. A previous study with a 2D barotropic model and field data revealed that several tidal constituents have a significant baroclinic component (the K1 in particular). Thus we embarked on another study with a 3D model to study the baroclinic effects on the residual and several selected tidal constituents. The 3D model uses a harmonic expansion in time and a finite element discretization in space. All nonlinear terms are retained, including quadratic bottom stress, advection and wave transport (continuity nonlinearity). The equations are solved as a global and a local problem, where the global problem is the solution of the wave equation formulation of the shallow water equations, and the local problem is the solution of the momentum equation for the vertical velocity profile. These equations are coupled to the advection-diffusion equation for density so that density gradient forcing is included in the momentum equations. However, the study presented here describes diagnostic calculations for the baroclinic residual circulation only. The model is sufficiently efficient that it encourages sensitivity testing with a large number of model runs. In this sense, the model is akin to an extension of analytical solutions to the domain of irregular geometry and bottom topography where this parameter space can be explored in some detail. In particular, the consequences of the sigma coordinate system used by the model are explored. Test cases using an idealized representation of the continental shelf, shelf break and shelf slope, lead to an estimation of the velocity errors caused by interpolation errors inherent in the sigma coordinate system. On the basis of these estimates, the computational grid used in the 2D model is found to have inadequate resolution. Thus a new grid is generated with increased
Xie, G.; Li, J.; Majer, E.; Zuo, D.
1998-07-01
This paper describes a new 3D parallel GILD electromagnetic (EM) modeling and nonlinear inversion algorithm. The algorithm consists of: (a) a new magnetic integral equation instead of the electric integral equation to solve the electromagnetic forward modeling and inverse problem; (b) a collocation finite element method for solving the magnetic integral and a Galerkin finite element method for the magnetic differential equations; (c) a nonlinear regularizing optimization method to make the inversion stable and of high resolution; and (d) a new parallel 3D modeling and inversion using a global integral and local differential domain decomposition technique (GILD). The new 3D nonlinear electromagnetic inversion has been tested with synthetic data and field data. The authors obtained very good imaging for the synthetic data and reasonable subsurface EM imaging for the field data. The parallel algorithm has high parallel efficiency over 90% and can be a parallel solver for elliptic, parabolic, and hyperbolic modeling and inversion. The parallel GILD algorithm can be extended to develop a high resolution and large scale seismic and hydrology modeling and inversion in the massively parallel computer.
An augmented Lagrangian finite element formulation for 3D contact of biphasic tissues.
Guo, Hongqiang; Spilker, Robert L
2014-01-01
Biphasic contact analysis is essential to obtain a complete understanding of soft tissue biomechanics, and the importance of physiological structure on the joint biomechanics has long been recognised; however, up to date, there are no successful developments of biphasic finite element contact analysis for three-dimensional (3D) geometries of physiological joints. The aim of this study was to develop a finite element formulation for biphasic contact of 3D physiological joints. The augmented Lagrangian method was used to enforce the continuity of contact traction and fluid pressure across the contact interface. The biphasic contact method was implemented in the commercial software COMSOL Multiphysics 4.2(®) (COMSOL, Inc., Burlington, MA). The accuracy of the implementation was verified using 3D biphasic contact problems, including indentation with a flat-ended indenter and contact of glenohumeral cartilage layers. The ability of the method to model multibody biphasic contact of physiological joints was proved by a 3D knee model. The 3D biphasic finite element contact method developed in this study can be used to study the biphasic behaviours of the physiological joints. PMID:23181617
Finite Element Code For 3D-Hydraulic Fracture Propagation Equations (3-layer).
1992-03-24
HYFRACP3D is a finite element program for simulation of a pseudo three-dimensional fracture geometries with a two-dimensional planar solution. The model predicts the height, width and winglength over time for a hydraulic fracture propagating in a three-layered system of rocks with variable rock mechanics properties.
NASA Technical Reports Server (NTRS)
Vos, R. G.; Straayer, J. W.
1975-01-01
The BOPACE 3-D is a finite element computer program, which provides a general family of three-dimensional isoparametric solid elements, and includes a new algorithm for improving the efficiency of the elastic-plastic-creep solution procedure. Theoretical, user, and programmer oriented sections are presented to describe the program.
NASA Technical Reports Server (NTRS)
Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.
1998-01-01
This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves
A finite element analysis of a 3D auxetic textile structure for composite reinforcement
NASA Astrophysics Data System (ADS)
Ge, Zhaoyang; Hu, Hong; Liu, Yanping
2013-08-01
This paper reports the finite element analysis of an innovative 3D auxetic textile structure consisting of three yarn systems (weft, warp and stitch yarns). Different from conventional 3D textile structures, the proposed structure exhibits an auxetic behaviour under compression and can be used as a reinforcement to manufacture auxetic composites. The geometry of the structure is first described. Then a 3D finite element model is established using ANSYS software and validated by the experimental results. The deformation process of the structure at different compression strains is demonstrated, and the validated finite element model is finally used to simulate the auxetic behaviour of the structure with different structural parameters and yarn properties. The results show that the auxetic behaviour of the proposed structure increases with increasing compression strain, and all the structural parameters and yarn properties have significant effects on the auxetic behaviour of the structure. It is expected that the study could provide a better understanding of 3D auxetic textile structures and could promote their application in auxetic composites.
2D-3D hybrid stabilized finite element method for tsunami runup simulations
NASA Astrophysics Data System (ADS)
Takase, S.; Moriguchi, S.; Terada, K.; Kato, J.; Kyoya, T.; Kashiyama, K.; Kotani, T.
2016-09-01
This paper presents a two-dimensional (2D)-three-dimensional (3D) hybrid stabilized finite element method that enables us to predict a propagation process of tsunami generated in a hypocentral region, which ranges from offshore propagation to runup to urban areas, with high accuracy and relatively low computational costs. To be more specific, the 2D shallow water equation is employed to simulate the propagation of offshore waves, while the 3D Navier-Stokes equation is employed for the runup in urban areas. The stabilized finite element method is utilized for numerical simulations for both of the 2D and 3D domains that are independently discretized with unstructured meshes. The multi-point constraint and transmission methods are applied to satisfy the continuity of flow velocities and pressures at the interface between the resulting 2D and 3D meshes, since neither their spatial dimensions nor node arrangements are consistent. Numerical examples are presented to demonstrate the performance of the proposed hybrid method to simulate tsunami behavior, including offshore propagation and runup to urban areas, with substantially lower computation costs in comparison with full 3D computations.
2D-3D hybrid stabilized finite element method for tsunami runup simulations
NASA Astrophysics Data System (ADS)
Takase, S.; Moriguchi, S.; Terada, K.; Kato, J.; Kyoya, T.; Kashiyama, K.; Kotani, T.
2016-05-01
This paper presents a two-dimensional (2D)-three-dimensional (3D) hybrid stabilized finite element method that enables us to predict a propagation process of tsunami generated in a hypocentral region, which ranges from offshore propagation to runup to urban areas, with high accuracy and relatively low computational costs. To be more specific, the 2D shallow water equation is employed to simulate the propagation of offshore waves, while the 3D Navier-Stokes equation is employed for the runup in urban areas. The stabilized finite element method is utilized for numerical simulations for both of the 2D and 3D domains that are independently discretized with unstructured meshes. The multi-point constraint and transmission methods are applied to satisfy the continuity of flow velocities and pressures at the interface between the resulting 2D and 3D meshes, since neither their spatial dimensions nor node arrangements are consistent. Numerical examples are presented to demonstrate the performance of the proposed hybrid method to simulate tsunami behavior, including offshore propagation and runup to urban areas, with substantially lower computation costs in comparison with full 3D computations.
Robust and scalable 3-D geo-electromagnetic modelling approach using the finite element method
NASA Astrophysics Data System (ADS)
Grayver, Alexander V.; Bürg, Markus
2014-07-01
We present a robust and scalable solver for time-harmonic Maxwell's equations for problems with large conductivity contrasts, wide range of frequencies, stretched grids and locally refined meshes. The solver is part of the fully distributed adaptive 3-D electromagnetic modelling scheme which employs the finite element method and unstructured non-conforming hexahedral meshes for spatial discretization using the open-source software deal.II. We use the complex-valued electric field formulation and split it into two real-valued equations for which we utilize an optimal block-diagonal pre-conditioner. Application of this pre-conditioner requires the solution of two smaller real-valued symmetric problems. We solve them by using either a direct solver or the conjugate gradient method pre-conditioned with the recently introduced auxiliary space technique. The auxiliary space pre-conditioner reformulates the original problem in form of several simpler ones, which are then solved using highly efficient algebraic multigrid methods. In this paper, we consider the magnetotelluric case and verify our numerical scheme by using COMMEMI 3-D models. Afterwards, we run a series of numerical experiments and demonstrate that the solver converges in a small number of iterations for a wide frequency range and variable problem sizes. The number of iterations is independent of the problem size, but exhibits a mild dependency on frequency. To test the stability of the method on locally refined meshes, we have implemented a residual-based a posteriori error estimator and compared it with uniform mesh refinement for problems up to 200 million unknowns. We test the scalability of the most time consuming parts of our code and show that they fulfill the strong scaling assumption as long as each MPI process possesses enough degrees of freedom to alleviate communication overburden. Finally, we refer back to a direct solver-based pre-conditioner and analyse its complexity in time. The results show
3D finite element analysis of porous Ti-based alloy prostheses.
Mircheski, Ile; Gradišar, Marko
2016-11-01
In this paper, novel designs of porous acetabular cups are created and tested with 3D finite element analysis (FEA). The aim is to develop a porous acetabular cup with low effective radial stiffness of the structure, which will be near to the architectural and mechanical behavior of the natural bone. For the realization of this research, a 3D-scanner technology was used for obtaining a 3D-CAD model of the pelvis bone, a 3D-CAD software for creating a porous acetabular cup, and a 3D-FEA software for virtual testing of a novel design of the porous acetabular cup. The results obtained from this research reveal that a porous acetabular cup from Ti-based alloys with 60 ± 5% porosity has the mechanical behavior and effective radial stiffness (Young's modulus in radial direction) that meet and exceed the required properties of the natural bone. The virtual testing with 3D-FEA of a novel design with porous structure during the very early stage of the design and the development of orthopedic implants, enables obtaining a new or improved biomedical implant for a relatively short time and reduced price. PMID:27015664
Weak concentration and wave operator for a 3D coupled nonlinear Schrödinger system
NASA Astrophysics Data System (ADS)
Pastor, Ademir
2015-02-01
Reported in this paper are results concerning the Cauchy problem and the dynamics for a cubic nonlinear Schrödinger system arising in nonlinear optics. A sharp criterion is given concerned with the dichotomy global existence versus finite time blow-up. When a radial solution blows up in finite time, we prove the concentration in the critical Lebesgue space. Sufficient condition for the scattering and the construction of the wave operator in the energy space is also provided.
Application of edge-based finite elements and vector ABCs in 3D scattering
NASA Technical Reports Server (NTRS)
Chatterjee, A.; Jin, J. M.; Volakis, John L.
1992-01-01
A finite element absorbing boundary condition (FE-ABC) solution of the scattering by arbitrary 3-D structures is considered. The computational domain is discretized using edge-based tetrahedral elements. In contrast to the node-based elements, edge elements can treat geometries with sharp edges, are divergence-less, and easily satisfy the field continuity condition across dielectric interfaces. They do, however, lead to a higher unknown count but this is balanced by the greater sparsity of the resulting finite element matrix. Thus, the computation time required to solve such a system iteratively with a given degree of accuracy is less than the traditional node-based approach. The purpose is to examine the derivation and performance of the ABC's when applied to 2-D and 3-D problems and to discuss the specifics of our FE-ABC implementation.
Numerical solution of 3-D magnetotelluric using vector finite element method
NASA Astrophysics Data System (ADS)
Prihantoro, Rudy; Sutarno, Doddy; Nurhasan
2015-09-01
Magnetotelluric (MT) is a passive electromagnetic (EM) method which measure natural variations of electric and magnetic vector fields at the Earth surface to map subsurface electrical conductivity/resistivity structure. In this study, we obtained numerical solution of three-dimensional (3-D) MT using vector finite element method by solving second order Maxwell differential equation describing diffusion of plane wave through the conductive earth. Rather than the nodes of the element, the edges of the element is used as a vector basis to overcome the occurrence of nonphysical solutions that usually faced by scalar (node based) finite element method. Electric vector fields formulation was used and the resulting system of equation was solved using direct solution method to obtain the electric vector field distribution throughout the earth resistivity model structure. The resulting MT response functions was verified with 1-D layered Earth and 3-D2 COMMEMI outcropping structure. Good agreement is achieved for both structure models.
3D modeling of high-Tc superconductors by finite element software
NASA Astrophysics Data System (ADS)
Zhang, Min; Coombs, T. A.
2012-01-01
A three-dimensional (3D) numerical model is proposed to solve the electromagnetic problems involving transport current and background field of a high-Tc superconducting (HTS) system. The model is characterized by the E-J power law and H-formulation, and is successfully implemented using finite element software. We first discuss the model in detail, including the mesh methods, boundary conditions and computing time. To validate the 3D model, we calculate the ac loss and trapped field solution for a bulk material and compare the results with the previously verified 2D solutions and an analytical solution. We then apply our model to test some typical problems such as superconducting bulk array and twisted conductors, which cannot be tackled by the 2D models. The new 3D model could be a powerful tool for researchers and engineers to investigate problems with a greater level of complicity.
Application of 3D X-ray CT data sets to finite element analysis
Bossart, P.L.; Martz, H.E.; Brand, H.R.; Hollerbach, K.
1995-08-31
Finite Element Modeling (FEM) is becoming more important as industry drives toward concurrent engineering. A fundamental hindrance to fully exploiting the power of FEM is the human effort required to acquire complex part geometry, particularly as-built geometry, as a FEM mesh. Many Quantitative Non Destructive Evaluation (QNDE) techniques that produce three-dimensional (3D) data sets provide a substantial reduction in the effort required to apply FEM to as-built parts. This paper describes progress at LLNL on the application of 3D X-ray computed tomography (CT) data sets to more rapidly produce high-quality FEM meshes of complex, as-built geometries. Issues related to the volume segmentation of the 3D CT data as well as the use of this segmented data to tailor generic hexahedral FEM meshes to part specific geometries are discussed. The application of these techniques to FEM analysis in the medical field is reported here.
The program FANS-3D (finite analytic numerical simulation 3-dimensional) and its applications
NASA Technical Reports Server (NTRS)
Bravo, Ramiro H.; Chen, Ching-Jen
1992-01-01
In this study, the program named FANS-3D (Finite Analytic Numerical Simulation-3 Dimensional) is presented. FANS-3D was designed to solve problems of incompressible fluid flow and combined modes of heat transfer. It solves problems with conduction and convection modes of heat transfer in laminar flow, with provisions for radiation and turbulent flows. It can solve singular or conjugate modes of heat transfer. It also solves problems in natural convection, using the Boussinesq approximation. FANS-3D was designed to solve heat transfer problems inside one, two and three dimensional geometries that can be represented by orthogonal planes in a Cartesian coordinate system. It can solve internal and external flows using appropriate boundary conditions such as symmetric, periodic and user specified.
3-d finite element model development for biomechanics: a software demonstration
Hollerbach, K.; Hollister, A.M.; Ashby, E.
1997-03-01
Finite element analysis is becoming an increasingly important part of biomechanics and orthopedic research, as computational resources become more powerful, and data handling algorithms become more sophisticated. Until recently, tools with sufficient power did not exist or were not accessible to adequately model complicated, three-dimensional, nonlinear biomechanical systems. In the past, finite element analyses in biomechanics have often been limited to two-dimensional approaches, linear analyses, or simulations of single tissue types. Today, we have the resources to model fully three-dimensional, nonlinear, multi-tissue, and even multi-joint systems. The authors will present the process of developing these kinds of finite element models, using human hand and knee examples, and will demonstrate their software tools.
Spatial parallelism of a 3D finite difference, velocity-stress elastic wave propagation code
Minkoff, S.E.
1999-12-01
Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately, finite difference simulations for 3D elastic wave propagation are expensive. The authors model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MPI library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speedup. Because I/O is handled largely outside of the time-step loop (the most expensive part of the simulation) the authors have opted for straight-forward broadcast and reduce operations to handle I/O. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ghost cells. When this communication is balanced against computation by allocating subdomains of reasonable size, they observe excellent scaled speedup. Allocating subdomains of size 25 x 25 x 25 on each node, they achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.
Spatial Parallelism of a 3D Finite Difference, Velocity-Stress Elastic Wave Propagation Code
MINKOFF,SUSAN E.
1999-12-09
Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately. finite difference simulations for 3D elastic wave propagation are expensive. We model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MP1 library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speed up. Because i/o is handled largely outside of the time-step loop (the most expensive part of the simulation) we have opted for straight-forward broadcast and reduce operations to handle i/o. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ''ghost cells''. When this communication is balanced against computation by allocating subdomains of reasonable size, we observe excellent scaled speed up. Allocating subdomains of size 25 x 25 x 25 on each node, we achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.
Finite Element Analysis of Thermo-Mechanical Properties of 3D Braided Composites
NASA Astrophysics Data System (ADS)
Jiang, Li-li; Xu, Guo-dong; Cheng, Su; Lu, Xia-mei; Zeng, Tao
2014-04-01
This paper presents a modified finite element model (FEM) to investigate the thermo-mechanical properties of three-dimensional (3D) braided composite. The effective coefficients of thermal expansion (CTE) and the meso-scale mechanical response of 3D braided composites are predicted. The effects of the braiding angle and fiber volume fraction on the effective CTE are evaluated. The results are compared to the experimental data available in the literature to demonstrate the accuracy and reliability of the present method. The tensile stress distributions of the representative volume element (RVE) are also outlined. It is found that the stress of the braiding yarn has a significant increase with temperature rise; on the other hand, the temperature change has an insignificant effect on the stress of the matrix. In addition, a rapid decrease in the tensile strength of 3D braided composites is observed with the increase in temperature. It is revealed that the thermal conditions have a significant effect on the strength of 3D braided composites. The present method provides an effective tool to predict the stresses of 3D braided composites under thermo-mechanical loading.
Non-linear 3D Born Shear Wave Tomography in Southeastern Asia
NASA Astrophysics Data System (ADS)
Cao, A.; Panning, M.; Kim, A.; Romanowicz, B.
2007-12-01
We have developed a 3D radially anisotropic shear velocity model of the upper mantle in southeastern Asia from the inversion of long period seismic multimode waveforms. Our approach is based on normal mode perturbation theory, specifically, on a recent modification of the Born approximation, which we call "N-Born", and which includes a non-linear term that allows the accurate inclusion of accumulated phase shifts which arise when the wavepath traverses a spatially extended region with a smooth velocity anomaly of constant sign. We apply the N-Born approximation in the forward modeling part and calculate linear 3D Born kernels in the inverse part. Our starting model is a 3D radially anisotropic model which we derived from a large dataset of teleseismic multimode long period waveforms in the period range 60 to 400 s, using a finite-frequency 2D approximation (NACT, Li and Romanowicz, 1995). This model covered a larger region of East Asia (longitude 30 to 150 degrees and latitude -10 to 60 degrees), while our N-Born model is restricted to a smaller subregion (longitude 75 to 150 degrees and latitude 0 to 45 degrees) for computational efficiency. In this subregion, our N-Born isotropic and anisotropic models are both parameterized at relatively short wavelengths corresponding to a spherical spline level 6 (~200km). Our N-Born model can fit waveforms as well as the NACT model, with up to ~ 83% variance reduction. While the models agree in general, the N-Born isotropic model shows a stronger fast velocity anomaly beneath the Tibetan plateau in the depth range of 150 km to 250 km, which disappears at greater depth, consistent with other studies. More importantly, the N-Born anisotropic model can recover well the downwelling structure associated with subducted slabs. Beneath the Tibet plateau, radial anisotropy shows VSH>VSV, which is indicative of horizontal rather than vertical flow and may help distinguish between end member models of the tectonics of Tibet.
NASA Technical Reports Server (NTRS)
Raju, I. S.; Newman, J. C., Jr.
1993-01-01
A computer program, surf3d, that uses the 3D finite-element method to calculate the stress-intensity factors for surface, corner, and embedded cracks in finite-thickness plates with and without circular holes, was developed. The cracks are assumed to be either elliptic or part eliptic in shape. The computer program uses eight-noded hexahedral elements to model the solid. The program uses a skyline storage and solver. The stress-intensity factors are evaluated using the force method, the crack-opening displacement method, and the 3-D virtual crack closure methods. In the manual the input to and the output of the surf3d program are described. This manual also demonstrates the use of the program and describes the calculation of the stress-intensity factors. Several examples with sample data files are included with the manual. To facilitate modeling of the user's crack configuration and loading, a companion program (a preprocessor program) that generates the data for the surf3d called gensurf was also developed. The gensurf program is a three dimensional mesh generator program that requires minimal input and that builds a complete data file for surf3d. The program surf3d is operational on Unix machines such as CRAY Y-MP, CRAY-2, and Convex C-220.
Charged-particle Gun Design with 3D Finite-element Methods
NASA Astrophysics Data System (ADS)
Humphries, Stanley
2002-04-01
The DARHT second-axis injector poses a major challenge for computer simulation. The relativistic electrons are subject to strong beam-generated electric and magnetic forces. The beam and applied fields are fully three-dimensional. Furthermore, accurate field calculations at surfaces are critical to model Child-law emission. Although several 2D relativistic beam codes are available, there is presently no 3D tool that can address all important processes in the DARHT injector. As a result, we created the OmniTrak 3D finite-element code suite. This talk gives a basic tutorial on finite-element methods with emphasis on electron gun design via the ray-tracing technique. Four main areas are covered: 1) the mesh as a tool to organize space, 2) transformation of the Poisson equation through the minimum residual principle, 3) orbit tracking in a complex environment and 4) handling self-consistent beam-generated fields. The components of a volume mesh (elements, nodes and facets) are reviewed. We consider motivations for choosing a 3D mesh style: structured versus unstructured, tetrahedrons versus hexahedrons. We discuss methods for taking volume integrals over arbitrary hexahedrons through normal coordinates and shape functions, leading to the fundamental field equations. The special problems of 3D magnetic field solutions and the advantages of the reduced potential method are outlined. Accurate field interpolations for orbit calculations require fast identification of occupied elements. A method for fast element identification that also yields the orbit penetration point on the element surface is described. The final topics are the assignment of charge and current to meshes from calculated orbits and techniques for space-charge-limited emission from multiple arbitrary 3D surfaces.
Ground motion simulations in Marmara (Turkey) region from 3D finite difference method
NASA Astrophysics Data System (ADS)
Aochi, Hideo; Ulrich, Thomas; Douglas, John
2016-04-01
In the framework of the European project MARSite (2012-2016), one of the main contributions from our research team was to provide ground-motion simulations for the Marmara region from various earthquake source scenarios. We adopted a 3D finite difference code, taking into account the 3D structure around the Sea of Marmara (including the bathymetry) and the sea layer. We simulated two moderate earthquakes (about Mw4.5) and found that the 3D structure improves significantly the waveforms compared to the 1D layer model. Simulations were carried out for different earthquakes (moderate point sources and large finite sources) in order to provide shake maps (Aochi and Ulrich, BSSA, 2015), to study the variability of ground-motion parameters (Douglas & Aochi, BSSA, 2016) as well as to provide synthetic seismograms for the blind inversion tests (Diao et al., GJI, 2016). The results are also planned to be integrated in broadband ground-motion simulations, tsunamis generation and simulations of triggered landslides (in progress by different partners). The simulations are freely shared among the partners via the internet and the visualization of the results is diffused on the project's homepage. All these simulations should be seen as a reference for this region, as they are based on the latest knowledge that obtained during the MARSite project, although their refinement and validation of the model parameters and the simulations are a continuing research task relying on continuing observations. The numerical code used, the models and the simulations are available on demand.
ATHENA 3D: A finite element code for ultrasonic wave propagation
NASA Astrophysics Data System (ADS)
Rose, C.; Rupin, F.; Fouquet, T.; Chassignole, B.
2014-04-01
The understanding of wave propagation phenomena requires use of robust numerical models. 3D finite element (FE) models are generally prohibitively time consuming. However, advances in computing processor speed and memory allow them to be more and more competitive. In this context, EDF R&D developed the 3D version of the well-validated FE code ATHENA2D. The code is dedicated to the simulation of wave propagation in all kinds of elastic media and in particular, heterogeneous and anisotropic materials like welds. It is based on solving elastodynamic equations in the calculation zone expressed in terms of stress and particle velocities. The particularity of the code relies on the fact that the discretization of the calculation domain uses a Cartesian regular 3D mesh while the defect of complex geometry can be described using a separate (2D) mesh using the fictitious domains method. This allows combining the rapidity of regular meshes computation with the capability of modelling arbitrary shaped defects. Furthermore, the calculation domain is discretized with a quasi-explicit time evolution scheme. Thereby only local linear systems of small size have to be solved. The final step to reduce the computation time relies on the fact that ATHENA3D has been parallelized and adapted to the use of HPC resources. In this paper, the validation of the 3D FE model is discussed. A cross-validation of ATHENA 3D and CIVA is proposed for several inspection configurations. The performances in terms of calculation time are also presented in the cases of both local computer and computation cluster use.
Finite-element 3D simulation tools for high-current relativistic electron beams
NASA Astrophysics Data System (ADS)
Humphries, Stanley; Ekdahl, Carl
2002-08-01
The DARHT second-axis injector is a challenge for computer simulations. Electrons are subject to strong beam-generated forces. The fields are fully three-dimensional and accurate calculations at surfaces are critical. We describe methods applied in OmniTrak, a 3D finite-element code suite that can address DARHT and the full range of charged-particle devices. The system handles mesh generation, electrostatics, magnetostatics and self-consistent particle orbits. The MetaMesh program generates meshes of conformal hexahedrons to fit any user geometry. The code has the unique ability to create structured conformal meshes with cubic logic. Organized meshes offer advantages in speed and memory utilization in the orbit and field solutions. OmniTrak is a versatile charged-particle code that handles 3D electric and magnetic field solutions on independent meshes. The program can update both 3D field solutions from the calculated beam space-charge and current-density. We shall describe numerical methods for orbit tracking on a hexahedron mesh. Topics include: 1) identification of elements along the particle trajectory, 2) fast searches and adaptive field calculations, 3) interpolation methods to terminate orbits on material surfaces, 4) automatic particle generation on multiple emission surfaces to model space-charge-limited emission and field emission, 5) flexible Child law algorithms, 6) implementation of the dual potential model for 3D magnetostatics, and 7) assignment of charge and current from model particle orbits for self-consistent fields.
Calculation by the finite element method of 3-D turbulent flow in a centrifugal pump
NASA Astrophysics Data System (ADS)
Combes, J. F.
1992-02-01
In order to solve industrial flow problems in complex geometries, a finite element code, N3S, was developed. It allows the computation of a wide variety of 2-D or 3-D unsteady incompressible flows, by solving the Reynolds averaged Navier-Stokes equations together with a k-epsilon turbulence model. Some recent developments of this code concern turbomachinery flows, where one has to take into account periodic boundary conditions, as well as Coriolis and centrifugal forces. The numerical treatment is based on a fractional step method: at each time step, an advection step is solved successively by means of a characteristic method; a diffusion step for the scalar terms; and finally, a Generalized Stokes Problem by using a preconditioned Uzawa algorithm. The space discretization uses a standard Galerkin finite element method with a mixed formulation for the velocity and pressure. An application is presented of this code to the flow inside a centrifugal pump which was extensively tested on several air and water test rigs, and for which many quasi-3-D or Euler calculations were reported. The present N3S calculation is made on a finite element mesh comprising about 28000 tetrahedrons and 43000 nodes.
NASA Technical Reports Server (NTRS)
Raju, I. S.
1992-01-01
A computer program that generates three-dimensional (3D) finite element models for cracked 3D solids was written. This computer program, gensurf, uses minimal input data to generate 3D finite element models for isotropic solids with elliptic or part-elliptic cracks. These models can be used with a 3D finite element program called surf3d. This report documents this mesh generator. In this manual the capabilities, limitations, and organization of gensurf are described. The procedures used to develop 3D finite element models and the input for and the output of gensurf are explained. Several examples are included to illustrate the use of this program. Several input data files are included with this manual so that the users can edit these files to conform to their crack configuration and use them with gensurf.
Justification for a 2D versus 3D fingertip finite element model during static contact simulations.
Harih, Gregor; Tada, Mitsunori; Dolšak, Bojan
2016-10-01
The biomechanical response of a human hand during contact with various products has not been investigated in details yet. It has been shown that excessive contact pressure on the soft tissue can result in discomfort, pain and also cumulative traumatic disorders. This manuscript explores the benefits and limitations of a simplified two-dimensional vs. an anatomically correct three-dimensional finite element model of a human fingertip. Most authors still use 2D FE fingertip models due to their simplicity and reduced computational costs. However we show that an anatomically correct 3D FE fingertip model can provide additional insight into the biomechanical behaviour. The use of 2D fingertip FE models is justified when observing peak contact pressure values as well as displacement during the contact for the given studied cross-section. On the other hand, an anatomically correct 3D FE fingertip model provides a contact pressure distribution, which reflects the fingertip's anatomy. PMID:26856769
NASA Technical Reports Server (NTRS)
Nakazawa, S.
1988-01-01
This annual status report presents the results of work performed during the fourth year of the 3-D Inelastic Analysis Methods for Hot Section Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of new computer codes permitting more accurate and efficient 3-D analysis of selected hot section components, i.e., combustor liners, turbine blades and turbine vanes. The computer codes embody a progression of math models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components. Volume 1 of this report discusses the special finite element models developed during the fourth year of the contract.
Finite-difference model for 3-D flow in bays and estuaries
Smith, Peter E.; Larock, Bruce E.
1993-01-01
This paper describes a semi-implicit finite-difference model for the numerical solution of three-dimensional flow in bays and estuaries. The model treats the gravity wave and vertical diffusion terms in the governing equations implicitly, and other terms explicitly. The model achieves essentially second-order accurate and stable solutions in strongly nonlinear problems by using a three-time-level leapfrog-trapezoidal scheme for the time integration.
NASA Astrophysics Data System (ADS)
Moortgat, Joachim; Firoozabadi, Abbas
2016-06-01
Problems of interest in hydrogeology and hydrocarbon resources involve complex heterogeneous geological formations. Such domains are most accurately represented in reservoir simulations by unstructured computational grids. Finite element methods accurately describe flow on unstructured meshes with complex geometries, and their flexible formulation allows implementation on different grid types. In this work, we consider for the first time the challenging problem of fully compositional three-phase flow in 3D unstructured grids, discretized by any combination of tetrahedra, prisms, and hexahedra. We employ a mass conserving mixed hybrid finite element (MHFE) method to solve for the pressure and flux fields. The transport equations are approximated with a higher-order vertex-based discontinuous Galerkin (DG) discretization. We show that this approach outperforms a face-based implementation of the same polynomial order. These methods are well suited for heterogeneous and fractured reservoirs, because they provide globally continuous pressure and flux fields, while allowing for sharp discontinuities in compositions and saturations. The higher-order accuracy improves the modeling of strongly non-linear flow, such as gravitational and viscous fingering. We review the literature on unstructured reservoir simulation models, and present many examples that consider gravity depletion, water flooding, and gas injection in oil saturated reservoirs. We study convergence rates, mesh sensitivity, and demonstrate the wide applicability of our chosen finite element methods for challenging multiphase flow problems in geometrically complex subsurface media.
Dynamic Analysis of 2D Electromagnetic Resonant Optical Scanner Using 3D Finite Element Method
NASA Astrophysics Data System (ADS)
Hirata, Katsuhiro; Hong, Sara; Maeda, Kengo
The optical scanner is a scanning device in which a laser beam is reflected by a mirror that can be rotated or oscillated. In this paper, we propose a new 2D electromagnetic resonant optical scanner that employs electromagnets and leaf springs. Torque characteristics and resonance characteristics of the scanner are analyzed using the 3D finite element method. The validity of the analysis is shown by comparing the characteristics inferred from the analysis with the characteristics of the prototype. Further, 2D resonance is investigated by introducing a superimposed-frequency current in a single coil.
Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration
NASA Astrophysics Data System (ADS)
Zhang, Y.; Key, K.; Ovall, J.; Holst, M.
2014-12-01
We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented
Isoparametric 3-D Finite Element Mesh Generation Using Interactive Computer Graphics
NASA Technical Reports Server (NTRS)
Kayrak, C.; Ozsoy, T.
1985-01-01
An isoparametric 3-D finite element mesh generator was developed with direct interface to an interactive geometric modeler program called POLYGON. POLYGON defines the model geometry in terms of boundaries and mesh regions for the mesh generator. The mesh generator controls the mesh flow through the 2-dimensional spans of regions by using the topological data and defines the connectivity between regions. The program is menu driven and the user has a control of element density and biasing through the spans and can also apply boundary conditions, loads interactively.
Equivalent Body Force Finite Elements Method and 3-D Earth Model Applied In 2004 Sumatra Earthquake
NASA Astrophysics Data System (ADS)
Qu, W.; Cheng, H.; Shi, Y.
2015-12-01
The 26 December 2004 Sumatra-Andaman earthquake with moment magnitude (Mw) of 9.1 to 9.3 is the first great earthquake recorded by digital broadband, high-dynamic-range seismometers and global positioning system (GPS) equipment, which recorded many high-quality geophysical data sets. The spherical curvature is not negligible in far field especially for large event and the real Earth is laterally inhomogeneity and the analytical results still are difficult to explain the geodetic measurements. We use equivalent body force finite elements method Zhang et al. (2015) and mesh the whole earth, to compute global co-seismic displacements using four fault slip models of the 2004 Sumatra earthquake provided by different authors. Comparisons of calculated co-seismic displacements and GPS show that the confidences are well in near field for four models, and the confidences are according to different models. In the whole four models, the Chlieh model (Chlieh et al., 2007) is the best as this slip model not only accord well with near field data but also far field data. And then we use the best slip model, Chlieh model to explore influence of three dimensional lateral earth structure on both layered spherically symmetric (PREM) and real 3-D heterogeneous earth model (Crust 1.0 model and GyPSuM). Results show that the effects of 3-D heterogeneous earth model are not negligible and decrease concomitantly with increasing distance from the epicenter. The relative effects of 3-D crust model are 23% and 40% for horizontal and vertical displacements, respectively. The effects of the 3-D mantle model are much smaller than that of 3-D crust model but with wider impacting area.
NASA Astrophysics Data System (ADS)
Moortgat, J.; Firoozabadi, A.
2013-12-01
Most problems of interest in hydrogeology and subsurface energy resources involve complex heterogeneous geological formations. Such domains are most naturally represented in numerical reservoir simulations by unstructured computational grids. Finite element methods are a natural choice to describe fluid flow on unstructured meshes, because the governing equations can be readily discretized for any grid-element geometry. In this work, we consider the challenging problem of fully compositional three-phase flow in 3D unstructured grids, discretized by tetrahedra, prisms, or hexahedra, and compare to simulations on 3D structured grids. We employ a combination of mixed hybrid finite element methods to solve for the pressure and flux fields in a fractional flow formulation, and higher-order discontinuous Galerkin methods for the mass transport equations. These methods are well suited to simulate flow in heterogeneous and fractured reservoirs, because they provide a globally continuous pressure and flux field, while allowing for sharp discontinuities in the phase properties, such as compositions and saturations. The increased accuracy from using higher-order methods improves the modeling of highly non-linear flow, such as gravitational and viscous fingering. We present several numerical examples to study convergence rates and the (lack of) sensitivity to gridding/mesh orientation, and mesh quality. These examples consider gravity depletion, water and gas injection in oil saturated subsurface reservoirs with species exchange between up to three fluid phases. The examples demonstrate the wide applicability of our chosen finite element methods in the study of challenging multiphase flow problems in porous, geometrically complex, subsurface media.
A 3D finite element ALE method using an approximate Riemann solution
Chiravalle, V. P.; Morgan, N. R.
2016-08-09
Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less
Parallel 3D Finite Element Numerical Modelling of DC Electron Guns
Prudencio, E.; Candel, A.; Ge, L.; Kabel, A.; Ko, K.; Lee, L.; Li, Z.; Ng, C.; Schussman, G.; /SLAC
2008-02-04
In this paper we present Gun3P, a parallel 3D finite element application that the Advanced Computations Department at the Stanford Linear Accelerator Center is developing for the analysis of beam formation in DC guns and beam transport in klystrons. Gun3P is targeted specially to complex geometries that cannot be described by 2D models and cannot be easily handled by finite difference discretizations. Its parallel capability allows simulations with more accuracy and less processing time than packages currently available. We present simulation results for the L-band Sheet Beam Klystron DC gun, in which case Gun3P is able to reduce simulation time from days to some hours.
Glacial isostatic adjustment on 3-D Earth models: a finite-volume formulation
NASA Astrophysics Data System (ADS)
Latychev, Konstantin; Mitrovica, Jerry X.; Tromp, Jeroen; Tamisiea, Mark E.; Komatitsch, Dimitri; Christara, Christina C.
2005-05-01
We describe and present results from a finite-volume (FV) parallel computer code for forward modelling the Maxwell viscoelastic response of a 3-D, self-gravitating, elastically compressible Earth to an arbitrary surface load. We implement a conservative, control volume discretization of the governing equations using a tetrahedral grid in Cartesian geometry and a low-order, linear interpolation. The basic starting grid honours all major radial discontinuities in the Preliminary Reference Earth Model (PREM), and the models are permitted arbitrary spatial variations in viscosity and elastic parameters. These variations may be either continuous or discontinuous at a set of grid nodes forming a 3-D surface within the (regional or global) modelling domain. In the second part of the paper, we adopt the FV methodology and a spherically symmetric Earth model to generate a suite of predictions sampling a broad class of glacial isostatic adjustment (GIA) data types (3-D crustal motions, long-wavelength gravity anomalies). These calculations, based on either a simple disc load history or a global Late Pleistocene ice load reconstruction (ICE-3G), are benchmarked against predictions generated using the traditional normal-mode approach to GIA. The detailed comparison provides a guide for future analyses (e.g. what grid resolution is required to obtain a specific accuracy?) and it indicates that discrepancies in predictions of 3-D crustal velocities less than 0.1 mm yr-1 are generally obtainable for global grids with ~3 × 106 nodes; however, grids of higher resolution are required to predict large-amplitude (>1 cm yr-1) radial velocities in zones of peak post-glacial uplift (e.g. James bay) to the same level of absolute accuracy. We conclude the paper with a first application of the new formulation to a 3-D problem. Specifically, we consider the impact of mantle viscosity heterogeneity on predictions of present-day 3-D crustal motions in North America. In these tests, the
A 3-D nonlinear recursive digital filter for video image processing
NASA Technical Reports Server (NTRS)
Bauer, P. H.; Qian, W.
1991-01-01
This paper introduces a recursive 3-D nonlinear digital filter, which is capable of performing noise suppression without degrading important image information such as edges in space or time. It also has the property of unnoticeable bandwidth reduction immediately after a scene change, which makes the filter an attractive preprocessor to many interframe compression algorithms. The filter consists of a nonlinear 2-D spatial subfilter and a 1-D temporal filter. In order to achieve the required computational speed and increase the flexibility of the filter, all of the linear shift-variant filter modules are of the IIR type.
Nonlinear dynamics of Airy-vortex 3D wave packets: emission of vortex light waves.
Driben, Rodislav; Meier, Torsten
2014-10-01
The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Because of the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and nonzero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse. PMID:25360922
Neutron radiographic image restoration using BM3D frames and nonlinear variance stabilization
NASA Astrophysics Data System (ADS)
Shuang, Qiao; Wei-jing, Zhao; Jia-ning, Sun
2015-07-01
Neutron radiography is a powerful tool for non-destructive investigations in industrial applications. However, the resulting images are degraded inevitably due to some physical limitations. In this paper, we propose a new scheme for neutron image restoration, which utilizes BM3D frames and nonlinear variance stabilization including generalized anscombe transformation and its exact unbiased inverse. Experimental results show that superior to the existing restoration methods, the proposed scheme improves the restoration quality efficiently and exhibits better visual results.
El-Anwar, Mohamed; Ghali, Rami; Aboelnagga, Mona
2016-01-01
AIM: This study aimed to estimate the stress patterns induced by the masticatory loads on a removable prosthesis supported and retained by bar splinted implants placed in the reconstructed mandible with two different clip materials and without clip, in the fibula-jaw bone and prosthesis using finite element analysis. METHODS: Two 3D finite element models were constructed, that models components were modeled on commercial CAD/CAM software then assembled into finite element package. Vertical loads were applied simulating the masticatory forces unilaterally in the resected site and bilaterally in the central fossa of the lower first molar as 100N (tension and compression). Analysis was based on the assumption full osseointegration between different types of bones, and between implants and fibula while fixing the top surface of the TMJ in place. RESULTS: The metallic bar connecting the three implants is insensitive to the clips material. Its supporting implants showed typical behavior with maximum stress values at the neck region. Fibula and jaw bone showed stresses within physiologic, while clips material effect seems to be very small due to its relatively small size. CONCLUSION: Switching loading force direction from tensile to compression did-not change the stresses and deformations distribution, but reversed their sign from positive to negative. PMID:27275353
A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains
NASA Technical Reports Server (NTRS)
Kandil, Osama A.
1998-01-01
Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.
NASA Astrophysics Data System (ADS)
Schaa, R.; Gross, L.; du Plessis, J.
2016-04-01
We present a general finite-element solver, escript, tailored to solve geophysical forward and inverse modeling problems in terms of partial differential equations (PDEs) with suitable boundary conditions. Escript’s abstract interface allows geoscientists to focus on solving the actual problem without being experts in numerical modeling. General-purpose finite element solvers have found wide use especially in engineering fields and find increasing application in the geophysical disciplines as these offer a single interface to tackle different geophysical problems. These solvers are useful for data interpretation and for research, but can also be a useful tool in educational settings. This paper serves as an introduction into PDE-based modeling with escript where we demonstrate in detail how escript is used to solve two different forward modeling problems from applied geophysics (3D DC resistivity and 2D magnetotellurics). Based on these two different cases, other geophysical modeling work can easily be realized. The escript package is implemented as a Python library and allows the solution of coupled, linear or non-linear, time-dependent PDEs. Parallel execution for both shared and distributed memory architectures is supported and can be used without modifications to the scripts.
Nonlinear probabilistic finite element models of laminated composite shells
NASA Technical Reports Server (NTRS)
Engelstad, S. P.; Reddy, J. N.
1993-01-01
A probabilistic finite element analysis procedure for laminated composite shells has been developed. A total Lagrangian finite element formulation, employing a degenerated 3-D laminated composite shell with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells.
NASA Technical Reports Server (NTRS)
Mangalgiri, P. D.; Prabhakaran, R.
1986-01-01
An algorithm for vectorized computation of stiffness matrices of an 8 noded isoparametric hexahedron element for geometric nonlinear analysis was developed. This was used in conjunction with the earlier 2-D program GAMNAS to develop the new program NAS3D for geometric nonlinear analysis. A conventional, modified Newton-Raphson process is used for the nonlinear analysis. New schemes for the computation of stiffness and strain energy release rates is presented. The organization the program is explained and some results on four sample problems are given. The study of CPU times showed that savings by a factor of 11 to 13 were achieved when vectorized computation was used for the stiffness instead of the conventional scalar one. Finally, the scheme of inputting data is explained.
Shaping of light beams by 3D direct laser writing on facets of nonlinear crystals.
Lightman, Shlomi; Gvishi, Raz; Hurvitz, Gilad; Arie, Ady
2015-10-01
We demonstrate experimentally spatial-mode conversions of light beams generated in a quadratic nonlinear process by micron-scale structures placed on the facets of nonlinear crystals. These structures were printed on the crystal facets using a three-dimensional (3D) direct laser writing system. The functional structures were designed to modify the phase of the beam at specific wavelengths, thereby enabling conversion of a fundamental Gaussian laser beam into different high-order Hermite-Gaussian modes, Laguerre-Gaussian modes, and zeroth-order Bessel beams of the second harmonic. This facet functionalization opens exciting new opportunities for robust and compact beam shaping in a nonlinear interaction without compromising the conversion efficiency. PMID:26421556
NASA Astrophysics Data System (ADS)
Hu, Shengsun; Guo, Chaobo; Wang, Dongpo; Wang, Zhijiang
2016-07-01
The nonuniform distributions of the residual stress were simulated by a 3D finite element model to analyze the elastic-plastic dynamic ultrasonic impact treatment (UIT) process of multiple impacts on the 2024 aluminum alloy. The evolution of the stress during the impact process was discussed. The successive impacts during the UIT process improve the uniformity of the plastic deformation and decrease the maximum compressive residual stress beneath the former impact indentations. The influences of different controlled parameters, including the initial impact velocity, pin diameter, pin tip, device moving, and offset distances, on the residual stress distributions were analyzed. The influences of the controlled parameters on the residual stress distributions are apparent in the offset direction due to the different surface coverage in different directions. The influences can be used to understand the UIT process and to obtain the desired residual stress by optimizing the controlled parameters.
A least-squares finite element method for 3D incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.
1993-01-01
The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.
Description of a parallel, 3D, finite element, hydrodynamics-diffusion code
Milovich, J L; Prasad, M K; Shestakov, A I
1999-04-11
We describe a parallel, 3D, unstructured grid finite element, hydrodynamic diffusion code for inertial confinement fusion (ICF) applications and the ancillary software used to run it. The code system is divided into two entities, a controller and a stand-alone physics code. The code system may reside on different computers; the controller on the user's workstation and the physics code on a supercomputer. The physics code is composed of separate hydrodynamic, equation-of-state, laser energy deposition, heat conduction, and radiation transport packages and is parallelized for distributed memory architectures. For parallelization, a SPMD model is adopted; the domain is decomposed into a disjoint collection of subdomains, one per processing element (PE). The PEs communicate using MPI. The code is used to simulate the hydrodynamic implosion of a spherical bubble.
An accurate quadrature technique for the contact boundary in 3D finite element computations
NASA Astrophysics Data System (ADS)
Duong, Thang X.; Sauer, Roger A.
2015-01-01
This paper presents a new numerical integration technique for 3D contact finite element implementations, focusing on a remedy for the inaccurate integration due to discontinuities at the boundary of contact surfaces. The method is based on the adaptive refinement of the integration domain along the boundary of the contact surface, and is accordingly denoted RBQ for refined boundary quadrature. It can be used for common element types of any order, e.g. Lagrange, NURBS, or T-Spline elements. In terms of both computational speed and accuracy, RBQ exhibits great advantages over a naive increase of the number of quadrature points. Also, the RBQ method is shown to remain accurate for large deformations. Furthermore, since the sharp boundary of the contact surface is determined, it can be used for various purposes like the accurate post-processing of the contact pressure. Several examples are presented to illustrate the new technique.
NASA Technical Reports Server (NTRS)
Nakazawa, S.
1987-01-01
This Annual Status Report presents the results of work performed during the third year of the 3-D Inelastic Analysis Methods for Hot Section Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of new computer codes that permit more accurate and efficient three-dimensional analysis of selected hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components. This report is presented in two volumes. Volume 1 describes effort performed under Task 4B, Special Finite Element Special Function Models, while Volume 2 concentrates on Task 4C, Advanced Special Functions Models.
3D frequency-domain finite-difference modeling of acoustic wave propagation
NASA Astrophysics Data System (ADS)
Operto, S.; Virieux, J.
2006-12-01
We present a 3D frequency-domain finite-difference method for acoustic wave propagation modeling. This method is developed as a tool to perform 3D frequency-domain full-waveform inversion of wide-angle seismic data. For wide-angle data, frequency-domain full-waveform inversion can be applied only to few discrete frequencies to develop reliable velocity model. Frequency-domain finite-difference (FD) modeling of wave propagation requires resolution of a huge sparse system of linear equations. If this system can be solved with a direct method, solutions for multiple sources can be computed efficiently once the underlying matrix has been factorized. The drawback of the direct method is the memory requirement resulting from the fill-in of the matrix during factorization. We assess in this study whether representative problems can be addressed in 3D geometry with such approach. We start from the velocity-stress formulation of the 3D acoustic wave equation. The spatial derivatives are discretized with second-order accurate staggered-grid stencil on different coordinate systems such that the axis span over as many directions as possible. Once the discrete equations were developed on each coordinate system, the particle velocity fields are eliminated from the first-order hyperbolic system (following the so-called parsimonious staggered-grid method) leading to second-order elliptic wave equations in pressure. The second-order wave equations discretized on each coordinate system are combined linearly to mitigate the numerical anisotropy. Secondly, grid dispersion is minimized by replacing the mass term at the collocation point by its weighted averaging over all the grid points of the stencil. Use of second-order accurate staggered- grid stencil allows to reduce the bandwidth of the matrix to be factorized. The final stencil incorporates 27 points. Absorbing conditions are PML. The system is solved using the parallel direct solver MUMPS developed for distributed
GPU-accelerated 3D neutron diffusion code based on finite difference method
Xu, Q.; Yu, G.; Wang, K.
2012-07-01
Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)
Ash3d: A finite-volume, conservative numerical model for ash transport and tephra deposition
Schwaiger, Hans F.; Denlinger, Roger P.; Mastin, Larry G.
2012-01-01
We develop a transient, 3-D Eulerian model (Ash3d) to predict airborne volcanic ash concentration and tephra deposition during volcanic eruptions. This model simulates downwind advection, turbulent diffusion, and settling of ash injected into the atmosphere by a volcanic eruption column. Ash advection is calculated using time-varying pre-existing wind data and a robust, high-order, finite-volume method. Our routine is mass-conservative and uses the coordinate system of the wind data, either a Cartesian system local to the volcano or a global spherical system for the Earth. Volcanic ash is specified with an arbitrary number of grain sizes, which affects the fall velocity, distribution and duration of transport. Above the source volcano, the vertical mass distribution with elevation is calculated using a Suzuki distribution for a given plume height, eruptive volume, and eruption duration. Multiple eruptions separated in time may be included in a single simulation. We test the model using analytical solutions for transport. Comparisons of the predicted and observed ash distributions for the 18 August 1992 eruption of Mt. Spurr in Alaska demonstrate to the efficacy and efficiency of the routine.
Multiple-mode Lamb wave scattering simulations using 3D elastodynamic finite integration technique.
Leckey, Cara A C; Rogge, Matthew D; Miller, Corey A; Hinders, Mark K
2012-02-01
We have implemented three-dimensional (3D) elastodynamic finite integration technique (EFIT) simulations to model Lamb wave scattering for two flaw-types in an aircraft-grade aluminum plate, a rounded rectangle flat-bottom hole and a disbond of the same shape. The plate thickness and flaws explored in this work include frequency-thickness regions where several Lamb wave modes exist and sometimes overlap in phase and/or group velocity. For the case of the flat-bottom hole the depth was incrementally increased to explore progressive changes in multiple-mode Lamb wave scattering due to the damage. The flat-bottom hole simulation results have been compared to experimental data and are shown to provide key insight for this well-defined experimental case by explaining unexpected results in experimental waveforms. For the rounded rectangle disbond flaw, which would be difficult to implement experimentally, we found that Lamb wave behavior differed significantly from the flat-bottom hole flaw. Most of the literature in this field is restricted to low frequency-thickness regions due to difficulties in interpreting data when multiple modes exist. We found that benchmarked 3D EFIT simulations can yield an understanding of scattering behavior for these higher frequency-thickness regions and in cases that would be difficult to set up experimentally. Additionally, our results show that 2D simulations would not have been sufficient for modeling the complicated scattering that occurred. PMID:21908011
NASA Technical Reports Server (NTRS)
Zhao, W.; Newman, J. C., Jr.; Sutton, M. A.; Wu, X. R.; Shivakumar, K. N.
1995-01-01
Stress intensity factors for quarter-elliptical corner cracks emanating from a circular hole are determined using a 3-D weight function method combined with a 3-D finite element method. The 3-D finite element method is used to analyze uncracked configuration and provide stress distribution in the region where crack is to occur. Using this stress distribution as input, the 3-D weight function method is used to determine stress intensity factors. Three different loading conditions, i.e. remote tension, remote bending and wedge loading, are considered for a wide range in geometrical parameters. The significance in using 3-D uncracked stress distribution and the difference between single and double corner cracks are studied. Typical crack opening displacements are also provided. Comparisons are made with solutions available in the literature.
NASA Technical Reports Server (NTRS)
Nakazawa, Shohei
1989-01-01
The user options available for running the MHOST finite element analysis package is described. MHOST is a solid and structural analysis program based on the mixed finite element technology, and is specifically designed for 3-D inelastic analysis. A family of 2- and 3-D continuum elements along with beam and shell structural elements can be utilized, many options are available in the constitutive equation library, the solution algorithms and the analysis capabilities. The outline of solution algorithms is discussed along with the data input and output, analysis options including the user subroutines and the definition of the finite elements implemented in the program package.
3D imaging and characterization of microlenses and microlens arrays using nonlinear microscopy
NASA Astrophysics Data System (ADS)
Krmpot, Aleksandar J.; Tserevelakis, George J.; Murić, Branka D.; Filippidis, George; Pantelić, Dejan V.
2013-05-01
In this work, nonlinear laser scanning microscopy was employed for the characterization and three-dimensional (3D) imaging of microlenses and microlens arrays. Third-harmonic generation and two-photon excitation fluorescence (TPEF) signals were recorded and the obtained data were further processed in order to generate 3D reconstructions of the examined samples. Femtosecond laser pulses (1028 nm) were utilized for excitation. Microlenses were manufactured on Tot'hema and eosin sensitized gelatin layers using a green (532 nm) continuous wave laser beam using the direct laser writing method. The profiles of the microlens surface were obtained from the radial cross-sections, using a triple-Gaussian fit. The analytical shapes of the profiles were also used for ray tracing. Furthermore, the volumes of the microlenses were determined with high precision. The TPEF signal arising from the volume of the material was recorded and the respective 3D spatial fluorescence distribution of the samples was mapped. Nonlinear microscopy modalities have been shown to be a powerful diagnostic tool for microlens characterization as they enable in-depth investigations of the structural properties of the samples, in a nondestructive manner.
A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials
NASA Astrophysics Data System (ADS)
Zhang, L.; Zhang, H. W.; Wu, J.; Yan, B.
2016-06-01
Bi-modulus materials with different mechanical responses in tension and compression are often found in civil, composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress directions. The original problem is transformed into a standard linear complementarity problem (LCP) by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke's algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative schemes. Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.
A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials
NASA Astrophysics Data System (ADS)
Zhang, L.; Zhang, H. W.; Wu, J.; Yan, B.
2015-10-01
Bi-modulus materials with different mechanical responses in tension and compression are often found in civil, composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress directions. The original problem is transformed into a standard linear complementarity problem (LCP) by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke's algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative schemes. Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.
Kolotilina, L.; Nikishin, A.; Yeremin, A.
1994-12-31
The solution of large systems of linear equations is a crucial bottleneck when performing 3D finite element analysis of structures. Also, in many cases the reliability and robustness of iterative solution strategies, and their efficiency when exploiting hardware resources, fully determine the scope of industrial applications which can be solved on a particular computer platform. This is especially true for modern vector/parallel supercomputers with large vector length and for modern massively parallel supercomputers. Preconditioned iterative methods have been successfully applied to industrial class finite element analysis of structures. The construction and application of high quality preconditioners constitutes a high percentage of the total solution time. Parallel implementation of high quality preconditioners on such architectures is a formidable challenge. Two common types of existing preconditioners are the implicit preconditioners and the explicit preconditioners. The implicit preconditioners (e.g. incomplete factorizations of several types) are generally high quality but require solution of lower and upper triangular systems of equations per iteration which are difficult to parallelize without deteriorating the convergence rate. The explicit type of preconditionings (e.g. polynomial preconditioners or Jacobi-like preconditioners) require sparse matrix-vector multiplications and can be parallelized but their preconditioning qualities are less than desirable. The authors present results of numerical experiments with Factorized Sparse Approximate Inverses (FSAI) for symmetric positive definite linear systems. These are high quality preconditioners that possess a large resource of parallelism by construction without increasing the serial complexity.
Characterizing the propagation of gravity waves in 3D nonlinear simulations of solar-like stars
NASA Astrophysics Data System (ADS)
Alvan, L.; Strugarek, A.; Brun, A. S.; Mathis, S.; Garcia, R. A.
2015-09-01
Context. The revolution of helio- and asteroseismology provides access to the detailed properties of stellar interiors by studying the star's oscillation modes. Among them, gravity (g) modes are formed by constructive interferences between progressive internal gravity waves (IGWs), propagating in stellar radiative zones. Our new 3D nonlinear simulations of the interior of a solar-like star allows us to study the excitation, propagation, and dissipation of these waves. Aims: The aim of this article is to clarify our understanding of the behavior of IGWs in a 3D radiative zone and to provide a clear overview of their properties. Methods: We use a method of frequency filtering that reveals the path of individual gravity waves of different frequencies in the radiative zone. Results: We are able to identify the region of propagation of different waves in 2D and 3D, to compare them to the linear raytracing theory and to distinguish between propagative and standing waves (g-modes). We also show that the energy carried by waves is distributed in different planes in the sphere, depending on their azimuthal wave number. Conclusions: We are able to isolate individual IGWs from a complex spectrum and to study their propagation in space and time. In particular, we highlight in this paper the necessity of studying the propagation of waves in 3D spherical geometry, since the distribution of their energy is not equipartitioned in the sphere.
Non-linear Tearing and Flux rope Formation in 3D Null Current Sheets
NASA Astrophysics Data System (ADS)
Wyper, P. F.; Pontin, D. I.
2014-12-01
The manner in which small scale structure affects the large scale reconnection process in realistic 3D geometries is still an unsolved problem. With the increase in computational resources and improvements in satellite instrumentation, signatures of flux ropes or "plasmoids" are now observed with increasing regularity, yet their formation and dynamics are poorly understood. It has been demonstrated that even at MHD scales, in 2D rapid non-linear tearing of Sweet-Parker-like layers forms multiple magnetic islands ("plasmoids") and allows the reconnection rate to become almost independent of the Lundquist number (the "plasmoid instability"). This work presents some of our recent theoretical work focussing on an analogous instability in a fully 3D geometry. Using results from a series of 3D high resolution MHD simulations, the formation and evolution of fully three dimensional "flux rope" structures following the 3D plasmoid instability will be presented, and their effects on the manner of the reconnection process as a whole discussed.
User's manuals for DYNA3D and DYNAP: nonlinear dynamic analysis of solids in three dimensions
Hallquist, J.O.
1981-07-01
This report provides a user's manual for DYNA3D, an explicit three-dimensional finite element code for analyzing the large deformation dynamic response of inelastic solids. A contact-impact algorithm permits gaps and sliding along material interfaces. By a specialization of this algorithm, such interfaces can be rigidly tied to admit variable zoning without the need of transition regions. Spatial discretization is achieved by the use of 8-node solid elements, and the equations-of-motion are integrated by the central difference method. Post-processors for DYNA3D include GRAPE for plotting deformed shapes and stress contours and DYNAP for plotting time histories. A user's manual for DYNAP is also provided in this report.
3D soliton-like bullets in nonlinear optics and Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Belyaeva, T. L.; Hasegawa, Akira; Kovachev, L. M.; Serkin, V. N.
2010-10-01
Mathematical similarities and parallels between two different physical objects, optical solitons and matter-wave solitons, both described by similar mathematical models: the nonlinear Schrodinger equation (NLSE) and the Gross-Pitaevskii equation (GPE) model, open the possibility to study both systems in parallel and because of the obvious complexity of experiments with matter-wave solitons, offer outstanding possibilities in studies of BEC system by performing experiments in the nonlinear optical system and vise versa. In this report we briefly overview recent theoretical studies of the existence and stability of 3D solitons. With contributions from major groups who have pioneered research in this field, the report describes the historical development of the subject, provides a background to the associated nonlinear optical processes, the generation mechanisms of soliton bullets. The main features of nonautonomous matter-wave solitons near the Feshbach resonance with continuously tuned scattering length are investigated. We focus on the most physically important situations where the applied magnetic field is varying in time linearly and periodically. In nonlinear optical applications, this kind of periodic graded-index nonlinear structure with alternating waveguiding and antiwaveguiding segments can be used to simulate different and complicated processes in the total scenario of matterwave soliton bullets generation.
Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method
NASA Technical Reports Server (NTRS)
Hrinda, Glenn A.
2006-01-01
Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.
A Multi-Compartment 3-D Finite Element Model of Rectocele and Its Interaction with Cystocele
Luo, Jiajia; Chen, Luyun; Fenner, Dee E.; Ashton-Miller, James A.; DeLancey, John O. L.
2015-01-01
We developed a subject-specific 3-D finite element model to understand the mechanics underlying formation of female pelvic organ prolapse, specifically a rectocele and its interaction with a cystocele. The model was created from MRI 3-D geometry of a healthy 45 year-old multiparous woman. It included anterior and posterior vaginal walls, levator ani muscle, cardinal and uterosacral ligaments, anterior and posterior arcus tendineus fascia pelvis, arcus tendineus levator ani, perineal body, perineal membrane and anal sphincter. Material properties were mostly from the literature. Tissue impairment was modeled as decreased tissue stiffness based on previous clinical studies. Model equations were solved using Abaqus v 6.11. The sensitivity of anterior and posterior vaginal wall geometry was calculated for different combinations tissue impairments under increasing intraabdominal pressure. Prolapse size was reported as POP-Q point at point Bp for rectocele and point Ba for cystocele. Results show that a rectocele resulted from impairments of the levator ani and posterior compartment support. For 20% levator and 85% posterior support impairments, simulated rectocele size (at POP-Q point: Bp) increased 0.29 mm/cm H2O without apical impairment and 0.36 mm/cm H2O with 60% apical impairment, as intraabdominal pressures increased from 0 to 150 cm H2O. Apical support impairment could result in the development of either a cystocele or rectocele. Simulated repair of posterior compartment support decreased rectocele but increased a preexisting cystocele. We conclude that development of rectocele and cystocele depend on the presence of anterior, posterior, levator and/or or apical support impairments, as well as the interaction of the prolapse with the opposing compartment. PMID:25757664
Accurate, finite-volume methods for 3D MHD on unstructured Lagrangian meshes
Barnes, D.C.; Rousculp, C.L.
1998-10-01
Previous 2D methods for magnetohydrodynamics (MHD) have contributed both to development of core code capability and to physics applications relevant to AGEX pulsed-power experiments. This strategy is being extended to 3D by development of a modular extension of an ASCI code. Extension to 3D not only increases complexity by problem size, but also introduces new physics, such as magnetic helicity transport. The authors have developed a method which incorporates all known conservation properties into the difference scheme on a Lagrangian unstructured mesh. Because the method does not depend on the mesh structure, mesh refinement is possible during a calculation to prevent the well known problem of mesh tangling. Arbitrary polyhedral cells are decomposed into tetrahedrons. The action of the magnetic vector potential, A {center_dot} {delta}l, is centered on the edges of this extended mesh. For ideal flow, this maintains {del} {center_dot} B = 0 to round-off error. Vertex forces are derived by the variation of magnetic energy with respect to vertex positions, F = {minus}{partial_derivative}W{sub B}/{partial_derivative}r. This assures symmetry as well as magnetic flux, momentum, and energy conservation. The method is local so that parallelization by domain decomposition is natural for large meshes. In addition, a simple, ideal-gas, finite pressure term has been included. The resistive diffusion part is calculated using the support operator method, to obtain an energy conservative, symmetric method on an arbitrary mesh. Implicit time difference equations are solved by preconditioned, conjugate gradient methods. Results of convergence tests are presented. Initial results of an annular Z-pinch implosion problem illustrate the application of these methods to multi-material problems.
Development of a 3D finite element model of lens microcirculation
2012-01-01
Background It has been proposed that in the absence of a blood supply, the ocular lens operates an internal microcirculation system. This system delivers nutrients, removes waste products and maintains ionic homeostasis in the lens. The microcirculation is generated by spatial differences in membrane transport properties; and previously has been modelled by an equivalent electrical circuit and solved analytically. While effective, this approach did not fully account for all the anatomical and functional complexities of the lens. To encapsulate these complexities we have created a 3D finite element computer model of the lens. Methods Initially, we created an anatomically-correct representative mesh of the lens. We then implemented the Stokes and advective Nernst-Plank equations, in order to model the water and ion fluxes respectively. Next we complemented the model with experimentally-measured surface ionic concentrations as boundary conditions and solved it. Results Our model calculated the standing ionic concentrations and electrical potential gradients in the lens. Furthermore, it generated vector maps of intra- and extracellular space ion and water fluxes that are proposed to circulate throughout the lens. These fields have only been measured on the surface of the lens and our calculations are the first 3D representation of their direction and magnitude in the lens. Conclusion Values for steady state standing fields for concentration and electrical potential plus ionic and fluid fluxes calculated by our model exhibited broad agreement with observed experimental values. Our model of lens function represents a platform to integrate new experimental data as they emerge and assist us to understand how the integrated structure and function of the lens contributes to the maintenance of its transparency. PMID:22992294
A 3-D implicit finite-volume model of shallow water flows
NASA Astrophysics Data System (ADS)
Wu, Weiming; Lin, Qianru
2015-09-01
A three-dimensional (3-D) model has been developed to simulate shallow water flows in large water bodies, such as coastal and estuarine waters. The eddy viscosity is determined using a newly modified mixing length model that uses different mixing length functions for the horizontal and vertical shear strain rates. The 3-D shallow water flow equations with the hydrostatic pressure assumption are solved using an implicit finite-volume method based on a quadtree (telescoping) rectangular mesh on the horizontal plane and the sigma coordinate in the vertical direction. The quadtree technique can locally refine the mesh around structures or in high-gradient regions by splitting a coarse cell into four child cells. The grid nodes are numbered with a one-dimensional index system that has unstructured grid feature for better grid flexibility. All the primary variables are arranged in a non-staggered grid system. Fluxes at cell faces are determined using a Rhie and Chow-type momentum interpolation, to avoid the possible spurious checkerboard oscillations caused by linear interpolation. Each of the discretized governing equations is solved iteratively using the flexible GMRES method with ILUT preconditioning, and coupling of water level and velocity among these equations is achieved by using the SIMPLEC algorithm with under-relaxation. The model has been tested in four cases, including steady flow near a spur-dyke, tidal flows in San Francisco Bay and Gironde Estuary, and wind-induced current in a flume. The calculated water levels and velocities are in good agreement with the measured values.
NASA Astrophysics Data System (ADS)
Kaus, B.; Popov, A.
2015-12-01
The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results
FERM3D: A finite element R-matrix electron molecule scattering code
NASA Astrophysics Data System (ADS)
Tonzani, Stefano
2007-01-01
FERM3D is a three-dimensional finite element program, for the elastic scattering of a low energy electron from a general polyatomic molecule, which is converted to a potential scattering problem. The code is based on tricubic polynomials in spherical coordinates. The electron-molecule interaction is treated as a sum of three terms: electrostatic, exchange, and polarization. The electrostatic term can be extracted directly from ab initio codes ( GAUSSIAN 98 in the work described here), while the exchange term is approximated using a local density functional. A local polarization potential based on density functional theory [C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785] describes the long range attraction to the molecular target induced by the scattering electron. Photoionization calculations are also possible and illustrated in the present work. The generality and simplicity of the approach is important in extending electron-scattering calculations to more complex targets than it is possible with other methods. Program summaryTitle of program:FERM3D Catalogue identifier:ADYL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYL_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested:Intel Xeon, AMD Opteron 64 bit, Compaq Alpha Operating systems or monitors under which the program has been tested:HP Tru64 Unix v5.1, Red Hat Linux Enterprise 3 Programming language used:Fortran 90 Memory required to execute with typical data:900 MB (neutral CO 2), 2.3 GB (ionic CO 2), 1.4 GB (benzene) No. of bits in a word:32 No. of processors used:1 Has the code been vectorized?:No No. of lines in distributed program, including test data, etc.:58 383 No. of bytes in distributed program, including test data, etc.:561 653 Distribution format:tar.gzip file CPC Program library subprograms used:ADDA, ACDP Nature of physical problem:Scattering of an
Kılıç, Emre Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
NASA Technical Reports Server (NTRS)
Nakazawa, Shohei
1991-01-01
Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.
2013-01-01
PURPOSE This study was accomplished to assess the biomechanical state of different retaining methods of bar implant-overdenture. MATERIALS AND METHODS Two 3D finite element models were designed. The first model included implant overdenture retained by Hader-clip attachment, while the second model included two extracoronal resilient attachment (ERA) studs added distally to Hader splint bar. A non-linear frictional contact type was assumed between overdentures and mucosa to represent sliding and rotational movements among different attachment components. A 200 N was applied at the molar region unilaterally and perpendicular to the occlusal plane. Additionally, the mandible was restrained at their ramus ends. The maximum equivalent stress and strain (von Mises) were recorded and analyzed at the bone-implant interface level. RESULTS The values of von Mises stress and strain of the first model at bone-implant interface were higher than their counterparts of the second model. Stress concentration and high value of strain were recognized surrounding implant of the unloaded side in both models. CONCLUSION There were different patterns of stress-strain distribution at bone-implant interface between the studied attachment designs. Hader bar-clip attachment showed better biomechanical behavior than adding ERA studs distal to hader bar. PMID:24049576
NASA Technical Reports Server (NTRS)
Wang, Ren H.
1991-01-01
A method of combined use of magnetic vector potential (MVP) based finite element (FE) formulations and magnetic scalar potential (MSP) based FE formulations for computation of three-dimensional (3D) magnetostatic fields is developed. This combined MVP-MSP 3D-FE method leads to considerable reduction by nearly a factor of 3 in the number of unknowns in comparison to the number of unknowns which must be computed in global MVP based FE solutions. This method allows one to incorporate portions of iron cores sandwiched in between coils (conductors) in current-carrying regions. Thus, it greatly simplifies the geometries of current carrying regions (in comparison with the exclusive MSP based methods) in electric machinery applications. A unique feature of this approach is that the global MSP solution is single valued in nature, that is, no branch cut is needed. This is again a superiority over the exclusive MSP based methods. A Newton-Raphson procedure with a concept of an adaptive relaxation factor was developed and successfully used in solving the 3D-FE problem with magnetic material anisotropy and nonlinearity. Accordingly, this combined MVP-MSP 3D-FE method is most suited for solution of large scale global type magnetic field computations in rotating electric machinery with very complex magnetic circuit geometries, as well as nonlinear and anisotropic material properties.
Acceleration of 3D Finite Difference AWP-ODC for seismic simulation on GPU Fermi Architecture
NASA Astrophysics Data System (ADS)
Zhou, J.; Cui, Y.; Choi, D.
2011-12-01
AWP-ODC, a highly scalable parallel finite-difference application, enables petascale 3D earthquake calculations. This application generates realistic dynamic earthquake source description and detailed physics-based anelastic ground motions at frequencies pertinent to safe building design. In 2010, the code achieved M8, a full dynamical simulation of a magnitude-8 earthquake on the southern San Andreas fault up to 2-Hz, the largest-ever earthquake simulation. Building on the success of the previous work, we have implemented CUDA on AWP-ODC to accelerate wave propagation on GPU platform. Our CUDA development aims on aggressive parallel efficiency, optimized global and shared memory access to make the best use of GPU memory hierarchy. The benchmark on NVIDIA Tesla C2050 graphics cards demonstrated many tens of speedup in single precision compared to serial implementation at a testing problem size, while an MPI-CUDA implementation is in the progress to extend our solver to multi-GPU clusters. Our CUDA implementation has been carefully verified for accuracy.
A NURBS-based generalized finite element scheme for 3D simulation of heterogeneous materials
NASA Astrophysics Data System (ADS)
Safdari, Masoud; Najafi, Ahmad R.; Sottos, Nancy R.; Geubelle, Philippe H.
2016-08-01
A 3D NURBS-based interface-enriched generalized finite element method (NIGFEM) is introduced to solve problems with complex discontinuous gradient fields observed in the analysis of heterogeneous materials. The method utilizes simple structured meshes of hexahedral elements that do not necessarily conform to the material interfaces in heterogeneous materials. By avoiding the creation of conforming meshes used in conventional FEM, the NIGFEM leads to significant simplification of the mesh generation process. To achieve an accurate solution in elements that are crossed by material interfaces, the NIGFEM utilizes Non-Uniform Rational B-Splines (NURBS) to enrich the solution field locally. The accuracy and convergence of the NIGFEM are tested by solving a benchmark problem. We observe that the NIGFEM preserves an optimal rate of convergence, and provides additional advantages including the accurate capture of the solution fields in the vicinity of material interfaces and the built-in capability for hierarchical mesh refinement. Finally, the use of the NIGFEM in the computational analysis of heterogeneous materials is discussed.
Finite element modeling of a 3D coupled foot-boot model.
Qiu, Tian-Xia; Teo, Ee-Chon; Yan, Ya-Bo; Lei, Wei
2011-12-01
Increasingly, musculoskeletal models of the human body are used as powerful tools to study biological structures. The lower limb, and in particular the foot, is of interest because it is the primary physical interaction between the body and the environment during locomotion. The goal of this paper is to adopt the finite element (FE) modeling and analysis approaches to create a state-of-the-art 3D coupled foot-boot model for future studies on biomechanical investigation of stress injury mechanism, foot wear design and parachute landing fall simulation. In the modeling process, the foot-ankle model with lower leg was developed based on Computed Tomography (CT) images using ScanIP, Surfacer and ANSYS. Then, the boot was represented by assembling the FE models of upper, insole, midsole and outsole built based on the FE model of the foot-ankle, and finally the coupled foot-boot model was generated by putting together the models of the lower limb and boot. In this study, the FE model of foot and ankle was validated during balance standing. There was a good agreement in the overall patterns of predicted and measured plantar pressure distribution published in literature. The coupled foot-boot model will be fully validated in the subsequent works under both static and dynamic loading conditions for further studies on injuries investigation in military and sports, foot wear design and characteristics of parachute landing impact in military. PMID:21676642
Rigorous interpolation near tilted interfaces in 3-D finite-difference EM modelling
NASA Astrophysics Data System (ADS)
Shantsev, Daniil V.; Maaø, Frank A.
2015-02-01
We present a rigorous method for interpolation of electric and magnetic fields close to an interface with a conductivity contrast. The method takes into account not only a well-known discontinuity in the normal electric field, but also discontinuity in all the normal derivatives of electric and magnetic tangential fields. The proposed method is applied to marine 3-D controlled-source electromagnetic modelling (CSEM) where sources and receivers are located close to the seafloor separating conductive seawater and resistive formation. For the finite-difference scheme based on the Yee grid, the new interpolation is demonstrated to be much more accurate than alternative methods (interpolation using nodes on one side of the interface or interpolation using nodes on both sides, but ignoring the derivative jumps). The rigorous interpolation can handle arbitrary orientation of interface with respect to the grid, which is demonstrated on a marine CSEM example with a dipping seafloor. The interpolation coefficients are computed by minimizing a misfit between values at the nearest nodes and linear expansions of the continuous field components in the coordinate system aligned with the interface. The proposed interpolation operators can handle either uniform or non-uniform grids and can be applied to interpolation for both sources and receivers.
Validation Studies of the Finite Orbit Width version of the CQL3D code
NASA Astrophysics Data System (ADS)
Petrov, Yu. V.; Harvey, R. W.
2014-10-01
The Finite-Orbit-Width (FOW) version of the CQL3D bounce-averaged Fokker-Planck (FP) code has been further developed and tested. The neoclassical radial transport appears naturally in this version by averaging the local collision coefficients along guiding center orbits, with a proper transformation matrix from local (R,Z) coordinates to the midplane computational coordinates, where the FP equation is solved. In a similar way, the local quasilinear rf diffusion terms give rise to additional radial transport of orbits. The main challenge is the internal boundary conditions (IBC) which add many elements into the matrix of coefficients for the solution of FPE on the computational grid, effectively making it a non-banded matrix (but still sparse). Steady state runs have been achieved at NERSC supercomputers in typically 10 time steps. Validation tests are performed for NSTX conditions, but using different scaling factors of equilibrium magnetic field, from 0.5 to 8.0. The bootstrap current calculations for ions show a reasonable agreement of current density profiles with Sauter et al. model equations which are based on 1st order expansion, although the magnitudes of currents may differ by up to 30%. Supported by USDOE grants SC0006614, ER54744, and ER44649.
A new 3D finite element model of the IEC 60318-1 artificial ear
NASA Astrophysics Data System (ADS)
Bravo, Agustín; Barham, Richard; Ruiz, Mariano; López, Juan Manuel; DeArcas, Guillermo; Recuero, Manuel
2008-08-01
The artificial ear specified in IEC 60318-1 is used for the measurement of headphones and has been designed to present an acoustic load equivalent to that of normal human ears. In this respect it is specified in terms of an acoustical impedance, and modelled by a lumped parameter approach. However, this has some inherent frequency limitations and becomes less valid as the acoustic wavelength approaches the characteristic dimensions within the device. In addition, when sound propagates through structures such as narrow tubes, annular slits or over sharp corners, noticeable thermal and viscous effects take place causing further departure from the lumped parameter model. A new numerical model has therefore been developed, which gives proper consideration to the aforementioned effects. Both kinds of losses can be simulated by means of the LMS Virtual Lab acoustic software which facilitates finite and boundary element modelling of the whole artificial ear. A full 3D model of the artificial ear has therefore been developed based on key dimensional data found in IEC 60318-1. The model has been used to calculate the acoustical impedance, and the results compared with the corresponding data determined from the lumped parameter model. The numerical simulation of the artificial ear has been shown to provide realistic results, and is a powerful tool for developing a detailed understanding of the device. It is also proving valuable in the revision of IEC 60318-1 that is currently in progress.
3D finite element simulation of effects of deflection rate on energy absorption for TRIP steel
NASA Astrophysics Data System (ADS)
Hayashi, Asuka; Pham, Hang; Iwamoto, Takeshi
2015-09-01
Recently, with the requirement of lighter weight and more safety for a design of automobile, energy absorption capability of structural materials has become important. TRIP (Transformation-induced Plasticity) steel is expected to apply to safety members because of excellent energy absorption capability and ductility. Past studies proved that such excellent characteristics in TRIP steel are dominated by strain-induced martensitic transformation (SIMT) during plastic deformation. Because SIMT strongly depends on deformation rate and temperature, an investigation of the effects of deformation rate and temperature on energy absorption in TRIP is essential. Although energy absorption capability of material can be estimated by J-integral experimentally by using pre-cracked specimen, it is difficult to determine volume fraction of martensite and temperature rise during the crack extension. In addition, their effects on J-integral, especially at high deformation rate in experiment might be quite hard. Thus, a computational prediction needs to be performed. In this study, bending deformation behavior of pre-cracked specimen until the onset point of crack extension are predicted by 3D finite element simulation based on the transformation kinetics model proposed by Iwamoto et al. (1998). It is challenged to take effects of temperature, volume fraction of martensite and deformation rate into account. Then, the mechanism for higher energy absorption characteristic will be discussed.
NASA Technical Reports Server (NTRS)
Nakazawa, Shohei
1989-01-01
The internal structure is discussed of the MHOST finite element program designed for 3-D inelastic analysis of gas turbine hot section components. The computer code is the first implementation of the mixed iterative solution strategy for improved efficiency and accuracy over the conventional finite element method. The control structure of the program is covered along with the data storage scheme and the memory allocation procedure and the file handling facilities including the read and/or write sequences.
NASA Astrophysics Data System (ADS)
Anderson, T. S.; Miller, R.; Greenfield, R.; Fisk, D.
2002-12-01
The propagation of seismic waves through regions of complex topography is not thoroughly understood. Surface waves, are of particular interest, as they are large in amplitude and can characterize the source depth, magnitude, and frequency content. The amplitude and frequency content of seismic waves that propagate in regions with large topographical variations are affected by both the scattering and blockage of the wave energy. The ability to predict the 3-d scattering due to topography will improve the understanding of both regional scale surface wave magnitudes, and refine surface wave discriminants as well as at the local scale (<2 km ) where it will aid in the development of rule of thumb guide lines for array sensor placement for real time sensing technologies. Ideally, when validating the numerical accuracy of a propagation model against field data, the input geologic parameters would be known and thus eliminates geology as a source of error in the calculation. In March of 2001, Kansas Geological Survey (KGS) performed a detailed seismic site characterization at the Smart Weapons Test Range, Yuma Proving Ground, Arizona. The result of the KGS characterization study is a high-resolution 3-d model that is used in our seismic simulations. The velocities Vs, Vp are calculated by tomography and refraction, attenuation coefficients estimated from the surface wave and from p-waves and are provided in a model with attributes resolved in 3-d to 0.5 meters. In the present work, we present comparisons of synthetic data with seismic data collected at the Smart Weapons Test Range to benchmark the accuracy achieved in simulating 3-d wave propagation in the vicinity of a topographical anomaly (trench). Synthetic seismograms are generated using a 3-d 8th order staggered grid visco-elastic finite difference code that accounts for topography. The geologic model is based on the Yuma site characterization. The size of these calculations required use of the DoD High Performance
Latour, Gaël; Echard, Jean-Philippe; Didier, Marie; Schanne-Klein, Marie-Claire
2012-10-22
We demonstrate multimodal nonlinear optical imaging of historical artifacts by combining Second Harmonic Generation (SHG) and Two-Photon Excited Fluorescence (2PEF) microscopies. We first identify the nonlinear optical response of materials commonly encountered in coatings of cultural heritage artifacts by analyzing one- and multi-layered model samples. We observe 2PEF signals from cochineal lake and sandarac and show that pigments and varnish films can be discriminated by exploiting their different emission spectral ranges as in luminescence linear spectroscopy. We then demonstrate SHG imaging of a filler, plaster, composed of bassanite particles which exhibit a non centrosymmetric crystal structure. We also show that SHG/2PEF imaging enables the visualization of wood microstructure through typically 60 µm-thick coatings by revealing crystalline cellulose (SHG signal) and lignin (2PEF signal) in the wood cell walls. Finally, in situ multimodal nonlinear imaging is demonstrated in a historical violin. SHG/2PEF imaging thus appears as a promising non-destructive and contactless tool for in situ 3D investigation of historical coatings and more generally for wood characterization and coating analysis at micrometer scale. PMID:23187225
Finite-Difference Algorithm for Simulating 3D Electromagnetic Wavefields in Conductive Media
NASA Astrophysics Data System (ADS)
Aldridge, D. F.; Bartel, L. C.; Knox, H. A.
2013-12-01
Electromagnetic (EM) wavefields are routinely used in geophysical exploration for detection and characterization of subsurface geological formations of economic interest. Recorded EM signals depend strongly on the current conductivity of geologic media. Hence, they are particularly useful for inferring fluid content of saturated porous bodies. In order to enhance understanding of field-recorded data, we are developing a numerical algorithm for simulating three-dimensional (3D) EM wave propagation and diffusion in heterogeneous conductive materials. Maxwell's equations are combined with isotropic constitutive relations to obtain a set of six, coupled, first-order partial differential equations governing the electric and magnetic vectors. An advantage of this system is that it does not contain spatial derivatives of the three medium parameters electric permittivity, magnetic permeability, and current conductivity. Numerical solution methodology consists of explicit, time-domain finite-differencing on a 3D staggered rectangular grid. Temporal and spatial FD operators have order 2 and N, where N is user-selectable. We use an artificially-large electric permittivity to maximize the FD timestep, and thus reduce execution time. For the low frequencies typically used in geophysical exploration, accuracy is not unduly compromised. Grid boundary reflections are mitigated via convolutional perfectly matched layers (C-PMLs) imposed at the six grid flanks. A shared-memory-parallel code implementation via OpenMP directives enables rapid algorithm execution on a multi-thread computational platform. Good agreement is obtained in comparisons of numerically-generated data with reference solutions. EM wavefields are sourced via point current density and magnetic dipole vectors. Spatially-extended inductive sources (current carrying wire loops) are under development. We are particularly interested in accurate representation of high-conductivity sub-grid-scale features that are common
SIMULATIONS OF 2D AND 3D THERMOCAPILLARY FLOWS BY A LEAST-SQUARES FINITE ELEMENT METHOD. (R825200)
Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank-Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matri...
The numerical integration and 3-D finite element formulation of a viscoelastic model of glass
Chambers, R.S.
1994-08-01
The use of glasses is widespread in making hermetic, insulating seals for many electronic components. Flat panel displays and fiber optic connectors are other products utilizing glass as a structural element. When glass is cooled from sealing temperatures, residual stresses are generated due to mismatches in thermal shrinkage created by the dissimilar material properties of the adjoining materials. Because glass is such a brittle material at room temperature, tensile residual stresses must be kept small to ensure durability and avoid cracking. Although production designs and the required manufacturing process development can be deduced empirically, this is an expensive and time consuming process that does not necessarily lead to an optimal design. Agile manufacturing demands that analyses be used to reduce development costs and schedules by providing insight and guiding the design process through the development cycle. To make these gains, however, viscoelastic models of glass must be available along with the right tool to use them. A viscoelastic model of glass can be used to simulate the stress and volume relaxation that occurs at elevated temperatures as the molecular structure of the glass seeks to equilibrate to the state of the supercooled liquid. The substance of the numerical treatment needed to support the implementation of the model in a 3-D finite element program is presented herein. An accurate second-order, central difference integrator is proposed for the constitutive equations, and numerical solutions are compared to those obtained with other integrators. Inherent convergence problems are reviewed and fixes are described. The resulting algorithms are generally applicable to the broad class of viscoelastic material models. First-order error estimates are used as a basis for developing a scheme for automatic time step controls, and several demonstration problems are presented to illustrate the performance of the methodology.
NASA Astrophysics Data System (ADS)
Bayona, Victor; Kindelan, Manuel
2013-10-01
Laminar flame propagation is an important problem in combustion modelling for which great advances have been achieved both in its theoretical understanding and in the numerical solution of the governing equations in 2D and 3D. Most of these numerical simulations use finite difference techniques on simple geometries (channels, ducts, ...) with equispaced nodes. The objective of this work is to explore the applicability of the radial basis function generated finite difference (RBF-FD) method to laminar flame propagation modelling. This method is specially well suited for the solution of problems with complex geometries and irregular boundaries. Another important advantage is that the method is independent of the dimension of the problem and, therefore, it is very easy to apply in 3D problems with complex geometries. In this work we use the RBF-FD method to compute 2D and 3D numerical results that simulate premixed laminar flames with different Lewis numbers propagating in open ducts.
Observation of Self-Similar Behavior of the 3D, Nonlinear Rayleigh-Taylor Instability
Sadot, O.; Smalyuk, V.A.; Delettrez, J.A.; Sangster, T.C.; Goncharov, V.N.; Meyerhofer, D.D.; Betti, R.; Shvarts, D.
2005-12-31
The Rayleigh-Taylor unstable growth of laser-seeded, 3D broadband perturbations was experimentally measured in the laser-accelerated, planar plastic foils. The first experimental observation showing the self-similar behavior of the bubble size and amplitude distributions under ablative conditions is presented. In the nonlinear regime, the modulation {sigma}{sub rms} grows as {alpha}{sub {sigma}}gt{sup 2}, where g is the foil acceleration, t is the time, and {alpha}{sub {sigma}} is constant. The number of bubbles evolves as N(t){proportional_to}({omega}t{radical}(g)+C){sup -4} and the average size evolves as <{lambda}>(t){proportional_to}{omega}{sup 2}gt{sup 2}, where C is a constant and {omega}=0.83{+-}0.1 is the measured scaled bubble-merging rate.
Integrated gravity and gravity gradient 3D inversion using the non-linear conjugate gradient
NASA Astrophysics Data System (ADS)
Qin, Pengbo; Huang, Danian; Yuan, Yuan; Geng, Meixia; Liu, Jie
2016-03-01
Gravity data, which are critical in mineral, oil, and gas exploration, are obtained from the vertical component of the gravity field, while gravity gradient data are measured from changes in the gravity field in three directions. However, few studies have sought to improve exploration techniques by integrating gravity and gravity gradient data using inversion methods. In this study, we developed a new method to integrate gravity and gravity gradient data in a 3D density inversion using the non-linear conjugate gradient (NLCG) method and the minimum gradient support (MGS) functional to regularize the 3D inverse problem and to obtain a clear and accurate image of the anomalous body. The NLCG algorithm, which is suitable for solving large-scale nonlinear optimization problems and requires no memory storage, was compared to the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm and the results indicated that the convergence rate of NLCG is slower, but that the storage requirement and computation time is lower. To counteract the decay in kernel function, we introduced a depth weighting function for anomalous bodies at the same depth, with information about anomalous body depth obtained from well log and seismic exploration data. For anomalous bodies at different depths, we introduced a spatial gradient weighting function to incorporate additional information obtained in the inversion. We concluded that the spatial gradient weighting function enhanced the spatial resolution of the recovered model. Furthermore, our results showed that including multiple components for inversion increased the resolution of the recovered model. We validated our model by applying our inversion method to survey data from Vinton salt dome, Louisiana, USA. The results showed good agreement with known geologic information; thus confirming the accuracy of this approach.
Development and evaluation of a 3D model observer with nonlinear spatiotemporal contrast sensitivity
NASA Astrophysics Data System (ADS)
Avanaki, Ali R. N.; Espig, Kathryn S.; Maidment, Andrew D. A.; Marchessoux, Cedric; Bakic, Predrag R.; Kimpe, Tom R. L.
2014-03-01
We investigate improvements to our 3D model observer with the goal of better matching human observer performance as a function of viewing distance, effective contrast, maximum luminance, and browsing speed. Two nonlinear methods of applying the human contrast sensitivity function (CSF) to a 3D model observer are proposed, namely the Probability Map (PM) and Monte Carlo (MC) methods. In the PM method, the visibility probability for each frequency component of the image stack, p, is calculated taking into account Barten's spatiotemporal CSF, the component modulation, and the human psychometric function. The probability p is considered to be equal to the perceived amplitude of the frequency component and thus can be used by a traditional model observer (e.g., LG-msCHO) in the space-time domain. In the MC method, each component is randomly kept with probability p or discarded with 1-p. The amplitude of the retained components is normalized to unity. The methods were tested using DBT stacks of an anthropomorphic breast phantom processed in a comprehensive simulation pipeline. Our experiments indicate that both the PM and MC methods yield results that match human observer performance better than the linear filtering method as a function of viewing distance, effective contrast, maximum luminance, and browsing speed.
3D modelling of non-linear visco-elasto-plastic crustal and lithospheric processes using LaMEM
NASA Astrophysics Data System (ADS)
Popov, Anton; Kaus, Boris
2016-04-01
LaMEM (Lithosphere and Mantle Evolution Model) is a three-dimensional thermo-mechanical numerical code to simulate crustal and lithospheric deformation. The code is based on a staggered finite difference (FDSTAG) discretization in space, which is a stable and very efficient technique to solve the (nearly) incompressible Stokes equations that does not suffer from spurious pressure modes or artificial compressibility (a typical feature of low-order finite element techniques). Higher order finite element methods are more accurate than FDSTAG methods under idealized test cases where the jump in viscosity is exactly aligned with the boundaries of the elements. Yet, geodynamically more realistic cases involve evolving subduction zones, nonlinear rheologies or localized plastic shear bands. In these cases, the viscosity pattern evolves spontaneously during a simulation or even during nonlinear iterations, and the advantages of higher order methods disappear and they all converge with approximately first order accuracy, similar to that of FDSTAG [1]. Yet, since FDSTAG methods have considerably less degrees of freedom than quadratic finite element methods, they require about an order of magnitude less memory for the same number of nodes in 3D which also implies that every matrix-vector multiplication is significantly faster. LaMEM is build on top of the PETSc library and uses the particle-in-cell technique to track material properties, history variables which makes it straightforward to incorporate effects like phase changes or chemistry. An internal free surface is present, together with (simple) erosion and sedimentation processes, and a number of methods are available to import complex geometries into the code (e.g, http://geomio.bitbucket.org). Customized Galerkin coupled geometric multigrid preconditioners are implemented which resulted in a good parallel scalability of the code (we have tested LaMEM on 458'752 cores [2]). Yet, the drawback of using FDSTAG
Study of nonlinear 3-D evolution of kinetic Alfvén wave and fluctuation spectra
NASA Astrophysics Data System (ADS)
Sharma, Prachi; Yadav, Nitin; Sharma, R. P.
2015-11-01
Waves and instabilities play a very crucial role in astrophysical plasmas e.g. solar wind, Geospace etc. The main objective of current study is to investigate the importance of nonlinear processes associated with kinetic Alfvén waves (KAWs) in order to understand the physical mechanism behind the magnetopause turbulence. Numerical simulation of the coupled equations guiding the dynamics of three dimensionally propagating kinetic Alfvén wave (KAW) and slow magnetosonic wave has been performed for intermediate beta plasma (i.e. me/mi ≪ β < 1, where β is thermal to magnetic pressure ratio) applicable to the magnetopause. A simplified semi-analytical model based on paraxial approach has also been developed. We have examined the field localization and associated power spectrum of 3-D kinetic Alfvén wave for this nonlinear interaction. Governing dynamical equations of KAW and slow magnetosonic wave get coupled when the ponderomotive force arising due to pump KAW is taken into account while studying the slow magnetosonic wave dynamics. The numerical prediction of power law scaling is just consistent with the observation of THEMIS spacecraft in the magnetopause.
A non-linear 3D printed electromagnetic vibration energy harvester
NASA Astrophysics Data System (ADS)
Constantinou, P.; Roy, S.
2015-12-01
This paper describes a novel electromagnetic energy harvester that exploits the low flexural modulus of ABS and comprises of a nonlinear mechanism to enhance the generated power and bandwidth. The device is printed using desktop additive manufacturing techniques (3D printing) that use thermoplastics. It has a ‘V’ spring topology and exhibits a softening spring non-linearity introduced through the magnetic arrangement, which introduces a monostable potential well. A model is presented and measurements correspond favourably. The produced prototype generates a peak power of approximately 2.5mW at a frame acceleration of 1g and has a power bandwidth of approximately 1.2→1.5Hz and 3.5→3.9Hz during up and down sweeps respectively. The device has a power density of 0.4mW/cm3 at a frame acceleration of 1g and a density of 0.04mW/cm3 from a generated power of 25μW at 0.1g.
Nonlinear Finite Element Analysis of FRP Strengthened Reinforced Concrete Beams
NASA Astrophysics Data System (ADS)
Sasmal, S.; Kalidoss, S.; Srinivas, V.
2012-12-01
This paper focuses on nonlinear analysis of parent and fiber reinforced polymer (FRP) strengthened reinforced concrete (RC) beam using general purpose finite element software, ANSYS. Further, it is aimed to investigate the suitability of different elements available in ANSYS library to represent FRP, epoxy and interface. 3-D structural RC solid element has been used to model concrete and truss element is employed for modeling the reinforcements. FRP has been modelled using 3-D membrane element and layered element with number of layers, epoxy is modelled using eight node brick element, and eight node layered solid shell is used to mathematically represent the concrete-FRP interface behavior. Initially, the validation of the numerical model for the efficacy of different elements (SOLID65 for concrete and LINK8 for reinforcement) and material models is carried out on the experimental beam reported in literature. The validated model, elements and material properties is used to evaluate the load-displacement and load-strain response behavior and crack patterns of the FRP strengthened RC beams. The numerical results indicated that significant improvement in the displacement in the strengthened RC beams with the advancement of cracks. The study shows that FRP with shell elements is recommended when single layer of FRP is used. When multi layered FRP is used, solid layered element can be a reasonably good choice whereas the epoxy matrix with linear solid element does not need further complicated model. Interfacial element makes the analysis minimally improved at the cost of complicated modeling issues and considerable computation time. Hence, for nonlinear analysis of usual strengthened structures, unless it is specifically required for, interface element may not be required and a full contact can be assumed at interface.
NASA Astrophysics Data System (ADS)
Oprsal, I.; Faeh, D.; Giardini, D.
2002-12-01
The disastrous Basel earthquake of October 18, 1356 (I0=X, M ≈ 6.9), appeared in, today seismically modest, Basel region (Upper Rhine Graben). The lack of strong ground motion seismic data can be effectively supplied by numerical modeling. We applied the 3D finite differences (FD) to predict ground motions which can be used for microzonation and hazard assessment studies. The FD method is formulated for topography models on irregular rectangular grids. It is a 3D explicit FD formulation of the hyperbolic partial differential equation (PDE). Elastodynamic PDE is solved in the time domain. The Hooke's isotropic inhomogeneous medium contains discontinuities and a topographic free surface. The 3D elastic FD modeling is applied on a newly established P and S-wave velocities structure model. This complex structure contains main interfaces and gradients inside some layers. It is adjacent to the earth surface and includes topography (Kind, Faeh and Giardini, 2002, A 3D Reference Model for the Area of Basel, in prep.). The first attempt was done for a double-couple point source and relatively simple source function. Numerical tests are planned for several finite-extent source histories because the 1356 Basel earthquake source features have not been well determined, yet. The presumed finite-extent source is adjacent to the free surface. The results are compared to the macroseismic information of the Basel area.
NASA Technical Reports Server (NTRS)
Zhao, W.; Newman, J. C., Jr.; Sutton, M. A.; Shivakumar, K. N.; Wu, X. R.
1995-01-01
Parallel with the work in Part-1, stress intensity factors for semi-elliptical surface cracks emanating from a circular hole are determined. The 3-D weight function method with the 3D finite element solutions for the uncracked stress distribution as in Part-1 is used for the analysis. Two different loading conditions, i.e. remote tension and wedge loading, are considered for a wide range in geometrical parameters. Both single and double surface cracks are studied and compared with other solutions available in the literature. Typical crack opening displacements are also provided.
3D Functional Elements Deep Inside Silicon with Nonlinear Laser Lithography
NASA Astrophysics Data System (ADS)
Tokel, Onur; Turnali, Ahmet; Ergecen, Emre; Pavlov, Ihor; Ilday, Fatih Omer
Functional optical and electrical elements fabricated on silicon (Si) constitute fundamental building blocks of electronics and Si-photonics. However, since the highly successful established lithography are geared towards surface processing, elements embedded inside Si simply do not exist. Here, we present a novel direct-laser writing method for positioning buried functional elements inside Si wafers. This new phenomenon is distinct from previous work, in that the surface of Si is not modified. By exploiting nonlinear interactions of a focused laser, permanent refractive index changes are induced inside Si. The imprinted index contrast is then used to demonstrate a plethora of functional elements and capabilities embedded inside Si. In particular, we demonstrate the first functional optical element inside Si, the first information-storage capability inside Si, creation of high-resolution subsurface holograms, buried multilevel structures, and complex 3D architectures in Si, none of which is currently possible with other methods. This new approach complements available techniques by taking advantage of the real estate under Si, and therefore can pave the way for creating entirely new multilevel devices through electronic-photonic integration.
NASA Astrophysics Data System (ADS)
Wendling, A.; Daniel, J. L.; Hivet, G.; Vidal-Sallé, E.; Boisse, P.
2015-12-01
Numerical simulation is a powerful tool to predict the mechanical behavior and the feasibility of composite parts. Among the available numerical approaches, as far as woven reinforced composites are concerned, 3D finite element simulation at the mesoscopic scale leads to a good compromise between realism and complexity. At this scale, the fibrous reinforcement is modeled by an interlacement of yarns assumed to be homogeneous that have to be accurately represented. Among the numerous issues induced by these simulations, the first one consists in providing a representative meshed geometrical model of the unit cell at the mesoscopic scale. The second one consists in enabling a fast data input in the finite element software (contacts definition, boundary conditions, elements reorientation, etc.) so as to obtain results within reasonable time. Based on parameterized 3D CAD modeling tool of unit-cells of dry fabrics already developed, this paper presents an efficient strategy which permits an automated meshing of the models with 3D hexahedral elements and to accelerate of several orders of magnitude the simulation data input. Finally, the overall modeling strategy is illustrated by examples of finite element simulation of the mechanical behavior of fabrics.
Coupled 2D-3D finite element method for analysis of a skin panel with a discontinuous stiffener
NASA Technical Reports Server (NTRS)
Wang, J. T.; Lotts, C. G.; Davis, D. D., Jr.; Krishnamurthy, T.
1992-01-01
This paper describes a computationally efficient analysis method which was used to predict detailed stress states in a typical composite compression panel with a discontinuous hat stiffener. A global-local approach was used. The global model incorporated both 2D shell and 3D brick elements connected by newly developed transition elements. Most of the panel was modeled with 2D elements, while 3D elements were employed to model the stiffener flange and the adjacent skin. Both linear and geometrically nonlinear analyses were performed on the global model. The effect of geometric nonlinearity induced by the eccentric load path due to the discontinuous hat stiffener was significant. The local model used a fine mesh of 3D brick elements to model the region at the end of the stiffener. Boundary conditions of the local 3D model were obtained by spline interpolation of the nodal displacements from the global analysis. Detailed in-plane and through-the-thickness stresses were calculated in the flange-skin interface near the end of the stiffener.
A feasibility study of a 3-D finite element solution scheme for aeroengine duct acoustics
NASA Technical Reports Server (NTRS)
Abrahamson, A. L.
1980-01-01
The advantage from development of a 3-D model of aeroengine duct acoustics is the ability to analyze axial and circumferential liner segmentation simultaneously. The feasibility of a 3-D duct acoustics model was investigated using Galerkin or least squares element formulations combined with Gaussian elimination, successive over-relaxation, or conjugate gradient solution algorithms on conventional scalar computers and on a vector machine. A least squares element formulation combined with a conjugate gradient solver on a CDC Star vector computer initially appeared to have great promise, but severe difficulties were encountered with matrix ill-conditioning. These difficulties in conditioning rendered this technique impractical for realistic problems.
Hallquist, J.O.
1981-01-01
A user's manual is provided for NIKE3D, a fully implicit three-dimensional finite element code for analyzing the large deformation static and dynamic response of inelastic solids. A contact-impact algorithm permits gaps and sliding along material interfaces. By a specialization of this algorithm, such interfaces can be rigidly tied to admit variable zoning without the need of transition regions. Spatial discretization is achieved by the use of 8-node constant pressure solid elements. Bandwidth minimization is optional. Post-processors for NIKE3D include GRAPE for plotting deformed shapes and stress contours and DYNAP for plotting time histories.
Non-linear 3-D Born shear waveform tomography in Southeast Asia
NASA Astrophysics Data System (ADS)
Panning, Mark P.; Cao, Aimin; Kim, Ahyi; Romanowicz, Barbara A.
2012-07-01
Southeast (SE) Asia is a tectonically complex region surrounded by many active source regions, thus an ideal test bed for developments in seismic tomography. Much recent development in tomography has been based on 3-D sensitivity kernels based on the first-order Born approximation, but there are potential problems with this approach when applied to waveform data. In this study, we develop a radially anisotropic model of SE Asia using long-period multimode waveforms. We use a theoretical 'cascade' approach, starting with a large-scale Eurasian model developed using 2-D Non-linear Asymptotic Coupling Theory (NACT) sensitivity kernels, and then using a modified Born approximation (nBorn), shown to be more accurate at modelling waveforms, to invert a subset of the data for structure in a subregion (longitude 75°-150° and latitude 0°-45°). In this subregion, the model is parametrized at a spherical spline level 6 (˜200 km). The data set is also inverted using NACT and purely linear 3-D Born kernels. All three final models fit the data well, with just under 80 per cent variance reduction as calculated using the corresponding theory, but the nBorn model shows more detailed structure than the NACT model throughout and has much better resolution at depths greater than 250 km. Based on variance analysis, the purely linear Born kernels do not provide as good a fit to the data due to deviations from linearity for the waveform data set used in this modelling. The nBorn isotropic model shows a stronger fast velocity anomaly beneath the Tibetan Plateau in the depth range of 150-250 km, which disappears at greater depth, consistent with other studies. It also indicates moderate thinning of the high-velocity plate in the middle of Tibet, consistent with a model where Tibet is underplated by Indian lithosphere from the south and Eurasian lithosphere from the north, in contrast to a model with continuous underplating by Indian lithosphere across the entire plateau. The n
NASA Technical Reports Server (NTRS)
1976-01-01
The development of two new shell finite elements for applications to large deflection problems is considered. The elements in question are doubly curved and of triangular and quadrilateral planform. They are restricted to small strains of elastic materials, and can accommodate large rotations. The elements described, which are based on relatively simple linear elements, make use of a new displacement function approach specifically designed for strongly nonlinear problems. The displacement function development for nonlinear applications is based on certain beam element formulations, and the strain-displacement equations are of a shallow shell type. Additional terms were included in these equations in an attempt to avoid the large errors characteristic of shallow shell elements in certain types of problems. An incremental nonlinear solution procedure specifically adopted to the element formulation was developed. The solution procedure is of combined incremental and total Lagrangian type, and uses a new updating scheme. A computer program was written to evaluate the developed formulations. This program can accommodate small element groups in arbitrary arrangements. Two simple programs were successfully solved. The results indicate that this new type of element has definite promise and should be a fruitful area for further research.
A fully nonlinear, mixed spectral and finite difference model for thermally driven, rotating flows
NASA Technical Reports Server (NTRS)
Miller, Timothy L.; Lu, Huei-Iin; Butler, Karen A.
1992-01-01
Finite difference in time and the meridional plane, in conjunction with a spectral technique in the azimuthal direction, are used to approximate the Navier-Stokes equations in a model that can simulate a variety of thermally driven rotating flows in cylindrical and spherical geometries. Axisymmetric flow, linearized waves relative to a fixed or changing axisymmetric flow, nonlinear waves without wave-wave interaction, and fully nonlinear 3D flow, can in this way be calculated. A reexamination is conducted of the steady baroclinic wave case previously treated by Williams (1971) and Quon (1976).
Smalyuk, V.A.; Sadot, O.; Delettrez, J.A.; Meyerhofer, D.D.; Regan, S.P.; Sangster, T.C.
2005-12-05
Nonlinear growth of 3-D broadband nonuniformities was measured near saturation levels using x-ray radiography in planar foils accelerated by laser light. The initial target modulations were seeded by laser nonuniformities and later amplified during acceleration by Rayleigh-Taylor instability. The nonlinear saturation velocities are measured for the first time and are found to be in excellent agreement with Haan predictions. The measured growth of long-wavelength modes is consistent with enhanced, nonlinear, long-wavelength generation in ablatively driven targets.
The NCOREL computer program for 3D nonlinear supersonic potential flow computations
NASA Technical Reports Server (NTRS)
Siclari, M. J.
1983-01-01
An innovative computational technique (NCOREL) was established for the treatment of three dimensional supersonic flows. The method is nonlinear in that it solves the nonconservative finite difference analog of the full potential equation and can predict the formation of supercritical cross flow regions, embedded and bow shocks. The method implicitly computes a conical flow at the apex (R = 0) of a spherical coordinate system and uses a fully implicit marching technique to obtain three dimensional cross flow solutions. This implies that the radial Mach number must remain supersonic. The cross flow solutions are obtained by using type dependent transonic relaxation techniques with the type dependency linked to the character of the cross flow velocity (i.e., subsonic/supersonic). The spherical coordinate system and marching on spherical surfaces is ideally suited to the computation of wing flows at low supersonic Mach numbers due to the elimination of the subsonic axial Mach number problems that exist in other marching codes that utilize Cartesian transverse marching planes.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2016-02-01
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less
Edge-based finite elements and vector ABCs applied to 3D scattering
NASA Technical Reports Server (NTRS)
Chatterjee, A.; Jin, J. M.; Volakis, John L.
1992-01-01
An edge based finite element formulation with vector absorbing boundary conditions is presented for scattering by composite structures having boundaries satisfying impedance and/or transition conditions. Remarkably accurate results are obtained by placing the mesh a small fraction of a wavelength away from the scatterer.
NASA Astrophysics Data System (ADS)
Belashov, Vasily
We study the formation, structure, stability and dynamics of the multidimensional soliton-like beam structures forming on the low-frequency branch of oscillation in the ionospheric and magnetospheric plasma for cases when beta=4pinT/B(2) <<1 and beta>1. In first case with the conditions omega
Nonlinear finite element modeling of THUNDER piezoelectric actuators
NASA Astrophysics Data System (ADS)
Taleghani, Barmac K.; Campbell, Joel F.
1999-06-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (Thin Layer Unimorph Ferroelectric Driver) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators
NASA Technical Reports Server (NTRS)
Taleghani, Barmac K.; Campbell, Joel F.
1999-01-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
3D Finite Element Analysis of Spider Non-isothermal Forging Process
NASA Astrophysics Data System (ADS)
Niu, Ling; Wei, Wei; Wei, Kun Xia; Alexandrov, Igor V.; Hu, Jing
2016-05-01
The differences of effective stress, effective strain, velocity field, and the load-time curves between the spider isothermal and non-isothermal forging processes are investigated by making full use of 3D FEA, and verified by the production experiment of spider forging. Effective stress is mainly concentrated on the pin, and becomes lower closer to the front of the pin. The maximum effective strain in the non-isothermal forging is lower than that in the isothermal. The great majority of strain in the non-isothermal forging process is 1.76, which is larger than the strain of 1.31 in the isothermal forging. The maximum load required in the isothermal forging is higher than that in the non-isothermal. The maximum experimental load and deformation temperature in the spider production are in good agreement with those in the non-isothermal FEA. The results indicate that the non-isothermal 3D FEA results can guide the design of the spider forging process.
3D Finite Element Analysis of Spider Non-isothermal Forging Process
NASA Astrophysics Data System (ADS)
Niu, Ling; Wei, Wei; Wei, Kun Xia; Alexandrov, Igor V.; Hu, Jing
2016-06-01
The differences of effective stress, effective strain, velocity field, and the load-time curves between the spider isothermal and non-isothermal forging processes are investigated by making full use of 3D FEA, and verified by the production experiment of spider forging. Effective stress is mainly concentrated on the pin, and becomes lower closer to the front of the pin. The maximum effective strain in the non-isothermal forging is lower than that in the isothermal. The great majority of strain in the non-isothermal forging process is 1.76, which is larger than the strain of 1.31 in the isothermal forging. The maximum load required in the isothermal forging is higher than that in the non-isothermal. The maximum experimental load and deformation temperature in the spider production are in good agreement with those in the non-isothermal FEA. The results indicate that the non-isothermal 3D FEA results can guide the design of the spider forging process.
Static & Dynamic Response of 3D Solids
1996-07-15
NIKE3D is a large deformations 3D finite element code used to obtain the resulting displacements and stresses from multi-body static and dynamic structural thermo-mechanics problems with sliding interfaces. Many nonlinear and temperature dependent constitutive models are available.
A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)
NASA Astrophysics Data System (ADS)
Lee, Jin
2014-05-01
The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM dynamic corel innovations include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), *Icosahedral grid optimization (Wang and Lee, 2011), * All differentials evaluated as three-dimensional finite-volume integrals around the control volume. The three-dimensional finite-volume solver in NIM is designed to improve pressure gradient calculation and orographic precipitation over complex terrain. NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as internal gravity wave, and mountain waves in Dynamical Cores Model Inter-comparisons Projects (DCMIP). Physical parameterizations suitable for NWP are incorporated into NIM dynamical core and successfully tested with multimonth aqua-planet simulations. Recently, NIM has started real data simulations using GFS initial conditions. Results from the idealized tests as well as real-data simulations will be shown in the conference.
Binary 3-D Markov Chain Random Fields: Finite-size Scaling Analysis of Percolation Properties
NASA Astrophysics Data System (ADS)
Harter, T.
2004-12-01
Percolation phenomena in random media have been extensively studied in a wide variety of fields in physics, chemistry, engineering, bio-, earth-, and environmental sciences. Most work has focused on uncorrelated random fields. The critical behavior in media with short-range correlations is thought to be identical to that in uncorrelated systems. However, the percolation threshold, pc, which is 0.3116 in uncorrelated media, has been observed to vary with the correlation scale and also with the random field type. Here, we present percolation properties and finite-size scaling effects in three-dimensional binary cubic lattices represented by correlated Markov-chain random fields and compare them to those in sequential Gaussian and sequential indicator random fields. We find that the computed percolation threshold in correlated random fields is significantly lower than in the uncorrelated lattice and decreases with increasing correlation scale. The rate of decrease rapidly flattens out for correlation lengths larger than 2-3 grid-blocks. At correlation scales of 5-6 grid blocks, pc is found to be 0.126 for the Markov chain random fields and slightly higher for sequential Gaussian and indicator random fields. The universal scaling constants for mean cluster size, backbone fraction, and connectivity are found to be consistent with results on uncorrelated lattices. For numerical studies, it is critical to understand finite-size effects on the percolation and associated phase connectivity properties of lattices. We present detailed statistical results on the percolation properties in finite sized lattice and their dependence on correlation scale. We show that appropriate grid resolution and choice of simulation boundaries is critical to properly simulate correlated natural geologic systems, which may display significant finite-size effects.
A 3D finite element simulation model for TBM tunnelling in soft ground
NASA Astrophysics Data System (ADS)
Kasper, Thomas; Meschke, Günther
2004-12-01
A three-dimensional finite element simulation model for shield-driven tunnel excavation is presented. The model takes into account all relevant components of the construction process (the soil and the ground water, the tunnel boring machine with frictional contact to the soil, the hydraulic jacks, the tunnel lining and the tail void grouting). The paper gives a detailed description of the model components and the stepwise procedure to simulate the construction process. The soil and the grout material are modelled as saturated porous media using a two-field finite element formulation. This allows to take into account the groundwater, the grouting pressure and the fluid interaction between the soil and slurry at the cutting face and between the soil and grout around the tail void. A Cam-Clay plasticity model is used to describe the material behaviour of cohesive soils. The cementitious grouting material in the tail void is modelled as an ageing elastic material with time-dependent stiffness and permeability. To allow for an automated computation of arbitrarily long and also curvilinear driving paths with suitable finite element meshes, the simulation procedure has been fully automated. The simulation of a tunnel advance in soft cohesive soil below the ground water table is presented and the results are compared with measurements taken from the literature. Copyright
NASA Astrophysics Data System (ADS)
Pereira, J. P.; Duarte, C. A.; Jiao, X.; Guoy, D.
2009-06-01
This paper presents a study of generalized enrichment functions for 3D curved crack fronts. Two coordinate systems used in the definition of singular curved crack front enrichment functions are analyzed. In the first one, a set of Cartesian coordinate systems defined along the crack front is used. In the second case, the geometry of the crack front is approximated by a set of curvilinear coordinate systems. A description of the computation of derivatives of enrichment functions and curvilinear base vectors is presented. The coordinate systems are automatically defined using geometrical information provided by an explicit representation of the crack surface. A detailed procedure to accurately evaluate the surface normal, conormal and tangent vectors along curvilinear crack fronts in explicit crack surface representations is also presented. An accurate and robust definition of orthonormal vectors along crack fronts is crucial for the proper definition of enrichment functions. Numerical experiments illustrate the accuracy and robustness of the proposed approaches.
Image forces on 3d dislocation structures in crystals of finite volume
El-Azab, A.
1999-07-01
The present work aims at studying the image stress and image Peach-Koehler force fields for three-dimensional dislocation configurations in a single crystal of finite volume. It is shown that the image stress field is significant within the entire crystal volume, and that the image Peach-Koehler force can be of the same order of magnitude as the direct interaction force calculated from the infinite domain solution. The results demonstrate that image stress gives rise to long-range interaction forces that are important in meso-scale dynamics of dislocation structures.
Image Forces on 3-D Dislocation Structures in Crystals of Finite Volume
El-Azab, Anter ); V.V. Bulatov
1999-01-01
The present work aims at studying the image stress and image Peach-Koehler force fields for three-dimensional dislocation configurations in a single crystal of finite volume. It is shown that the image stress field is significant within the entire crystal volume, and that the image Peach-Koehler force can be of the same order of magnitude as the direct interaction force calculated from the infinite domain solution. The results demonstrate that image stress gives rise to long-range interaction forces that are important in meso-scale dynamics of dislocation structures.
A Lagrange-Galerkin hp-Finite Element Method for a 3D Nonhydrostatic Ocean Model
NASA Astrophysics Data System (ADS)
Galán del Sastre, Pedro; Bermejo, Rodolfo
2016-03-01
We introduce in this paper a Lagrange-Galerkin hp-finite element method to calculate the numerical solution of a nonhydrostatic ocean model. The Lagrange-Galerkin method yields a Stokes-like problem the solution of which is computed by a second-order rotational splitting scheme that separates the calculation of the velocity and pressure, the latter is decomposed into hydrostatic and nonhydrostatic components. We have tested the method in flows where the nonhydrostatic effects are important. The results are very encouraging.
NASA Technical Reports Server (NTRS)
Leser, Patrick E.; Hochhalter, Jacob D.; Newman, John A.; Leser, William P.; Warner, James E.; Wawrzynek, Paul A.; Yuan, Fuh-Gwo
2015-01-01
Utilizing inverse uncertainty quantification techniques, structural health monitoring can be integrated with damage progression models to form probabilistic predictions of a structure's remaining useful life. However, damage evolution in realistic structures is physically complex. Accurately representing this behavior requires high-fidelity models which are typically computationally prohibitive. In the present work, a high-fidelity finite element model is represented by a surrogate model, reducing computation times. The new approach is used with damage diagnosis data to form a probabilistic prediction of remaining useful life for a test specimen under mixed-mode conditions.
Nonlinear structural finite element model updating and uncertainty quantification
NASA Astrophysics Data System (ADS)
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.
2015-04-01
This paper presents a framework for nonlinear finite element (FE) model updating, in which state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with the maximum likelihood estimation method (MLE) to estimate time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure. The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem. A proof-of-concept example, consisting of a cantilever steel column representing a bridge pier, is provided to verify the proposed nonlinear FE model updating framework.
Finite rotation and nonlinear beam kinematics
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.
1987-01-01
Standard means of representing finite rotation in rigid-body kinematics, including orientation angles, Euler parameters, and Rodrigues parameters, are reviewed and compared. General kinematical relations for a beam theory that treats arbitrarily large rotation are then presented. The standard methods of representing finite rotations are applied to these kinematical expressions, and comparison is made among the standard methods and additional methods found in the literature, such as quasi-coordinates and linear combinations of projection angles. The method of Rodrigues parameters is shown to stand out for both its simplicity and generality when applied to beam kinematics, a result that is really missing from the literature.
Finite Orbit Width versions of the CQL3D code: Hybrid-FOW and Full-FOW
NASA Astrophysics Data System (ADS)
Petrov, Yu. V.; Harvey, R. W.
2012-10-01
Finite-Orbit-Width (FOW) effects are being added into the CQL3D bounce-averaged Fokker-Planck code [1] using two main options. In the Hybrid-FOW option, partial FOW capabilities are implemented which add FOW features into the particle source (NB) operator, RF quasilinear operator, diagnostics, and guiding center orbit losses with gyro-radius correction. Collisions remain Zero-Orbit-Width (ZOW). The Hybrid-FOW version provides a greatly improved agreement with signals measured by the NSTX Fast Ion Diagnostic [2]. The advantage of the Hybrid-FOW version is that run time increases by only a factor of two compared to ZOW runs. The Full-FOW option further adds neoclassical radial transport features into the FP coding. The collisional coefficients are averaged along guiding center orbits, with a proper transformation matrix from local coordinates to the midplane coordinates, where the FP equation is solved. All radial terms are included. The computations are parallelized in velocity-grid index, typically using 128 CPU cores. We emphasize that this theory includes nonthermal and full-orbit, not first order correction, neoclassical theory. [4pt] [1] R.W. Harvey and M. McCoy, ``The CQL3D Fokker Planck Code,'' www.compxco.com/cql3d [0pt] [2] R.W. Harvey, Yu. Petrov, D. Liu, W. Heidbrink, P. Bonoli, this mtg (2012)
The Combined Finite-Discrete Element Method applied to the Study of Rock Fracturing Behavior in 3D
Rougier, Esteban; Bradley, Christopher R.; Broom, Scott T.; Knight, Earl E.; Munjiza, Ante; Sussman, Aviva J.; Swift, Robert P.
2011-01-01
Since its introduction the combined finite-discrete element method (FEM/DEM), has become an excellent tool to address a wide range of problems involving fracturing and fragmentation of solids. Within the context of rock mechanics, the FEM/DEM method has been applied to many complex industrial problems such as block caving, deep mining techniques, rock blasting, seismic waves, packing problems, rock crushing problems, etc. In the real world most of the problems involving fracture and fragmentation of solids are three dimensional problems. With the aim of addressing these problems an improved 2D/3D FEM/DEM capability has been developed at Los Alamos National Laboratory (LANL). These capabilities include state of the art 3D contact detection, contact interaction, constitutive material models, and fracture models. In this paper, Split Hopkinson Pressure Bar (SHPB) Brazilian experiments are simulated using this improved 2D/3D FEM/DEM approach which is implemented in LANL's MUNROU (Munjiza-Rougier) code. The results presented in this work show excellent agreement with both the SHPB experiments and previous 2D numerical simulations performed by other FEM/DEM research groups.
NASA Astrophysics Data System (ADS)
Haddag, B.; Kagnaya, T.; Nouari, M.; Cutard, T.
2013-01-01
Modelling machining operations allows estimating cutting parameters which are difficult to obtain experimentally and in particular, include quantities characterizing the tool-workpiece interface. Temperature is one of these quantities which has an impact on the tool wear, thus its estimation is important. This study deals with a new modelling strategy, based on two steps of calculation, for analysis of the heat transfer into the cutting tool. Unlike the classical methods, considering only the cutting tool with application of an approximate heat flux at the cutting face, estimated from experimental data (e.g. measured cutting force, cutting power), the proposed approach consists of two successive 3D Finite Element calculations and fully independent on the experimental measurements; only the definition of the behaviour of the tool-workpiece couple is necessary. The first one is a 3D thermomechanical modelling of the chip formation process, which allows estimating cutting forces, chip morphology and its flow direction. The second calculation is a 3D thermal modelling of the heat diffusion into the cutting tool, by using an adequate thermal loading (applied uniform or non-uniform heat flux). This loading is estimated using some quantities obtained from the first step calculation, such as contact pressure, sliding velocity distributions and contact area. Comparisons in one hand between experimental data and the first calculation and at the other hand between measured temperatures with embedded thermocouples and the second calculation show a good agreement in terms of cutting forces, chip morphology and cutting temperature.
NASA Astrophysics Data System (ADS)
Gu, Xuejun; Jelen, Urszula; Li, Jinsheng; Jia, Xun; Jiang, Steve B.
2011-06-01
Targeting at the development of an accurate and efficient dose calculation engine for online adaptive radiotherapy, we have implemented a finite-size pencil beam (FSPB) algorithm with a 3D-density correction method on graphics processing unit (GPU). This new GPU-based dose engine is built on our previously published ultrafast FSPB computational framework (Gu et al 2009 Phys. Med. Biol. 54 6287-97). Dosimetric evaluations against Monte Carlo dose calculations are conducted on ten IMRT treatment plans (five head-and-neck cases and five lung cases). For all cases, there is improvement with the 3D-density correction over the conventional FSPB algorithm and for most cases the improvement is significant. Regarding the efficiency, because of the appropriate arrangement of memory access and the usage of GPU intrinsic functions, the dose calculation for an IMRT plan can be accomplished well within 1 s (except for one case) with this new GPU-based FSPB algorithm. Compared to the previous GPU-based FSPB algorithm without 3D-density correction, this new algorithm, though slightly sacrificing the computational efficiency (~5-15% lower), has significantly improved the dose calculation accuracy, making it more suitable for online IMRT replanning.
Gu, Xuejun; Jelen, Urszula; Li, Jinsheng; Jia, Xun; Jiang, Steve B
2011-06-01
Targeting at the development of an accurate and efficient dose calculation engine for online adaptive radiotherapy, we have implemented a finite-size pencil beam (FSPB) algorithm with a 3D-density correction method on graphics processing unit (GPU). This new GPU-based dose engine is built on our previously published ultrafast FSPB computational framework (Gu et al 2009 Phys. Med. Biol. 54 6287-97). Dosimetric evaluations against Monte Carlo dose calculations are conducted on ten IMRT treatment plans (five head-and-neck cases and five lung cases). For all cases, there is improvement with the 3D-density correction over the conventional FSPB algorithm and for most cases the improvement is significant. Regarding the efficiency, because of the appropriate arrangement of memory access and the usage of GPU intrinsic functions, the dose calculation for an IMRT plan can be accomplished well within 1 s (except for one case) with this new GPU-based FSPB algorithm. Compared to the previous GPU-based FSPB algorithm without 3D-density correction, this new algorithm, though slightly sacrificing the computational efficiency (∼5-15% lower), has significantly improved the dose calculation accuracy, making it more suitable for online IMRT replanning. PMID:21558589
Orthodontic intrusion of maxillary incisors: a 3D finite element method study
Saga, Armando Yukio; Maruo, Hiroshi; Argenta, Marco André; Maruo, Ivan Toshio; Tanaka, Orlando Motohiro
2016-01-01
Objective: In orthodontic treatment, intrusion movement of maxillary incisors is often necessary. Therefore, the objective of this investigation is to evaluate the initial distribution patterns and magnitude of compressive stress in the periodontal ligament (PDL) in a simulation of orthodontic intrusion of maxillary incisors, considering the points of force application. Methods: Anatomic 3D models reconstructed from cone-beam computed tomography scans were used to simulate maxillary incisors intrusion loading. The points of force application selected were: centered between central incisors brackets (LOAD 1); bilaterally between the brackets of central and lateral incisors (LOAD 2); bilaterally distal to the brackets of lateral incisors (LOAD 3); bilaterally 7 mm distal to the center of brackets of lateral incisors (LOAD 4). Results and Conclusions: Stress concentrated at the PDL apex region, irrespective of the point of orthodontic force application. The four load models showed distinct contour plots and compressive stress values over the midsagittal reference line. The contour plots of central and lateral incisors were not similar in the same load model. LOAD 3 resulted in more balanced compressive stress distribution. PMID:27007765
Nonlinear rheology in ASPECT: benchmarking and an application to 3D subduction
NASA Astrophysics Data System (ADS)
Glerum, Anne; Thieulot, Cedric; Fraters, Menno; Spakman, Wim
2014-05-01
ASPECT (Advanced Solver for Problems in Earth's ConvecTion) is a promising new code designed for modelling thermal convection in the mantle (Kronbichler et al. 2012). The massively parallel code uses state-of-the-art numerical methods, such as high performance solvers and adaptive mesh refinement. It builds on tried-and-well-tested libraries and works with plug-ins allowing easy extension to fine-tune it to the user's specific needs. We extended the code by implementing a frictional plasticity criterion that can be combined with a viscous creep rheology, allowing for thermo-mechanically coupled visco-plastic flow. This way we can accommodate for the nonlinear behavior of the Earth's materials and incorporate for instance the localization of deformation through plastic yielding. This has been shown to be of great importance for modelling lithosphere deformation. Three well-known benchmarks are used to test and validate our implementation of plasticity: the punch benchmark (e.g. Thieulot et al. 2008), which considers the indentation of a perfectly plastic material and allows for comparison with an analytical solution; the brick benchmark (Kaus 2010), performed in both a compressional and tensional regime with shear band angles bounded by results of other codes and theory; and the sandbox experiment by Buiter et al. (2006) modelling the time evolution of the extension of viscous and plastic layers in the presence of a free surface. We further showcase ASPECT's capabilities with a more geodynamical application: the subduction of an oceanic plate in a three-dimensional thermo-mechanically coupled system. We compare the use of nonlinear rheologies versus that of constant mantle and plate viscosities with an adaptation of the subducting/overriding plate setup of Schellart and Moresi (2013). These models also demonstrate how the adaptive mesh refinement allows for high resolutions locally while the code remains computationally efficient even in the presence of large
3D finite element modelling of guided wave scattering at delaminations in composites
NASA Astrophysics Data System (ADS)
Murat, Bibi Intan Suraya; Fromme, Paul
2016-02-01
Carbon fiber laminate composites are increasingly used for aerospace structures as they offer a number of advantages including a good strength to weight ratio. However, impact during the operation and servicing of the aircraft can lead to barely visible and difficult to detect damage. Depending on the severity of the impact, delaminations can occur, reducing the load carrying capacity of the structure. Efficient nondestructive testing of composite panels can be achieved using guided ultrasonic waves propagating along the structure. The guided wave (A0 Lamb wave mode) scattering at delaminations was modeled using full three-dimensional Finite Element (FE) simulations. The influence of the delamination size was systematically investigated from a parameter study. A significant influence of the delamination width on the guided wave scattering was found, especially on the angular dependency of the scattered guided wave amplitude. The sensitivity of guided ultrasonic waves for the detection of delamination damage in composite panels is discussed.
Active tectonics in Taiwan: insights from a 3-D viscous finite element model
NASA Astrophysics Data System (ADS)
Sun, Yujun; Liu, Mian; Dong, Shuwen; Zhang, Huai; Shi, Yaolin
2015-12-01
Taiwan is a young orogenic belt with complex spatial distributions of deformation and earthquakes. We have constructed a three-dimensional finite element model to explore how the interplays between lithospheric structure and plate boundary processes control the distribution of stress and strain rates in the Taiwan region. The model assumes a liberalized power-law rheology and incorporates main lithospheric structures; the model domain is loaded by the present-day crustal velocity applied at its boundaries. The model successfully reproduces the main features of the GPS-measured strain rate patterns and the earthquake-indicated stress states in the Taiwan region. The best fitting model requires the viscosity of the lower crust to be two orders of magnitude lower than that of the upper crust and lithospheric mantle. The calculated deviatoric stress is high in regions of thrust faulting and low in regions of extensional and strike-slip faulting, consistent with the spatial pattern of seismic intensity in Taiwan.
Finite element methods of analysis for 3D inviscid compressible flows
NASA Technical Reports Server (NTRS)
Peraire, Jaime
1990-01-01
The applicants have developed a finite element based approach for the solution of three-dimensional compressible flows. The procedure enables flow solutions to be obtained on tetrahedral discretizations of computational domains of complex form. A further development was the incorporation of a solution adaptive mesh strategy in which the adaptivity is achieved by complete remeshing of the solution domain. During the previous year, the applicants were working with the Advanced Aerodynamics Concepts Branch at NASA Ames Research Center with an implementation of the basic meshing and solution procedure. The objective of the work to be performed over this twelve month period was the transfer of the adaptive mesh technology and also the undertaking of basic research into alternative flow algorithms for the Euler equations on unstructured meshes.
Simulation of dielectrophoretic assembly of carbon nanotubes using 3D finite element analysis.
Berger, S D; McGruer, N E; Adams, G G
2015-04-17
One of the most important methods for selective and repeatable assembly of carbon nanotubes (CNTs) is alternating current dielectrophoresis (DEP). This method has been demonstrated experimentally as a viable technique for nano-scale manufacturing of novel CNT based devices. Previous numerical analyses have studied the motion of nanotubes, the volume from which they are assembled, and the rate of assembly, but have been restricted by various simplifying assumptions. In this paper we present a method for simulating the motion and behavior of CNTs subjected to dielectrophoresis using a three-dimensional electrostatic finite element analysis. By including the CNT in the finite element model, we can accurately predict the effect of the CNT on the electric field and the resulting force distribution across the CNT can be determined. We have used this information to calculate the motion of CNTs assembling onto the electrodes, and show how they tend to move towards the center of an electrode and come into contact at highly skewed angles. Our analysis suggests that the CNTs move to the electrode gap only after initially contacting the electrodes. We have also developed a model of the elastic deformation of CNTs as they approach the electrodes demonstrating how the induced forces can significantly alter the CNT shape during assembly. These results show that the CNT does not behave as a rigid body when in close proximity to the electrodes. In the future this method can be applied to a variety of real electrode geometries on a case-by-case basis and will provide more detailed insight into the specific motion and assembly parameters necessary for effective DEP assembly. PMID:25804394
Simulation of dielectrophoretic assembly of carbon nanotubes using 3D finite element analysis
NASA Astrophysics Data System (ADS)
Berger, S. D.; McGruer, N. E.; Adams, G. G.
2015-04-01
One of the most important methods for selective and repeatable assembly of carbon nanotubes (CNTs) is alternating current dielectrophoresis (DEP). This method has been demonstrated experimentally as a viable technique for nano-scale manufacturing of novel CNT based devices. Previous numerical analyses have studied the motion of nanotubes, the volume from which they are assembled, and the rate of assembly, but have been restricted by various simplifying assumptions. In this paper we present a method for simulating the motion and behavior of CNTs subjected to dielectrophoresis using a three-dimensional electrostatic finite element analysis. By including the CNT in the finite element model, we can accurately predict the effect of the CNT on the electric field and the resulting force distribution across the CNT can be determined. We have used this information to calculate the motion of CNTs assembling onto the electrodes, and show how they tend to move towards the center of an electrode and come into contact at highly skewed angles. Our analysis suggests that the CNTs move to the electrode gap only after initially contacting the electrodes. We have also developed a model of the elastic deformation of CNTs as they approach the electrodes demonstrating how the induced forces can significantly alter the CNT shape during assembly. These results show that the CNT does not behave as a rigid body when in close proximity to the electrodes. In the future this method can be applied to a variety of real electrode geometries on a case-by-case basis and will provide more detailed insight into the specific motion and assembly parameters necessary for effective DEP assembly.
A Simulation of crustal deformation around sourthwest Japan using 3D Finite Element Method
NASA Astrophysics Data System (ADS)
Oma, T.; Ito, T.; Sasajima, R.
2015-12-01
In southwest Japan, the Philippine Sea plate is subducting beneath the Amurian plate at the Nankai Trough. Megathrust earthquakes have been occurred with recurrence intervals of about 100-150 years. Previous studies have estimated co-seismic slip distribution at the 1944 Tokankai and the 1946 Nankai earthquakes and interplate plate coupling along the Nankai Trough. Many of previous studies employed a homogeneous elastic half space or elastic and viscoelastic layers structure. However, these assumptions as mentioned above are inadequate, since inhomogeneous structure is exceled in the real earth result from subducting plate. Therefore, in order to estimate the effect of inhomogeneous structure on the crustal deformation, we calculate crustal deformation due to Megathrust earthquake using 3-dimensional Finite Element Method (FEM). We use FEM software PyLith v2.1. In this study, we construct a finite element mesh with the region of 3000km(SW) × 2300km(NS) × 400km(depth) cover Japanese Islands, using Cubit 13.0. This mesh is considered topography, the Philippine Sea plate, the Pacific plate, Moho discontinuity, and curvature of the earth. In order to examine differences of surface displacement between inhomogeneous and homogeneous structures, we use co-seismic slip distribution of the 1944 and 1946 earthquakes estimated by Sagiya and Thatcher (1999). In result, surface elastic response under inhomogeneous structure becomes 30% larger than it's homogeneous structure at the Muroto cape. This difference indicates that co-seismic slip or plate coupling distribution estimated from Green's function under an assumption of homogeneous structure is overestimated. Then, we calculate viscoelastic response assuming Maxwell rheology model and viscosity as 1×1019. As a result, predicted horizontal velocity of viscoelastic response due to the events corresponds to 10 % of observed present deformation. It suggest that spatial pattern of plate coupling might be change when we
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
NASA Astrophysics Data System (ADS)
Fisher, Travis C.; Carpenter, Mark H.
2013-11-01
Nonlinear entropy stability is used to derive provably stable high-order finite difference operators including boundary closure stencils, for the compressible Navier-Stokes equations. A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks. Viscous terms are approximated using conservative, entropy stable, narrow-stencil finite difference operators. The efficacy of the new discrete operators is demonstrated using both smooth and discontinuous test cases.
Linear and nonlinear instability and ligament dynamics in 3D laminar two-layer liquid/liquid flows
NASA Astrophysics Data System (ADS)
Ó Náraigh, Lennon; Valluri, Prashant; Scott, David; Bethune, Iain; Spelt, Peter
2013-11-01
We consider the linear and nonlinear stability of two-phase density-matched but viscosity contrasted fluids subject to laminar Poiseuille flow in a channel, paying particular attention to the formation of three-dimensional waves. The Orr-Sommerfeld-Squire analysis is used along with DNS of the 3D two-phase Navier-Stokes equations using our newly launched TPLS Solver (http://edin.ac/10cRKzS). For the parameter regimes considered, we demonstrate the existence of two distinct mechanisms whereby 3D waves enter the system, and dominate at late time. There exists a direct route, whereby 3D waves are amplified by the standard linear mechanism; for certain parameter classes, such waves grow at a rate less than but comparable to that of most-dangerous two-dimensional mode. Additionally, there is a weakly nonlinear route, whereby a purely spanwise wave couples to a streamwise mode and grows exponentially. We demonstrate these mechanisms in isolation and in concert. Consideration is also given to the ultimate state of these waves: persistent three-dimensional nonlinear waves are stretched and distorted by the base flow, thereby producing regimes of ligaments, ``sheets,'' or ``interfacial turbulence.'' HECToR RAP/dCSE Project e174, HPC-Europa 2.
Sutradhar, Alok; Park, Jaejong; Carrau, Diana; Miller, Michael J
2014-09-01
With the dawn of 3D printing technology, patient-specific implant designs are set to have a paradigm shift. A topology optimization method in designing patient-specific craniofacial implants has been developed to ensure adequate load transfer mechanism and restore the form and function of the mid-face. Patient-specific finite element models are used to design these implants and to validate whether they are viable for physiological loading such as mastication. Validation of these topology optimized finite element models using mechanical testing is a critical step. Instead of inserting the implants into a cadaver or patient, we embed the implants into the computer-aided skull model of a patient and, fuse them together to 3D print the complete skull model with the implant. Masticatory forces are applied in the molar region to simulate chewing and measure the stress-strain trajectory. Until recently, strain gages have been used to measure strains for validation. Digital Image Correlation (DIC) method is a relatively new technique for full-field strain measurement which provides a continuous deformation field data. The main objective of this study is to validate the finite element model of patient-specific craniofacial implants against the strain data from the DIC obtained during the mastication simulation and show that the optimized shapes provide adequate load-transfer mechanism. Patient-specific models are obtained from CT scans. The principal maximum and minimum strains are compared. The computational and experimental approach to designing patient-specific implants proved to be a viable technique for mid-face craniofacial reconstruction. PMID:24992729
Study of Multi Pass Equal Channel Angular Pressing Using 3D Finite Element Analysis
NASA Astrophysics Data System (ADS)
Setia, Rajat; Sharma, Rahul Swarup; Sharma, Shanti Swarup; Raj, K. Hans
2011-01-01
Equal Channel Angular Pressing (ECAP) has emerged as most prominent Severe Plastic Deformation (SPD) technique used to produce an ultrafine grained (UFG) structure in metals in order to improve their mechanical and physical properties. In this work Finite Element modeling of ECAP is attempted in FORGE 2007 environment. Four passes of the ECAP process of 10mm square shaped AL 6061 billet were carried out for routes A, BA and C for different channel angles and values of coefficient of friction to investigate their influence on the billet. The models were developed assuming a range of friction conditions at the billet-die contact region considering eight distinct friction coefficient (μ) values of 0.0, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35 and 0.40, respectively. The simulations are carried out using three distinct situations of die channel angles (Φ), 90°, 105°, and 120° respectively. Route `BA' emerged as a better method among the three routes studied and 90° channel angle appeared to be optimal in terms of producing high equivalent strain.
Accurate 3-D finite difference computation of traveltimes in strongly heterogeneous media
NASA Astrophysics Data System (ADS)
Noble, M.; Gesret, A.; Belayouni, N.
2014-12-01
Seismic traveltimes and their spatial derivatives are the basis of many imaging methods such as pre-stack depth migration and tomography. A common approach to compute these quantities is to solve the eikonal equation with a finite-difference scheme. If many recently published algorithms for resolving the eikonal equation do now yield fairly accurate traveltimes for most applications, the spatial derivatives of traveltimes remain very approximate. To address this accuracy issue, we develop a new hybrid eikonal solver that combines a spherical approximation when close to the source and a plane wave approximation when far away. This algorithm reproduces properly the spherical behaviour of wave fronts in the vicinity of the source. We implement a combination of 16 local operators that enables us to handle velocity models with sharp vertical and horizontal velocity contrasts. We associate to these local operators a global fast sweeping method to take into account all possible directions of wave propagation. Our formulation allows us to introduce a variable grid spacing in all three directions of space. We demonstrate the efficiency of this algorithm in terms of computational time and the gain in accuracy of the computed traveltimes and their derivatives on several numerical examples.
Bone stress and strain modification in diastema closure: 3D analysis using finite element method.
Geramy, Allahyar; Bouserhal, Joseph; Martin, Domingo; Baghaeian, Pedram
2015-09-01
The aim of this study was to analyse the stress and strain distribution in the alveolar bone between two central incisors in the process of diastema closure with a constant force. A 3-dimensional computer modeling based on finite element techniques was used for this purpose. A model of an anterior segment of the mandible containing cortical bone, spongy bone, gingivae, PDL and two central incisors with a bracket in the labial surface of each tooth were designed. The von Mises stress and strain was evaluated in alveolar bone along a path of nodes defined in a cresto-apical direction in the midline between two teeth. It was observed that stress and strain of alveolar bone increased in midline with a constant force to close the diastema regardless of the type of movement in gradual steps of diastema closure, however the stress was higher in the tipping movement than the bodily so it can be suggested that a protocol of force system modification should be introduced to compensate for the stress and strain changes caused by the reduced distance to avoid the unwanted stress alteration during the diastema closure. PMID:26277458
Electron scattering from large molecules: a 3d finite element R-matrix approach
NASA Astrophysics Data System (ADS)
Tonzani, Stefano; Greene, Chris H.
2005-05-01
To solve the Schr"odinger equation for scattering of a low energy electron from a molecule, we present a three-dimensional finite element R-matrix method [S. Tonzani and C. H. Greene, J. Chem. Phys. 122 01411, (2005)]. Using the static exchange and local density approximations, we can use directly the molecular potentials extracted from ab initio codes (GAUSSIAN 98 in the work described here). A local polarization potential based on density functional theory [F. A. Gianturco and A. Rodriguez-Ruiz, Phys. Rev. A 47, 1075 (1993)] approximately describes the long range attraction to the molecular target induced by the scattering electron without adjustable parameters. We have used this approach successfully in calculations of cross sections for small and medium sized molecules (like SF6, XeF6, C60 and Uracil). This method will be useful to treat the electron-induced dynamics of extended molecular systems, possibly of biological interest, where oth er more complex ab initio methods are difficult to apply.
Finite element methods for nonlinear elastostatic problems in rubber elasticity
NASA Technical Reports Server (NTRS)
Oden, J. T.; Becker, E. B.; Miller, T. H.; Endo, T.; Pires, E. B.
1983-01-01
A number of finite element methods for the analysis of nonlinear problems in rubber elasticity are outlined. Several different finite element schemes are discussed. These include the augmented Lagrangian method, continuation or incremental loading methods, and associated Riks-type methods which have the capability of incorporating limit point behavior and bifurcations. Algorithms for the analysis of limit point behavior and bifurcations are described and the results of several numerical experiments are presented. In addition, a brief survey of some recent work on modelling contact and friction in elasticity problems is given. These results pertain to the use of new nonlocal and nonlinear friction laws.
NASA Astrophysics Data System (ADS)
Korneev, V. G.
2012-09-01
BPS is a well known an efficient and rather general domain decomposition Dirichlet-Dirichlet type preconditioner, suggested in the famous series of papers Bramble, Pasciak and Schatz (1986-1989). Since then, it has been serving as the origin for the whole family of domain decomposition Dirichlet-Dirichlet type preconditioners-solvers as for h so hp discretizations of elliptic problems. For its original version, designed for h discretizations, the named authors proved the bound O(1 + log2 H/ h) for the relative condition number under some restricting conditions on the domain decomposition and finite element discretization. Here H/ h is the maximal relation of the characteristic size H of a decomposition subdomain to the mesh parameter h of its discretization. It was assumed that subdomains are images of the reference unite cube by trilinear mappings. Later similar bounds related to h discretizations were proved for more general domain decompositions, defined by means of coarse tetrahedral meshes. These results, accompanied by the development of some special tools of analysis aimed at such type of decompositions, were summarized in the book of Toselli and Widlund (2005). This paper is also confined to h discretizations. We further expand the range of admissible domain decompositions for constructing BPS preconditioners, in which decomposition subdomains can be convex polyhedrons, satisfying some conditions of shape regularity. We prove the bound for the relative condition number with the same dependence on H/ h as in the bound given above. Along the way to this result, we simplify the proof of the so called abstract bound for the relative condition number of the domain decomposition preconditioner. In the part, related to the analysis of the interface sub-problem preconditioning, our technical tools are generalization of those used by Bramble, Pasciak and Schatz.
An Efficient Vector Finite Element Method for Nonlinear Electromagnetic Modeling
Fisher, A C; White, D A; Rodrigue, G H
2006-06-27
We have developed a mixed Vector Finite Element Method (VFEM) for Maxwell's equations with a nonlinear polarization term. The method allows for discretization of complicated geometries with arbitrary order representations of the B and E fields. In this paper we will describe the method and a series of optimizations that significantly reduce the computational cost. Additionally, a series of test simulations will be presented to validate the method. Finally, a nonlinear waveguide mode mixing example is presented and discussed.
Progress in the Peeling-Ballooning Model of ELMs: Numerical Studies of 3D Nonlinear ELM Dynamics
Snyder, P B; Wilson, H R; Xu, X Q
2004-12-13
Nonlinear simulations with the 3D electromagnetic two-fluid BOUT code are employed to study the dynamics of edge localized modes (ELMs) driven by intermediate wavelength peeling-ballooning modes. It is found that the early behavior of the modes is similar to expectations from linear, ideal peeling-ballooning mode theory, with the modes growing linearly at a fraction of the Alfven frequency. In the non-linear phase, the modes grow explosively, forming a number of extended filaments which propagate rapidly from the outer closed flux region into the open flux region toward the outer wall. Similarities to non-linear linear ballooning theory, as well as additional complexities are observed. Comparison to observations reveals a number of similarities. Implications of the simulations and proposals for the dynamics of the full ELM crash are discussed.
PROGRESS IN THE PEELING-BALLOONING MODEL OF ELMS: NUMERICAL STUDIES OF 3D NONLINEAR ELM DYNAMICS
SNYDER,P.B; WILSON,H.R; XU,X.Q
2004-11-01
Nonlinear simulations with the 3D electromagnetic two-fluid BOUT code are employed to study the dynamics of edge localized modes (ELMs) driven by intermediate wavelength peeling-ballooning modes. It is found that the early behavior of the modes is similar to expectations from linear, ideal peeling-ballooning mode theory, with the modes growing linearly at a fraction of the Alfven frequency. In the nonlinear phase, the modes grow explosively, forming a number of extended filaments which propagate rapidly from the outer closed flux region into the open flux region toward the outboard wall. Similarities to non-linear ballooning theory, as well as additional complexities are observed. Comparison to observations reveals a number of similarities. Implications of the simulations and proposals for the dynamics of the full ELM crash are discussed.
NASA Astrophysics Data System (ADS)
Yakura, S. Joe
2001-06-01
The Perfectly Matched Layer (PML) method is used to absorb outgoing electromanetic waves in finite difference time domain (FDTD) numerical simulations to create the notion of infinity within the finite numerical simulation volume. Starting with unsplit-field uniaxial PML formulation, a FDTD/PML algorithm, that is accurate to second order in time, is obtained for the first time using the piecewise-linear approximation for linear and nonlinear dispersive media. Use of the FDTD/PML algorithm results in the proper long time limit behavior where the electric field value decrease exponentially to zero inside a PML medium long after an electromagnetic pulse is incident on the PML medium. The behavior is consistent with the other PML algorithm, such as Gedney's two-step approach in the case of the linear dispersive medium. Also, in the case of the nonlinear dispersive medium, FDTD/PML algorithm reduces to the usual nonlinear dispersive FDTD algorithm [1] in the absence of the PML interface. Ref. [1]: S. J. Yakura, J. MacGillivray and David Dietz, "Finite-Difference Time-Domain Calculations Based on Recursive Convolution Approach for Propagation of Electromagnetic Waves in Nonlinear Dispersive Media," Accepted for publication in the Applied Computational Electromagnetics Society (ACES) Journal in 2001.
Simulating hydroplaning of submarine landslides by quasi 3D depth averaged finite element method
NASA Astrophysics Data System (ADS)
De Blasio, Fabio; Battista Crosta, Giovanni
2014-05-01
G.B. Crosta, H. J. Chen, and F.V. De Blasio Dept. Of Earth and Environmental Sciences, Università degli Studi di Milano Bicocca, Milano, Italy Klohn Crippen Berger, Calgary, Canada Subaqueous debris flows/submarine landslides, both in the open ocean as well as in fresh waters, exhibit extremely high mobility, quantified by a ratio between vertical to horizontal displacement of the order 0.01 or even much less. It is possible to simulate subaqueous debris flows with small-scale experiments along a flume or a pool using a cohesive mixture of clay and sand. The results have shown a strong enhancement of runout and velocity compared to the case in which the same debris flow travels without water, and have indicated hydroplaning as a possible explanation (Mohrig et al. 1998). Hydroplaning is started when the snout of the debris flow travels sufficiently fast. This generates lift forces on the front of the debris flow exceeding the self-weight of the sediment, which so begins to travel detached from the bed, literally hovering instead of flowing. Clearly, the resistance to flow plummets because drag stress against water is much smaller than the shear strength of the material. The consequence is a dramatic increase of the debris flow speed and runout. Does the process occur also for subaqueous landslides and debris flows in the ocean, something twelve orders of magnitude larger than the experimental ones? Obviously, no experiment will ever be capable to replicate this size, one needs to rely on numerical simulations. Results extending a depth-integrated numerical model for debris flows (Imran et al., 2001) indicate that hydroplaning is possible (De Blasio et al., 2004), but more should be done especially with alternative numerical methodologies. In this work, finite element methods are used to simulate hydroplaning using the code MADflow (Chen, 2014) adopting a depth averaged solution. We ran some simulations on the small scale of the laboratory experiments, and secondly
3D Finite-Difference Modeling of Acoustic Radiation from Seismic Sources
NASA Astrophysics Data System (ADS)
Chael, E. P.; Aldridge, D. F.; Jensen, R. P.
2013-12-01
Shallow seismic events, earthquakes as well as explosions, often generate acoustic waves in the atmosphere observable at local or even regional distances. Recording both the seismic and acoustic signals can provide additional constraints on source parameters such as epicenter coordinates, depth, origin time, moment, and mechanism. Recent advances in finite-difference (FD) modeling methods enable accurate numerical treatment of wave propagation across the ground surface between the (solid) elastic and (fluid) acoustic domains. Using a fourth-order, staggered-grid, velocity-stress FD algorithm, we are investigating the effects of various source parameters on the acoustic (or infrasound) signals transmitted from the solid earth into the atmosphere. Compressional (P), shear (S), and Rayleigh waves all radiate some acoustic energy into the air at the ground surface. These acoustic wavefronts are typically conical in shape, since their phase velocities along the surface exceed the sound speed in air. Another acoustic arrival with a spherical wavefront can be generated from the vicinity of the epicenter of a shallow event, due to the strong vertical ground motions directly above the buried source. Images of acoustic wavefields just above the surface reveal the radiation patterns and relative amplitudes of the various arrivals. In addition, we compare the relative effectiveness of different seismic source mechanisms for generating acoustic energy. For point sources at a fixed depth, double-couples with almost any orientation produce stronger acoustic signals than isotropic explosions, due to higher-amplitude S and Rayleigh waves. Of course, explosions tend to be shallower than most earthquakes, which can offset the differences due to mechanism. Low-velocity material in the shallow subsurface acts to increase vertical seismic motions there, enhancing the coupling to acoustic waves in air. If either type of source breaks the surface (e.g., an earthquake with surface rupture
Nonlinear susceptibilities of finite conjugated organic polymers
NASA Technical Reports Server (NTRS)
Beratan, David N.; Onuchic, Jose Nelson; Perry, Joseph W.
1987-01-01
Tight-binding calculations of the length dependence of the third-order molecular hyperpolarizability for polyenes and polyynes are reported. The pi-electron wave functions were determined by exploiting the limited translational symmetry of the molecules. Perturbation theory was used to calculate the longitudinal component of the electronic nonresonant hyperpolarizability. This is the first two-'band' calculation of third-order hyperpolarizabilities on finite pi-electron systems of varying length. In contrast to the results of the one-'band' models, the hyperpolarizability densities increase rapidly and then, after about 10-15 repeating units, approach an asymptotic value.
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
NASA Technical Reports Server (NTRS)
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
NASA Astrophysics Data System (ADS)
Sakai, Hirotaka; Urakawa, Fumihiro; Aikawa, Akira; Namura, Akira
The vibration of concrete sleepers is an important factor engendering track deterioration. In this paper, we created a three-dimensional finite element model to reproduce a prestressed concrete (PC) sleeper in detail, expressing influence of ballast layers with a 3D spring series and dampers to reproduce their vibration and dynamic characteristics. Determination of these parameters bases on the experimental modal analysis using an impact excitation technique for PC sleepers by adjusting the accelerance between the analytical results and experimental results. Furthermore, we compared the difference of these characteristics between normal sleepers and those with some structural modifications. Analytical results clarified that such means as sleeper width extension and increased sleeper thickness will influence the reduction of ballasted track vibration as improvements of PC sleepers.
NASA Astrophysics Data System (ADS)
Vattré, A.; Devincre, B.; Feyel, F.; Gatti, R.; Groh, S.; Jamond, O.; Roos, A.
2014-02-01
A unified model coupling 3D dislocation dynamics (DD) simulations with the finite element (FE) method is revisited. The so-called Discrete-Continuous Model (DCM) aims to predict plastic flow at the (sub-)micron length scale of materials with complex boundary conditions. The evolution of the dislocation microstructure and the short-range dislocation-dislocation interactions are calculated with a DD code. The long-range mechanical fields due to the dislocations are calculated by a FE code, taking into account the boundary conditions. The coupling procedure is based on eigenstrain theory, and the precise manner in which the plastic slip, i.e. the dislocation glide as calculated by the DD code, is transferred to the integration points of the FE mesh is described in full detail. Several test cases are presented, and the DCM is applied to plastic flow in a single-crystal Nickel-based superalloy.
Finite-Orbit-Width version of the CQL3D for description of RF-enhanced neoclassical transport
NASA Astrophysics Data System (ADS)
Petrov, Yu. V.; Harvey, R. W.
2015-12-01
The CQL3D bounce-averaged Fokker-Planck (FP) code [l] has been upgraded to include Finite-Orbit-Width (FOW) effects. The calculations can be done either with a fast Hybrid-FOW option or with a slower but neoclassically complete full-FOW option. The neoclassical radial transport appears naturally in the full-FOW version by averaging the local collision coefficients along guiding center orbits, with a proper transformation matrix from local (R, Z) coordinates to the midplane computational coordinates, where the FP equation is solved. In a similar way, the local quasilinear rf diffusion terms give rise to additional radial transport of orbits. The results of validation tests for the full-FOW version are presented.
Edge-based finite element approach to the simulation of geoelectromagnetic induction in a 3-D sphere
NASA Astrophysics Data System (ADS)
Yoshimura, Ryokei; Oshiman, Naoto
2002-02-01
We present a new simulator based on an edge-based finite element method (FEM) for computing the global-scale electromagnetic (EM) induction responses in a 3-D conducting sphere excited by an external source current for a variety of frequencies. The formulation is in terms of the magnetic vector potential. The edge-element approach assigns the degrees of freedom to the edges rather than to the nodes of the element. This edge-element strictly satisfies the discontinuity of the normal boundary conditions without considering the enforced normal boundary conditions that are usually practiced in a node-based FEM. To verify our simulation code, we compare our results with those of other solvers for two test computations, corresponding to azimuthally symmetric and asymmetric models. The results are in good agreement with one another.
NASA Astrophysics Data System (ADS)
Giasin, Khaled; Ayvar-Soberanis, Sabino; French, Toby; Phadnis, Vaibhav
2016-07-01
Machining Glass fibre aluminium reinforced epoxy (GLARE) is cumbersome due to distinctively different mechanical and thermal properties of its constituents, which makes it challenging to achieve damage-free holes with the acceptable surface quality. The proposed work focuses on the study of the machinability of thin (~2.5 mm) GLARE laminate. Drilling trials were conducted to analyse the effect of feed rate and spindle speed on the cutting forces and hole quality. The resulting hole quality metrics (surface roughness, hole size, circularity error, burr formation and delamination) were assessed using surface profilometry and optical scanning techniques. A three dimensional (3D) finite-element (FE) model of drilling GLARE laminate was also developed using ABAQUS/Explicit to help understand the mechanism of drilling GLARE. The homogenised ply-level response of GLARE laminate was considered in the FE model to predict cutting forces in the drilling process.
NASA Astrophysics Data System (ADS)
Umar Alkali, Adam; Lenggo Ginta, Turnad; Majdi Abdul-Rani, Ahmad
2015-04-01
This paper presents a 3D transient finite element modelling of the workpiece temperature field produced during the travelling heat sourced from oxyacetylene flame. The proposed model was given in terms of preheat-only test applicable during thermally enhanced machining using the oxyacetylene flame as a heat source. The FEA model as well as the experimental test investigated the surface temperature distribution on 316L stainless steel at scanning speed of 100mm/min, 125mm/min 160mm/min, 200mm/min and 250mm/min. The parametric properties of the heat source maintained constant are; lead distance Ld =10mm, focus height Fh=7.5mm, oxygen gas pressure Poxy=15psi and acetylene gas pressure Pacty=25psi. An experimental validation of the temperature field induced on type 316L stainless steel reveal that temperature distribution increases when the travelling speed decreases.
ZIP3D: An elastic and elastic-plastic finite-element analysis program for cracked bodies
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Newman, J. C., Jr.
1990-01-01
ZIP3D is an elastic and an elastic-plastic finite element program to analyze cracks in three dimensional solids. The program may also be used to analyze uncracked bodies or multi-body problems involving contacting surfaces. For crack problems, the program has several unique features including the calculation of mixed-mode strain energy release rates using the three dimensional virtual crack closure technique, the calculation of the J integral using the equivalent domain integral method, the capability to extend the crack front under monotonic or cyclic loading, and the capability to close or open the crack surfaces during cyclic loading. The theories behind the various aspects of the program are explained briefly. Line-by-line data preparation is presented. Input data and results for an elastic analysis of a surface crack in a plate and for an elastic-plastic analysis of a single-edge-crack-tension specimen are also presented.
3D Finite Element Model for Writing Long-Period Fiber Gratings by CO2 Laser Radiation
Coelho, João M. P.; Nespereira, Marta; Abreu, Manuel; Rebordão, José
2013-01-01
In the last years, mid-infrared radiation emitted by CO2 lasers has become increasing popular as a tool in the development of long-period fiber gratings. However, although the development and characterization of the resulting sensing devices have progressed quickly, further research is still necessary to consolidate functional models, especially regarding the interaction between laser radiation and the fiber's material. In this paper, a 3D finite element model is presented to simulate the interaction between laser radiation and an optical fiber and to determine the resulting refractive index change. Dependence with temperature of the main parameters of the optical fiber materials (with special focus on the absorption of incident laser radiation) is considered, as well as convection and radiation losses. Thermal and residual stress analyses are made for a standard single mode fiber, and experimental results are presented. PMID:23941908
pF3d simulations of nonlinear backward stimulated Raman scatter in a multi-speckle environment
NASA Astrophysics Data System (ADS)
Dodd, E. S.; Bezzerides, B.; Dubois, D. F.; Vu, H. X.
2008-11-01
Kinetic simulations of backward stimulated Raman scattering (BSRS) have shown that, in regimes of strong Landau damping of the BSRS Langmuir wave (LW), the reflectivity can exceed that predicted by linear analysis [1]. This is a result of electron trapping in the LW, which decreases Landau damping, and creates a frequency shift. Above a threshold, determined by the competition of trapping and collisional diffusion, the frequency shift becomes the dominant saturation mechanism for BSRS. This includes the transverse modulational instability [2]. However, one must use a code that models the nonlinear microscopic behavior along with the macroscopic evolution of the laser beam and background plasma. Here, we discuss work on implementing an empirical model for this effect in the pF3d code [3]. The model has been tested by comparing pF3d single-hot-spot simulations against theoretical calculations of the inflation threshold. We will discuss our current effort, using pF3d, to understand how the onset of nonlinear LW behavior is affected by inter-speckle interactions. [1] H. X. Vu, et al., Phys. Plasmas 14 012702 (2007). [2] H. A. Rose, and L. Yin, Phys. Plasmas 15 042311 (2008). [3] R. L. Berger, et al., Phys Plasmas 5 4337 (1998).
Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation
NASA Astrophysics Data System (ADS)
Costa, Carlos A. N.; Campos, Itamara S.; Costa, Jessé C.; Neto, Francisco A.; Schleicher, Jörg; Novais, Amélia
2013-08-01
Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality.
Nonlinear evolution of Alfven waves in a finite beta plasma
Som, B.K. ); Dasgupta, B.; Patel, V.L. ); Gupta, M.R. )
1989-12-01
A general form of the derivative nonlinear Schroedinger (DNLS) equation, describing the nonlinear evolution of Alfven waves propagating parallel to the magnetic field, is derived by using two-fluid equations with electron and ion pressure tensors obtained from Braginskii (in {ital Reviews} {ital of} {ital Plasma Physics} (Consultants Bureau, New York, 1965), Vol. 1, p. 218). This equation is a mixed version of the nonlinear Schroedinger (NLS) equation and the DNLS, as it contains an additional cubic nonlinear term that is of the same order as the derivative of the nonlinear terms, a term containing the product of a quadratic term, and a first-order derivative. It incorporates the effects of finite beta, which is an important characteristic of space and laboratory plasmas.
NASA Astrophysics Data System (ADS)
Vattré, A.; Denoual, C.
2016-07-01
A thermodynamically consistent framework for combining nonlinear elastoplasticity and multivariant phase-field theory is formulated at large strains. In accordance with the Clausius-Duhem inequality, the Helmholtz free energy and time-dependent constitutive relations give rise to displacive driving forces for pressure-induced martensitic phase transitions in materials. Inelastic forces are obtained by using a representation of the energy landscape that involves the concept of reaction pathways with respect to the point group symmetry operations of crystal lattices. On the other hand, additional elastic forces are derived for the most general case of large strains and rotations, as well as nonlinear, anisotropic, and different elastic pressure-dependent properties of phases. The phase-field formalism coupled with finite elastoplastic deformations is implemented into a three-dimensional Lagrangian finite element approach and is applied to analyze the iron body-centered cubic (α-Fe) into hexagonal close-packed (ɛ-Fe) phase transitions under high hydrostatic compression. The simulations exhibit the major role played by the plastic deformation in the morphological and microstructure evolution processes. Due to the strong long-range elastic interactions between variants without plasticity, a forward α → ɛ transition is energetically unfavorable and remains incomplete. However, plastic dissipation releases considerably the stored strain energy, leading to the α ↔ ɛ ↔α‧ (forward and reverse) polymorphic phase transformations with an unexpected selection of variants.
Efficient Nonlinear Atomization Model for Thin 3D Free Liquid Films
NASA Astrophysics Data System (ADS)
Mehring, Carsten
2007-03-01
Reviewed is a nonlinear reduced-dimension thin-film model developed by the author and aimed at the prediction of spray formation from thin films such as those found in gas-turbine engines (e.g., prefilming air-blast atomizers), heavy-fuel-oil burners (e.g., rotary-cup atomizers) and in the paint industry (e.g., flat-fan atomizers). Various implementations of the model focusing on different model-aspects, i.e., effect of film geometry, surface tension, liquid viscosity, coupling with surrounding gas-phase flow, influence of long-range intermolecular forces during film rupture are reviewed together with a validation of the nonlinear wave propagation characteristics predicted by the model for inviscid planar films using a two-dimensional vortex- method. An extension and generalization of the current nonlinear film model for implementation into a commercial flow- solver is outlined.
NASA Technical Reports Server (NTRS)
Costiner, Sorin; Taasan, Shlomo
1994-01-01
This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.
Computerized symbolic manipulation in nonlinear finite element analysis
NASA Technical Reports Server (NTRS)
Noor, A. K.; Andersen, C. M.
1981-01-01
The potential of using computerized symbolic manipulation in the development of nonlinear finite elements is discussed. Three tasks which can be efficiently performed using computerized symbolic manipulation are identified: (1) generation of algebraic expressions for the stiffness coefficients of nonlinear finite elements, (2) generation of FORTRAN source code for numerical evaluation of stiffness coefficients, and (3) checking the correctness of the FORTRAN statements for the arrays of coefficients. The symbolic and algebraic manipulation system MACSYMA is used in the present study. Two sample MACSYMA programs are presented for the development of the nonlinear stiffness coefficients of two-dimensional, shear-flexible, doubly-curved deep shell elements. The first program is for displacement models and the second program is for mixed models with discontinuous stress-resultant fields at interelement boundaries.
Surface subsidence prediction by nonlinear finite-element analysis
Najjar, Y. . Dept. of Civil Engineering); Zaman, M. . School of Civil Engineering and Environmental Science)
1993-11-01
An improved two-dimensional plane-strain numerical procedure based on the incremental-iterative nonlinear finite-element is developed to predict ground subsidence caused by underground mining. The procedure emphasizes the use of the following features: (1) an appropriate constitutive model that can accurately describe the nonlinear behavior of geological strata; and (2) an accurate algorithm for simulation of excavation sequences consistent with the actual underground mining process. The computer code is used to analyze a collapse that occurred in the Blue Goose Lease [number sign]1 Mine in northeastern Oklahoma. A parametric study is conducted to investigate the effects of some selected factors on the shape and extent of subsidence profiles. Analyses of the numerical results indicate that the nonlinear finite-element technique can be employed to meaningfully predict and characterize the potential for ground subsidence due to underground mining.
On the Finite-Time Splash and Splat Singularities for the 3-D Free-Surface Euler Equations
NASA Astrophysics Data System (ADS)
Coutand, Daniel; Shkoller, Steve
2014-01-01
We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in Castro et al. (Splash singularity for water waves, http://arxiv.org/abs/1106.2120v2, 2011), wherein the evolving 2-D hypersurface, the moving boundary of the fluid domain, self-intersects at a point (or on surface). Such singularities can occur when the crest of a breaking wave falls unto its trough, or in the study of drop impact upon liquid surfaces. Our approach is founded upon the Lagrangian description of the free-boundary problem, combined with a novel approximation scheme of a finite collection of local coordinate charts; as such we are able to analyze a rather general set of geometries for the evolving 2-D free-surface of the fluid. We do not assume the fluid is irrotational, and as such, our method can be used for a number of other fluid interface problems, including compressible flows, plasmas, as well as the inclusion of surface tension effects.
NASA Astrophysics Data System (ADS)
Mulder, W. A.; Zhebel, E.; Minisini, S.
2014-02-01
We analyse the time-stepping stability for the 3-D acoustic wave equation, discretized on tetrahedral meshes. Two types of methods are considered: mass-lumped continuous finite elements and the symmetric interior-penalty discontinuous Galerkin method. Combining the spatial discretization with the leap-frog time-stepping scheme, which is second-order accurate and conditionally stable, leads to a fully explicit scheme. We provide estimates of its stability limit for simple cases, namely, the reference element with Neumann boundary conditions, its distorted version of arbitrary shape, the unit cube that can be partitioned into six tetrahedra with periodic boundary conditions and its distortions. The Courant-Friedrichs-Lewy stability limit contains an element diameter for which we considered different options. The one based on the sum of the eigenvalues of the spatial operator for the first-degree mass-lumped element gives the best results. It resembles the diameter of the inscribed sphere but is slightly easier to compute. The stability estimates show that the mass-lumped continuous and the discontinuous Galerkin finite elements of degree 2 have comparable stability conditions, whereas the mass-lumped elements of degree one and three allow for larger time steps.
Desai, Shrikar R.; Karthikeyan, I.; Gaddale, Reetika
2013-01-01
Purpose: The purpose of this finite element study was to compare the stresses, strains, and displacements of double versus single implant in immediate loading for replacing mandibular molar. Materials and Methods: Two 3D FEM (finite element method) models were made to simulate implant designs. The first model used 5-mm-wide diameter implant to support a single molar crown. The second model used 3.75-3.75 double implant design. Anisotropic properties were assigned to bone model. Each model was analyzed with single force magnitude (100 N) in vertical axis. Results: This FEM study suggested that micromotion can be controlled better for double implants compared to single wide-diameter implants. The Von Mises stress for double implant showed 74.44% stress reduction compared to that of 5-mm implant. The Von Mises elastic strain was reduced by 61% for double implant compared to 5-mm implant. Conclusion: Within the limitations of the study, when the mesiodistal space for artificial tooth is more than 12.5 mm, under immediate loading, the double implant support should be considered. PMID:24554890
Preliminary simulation of a M6.5 earthquake on the Seattle Fault using 3D finite-difference modeling
Stephenson, William J.; Frankel, Arthur D.
2000-01-01
A three-dimensional finite-difference simulation of a moderate-sized (M 6.5) thrust-faulting earthquake on the Seattle fault demonstrates the effects of the Seattle Basin on strong ground motion in the Puget lowland. The model area includes the cities of Seattle, Bremerton and Bellevue. We use a recently developed detailed 3D-velocity model of the Seattle Basin in these simulations. The model extended to 20-km depth and assumed rupture on a finite fault with random slip distribution. Preliminary results from simulations of frequencies 0.5 Hz and lower suggest amplification can occur at the surface of the Seattle Basin by the trapping of energy in the Quaternary sediments. Surface waves generated within the basin appear to contribute to amplification throughout the modeled region. Several factors apparently contribute to large ground motions in downtown Seattle: (1) radiation pattern and directivity from the rupture; (2) amplification and energy trapping within the Quaternary sediments; and (3) basin geometry and variation in depth of both Quaternary and Tertiary sediments
NASA Astrophysics Data System (ADS)
Li, Y.; Han, B.; Métivier, L.; Brossier, R.
2016-09-01
We investigate an optimal fourth-order staggered-grid finite-difference scheme for 3D frequency-domain viscoelastic wave modeling. An anti-lumped mass strategy is incorporated to minimize the numerical dispersion. The optimal finite-difference coefficients and the mass weighting coefficients are obtained by minimizing the misfit between the normalized phase velocities and the unity. An iterative damped least-squares method, the Levenberg-Marquardt algorithm, is utilized for the optimization. Dispersion analysis shows that the optimal fourth-order scheme presents less grid dispersion and anisotropy than the conventional fourth-order scheme with respect to different Poisson's ratios. Moreover, only 3.7 grid-points per minimum shear wavelength are required to keep the error of the group velocities below 1%. The memory cost is then greatly reduced due to a coarser sampling. A parallel iterative method named CARP-CG is used to solve the large ill-conditioned linear system for the frequency-domain modeling. Validations are conducted with respect to both the analytic viscoacoustic and viscoelastic solutions. Compared with the conventional fourth-order scheme, the optimal scheme generates wavefields having smaller error under the same discretization setups. Profiles of the wavefields are presented to confirm better agreement between the optimal results and the analytic solutions.
NASA Astrophysics Data System (ADS)
Schultz, A.
2010-12-01
describe our ongoing efforts to achieve massive parallelization on a novel hybrid GPU testbed machine currently configured with 12 Intel Westmere Xeon CPU cores (or 24 parallel computational threads) with 96 GB DDR3 system memory, 4 GPU subsystems which in aggregate contain 960 NVidia Tesla GPU cores with 16 GB dedicated DDR3 GPU memory, and a second interleved bank of 4 GPU subsystems containing in aggregate 1792 NVidia Fermi GPU cores with 12 GB dedicated DDR5 GPU memory. We are applying domain decomposition methods to a modified version of Weiss' (2001) 3D frequency domain full physics EM finite difference code, an open source GPL licensed f90 code available for download from www.OpenEM.org. This will be the core of a new hybrid 3D inversion that parallelizes frequencies across CPUs and individual forward solutions across GPUs. We describe progress made in modifying the code to use direct solvers in GPU cores dedicated to each small subdomain, iteratively improving the solution by matching adjacent subdomain boundary solutions, rather than iterative Krylov space sparse solvers as currently applied to the whole domain.
NASA Technical Reports Server (NTRS)
Padovan, Joe
1986-01-01
In a three part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modelled by fractional integro-differential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator. In the second and third parts of the paper, 3-D extensions are developed along with transient contact strategies enabling the handling of impacts with obstructions. Overall, the various developments are benchmarked via comprehensive 2- and 3-D simulations. These are correlated with experimental data to define modelling capabilities.
Non-linear dynamic analysis of ancient masonry structures by 3D rigid block models
NASA Astrophysics Data System (ADS)
Orduña, Agustin; Ayala, A. Gustavo
2015-12-01
This work presents a formulation for non-linear dynamic analysis of unreinforced masonry structures using rigid block models. This procedure is akin to the distinct element family of methods, nevertheless, we assume that small displacements occur and, therefore, the formulation does not involve the search for new contacts between blocks. This proposal is also related to the rigid element method, although, in this case we use full three-dimensional models and a more robust interface formulation.
Nonlinear analysis of structures. [within framework of finite element method
NASA Technical Reports Server (NTRS)
Armen, H., Jr.; Levine, H.; Pifko, A.; Levy, A.
1974-01-01
The development of nonlinear analysis techniques within the framework of the finite-element method is reported. Although the emphasis is concerned with those nonlinearities associated with material behavior, a general treatment of geometric nonlinearity, alone or in combination with plasticity is included, and applications presented for a class of problems categorized as axisymmetric shells of revolution. The scope of the nonlinear analysis capabilities includes: (1) a membrane stress analysis, (2) bending and membrane stress analysis, (3) analysis of thick and thin axisymmetric bodies of revolution, (4) a general three dimensional analysis, and (5) analysis of laminated composites. Applications of the methods are made to a number of sample structures. Correlation with available analytic or experimental data range from good to excellent.
Quantitative 3D molecular cutaneous absorption in human skin using label free nonlinear microscopy.
Chen, Xueqin; Grégoire, Sébastien; Formanek, Florian; Galey, Jean-Baptiste; Rigneault, Hervé
2015-02-28
Understanding the penetration mechanisms of drugs into human skin is a key issue in pharmaceutical and cosmetics research. To date, the techniques available for percutaneous penetration of compounds fail to provide a quantitative 3D map of molecular concentration distribution in complex tissues as the detected microscopy images are an intricate combination of concentration distribution and laser beam attenuation upon deep penetration. Here we introduce and validate a novel framework for imaging and reconstructing molecular concentration within the depth of artificial and human skin samples. Our approach combines the use of deuterated molecular compounds together with coherent anti-Stokes Raman scattering spectroscopy and microscopy that permits targeted molecules to be unambiguously discriminated within skin layers. We demonstrate both intercellular and transcellular pathways for different active compounds, together with in-depth concentration profiles reflecting the detailed skin barrier architecture. This method provides an enabling platform for establishing functional activity of topically applied products. PMID:25550155
Nonlinear Evolution of a 3D Inertial Alfvén Wave and Its Implication in Particle Acceleration
NASA Astrophysics Data System (ADS)
Sharma, Prachi; Yadav, Nitin; Sharma, R. P.
2016-03-01
A simulation based on a pseudo-spectral method has been performed in order to study particle acceleration. A model for the acceleration of charged particles by field localization is developed for the low-β plasma. For this purpose, a fractional diffusion approach has been employed. The nonlinear interaction between a 3D inertial Alfvén wave and a slow magnetosonic wave has been examined, and the dynamical equations of these two waves in the presence of ponderomotive nonlinearity have been solved numerically. The nonlinear evolution of the inertial Alfvén wave in the presence of slow magnetosonic wave undergoes a filamentation instability and results in field intensity localization. The results obtained show the localization and power spectrum of inertial Alfvén wave due to nonlinear coupling. The scaling obtained after the first break point of the magnetic power spectrum has been used to calculate the formation of the thermal tail of energetic particles in the solar corona.
NASA Astrophysics Data System (ADS)
Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María
2014-06-01
We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the
Eraslan, Oğuz; Inan, Ozgür
2010-08-01
The biomechanical behavior of implant thread plays an important role on stresses at implant-bone interface. Information about the effect of different thread profiles upon the bone stresses is limited. The purpose of this study was to evaluate the effects of different implant thread designs on stress distribution characteristics at supporting structures. In this study, three-dimensional (3D) finite element (FE) stress-analysis method was used. Four types of 3D mathematical models simulating four different thread-form configurations for a solid screw implant was prepared with supporting bone structure. V-thread (1), buttress (2), reverse buttress (3), and square thread designs were simulated. A 100-N static axial occlusal load was applied to occlusal surface of abutment to calculate the stress distributions. Solidworks/Cosmosworks structural analysis programs were used for FE modeling/analysis. The analysis of the von Mises stress values revealed that maximum stress concentrations were located at loading areas of implant abutments and cervical cortical bone regions for all models. Stress concentration at cortical bone (18.3 MPa) was higher than spongious bone (13.3 MPa), and concentration of first thread (18 MPa) was higher than other threads (13.3 MPa). It was seen that, while the von Mises stress distribution patterns at different implant thread models were similar, the concentration of compressive stresses were different. The present study showed that the use of different thread form designs did not affect the von Mises concentration at supporting bone structure. However, the compressive stress concentrations differ by various thread profiles. PMID:19543925
Hribar, K C; Finlay, D; Ma, X; Qu, X; Ondeck, M G; Chung, P H; Zanella, F; Engler, A J; Sheikh, F; Vuori, K; Chen, S C
2015-06-01
Long-term culture and monitoring of individual multicellular spheroids and embryoid bodies (EBs) remains a challenge for in vitro cell propagation. Here, we used a continuous 3D projection printing approach - with an important modification of nonlinear exposure - to generate concave hydrogel microstructures that permit spheroid growth and long-term maintenance, without the need for spheroid transfer. Breast cancer spheroids grown to 10 d in the concave structures showed hypoxic cores and signs of necrosis using immunofluorescent and histochemical staining, key features of the tumor microenvironment in vivo. EBs consisting of induced pluripotent stem cells (iPSCs) grown on the hydrogels demonstrated narrow size distribution and undifferentiated markers at 3 d, followed by signs of differentiation by the presence of cavities and staining of the three germ layers at 10 d. These findings demonstrate a new method for long-term (e.g. beyond spheroid formation at day 2, and with media exchange) 3D cell culture that should be able to assist in cancer spheroid studies as well as embryogenesis and patient-derived disease modeling with iPSC EBs. PMID:25900329
Hribar, K.C; Finlay, D.; Ma, X.; Qu, X.; Ondeck, M. G.; Chung, P. H.; Zanella, F.; Engler, A. J.; Sheikh, F.; Vuori, K.; Chen, S.
2015-01-01
Long-term culture and monitoring of individual multicellular spheroids and embryoid bodies (EBs) remains a challenge for in vitro cell propogation. Here, we used a continuous 3D projection printing approach – with an important modification of nonlinear exposure — to generate concave hydrogel microstructures that permit spheroid growth and long-term maintenance, without the need for spheroid transfer. Breast cancer spheroids grown to 10 d in the concave structures showed hypoxic cores and signs of necrosis using immunofluorescent and histochemical staining, key features of the tumor microenvironment in vivo. EBs consisting of induced pluripotent stem cells (iPSCs) grown on the hydrogels demonstrated narrow size distribution and undifferentiated markers at 3 d, followed by signs of differentiation by the presence of cavities and staining of the three germ layers at 10 d. These findings demonstrate a new method for long-term (e.g. beyond spheroid formation at day 2, and with media exchange) 3D cell culture that should be able to assist in cancer spheroid studies as well as embryogenesis and patient-derived disease modeling with iPSC EBs. PMID:25900329
Hsu, Christina M. L.; Palmeri, Mark L.; Segars, W. Paul; Veress, Alexander I.; Dobbins, James T.
2011-01-01
Purpose: The authors previously introduced a methodology to generate a realistic three-dimensional (3D), high-resolution, computer-simulated breast phantom based on empirical data. One of the key components of such a phantom is that it provides a means to produce a realistic simulation of clinical breast compression. In the current study, they have evaluated a finite element (FE) model of compression and have demonstrated the effect of a variety of mechanical properties on the model using a dense mesh generated from empirical breast data. While several groups have demonstrated an effective compression simulation with lower density finite element meshes, the presented study offers a mesh density that is able to model the morphology of the inner breast structures more realistically than lower density meshes. This approach may prove beneficial for multimodality breast imaging research, since it provides a high level of anatomical detail throughout the simulation study. Methods: In this paper, the authors describe methods to improve the high-resolution performance of a FE compression model. In order to create the compressible breast phantom, dedicated breast CT data was segmented and a mesh was generated with 4-noded tetrahedral elements. Using an explicit FE solver to simulate breast compression, several properties were analyzed to evaluate their effect on the compression model including: mesh density, element type, density, and stiffness of various tissue types, friction between the skin and the compression plates, and breast density. Following compression, a simulated projection was generated to demonstrate the ability of the compressible breast phantom to produce realistic simulated mammographic images. Results: Small alterations in the properties of the breast model can change the final distribution of the tissue under compression by more than 1 cm; which ultimately results in different representations of the breast model in the simulated images. The model
NASA Astrophysics Data System (ADS)
Simpson, D. G.; Lipatov, A. S.; Sittler, E. C.; Cooper, J. F.; Hartle, R. E.; Sarantos, M.
2012-12-01
In this report we discuss the results of a 3D hybrid modeling of the interaction between Saturn's magnetosphere and Titan's atmosphere/ionosphere for the T5 encounter. The T5 flyby is the only encounter when the two main ionizing sources of Titan's atmosphere, solar radiation and corotating plasma, align quasi-anti-parallel. The model is based on recent analysis of the Cassini Plasma Spectrometer (CAPS) and the Cassini Ion and Neutral Mass Spectrometer (INMS) measurements during the T5 flyby through Titan's ram-side and polar ionosphere [1,2]. Magnetic field data was used from the MAG instrument [3]. In our model the background ions (O+, H+), all pickup ions, and ionospheric ions are considered as a particles, whereas the electrons are described as a fluid (see e.g. [4]). Inhomogeneous photoionization (in the dayside ionosphere), electron-impact ionization, and charge exchange are included in our model. The temperature of the background electrons and pickup electrons was also incorporated into the generalized Ohm's law. We also take into account collisions between ions and neutrals. In our hybrid simulations we use Chamberlain profiles for the exosphere's components. The moon is considered as a weakly conducting body. The first results of our hybrid modeling show a strong asymmetry in the background (H+, O+) and pickup (H2+, N2+, CH4+) ion density profiles. Such strong asymmetry cannot be explained by a single-fluid multi-species 3D MHD model [5], which includes complex chemistry but does not produce finite gyroradius and kinetic effects. References [1] Sittler, et al., Energy Deposition Processes in Titan's Atmosphere and Its Induced Magnetosphere. In: Titan from Cassini-Huygens, Brown, R.H., Lebreton, J.P., Waite, J.H., Eds., Springer, (Dordrecht, Heidelberg, London, New York), pp. 393-455, 2010. [2] Agren, K., et al., On magnetosphere electron impact ionization and dynamics in Titan's ram-side and polar ionosphere -- a Cassini case study, Ann. Geophys., 25, 2359
NASA Technical Reports Server (NTRS)
Krueger, Ronald; Paris, Isbelle L.; OBrien, T. Kevin; Minguet, Pierre J.
2004-01-01
The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane-strain elements as well as three different generalized plane strain type approaches were performed. The computed skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with delamination length. For more accurate predictions, however, a three-dimensional analysis is required.
Wu, Yicong; Leng, Yuxin; Xi, Jiefeng; Li, Xingde
2009-01-01
An extremely compact all-fiber-optic scanning endomicroscopy system was developed for two-photon fluorescence (TPF) and second harmonic generation (SHG) imaging of biological samples. A conventional double-clad fiber (DCF) was employed in the endomicroscope for single-mode femtosecond pulse delivery, multimode nonlinear optical signals collection and fast two-dimensional scanning. A single photonic bandgap fiber (PBF) with negative group velocity dispersion at two-photon excitation wavelength (i.e. ~810 nm) was used for pulse prechirping in replacement of a bulky grating/lens-based pulse stretcher. The combined use of DCF and PBF in the endomicroscopy system made the endomicroscope basically a plug-and-play unit. The excellent imaging ability of the extremely compact all-fiber-optic nonlinear optical endomicroscopy system was demonstrated by SHG imaging of rat tail tendon and depth-resolved TPF imaging of epithelial tissues stained with acridine orange. The preliminary results suggested the promising potential of this extremely compact all-fiber-optic endomicroscopy system for real-time assessment of both epithelial and stromal structures in luminal organs. PMID:19434122
A survey of the core-congruential formulation for geometrically nonlinear TL finite elements
NASA Technical Reports Server (NTRS)
Felippa, Carlos A.; Crivelli, Luis A.; Haugen, Bjorn
1994-01-01
This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.
Development of a moderately sized finite element program for nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Haisler, W. E.
1977-01-01
AGGIE 1 is a computer program for predicting the linear and nonlinear, static and dynamic structural response of two- and three-dimensional continuum solids. The program is based on isoparametric finite elements and allows for 2-D plane stress, plane strain, and axisymmetric analyses and general 3-D analyses. Large strain kinematics is based on the total Lagrangian formulation. Materially nonlinear models include several elastic-plastic work-hardening models as well as an incompressible Mooney-Rivlin model. Included in this report is a brief description of the theoretical bases of the program, the material models used, the element library and the overall program organization. Instructions for data input preparation are given in detail. Several sample problems are given along with the required program input and program generated solutions.
Frankel, Arthur D.; Stephenson, William J.; Carver, David L.; Williams, Robert A.; Odum, Jack K.; Rhea, Susan
2007-01-01
This report presents probabilistic seismic hazard maps for Seattle, Washington, based on over 500 3D simulations of ground motions from scenario earthquakes. These maps include 3D sedimentary basin effects and rupture directivity. Nonlinear site response for soft-soil sites of fill and alluvium was also applied in the maps. The report describes the methodology for incorporating source and site dependent amplification factors into a probabilistic seismic hazard calculation. 3D simulations were conducted for the various earthquake sources that can affect Seattle: Seattle fault zone, Cascadia subduction zone, South Whidbey Island fault, and background shallow and deep earthquakes. The maps presented in this document used essentially the same set of faults and distributed-earthquake sources as in the 2002 national seismic hazard maps. The 3D velocity model utilized in the simulations was validated by modeling the amplitudes and waveforms of observed seismograms from five earthquakes in the region, including the 2001 M6.8 Nisqually earthquake. The probabilistic seismic hazard maps presented here depict 1 Hz response spectral accelerations with 10%, 5%, and 2% probabilities of exceedance in 50 years. The maps are based on determinations of seismic hazard for 7236 sites with a spacing of 280 m. The maps show that the most hazardous locations for this frequency band (around 1 Hz) are soft-soil sites (fill and alluvium) within the Seattle basin and along the inferred trace of the frontal fault of the Seattle fault zone. The next highest hazard is typically found for soft-soil sites in the Duwamish Valley south of the Seattle basin. In general, stiff-soil sites in the Seattle basin exhibit higher hazard than stiff-soil sites outside the basin. Sites with shallow bedrock outside the Seattle basin have the lowest estimated hazard for this frequency band.
A triangular thin shell finite element: Nonlinear analysis. [structural analysis
NASA Technical Reports Server (NTRS)
Thomas, G. R.; Gallagher, R. H.
1975-01-01
Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.
Nonlinear gyrokinetic theory for finite-BETA plasmas
Hahm, T.S.; Lee, W.W.; Brizard, A.
1988-02-01
A self-consistent and energy-conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell's equations for finite-..beta.. plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formation is valid for arbitrary values of k/perpendicular//rho//sub i/ and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numerical studies based on the existing gyrokinetic particle simulation techniques. 31 refs.
Fast spatial beam shaping by acousto-optic diffraction for 3D non-linear microscopy.
Akemann, Walther; Léger, Jean-François; Ventalon, Cathie; Mathieu, Benjamin; Dieudonné, Stéphane; Bourdieu, Laurent
2015-11-01
Acousto-optic deflection (AOD) devices offer unprecedented fast control of the entire spatial structure of light beams, most notably their phase. AOD light modulation of ultra-short laser pulses, however, is not straightforward to implement because of intrinsic chromatic dispersion and non-stationarity of acousto-optic diffraction. While schemes exist to compensate chromatic dispersion, non-stationarity remains an obstacle. In this work we demonstrate an efficient AOD light modulator for stable phase modulation using time-locked generation of frequency-modulated acoustic waves at the full repetition rate of a high power laser pulse amplifier of 80 kHz. We establish the non-local relationship between the optical phase and the generating acoustic frequency function and verify the system for temporal stability, phase accuracy and generation of non-linear two-dimensional phase functions. PMID:26561090
Slave finite elements: The temporal element approach to nonlinear analysis
NASA Technical Reports Server (NTRS)
Gellin, S.
1984-01-01
A formulation method for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the element domain, and only explicit integration over space and time. While applications are general, the plate and shell elements that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.
NASA Astrophysics Data System (ADS)
Yonetsu, Daigo; Tanaka, Kazufumi; Hara, Takehisa
In recent years, induction-heating (IH) cookers that can be used to heat nonmagnetic metals such as aluminum have been produced. Occasionally, a light pan moves on a glass plate due to buoyancy when heated by an IH cooker. In some IH cookers, an aluminum plate is mounted between the glass plate and the coil in order to reduce the buoyancy effect. The objective of this research is to evaluate the buoyancy-reduction effect and the heating effect of buoyancy-reduction plates. Eddy current analysis is carried out by 3D finite element method, and the electromagnetic force and the heat distribution on the heating plate are calculated. After this calculation is performed, the temperature distribution of the heating plate is calculated by heat transfer analysis. It is found that the shape, area, and the position of the buoyancy reduction plate strongly affect the buoyancy and the heat distribution. The impact of the shape, area, and position of the buoyancy reduction plate was quantified. The phenomena in the heating were elucidated qualitatively.
Application of the Finite Orbit Width Version of the CQL3D Code to NBI +RF Heating of NSTX Plasma
NASA Astrophysics Data System (ADS)
Petrov, Yu. V.; Harvey, R. W.
2015-11-01
The CQL3D bounce-averaged Fokker-Planck (FP) code has been upgraded to include Finite-Orbit-Width (FOW) effects. The calculations can be done either with a fast Hybrid-FOW option or with a slower but neoclassically complete full-FOW option. The banana regime neoclassical radial transport appears naturally in the full-FOW version by averaging the local collision coefficients along guiding center orbits, with a proper transformation matrix from local (R, Z) coordinates to the midplane computational coordinates, where the FP equation is solved. In a similar way, the local quasilinear rf diffusion terms give rise to additional radial transport of orbits. The full-FOW version is applied to simulation of ion heating in NSTX plasma. It is demonstrated that it can describe the physics of transport phenomena in plasma with auxiliary heating, in particular, the enhancement of the radial transport of ions by RF heating and the occurrence of the bootstrap current. Because of the bounce-averaging on the FPE, the results are obtained in a relatively short computational time. A typical full-FOW run time is 30 min using 140 MPI cores. Due to an implicit solver, calculations with a large time step (tested up to dt = 0.5 sec) remain stable. Supported by USDOE grants SC0006614, ER54744, and ER44649.
NASA Astrophysics Data System (ADS)
Zhang, Qi-Hua
2015-10-01
Finite element generation of complicated fracture networks is the core issue and source of technical difficulty in three-dimensional (3-D) discrete fracture network (DFN) flow models. Due to the randomness and uncertainty in the configuration of a DFN, the intersection lines (traces) are arbitrarily distributed in each face (fracture and other surfaces). Hence, subdivision of the fractures is an issue relating to subdivision of two-dimensional (2-D) domains with arbitrarily-distributed constraints. When the DFN configuration is very complicated, the well-known approaches (e.g. Voronoi Delaunay-based methods and advancing-front techniques) cannot operate properly. This paper proposes an algorithm to implement end-to-end connection between traces to subdivide 2-D domains into closed loops. The compositions of the vertices in the common edges between adjacent loops (which may belong to a single fracture or two connected fractures) are thus ensured to be topologically identical. The paper then proposes an approach for triangulating arbitrary loops which does not add any nodes to ensure consistency of the meshes at the common edges. In addition, several techniques relating to tolerance control and improving code robustness are discussed. Finally, the equivalent permeability of the rock mass is calculated for some very complicated DFNs (the DFN may contain 1272 fractures, 633 connected fractures, and 16,270 closed loops). The results are compared with other approaches to demonstrate the veracity and efficiency of the approach proposed in this paper.
Modeling of Nonlinear Mechanical Behavior for 3D Needled C/C-SiC Composites Under Tensile Load
NASA Astrophysics Data System (ADS)
Xie, Junbo; Fang, Guodong; Chen, Zhen; Liang, Jun
2016-04-01
This paper established a macroscopic constitutive model to describe the nonlinear stress-strain behavior of 3D needled C/C-SiC composites under tensile load. Extensive on- and off-axis tensile tests were performed to investigate the macroscopic mechanical behavior and damage characteristics of the composites. The nonlinear mechanical behavior of the material was mainly induced by matrix tensile cracking and fiber/matrix debonding. Permanent deformations and secant modulus degradation were observed in cyclic loading-unloading tests. The nonlinear stress-strain relationship of the material could be described macroscopically by plasticity deformation and stiffness degradation. In the proposed model, we employed a plasticity theory with associated plastic flow rule to describe the evolution of plastic strains. A novel damage variable was also introduced to characterize the stiffness degradation of the material. The damage evolution law was derived from the statistical distribution of material strength. Parameters of the proposed model can be determined from off-axis tensile tests. Stress-strain curves predicted by this model showed reasonable agreement with experimental results.
Modeling of Nonlinear Mechanical Behavior for 3D Needled C/C-SiC Composites Under Tensile Load
NASA Astrophysics Data System (ADS)
Xie, Junbo; Fang, Guodong; Chen, Zhen; Liang, Jun
2016-08-01
This paper established a macroscopic constitutive model to describe the nonlinear stress-strain behavior of 3D needled C/C-SiC composites under tensile load. Extensive on- and off-axis tensile tests were performed to investigate the macroscopic mechanical behavior and damage characteristics of the composites. The nonlinear mechanical behavior of the material was mainly induced by matrix tensile cracking and fiber/matrix debonding. Permanent deformations and secant modulus degradation were observed in cyclic loading-unloading tests. The nonlinear stress-strain relationship of the material could be described macroscopically by plasticity deformation and stiffness degradation. In the proposed model, we employed a plasticity theory with associated plastic flow rule to describe the evolution of plastic strains. A novel damage variable was also introduced to characterize the stiffness degradation of the material. The damage evolution law was derived from the statistical distribution of material strength. Parameters of the proposed model can be determined from off-axis tensile tests. Stress-strain curves predicted by this model showed reasonable agreement with experimental results.
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
NASA Technical Reports Server (NTRS)
Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)
2001-01-01
Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.
Linear Stability and Nonlinear Evolution of 3D Vortices in Rotating Stratified Flows
NASA Astrophysics Data System (ADS)
Mahdinia, Mani; Hassanzadeh, Pedram; Marcus, Philip
2014-11-01
Axisymmetric Gaussian vortices are widely-used to model oceanic vortices. We study their stability in rotating, stratified flows by using the full Boussinesq equations. We created a stability map as a function of the Burger and Rossby numbers of the vortices. We computed the linear growth rates of the most-unstable eigenmodes and their corresponding eigenmodes. Our map shows a significant cyclone/anti-cyclone asymmetry. The vortices are linearly unstable in most of the parameter space that we studied. However, the anticyclonic vortices, over most of the parameter space, have eigenmodes with only very weak growth rates - longer than 50 vortex turn-around times. For oceanic vortices, that time corresponds to several months, so we argue that this slow growth rate means that the oceanic anticyclones lifetimes are not determined by linear stability, but by other processes. We also use our full, nonlinear simulations to show an example of an unstable cyclone with a very fast growing linear eigenmodes. However, we show that cyclone quickly redistributes its vorticity and becomes a stable tripole with a large core that is nearly axisymmetric.
Sotelo, Julio; Urbina, Jesus; Valverde, Israel; Tejos, Cristian; Irarrazaval, Pablo; Andia, Marcelo E; Uribe, Sergio; Hurtado, Daniel E
2016-06-01
Several 2D methods have been proposed to estimate WSS and OSI from PC-MRI, neglecting the longitudinal velocity gradients that typically arise in cardiovascular flow, particularly on vessel geometries whose cross section and centerline orientation strongly vary in the axial direction. Thus, the contribution of longitudinal velocity gradients remains understudied. In this work, we propose a 3D finite-element method for the quantification of WSS and OSI from 3D-CINE PC-MRI that accounts for both in-plane and longitudinal velocity gradients. We demonstrate the convergence and robustness of the method on cylindrical geometries using a synthetic phantom based on the Poiseuille flow equation. We also show that, in the presence of noise, the method is both stable and accurate. Using computational fluid dynamics simulations, we show that the proposed 3D method results in more accurate WSS estimates than those obtained from a 2D analysis not considering out-of-plane velocity gradients. Further, we conclude that for irregular geometries the accurate prediction of WSS requires the consideration of longitudinal gradients in the velocity field. Additionally, we compute 3D maps of WSS and OSI for 3D-CINE PC-MRI data sets from an aortic phantom and sixteen healthy volunteers and two patients. The OSI values show a greater dispersion than WSS, which is strongly dependent on the PC-MRI resolution. We envision that the proposed 3D method will improve the estimation of WSS and OSI from 3D-CINE PC-MRI images, allowing for more accurate estimates in vessels with pathologies that induce high longitudinal velocity gradients, such as coarctations and aneurisms. PMID:26780787
Lee, Shiu-Hang; Kamae, Tuneyoshi; Ellison, Donald C.
2008-07-02
We present a 3-dimensional model of supernova remnants (SNRs) where the hydrodynamical evolution of the remnant is modeled consistently with nonlinear diffusive shock acceleration occurring at the outer blast wave. The model includes particle escape and diffusion outside of the forward shock, and particle interactions with arbitrary distributions of external ambient material, such as molecular clouds. We include synchrotron emission and cooling, bremsstrahlung radiation, neutral pion production, inverse-Compton (IC), and Coulomb energy-loss. Boardband spectra have been calculated for typical parameters including dense regions of gas external to a 1000 year old SNR. In this paper, we describe the details of our model but do not attempt a detailed fit to any specific remnant. We also do not include magnetic field amplification (MFA), even though this effect may be important in some young remnants. In this first presentation of the model we don't attempt a detailed fit to any specific remnant. Our aim is to develop a flexible platform, which can be generalized to include effects such as MFA, and which can be easily adapted to various SNR environments, including Type Ia SNRs, which explode in a constant density medium, and Type II SNRs, which explode in a pre-supernova wind. When applied to a specific SNR, our model will predict cosmic-ray spectra and multi-wavelength morphology in projected images for instruments with varying spatial and spectral resolutions. We show examples of these spectra and images and emphasize the importance of measurements in the hard X-ray, GeV, and TeV gamma-ray bands for investigating key ingredients in the acceleration mechanism, and for deducing whether or not TeV emission is produced by IC from electrons or pion-decay from protons.
Väänänen, Sami P; Grassi, Lorenzo; Flivik, Gunnar; Jurvelin, Jukka S; Isaksson, Hanna
2015-08-01
Areal bone mineral density (aBMD), as measured by dual-energy X-ray absorptiometry (DXA), predicts hip fracture risk only moderately. Simulation of bone mechanics based on DXA imaging of the proximal femur, may help to improve the prediction accuracy. Therefore, we collected three (1-3) image sets, including CT images and DXA images of 34 proximal cadaver femurs (set 1, including 30 males, 4 females), 35 clinical patient CT images of the hip (set 2, including 27 males, 8 females) and both CT and DXA images of clinical patients (set 3, including 12 female patients). All CT images were segmented manually and landmarks were placed on both femurs and pelvises. Two separate statistical appearance models (SAMs) were built using the CT images of the femurs and pelvises in sets 1 and 2, respectively. The 3D shape of the femur was reconstructed from the DXA image by matching the SAMs with the DXA images. The orientation and modes of variation of the SAMs were adjusted to minimize the sum of the absolute differences between the projection of the SAMs and a DXA image. The mesh quality and the location of the SAMs with respect to the manually placed control points on the DXA image were used as additional constraints. Then, finite element (FE) models were built from the reconstructed shapes. Mean point-to-surface distance between the reconstructed shape and CT image was 1.0 mm for cadaver femurs in set 1 (leave-one-out test) and 1.4 mm for clinical subjects in set 3. The reconstructed volumetric BMD showed a mean absolute difference of 140 and 185 mg/cm(3) for set 1 and set 3 respectively. The generation of the SAM and the limitation of using only one 2D image were found to be the most significant sources of errors in the shape reconstruction. The noise in the DXA images had only small effect on the accuracy of the shape reconstruction. DXA-based FE simulation was able to explain 85% of the CT-predicted strength of the femur in stance loading. The present method can be used to
Non-linear dynamics of viscous bilayers subjected to an electric field: 3D phase field simulations
NASA Astrophysics Data System (ADS)
Dritselis, Christos; Karapetsas, George; Bontozoglou, Vasilis
2014-11-01
The scope of this work is to investigate the non-linear dynamics of the electro-hydrodynamic instability of a bilayer of immiscible liquids. We consider the case of two viscous films which is separated from the top electrode by air. We assume that the liquids are perfect dielectrics and consider the case of both flat and patterned electrodes. We develop a computational model using the diffuse interface method and carry out 3D numerical simulations fully accounting for the flow and electric field in all phases. We perform a parametric study and investigate the influence of the electric properties of fluids, applied voltage and various geometrical characteristics of the mask. The authors acknowledge the support by the General Secretariat of Research and Technology of Greece under the action ``Supporting Postdoctoral Researchers'' (Grant Number PE8/906), co-funded by the European Social Fund and National Resources.
Super non-linear RRAM with ultra-low power for 3D vertical nano-crossbar arrays.
Luo, Qing; Xu, Xiaoxin; Liu, Hongtao; Lv, Hangbing; Gong, Tiancheng; Long, Shibing; Liu, Qi; Sun, Haitao; Banerjee, Writam; Li, Ling; Gao, Jianfeng; Lu, Nianduan; Liu, Ming
2016-08-25
Vertical crossbar arrays provide a cost-effective approach for high density three-dimensional (3D) integration of resistive random access memory. However, an individual selector device is not allowed to be integrated with the memory cell separately. The development of V-RRAM has impeded the lack of satisfactory self-selective cells. In this study, we have developed a high performance bilayer self-selective device using HfO2 as the memory switching layer and a mixed ionic and electron conductor as the selective layer. The device exhibits high non-linearity (>10(3)) and ultra-low half-select leakage (<0.1 pA). A four layer vertical crossbar array was successfully demonstrated based on the developed self-selective device. High uniformity, ultra-low leakage, sub-nA operation, self-compliance, and excellent read/write disturbance immunity were achieved. The robust array level performance shows attractive potential for low power and high density 3D data storage applications. PMID:27510434
NASA Astrophysics Data System (ADS)
Kis, M.; Detzky, G.; Koppán, A.
2012-04-01
phenomenon in general. Authors calculated the deformations of a simple-geometry 3D cavity, which is caused by variable gravity loads. Dependence of the cavity effect on changing of distinct elastic properties in categorized models has been investigated. Authors introduced qualifying parameter fields calculated using the results of the FE modelling (nodal displacements as a model answer for the gravity load), in order to characterize the effect. Modelling results can be used as an estimation not only for the absolute cavity effect rate of the intended arrangement, furthermore the sensitivity of the given system against a particular geometric property. As an application example finite element modelling were carried out in order to estimate the influence of the complicated cavity system surrounding the "Budapest-Matyashegy" Gravity and Geodynamical Observatory of the Eotvos Lorand Geophysical Institute of Hungary.
NASA Technical Reports Server (NTRS)
1976-01-01
A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity.
ERIC Educational Resources Information Center
Nazari, Mohammad Ali; Perrier, Pascal; Payan, Yohan
2013-01-01
Purpose: The authors aimed to design a distributed lambda model (DLM), which is well adapted to implement three-dimensional (3-D), finite-element descriptions of muscles. Method: A muscle element model was designed. Its stress-strain relationships included the active force-length characteristics of the ? model along the muscle fibers, together…
NASA Astrophysics Data System (ADS)
Kanellopoulos, V. N.; Webb, J. P.
1993-03-01
A 3D vector analysis of plane wave scattering by a metallic sphere using finite elements and Absorbing Boundary Conditions (ABCs) is presented. The ABCs are applied on the outer surface that truncates the infinitely extending domain. Mixed order curvilinear covariantprojection elements are used to avoid spurious corruptions. The second order ABC is superior to the first at no extra computational cost. The errors due to incomplete absorption decrease as the outer surface is moved further away from the scatterer. An error of about 1% in near-field values was obtained with the second order ABC, when the outer surface was less than half a wavelength from the scatterer. Une analyse tridimensionnelle vectorielle de la diffusion d'onde plane sur une sphère métallique utilisant des éléments finis et des Conditions aux Limites Absorbantes (CLA) est présentée. Les CLA sont appliquées sur la surface exteme tronquant le domaine s'étendant à l'infini. Des éléments curvilignes mixtes utilisant des projections covariantes sont utilisés pour éviter des solutions parasites. La CLA de second ordre est supérieure à celle de premier ordre sans effort de calcul additionnel. Les erreurs dues à l'absorption incomplète décroissent à mesure que l'on déplace la surface externe à une distance croissante du diffuseur. Un taux d'erreur d'environ 1 % dans les valeurs du champ proche a été obtenu avec les CLA de second ordre lorsque la surface externe était placée à une distance inférieure à une demi-longueur de la source de diffusion.
Lin, Jie; Zheng, Zhiqiang; Shinya, Akikazu; Matinlinna, Jukka Pekka; Botelho, Michael George; Shinya, Akiyoshi
2015-09-01
The purpose of this in vitro study was to compare the stress distribution and natural frequency of different shape and thickness retainer designs for maxillary posterior resin-bonded prostheses using finite element (FE) method. A 3D FE model of a three unit posterior resin-bonded prosthesis analysis model was generated. Three different shaped retainer designs, viz. C-shaped (three axial surface wraparounds), D-shaped (three axial surface wraparounds with central groove) and O-shaped (360° wraparounds), and three different thicknesses, viz., 0.4, 0.8, and 1.2 mm, resin-bonded prostheses were used in this study. The resin-bonded prosthesis analysis model was imported into an FE analysis software (ANSYS 10.0, ANSYS, USA) and attribution of material properties. The nodes at the bottom surface of the roots were assigned fixed zero displacement in the three spatial dimensions. A simulated angle of 45° loading of a 100 N force was applied to the node of the pontic lingual cusp surface. The stress distributions and corresponding natural frequencies were analyzed and resolved. The C-shaped retainer for 0.4 mm thickness recorded the greatest von Mises stresses of 71.4 MPa for all three groups. C-shaped, D-shaped and O-shaped retainer presented natural frequencies 3,988, 7,754, and 10,494 Hz, respectively. D-shaped retainer and O-shaped retainer increased natural frequencies and structural rigidity over the traditional C-shaped retainer. The maximum von Mises stresses values of the remaining tooth and prosthesis decreased with greater retainer thickness. D-shaped retainer and O-shaped retainer increased natural frequencies and structural rigidity over the traditional C-shaped retainer. PMID:25200313
Holford, D.J.
1994-01-01
This document is a user`s manual for the Rn3D finite element code. Rn3D was developed to simulate gas flow and radon transport in variably saturated, nonisothermal porous media. The Rn3D model is applicable to a wide range of problems involving radon transport in soil because it can simulate either steady-state or transient flow and transport in one-, two- or three-dimensions (including radially symmetric two-dimensional problems). The porous materials may be heterogeneous and anisotropic. This manual describes all pertinent mathematics related to the governing, boundary, and constitutive equations of the model, as well as the development of the finite element equations used in the code. Instructions are given for constructing Rn3D input files and executing the code, as well as a description of all output files generated by the code. Five verification problems are given that test various aspects of code operation, complete with example input files, FORTRAN programs for the respective analytical solutions, and plots of model results. An example simulation is presented to illustrate the type of problem Rn3D is designed to solve. Finally, instructions are given on how to convert Rn3D to simulate systems other than radon, air, and water.
NASA Astrophysics Data System (ADS)
Boscheri, Walter; Dumbser, Michael
2014-10-01
In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with
A nonlinear dynamic finite element approach for simulating muscular hydrostats.
Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A
2014-01-01
An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching. PMID:23025686
Three-dimensional finite-difference modeling of non-linear ground notion
Jones, E.M.; Olsen, K.B.
1997-08-01
We present a hybrid finite-difference technique capable of modeling non-linear soil amplification from the 3-D finite-fault radiation pattern for earthquakes in arbitrary earth models. The method is applied to model non-linear effects in the soils of the San Fernando Valley (SFV) from the 17 January 1994 M 6.7 Northridge earthquake. 0-7 Hz particle velocities are computed for an area of 17 km by 19 km immediately above the causative fault and 5 km below the surface where peak strike-parallel, strike-perpendicular, vertical, and total velocities reach values of 71 cm/s, 145 cm/s, 152 cm/s, and 180 cm/s, respectively. Selected Green`s functions and a soil model for the SFV are used to compute the approximate stress level during the earthquake, and comparison to the values for near-surface alluvium at the U.S. Nevada Test Site suggests that the non-linear regime may have been entered. We use selected values from the simulated particle velocity distribution at 5 km depth to compute the non-linear response in a soil column below a site within the Van Norman Complex in SFV, where the strongest ground motion was recorded. Since site-specific non- linear material parameters from the SFV are currently unavailable, values are taken from analyses of observed Test Site ground motions. Preliminary results show significant reduction of spectral velocities at the surface normalized to the peak source velocity due to non-linear effects when the peak velocity increases from 32 cm/s (approximately linear case) to 64 cm/s (30-92%), 93 cm/s (7-83%), and 124 cm/s (2-70%). The largest reduction occurs for frequencies above 1 Hz.
Nie, Weijie; Jia, Yuechen; Vázquez de Aldana, Javier R.; Chen, Feng
2016-01-01
Integrated photonic devices with beam splitting function are intriguing for a broad range of photonic applications. Through optical-lattice-like cladding waveguide structures fabricated by direct femtosecond laser writing, the light propagation can be engineered via the track-confined refractive index profiles, achieving tailored output beam distributions. In this work, we report on the fabrication of 3D laser-written optical-lattice-like structures in a nonlinear KTP crystal to implement 1 × 4 beam splitting. Second harmonic generation (SHG) of green light through these nonlinear waveguide beam splitter structures provides the capability for the compact visible laser emitting devices. With Type II phase matching of the fundamental wavelength (@ 1064 nm) to second harmonic waves (@ 532 nm), the frequency doubling has been achieved through this three-dimensional beam splitter. Under 1064-nm continuous-wave fundamental-wavelength pump beam, guided-wave SHG at 532 nm are measured with the maximum power of 0.65 mW and 0.48 mW for waveguide splitters (0.67 mW and 0.51 mW for corresponding straight channel waveguides), corresponding to a SH conversion efficiency of approximately ~14.3%/W and 13.9%/W (11.2%/W, 11.3%/W for corresponding straight channel waveguides), respectively. This work paves a way to fabricate compact integrated nonlinear photonic devices in a single chip with beam dividing functions. PMID:26924255
Nie, Weijie; Jia, Yuechen; Vázquez de Aldana, Javier R; Chen, Feng
2016-01-01
Integrated photonic devices with beam splitting function are intriguing for a broad range of photonic applications. Through optical-lattice-like cladding waveguide structures fabricated by direct femtosecond laser writing, the light propagation can be engineered via the track-confined refractive index profiles, achieving tailored output beam distributions. In this work, we report on the fabrication of 3D laser-written optical-lattice-like structures in a nonlinear KTP crystal to implement 1 × 4 beam splitting. Second harmonic generation (SHG) of green light through these nonlinear waveguide beam splitter structures provides the capability for the compact visible laser emitting devices. With Type II phase matching of the fundamental wavelength (@ 1064 nm) to second harmonic waves (@ 532 nm), the frequency doubling has been achieved through this three-dimensional beam splitter. Under 1064-nm continuous-wave fundamental-wavelength pump beam, guided-wave SHG at 532 nm are measured with the maximum power of 0.65 mW and 0.48 mW for waveguide splitters (0.67 mW and 0.51 mW for corresponding straight channel waveguides), corresponding to a SH conversion efficiency of approximately ~14.3%/W and 13.9%/W (11.2%/W, 11.3%/W for corresponding straight channel waveguides), respectively. This work paves a way to fabricate compact integrated nonlinear photonic devices in a single chip with beam dividing functions. PMID:26924255
NASA Astrophysics Data System (ADS)
Nie, Weijie; Jia, Yuechen; Vázquez de Aldana, Javier R.; Chen, Feng
2016-02-01
Integrated photonic devices with beam splitting function are intriguing for a broad range of photonic applications. Through optical-lattice-like cladding waveguide structures fabricated by direct femtosecond laser writing, the light propagation can be engineered via the track-confined refractive index profiles, achieving tailored output beam distributions. In this work, we report on the fabrication of 3D laser-written optical-lattice-like structures in a nonlinear KTP crystal to implement 1 × 4 beam splitting. Second harmonic generation (SHG) of green light through these nonlinear waveguide beam splitter structures provides the capability for the compact visible laser emitting devices. With Type II phase matching of the fundamental wavelength (@ 1064 nm) to second harmonic waves (@ 532 nm), the frequency doubling has been achieved through this three-dimensional beam splitter. Under 1064-nm continuous-wave fundamental-wavelength pump beam, guided-wave SHG at 532 nm are measured with the maximum power of 0.65 mW and 0.48 mW for waveguide splitters (0.67 mW and 0.51 mW for corresponding straight channel waveguides), corresponding to a SH conversion efficiency of approximately ~14.3%/W and 13.9%/W (11.2%/W, 11.3%/W for corresponding straight channel waveguides), respectively. This work paves a way to fabricate compact integrated nonlinear photonic devices in a single chip with beam dividing functions.
Probabilistic nonlinear finite element analysis of composite structures
NASA Technical Reports Server (NTRS)
Engelstad, S. P.; Reddy, J. N.
1993-01-01
A probabilistic finite element analysis procedure for laminated composite shells is developed. A total Lagrangian finite element formulation, employing a degenerated three-dimensional laminated composite shell element with the full Green-Lagrange strains and first-order shear deformable kinematics, is used. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed, and results are presented in the form of mean and variance of the structural response. Reliability calculations are made by using the first-order reliability method combined with sensitivity derivatives from the finite element analysis. Both ply-level and micromechanics-level random variables are incorporated, the latter by means of the Aboudi micromechanics model. Two sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. In general, the procedure is quite effective in determining the response statistics and reliability for linear and geometric nonlinear behavior of laminated composite shells.
NASA Technical Reports Server (NTRS)
Parikh, Paresh; Pirzadeh, Shahyar; Loehner, Rainald
1990-01-01
A set of computer programs for 3-D unstructured grid generation, fluid flow calculations, and flow field visualization was developed. The grid generation program, called VGRID3D, generates grids over complex configurations using the advancing front method. In this method, the point and element generation is accomplished simultaneously, VPLOT3D is an interactive, menudriven pre- and post-processor graphics program for interpolation and display of unstructured grid data. The flow solver, VFLOW3D, is an Euler equation solver based on an explicit, two-step, Taylor-Galerkin algorithm which uses the Flux Corrected Transport (FCT) concept for a wriggle-free solution. Using these programs, increasingly complex 3-D configurations of interest to aerospace community were gridded including a complete Space Transportation System comprised of the space-shuttle orbitor, the solid-rocket boosters, and the external tank. Flow solutions were obtained on various configurations in subsonic, transonic, and supersonic flow regimes.
PLANS: A finite element program for nonlinear analysis of structures. Volume 1: Theoretical manual
NASA Technical Reports Server (NTRS)
Pifko, A.; Levine, H. S.; Armen, H., Jr.
1975-01-01
The PLANS system is described which is a finite element program for nonlinear analysis. The system represents a collection of special purpose computer programs each associated with a distinct physical problem class. Modules of PLANS specifically referenced and described in detail include: (1) REVBY, for the plastic analysis of bodies of revolution; (2) OUT-OF-PLANE, for the plastic analysis of 3-D built-up structures where membrane effects are predominant; (3) BEND, for the plastic analysis of built-up structures where bending and membrane effects are significant; (4) HEX, for the 3-D elastic-plastic analysis of general solids; and (5) OUT-OF-PLANE-MG, for material and geometrically nonlinear analysis of built-up structures. The SATELLITE program for data debugging and plotting of input geometries is also described. The theoretical foundations upon which the analysis is based are presented. Discussed are the form of the governing equations, the methods of solution, plasticity theories available, a general system description and flow of the programs, and the elements available for use.
Mason, W.E.
1983-03-01
A set of finite element codes for the solution of nonlinear, two-dimensional (TACO2D) and three-dimensional (TACO3D) heat transfer problems. Performs linear and nonlinear analyses of both transient and steady state heat transfer problems. Has the capability to handle time or temperature dependent material properties. Materials may be either isotropic or orthotropic. A variety of time and temperature dependent boundary conditions and loadings are available including temperature, flux, convection, radiation, and internal heat generation.
NASA Astrophysics Data System (ADS)
Liu, Yang; Sen, Mrinal K.
2011-09-01
Most conventional finite-difference methods adopt second-order temporal and (2M)th-order spatial finite-difference stencils to solve the 3D acoustic wave equation. When spatial finite-difference stencils devised from the time-space domain dispersion relation are used to replace these conventional spatial finite-difference stencils devised from the space domain dispersion relation, the accuracy of modelling can be increased from second-order along any directions to (2M)th-order along 48 directions. In addition, the conventional high-order spatial finite-difference modelling accuracy can be improved by using a truncated finite-difference scheme. In this paper, we combine the time-space domain dispersion-relation-based finite difference scheme and the truncated finite-difference scheme to obtain optimised spatial finite-difference coefficients and thus to significantly improve the modelling accuracy without increasing computational cost, compared with the conventional space domain dispersion-relation-based finite difference scheme. We developed absorbing boundary conditions for the 3D acoustic wave equation, based on predicting wavefield values in a transition area by weighing wavefield values from wave equations and one-way wave equations. Dispersion analyses demonstrate that high-order spatial finite-difference stencils have greater accuracy than low-order spatial finite-difference stencils for high frequency components of wavefields, and spatial finite-difference stencils devised in the time-space domain have greater precision than those devised in the space domain under the same discretisation. The modelling accuracy can be improved further by using the truncated spatial finite-difference stencils. Stability analyses show that spatial finite-difference stencils devised in the time-space domain have better stability condition. Numerical modelling experiments for homogeneous, horizontally layered and Society of Exploration Geophysicists/European Association of
NASA Astrophysics Data System (ADS)
Borisov, Dmitry; Singh, Satish C.; Fuji, Nobuaki
2015-09-01
Seismic full waveform inversion is an objective method to estimate elastic properties of the subsurface and is an important area of research, particularly in seismic exploration community. It is a data-fitting approach, where the difference between observed and synthetic data is minimized iteratively. Due to a very high computational cost, the practical implementation of waveform inversion has so far been restricted to a 2-D geometry with different levels of physics incorporated in it (e.g. elasticity/viscoelasticity) or to a 3-D geometry but using an acoustic approximation. However, the earth is three-dimensional, elastic and heterogeneous and therefore a full 3-D elastic inversion is required in order to obtain more accurate and valuable models of the subsurface. Despite the recent increase in computing power, the application of 3-D elastic full waveform inversion to real-scale problems remains quite challenging on the current computer architecture. Here, we present an efficient method to perform 3-D elastic full waveform inversion for time-lapse seismic data using a finite-difference injection method. In this method, the wavefield is computed in the whole model and is stored on a surface above a finite volume where the model is perturbed and localized inversion is performed. Comparison of the final results using the 3-D finite-difference injection method and conventional 3-D inversion performed within the whole volume shows that our new method provides significant reductions in computational time and memory requirements without any notable loss in accuracy. Our approach shows a big potential for efficient reservoir monitoring in real time-lapse experiments.
Doulamis, Nikolaos D; Doulamis, Anastasios D; Panagakis, Athanasios; Dolkas, Konstantinos; Varvarigou, Theodora A; Varvarigos, Emmanuel
2004-04-01
Implementation of a commercial application to a grid infrastructure introduces new challenges in managing the quality-of-service (QoS) requirements, most stem from the fact that negotiation on QoS between the user and the service provider should strictly be satisfied. An interesting commercial application with a wide impact on a variety of fields, which can benefit from the computational grid technologies, is three-dimensional (3-D) rendering. In order to implement, however, 3-D rendering to a grid infrastructure, we should develop appropriate scheduling and resource allocation mechanisms so that the negotiated (QoS) requirements are met. Efficient scheduling schemes require modeling and prediction of rendering workload. In this paper workload prediction is addressed based on a combined fuzzy classification and neural network model. Initially, appropriate descriptors are extracted to represent the synthetic world. The descriptors are obtained by parsing RIB formatted files, which provides a general structure for describing computer-generated images. Fuzzy classification is used for organizing rendering descriptor so that a reliable representation is accomplished which increases the prediction accuracy. Neural network performs workload prediction by modeling the nonlinear input-output relationship between rendering descriptors and the respective computational complexity. To increase prediction accuracy, a constructive algorithm is adopted in this paper to train the neural network so that network weights and size are simultaneously estimated. Then, a grid scheduler scheme is proposed to estimate the queuing order that the tasks should be executed and the most appopriate processor assignment so that the demanded QoS are satisfied as much as possible. A fair scheduling policy is considered as the most appropriate. Experimental results on a real grid infrastructure are presented to illustrate the efficiency of the proposed workload prediction--scheduling algorithm
Nonlinear explicit transient finite element analysis on the Intel Delta
Plaskacz, E.J.; Ramirez, M.R.; Gupta, S.
1993-03-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Nonlinear explicit transient finite element analysis on the Intel Delta
Plaskacz, E.J. ); Ramirez, M.R.; Gupta, S. . Dept. of Civil Engineering)
1993-01-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Explicit 3-D Hydrodynamic FEM Program
2000-11-07
DYNA3D is a nonlinear explicit finite element code for analyzing 3-D structures and solid continuum. The code is vectorized and available on several computer platforms. The element library includes continuum, shell, beam, truss and spring/damper elements to allow maximum flexibility in modeling physical problems. Many materials are available to represent a wide range of material behavior, including elasticity, plasticity, composites, thermal effects and rate dependence. In addition, DYNA3D has a sophisticated contact interface capability, includingmore » frictional sliding, single surface contact and automatic contact generation.« less
Explicit 3-D Hydrodynamic FEM Program
2000-11-07
DYNA3D is a nonlinear explicit finite element code for analyzing 3-D structures and solid continuum. The code is vectorized and available on several computer platforms. The element library includes continuum, shell, beam, truss and spring/damper elements to allow maximum flexibility in modeling physical problems. Many materials are available to represent a wide range of material behavior, including elasticity, plasticity, composites, thermal effects and rate dependence. In addition, DYNA3D has a sophisticated contact interface capability, including frictional sliding, single surface contact and automatic contact generation.
Nonlinear finite-element analysis of nanoindentation of viral capsids
NASA Astrophysics Data System (ADS)
Gibbons, Melissa M.; Klug, William S.
2007-03-01
Recent atomic force microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick-shell models are proposed for two capsids: the spherical cowpea chlorotic mottle virus (CCMV), and the ellipsocylindrical bacteriophage ϕ29 . As analyzed by the finite-element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive particulars, and greatly influenced by geometric and kinematic details. Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness. Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young’s moduli of ≈280-360MPa for CCMV and ≈4.5GPa for ϕ29 .
NASA Astrophysics Data System (ADS)
Cooper, W. A.; Graves, J. P.; Duval, B. P.; Porte, L.; Reimerdes, H.; Sauter, O.; Tran, T.-M.
2015-12-01
> Novel free boundary magnetohydrodynamic equilibrium states with spontaneous three-dimensional (3-D) deformations of the plasma-vacuum interface are computed. The structures obtained look like saturated ideal external kink/peeling modes. Large edge pressure gradients yield toroidal mode number distortions when the edge bootstrap current is large and higher corrugations when this current is small. Linear ideal MHD stability analyses confirm the nonlinear saturated ideal kink equilibrium states produced and we can identify the Pfirsch-Schlüter current as the main linear instability driving mechanism when the edge pressure gradient is large. The dominant non-axisymmetric component of this Pfirsch-Schlüter current drives a near resonant helical parallel current density ribbon that aligns with the near vanishing magnetic shear region caused by the edge bootstrap current. This current ribbon is a manifestation of the outer mode previously found on JET (Solano 2010). We claim that the equilibrium corrugations describe structures that are commonly observed in quiescent H-mode tokamak discharges.
Sarens, Bart; Verstraeten, Bert; Glorieux, Christ; Kalogiannakis, Georgios; Van Hemelrijck, Danny
2010-06-01
Full-field dynamic shearography and laser Doppler vibrometric scanning are used to investigate the local contact acoustic nonlinear generation of delamination-induced effects on the vibration of a harmonically excited composite plate containing an artificial defect. Nonlinear elastic behavior caused by the stress-dependent boundary conditions at the delamination interfaces of a circular defect is also simulated by a 3-D second-order, finite-difference, staggered-grid model (displacement-stress formulation). Both the experimental and simulated data reveal an asymmetric motion of the layer above the delamination, which acts as a membrane vibrating with enhanced displacement amplitude around a finite offset displacement. The spectrum of the membrane motion is enriched with clapping-induced harmonics of the excitation frequency. In case of a sufficiently thin and soft membrane, the simulations reveal clear modal behavior at sub-harmonic frequencies caused by inelastic clapping. PMID:20529713
Djoudi, Farid
2013-01-01
Two separate themes are presented in this paper. Aims The first theme is to present a graphical modeling approach of human anatomical structures namely, the femur and the tibia. The second theme involves making a finite element analysis of stresses, displacements and deformations in prosthetic implants (the femoral implant and the polyethylene insert). Objectives The graphical modeling approach comes in two parts. The first is the segmentation of MRI scanned images, retrieved in DICOM format for edge detection. In the second part, 3D-CAD models are generated from the results of the segmentation stage. The finite element analysis is done by first extracting the prosthetic implants from the reconstructed 3D-CAD model, then do a finite element analysis of these implants under objectively determined conditions such as; forces, allowed displacements, the materials composing implant, and the coefficient of friction. Conclusion The objective of this work is to implement an interface for exchanging data between 2D MRI images obtained from a medical diagnosis of a patient and the 3D-CAD model used in various applications, such as; the extraction of the implants, stress analysis at the knee joint and can serve as an aid to surgery, also predict the behavior of the prosthetic implants vis-a-vis the forces acting on the knee joints. PMID:24396234
Comparison of 3-D finite element model of ashlar masonry with 2-D numerical models of ashlar masonry
NASA Astrophysics Data System (ADS)
Beran, Pavel
2016-06-01
3-D state of stress in heterogeneous ashlar masonry can be also computed by several suitable chosen 2-D numerical models of ashlar masonry. The results obtained from 2-D numerical models well correspond to the results obtained from 3-D numerical model. The character of thermal stress is the same. While using 2-D models the computational time is reduced more than hundredfold and therefore this method could be used for computation of thermal stresses during long time periods with 10 000 of steps.
NASA Astrophysics Data System (ADS)
Lu, W.; Tzoufras, M.; Joshi, C.; Tsung, F. S.; Mori, W. B.; Vieira, J.; Fonseca, R. A.; Silva, L. O.
2007-06-01
The extraordinary ability of space-charge waves in plasmas to accelerate charged particles at gradients that are orders of magnitude greater than in current accelerators has been well documented. We develop a phenomenological framework for laser wakefield acceleration (LWFA) in the 3D nonlinear regime, in which the plasma electrons are expelled by the radiation pressure of a short pulse laser, leading to nearly complete blowout. Our theory provides a recipe for designing a LWFA for given laser and plasma parameters and estimates the number and the energy of the accelerated electrons whether self-injected or externally injected. These formulas apply for self-guided as well as externally guided pulses (e.g. by plasma channels). We demonstrate our results by presenting a sample particle-in-cell (PIC) simulation of a 30fs, 200 TW laser interacting with a 0.75 cm long plasma with density 1.5×1018cm-3 to produce an ultrashort (10 fs) monoenergetic bunch of self-injected electrons at 1.5 GeV with 0.3 nC of charge. For future higher-energy accelerator applications, we propose a parameter space, which is distinct from that described by Gordienko and Pukhov [Phys. Plasmas 12, 043109 (2005)PHPAEN1070-664X10.1063/1.1884126] in that it involves lower plasma densities and wider spot sizes while keeping the intensity relatively constant. We find that this helps increase the output electron beam energy while keeping the efficiency high.
Nonlinear triggered lightning models for use in finite difference calculations
NASA Technical Reports Server (NTRS)
Rudolph, Terence; Perala, Rodney A.; Ng, Poh H.
1989-01-01
Two nonlinear triggered lightning models have been developed for use in finite difference calculations. Both are based on three species of air chemistry physics and couple nonlinearly calculated air conductivity to Maxwell's equations. The first model is suitable for use in three-dimensional modeling and has been applied to the analysis of triggered lightning on the NASA F106B Thunderstorm Research Aircraft. The model calculates number densities of positive ions, negative ions, and electrons as a function of time and space through continuity equations, including convective derivative terms. The set of equations is closed by using experimentally determined mobilities, and the mobilities are also used to determine the air conductivity. Results from the model's application to the F106B are shown. The second model is two-dimensional and incorporates an enhanced air chemistry formulation. Momentum conservation equations replace the mobility assumption of the first model. Energy conservation equations for neutrals, heavy ions, and electrons are also used. Energy transfer into molecular vibrational modes is accounted for. The purpose for the enhanced model is to include the effects of temperature into the air breakdown, a necessary step if the model is to simulate more than the very earliest stages of breakdown. Therefore, the model also incorporates a temperature-dependent electron avalanche rate. Results from the model's application to breakdown around a conducting ellipsoid placed in an electric field are shown.
Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers.
Cai, Qin; Hsieh, Meng-Juei; Wang, Jun; Luo, Ray
2010-01-12
We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in our analysis. We investigated the role of linear solvers in its performance by incorporating the incomplete Cholesky conjugate gradient and the geometric multigrid into its inner linear loop. We tailored and optimized both linear solvers for faster convergence rate. In addition, we explored strategies to optimize the successive over-relaxation method to reduce its convergence failures without too much sacrifice in its convergence rate. Specifically we attempted to adaptively change the relaxation parameter and to utilize the damping strategy from the inexact Newton method to improve the successive over-relaxation method. Our analysis shows that the nonlinear methods accompanied with a functional-assisted strategy, such as the conjugate gradient method and the inexact Newton method, can guarantee convergence in the tested molecules. Especially the inexact Newton method exhibits impressive performance when it is combined with highly efficient linear solvers that are tailored for its special requirement. PMID:24723843
Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature
Rudd, R E; Broughton, J Q
2005-05-30
Coarse-grained molecular dynamics (CGMD) is a technique developed as a concurrent multiscale model that couples conventional molecular dynamics (MD) to a more coarse-grained description of the periphery. The coarse-grained regions are modeled on a mesh in a formulation that generalizes conventional finite element modeling (FEM) of continuum elasticity. CGMD is derived solely from the MD model, however, and has no continuum parameters. As a result, it provides a coupling that is smooth and provides control of errors that arise at the coupling between the atomistic and coarse-grained regions. In this article, we elaborate on the formulation of CGMD, describing in detail how CGMD is applied to anharmonic solids and finite temperature simulations. As tests of CGMD, we present in detail the calculation of the phonon spectra for solid argon and tantalum in 3D, demonstrating how CGMD provides a better description of the elastic waves than that provided by FEM. We also present elastic wave scattering calculations that show the elastic wave scattering is more benign in CGMD than FEM. We also discuss the dependence of scattering on the properties of the mesh. We introduce a rigid approximation to CGMD that eliminates internal relaxation, similar to the Quasicontinuum technique, and compare it to the full CGMD.
FEMFLOW3D; a finite-element program for the simulation of three-dimensional aquifers; version 1.0
Durbin, Timothy J.; Bond, Linda D.
1998-01-01
This document also includes model validation, source code, and example input and output files. Model validation was performed using four test problems. For each test problem, the results of a model simulation with FEMFLOW3D were compared with either an analytic solution or the results of an independent numerical approach. The source code, written in the ANSI x3.9-1978 FORTRAN standard, and the complete input and output of an example problem are listed in the appendixes.
Pavarino, E.; Neves, L. A.; Machado, J. M.; de Godoy, M. F.; Shiyou, Y.; Momente, J. C.; Zafalon, G. F. D.; Pinto, A. R.; Valêncio, C. R.
2013-01-01
The Finite Element Method is a well-known technique, being extensively applied in different areas. Studies using the Finite Element Method (FEM) are targeted to improve cardiac ablation procedures. For such simulations, the finite element meshes should consider the size and histological features of the target structures. However, it is possible to verify that some methods or tools used to generate meshes of human body structures are still limited, due to nondetailed models, nontrivial preprocessing, or mainly limitation in the use condition. In this paper, alternatives are demonstrated to solid modeling and automatic generation of highly refined tetrahedral meshes, with quality compatible with other studies focused on mesh generation. The innovations presented here are strategies to integrate Open Source Software (OSS). The chosen techniques and strategies are presented and discussed, considering cardiac structures as a first application context. PMID:23762031
NASA Technical Reports Server (NTRS)
Ponchak, George E.; Dalton, Edan; Tentzeris, Emmanouil M.; Papapolymerou, John; Williams, W. Dan (Technical Monitor)
2001-01-01
Three-dimensional circuits built upon multiple layers of polyimide are required for constructing Si/SiGe monolithic microwave/millimeter-wave integrated circuits on complementary metal oxide semiconductor (CMOS) (low resistivity) Si wafers. Thin film microstrip lines (TFMS) with finite width ground planes embedded in the polyimide are often used. However, the closely spaced TFMS lines are susceptible to high levels of coupling, which degrades circuit performance. In this paper, Finite Difference Time Domain (FDTD) analysis and experimental measurements are used to show that the ground planes must be connected by via holes to reduce coupling in both the forward and backward directions.
Fessler, H.; Edwards, C.D.
1983-05-01
Combined strip and rosette gauge measurements and results from three-dimensional, finite element calculations are in excellent agreement with frozen stress photoelastic results for an efficient shape of cast-steel node under axial, brace loading. Three different meshes showed that two layers of elements through the thickness are needed.
NASA Astrophysics Data System (ADS)
Romano, Fabrizio; Trasatti, Elisa; Lorito, Stefano; Piromallo, Claudia; Piatanesi, Alessio; Cocco, Massimo; Murphy, Shane; Tonini, Roberto; Volpe, Manuela; Brizuela, Beatriz
2016-04-01
The study of the 2011 Tohoku earthquake revealed some new aspects in the rupture process of a megathrust event. Indeed, despite its magnitude Mw 9.0, this earthquake was characterized by a spatially limited rupture area and, contrary to the common view that the shallow portion of the subduction interface mainly experiences aseismic slip, the seismic rupture propagated onto the Japan trench with very large slip (> 50 m). Starting from slip distributions obtained by joint inversion of tsunami and geodetic data, we discuss the sensitivity of the tsunami impact predictions to the complexity of the modelling strategy. We use numerical tools ranging from a homogeneous half-space dislocation model (considering only vertical sea-floor displacement and tsunami propagation in the linear shallow-water approximation) to the more complex 3D-FEM model (with heterogeneous elastic parameters derived from 3D seismic tomography), including horizontal displacement and non-hydrostatic dispersive tsunami modeling. This research is funded by the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 603839 (Project ASTARTE - Assessment, Strategy and Risk Reduction for Tsunamis in Europe)
NASA Technical Reports Server (NTRS)
Ross, M. D.; Linton, S. W.; Parnas, B. R.
2000-01-01
A quasi-three-dimensional finite-volume numerical simulator was developed to study passive voltage spread in vestibular macular afferents. The method, borrowed from computational fluid dynamics, discretizes events transpiring in small volumes over time. The afferent simulated had three calyces with processes. The number of processes and synapses, and direction and timing of synapse activation, were varied. Simultaneous synapse activation resulted in shortest latency, while directional activation (proximal to distal and distal to proximal) yielded most regular discharges. Color-coded visualizations showed that the simulator discretized events and demonstrated that discharge produced a distal spread of voltage from the spike initiator into the ending. The simulations indicate that directional input, morphology, and timing of synapse activation can affect discharge properties, as must also distal spread of voltage from the spike initiator. The finite volume method has generality and can be applied to more complex neurons to explore discrete synaptic effects in four dimensions.
Naveau, Adrien; Renault, Patrick; Pierrisnard, Laurent
2009-06-01
This three dimensional Finite Element Analysis study investigated stress distribution and intensity in implants restored with cemented or screwed crown. Two parameters varied: interarch space and abutment height. Highest stresses occurred at the cervical area in all models. Stresses increased mainly with vertical interarch space highness, and secondarily with abutments shortness. From a mechanical point of view, bone and prosthetics components supporting cemented crowns were not as solicited as with screwed crowns. PMID:19645311
NASA Astrophysics Data System (ADS)
Zang, Mengyan; Gao, Wei; Lei, Zhou
2011-11-01
A contact algorithm in the context of the combined discrete element (DE) and finite element (FE) method is proposed. The algorithm, which is based on the node-to-surface method used in finite element method, treats each spherical discrete element as a slave node and the surfaces of the finite element domain as the master surfaces. The contact force on the contact interface is processed by using a penalty function method. Afterward, a modification of the combined DE/FE method is proposed. Following that, the corresponding numerical code is implemented into the in-house developed code. To test the accuracy of the proposed algorithm, the impact between two identical bars and the vibration process of a laminated glass plate under impact of elastic sphere are simulated in elastic range. By comparing the results with the analytical solution and/or that calculated by using LS-DYNA, it is found that they agree with each other very well. The accuracy of the algorithm proposed in this paper is proved.
Roveri, D S; Sant'Anna, G M; Bertan, H H; Mologni, J F; Alves, M A R; Braga, E S
2016-01-01
This paper presents a 3D computational framework for evaluating electrostatic properties of a single field emitter characterized by the hemisphere-on-post geometry. Numerical simulations employed the finite elements method by using Ansys-Maxwell software. Extensive parametric simulations were focused on the threshold distance from which the emitter field enhancement factor (γ) becomes independent from the anode-substrate gap (G). This investigation allowed demonstrating that the ratio between G and the emitter height (h) is a reliable reference for a broad range of emitter dimensions; furthermore, results permitted establishing G/h ≥ 2.2 as the threshold condition for setting the anode without affecting γ. PMID:26555324
Bayesian sensitivity analysis of a nonlinear finite element model
NASA Astrophysics Data System (ADS)
Becker, W.; Oakley, J. E.; Surace, C.; Gili, P.; Rowson, J.; Worden, K.
2012-10-01
A major problem in uncertainty and sensitivity analysis is that the computational cost of propagating probabilistic uncertainty through large nonlinear models can be prohibitive when using conventional methods (such as Monte Carlo methods). A powerful solution to this problem is to use an emulator, which is a mathematical representation of the model built from a small set of model runs at specified points in input space. Such emulators are massively cheaper to run and can be used to mimic the "true" model, with the result that uncertainty analysis and sensitivity analysis can be performed for a greatly reduced computational cost. The work here investigates the use of an emulator known as a Gaussian process (GP), which is an advanced probabilistic form of regression. The GP is particularly suited to uncertainty analysis since it is able to emulate a wide class of models, and accounts for its own emulation uncertainty. Additionally, uncertainty and sensitivity measures can be estimated analytically, given certain assumptions. The GP approach is explained in detail here, and a case study of a finite element model of an airship is used to demonstrate the method. It is concluded that the GP is a very attractive way of performing uncertainty and sensitivity analysis on large models, provided that the dimensionality is not too high.
Highly accurate adaptive finite element schemes for nonlinear hyperbolic problems
NASA Astrophysics Data System (ADS)
Oden, J. T.
1992-08-01
This document is a final report of research activities supported under General Contract DAAL03-89-K-0120 between the Army Research Office and the University of Texas at Austin from July 1, 1989 through June 30, 1992. The project supported several Ph.D. students over the contract period, two of which are scheduled to complete dissertations during the 1992-93 academic year. Research results produced during the course of this effort led to 6 journal articles, 5 research reports, 4 conference papers and presentations, 1 book chapter, and two dissertations (nearing completion). It is felt that several significant advances were made during the course of this project that should have an impact on the field of numerical analysis of wave phenomena. These include the development of high-order, adaptive, hp-finite element methods for elastodynamic calculations and high-order schemes for linear and nonlinear hyperbolic systems. Also, a theory of multi-stage Taylor-Galerkin schemes was developed and implemented in the analysis of several wave propagation problems, and was configured within a general hp-adaptive strategy for these types of problems. Further details on research results and on areas requiring additional study are given in the Appendix.
Verri, Fellippo Ramos; Cruz, Ronaldo Silva; de Souza Batista, Victor Eduardo; Almeida, Daniel Augusto de Faria; Verri, Ana Caroline Gonçales; Lemos, Cleidiel Aparecido de Araújo; Santiago Júnior, Joel Ferreira; Pellizzer, Eduardo Piza
2016-11-01
The aim of this study was to assess stress/strain of different implant modeling simplifications by 3D-FEA. Three variation of external hexagon implant (Ø3.75 × 10 mm) supporting one molar crown were simulated: A (no threads); B (slightly threads simplification); C (original design). 200 N (axial) and 100 N (oblique) were applied. Cortical bone was evaluated by maximum principal stress and microstrain qualitatively and quantitatively (ANOVA and Tukey post hoc (p < 0.05)). Higher stress levels (p < 0.05) were observed in model A. Models B and C presented similar stress transmission. It was possible to conclude that slightly simplification should be used for studies evaluating stress transferring for bone tissue. PMID:27082041
Stress analysis of a rectangular implant in laminated composites using 2-D and 3-D finite elements
NASA Technical Reports Server (NTRS)
Chow, Wai T.; Graves, Michael J.
1992-01-01
An analysis method using the FEM based on the Hellinger-Reissner variation principle has been developed to determine the 3-D stresses and displacements near a rectangular implant inside a laminated composite material. Three-dimensional elements are employed in regions where the interlaminar stress is considered to be significant; 2-D elements are used in other areas. Uniaxially loaded graphite-epoxy laminates have been analyzed; the implant was modeled as four plies of 3501/6 epoxy located in the middle of the laminate. It is shown that the interlaminar stresses are an order of magnitude lower than the stress representing the applied far-field load. The stress concentration factors of both the interlaminar and in-plane stresses depend on the stacking sequence of the laminate.
Saha, Debashish; Babler, Matthaus U; Holzner, Markus; Soos, Miroslav; Lüthi, Beat; Liberzon, Alex; Kinzelbach, Wolfgang
2016-01-12
Aggregates grown in mild shear flow are released, one at a time, into homogeneous isotropic turbulence, where their motion and intermittent breakup is recorded by three-dimensional particle tracking velocimetry (3D-PTV). The aggregates have an open structure with a fractal dimension of ∼2.2, and their size is 1.4 ± 0.4 mm, which is large, compared to the Kolmogorov length scale (η = 0.15 mm). 3D-PTV of flow tracers allows for the simultaneous measurement of aggregate trajectories and the full velocity gradient tensor along their pathlines, which enables us to access the Lagrangian stress history of individual breakup events. From this data, we found no consistent pattern that relates breakup to the local flow properties at the point of breakup. Also, the correlation between the aggregate size and both shear stress and normal stress at the location of breakage is found to be weaker, when compared with the correlation between size and drag stress. The analysis suggests that the aggregates are mostly broken due to the accumulation of the drag stress over a time lag on the order of the Kolmogorov time scale. This finding is explained by the fact that the aggregates are large, which gives their motion inertia and increases the time for stress propagation inside the aggregate. Furthermore, it is found that the scaling of the largest fragment and the accumulated stress at breakup follows an earlier established power law, i.e., dfrag ∼ σ(-0.6) obtained from laminar nozzle experiments. This indicates that, despite the large size and the different type of hydrodynamic stress, the microscopic mechanism causing breakup is consistent over a wide range of aggregate size and stress magnitude. PMID:26646289
Santee, G.E. Jr.; Chang, F.H.; Mortensen, G.A.; Brockett, G.F.; Gross, M.B.; Belytschko, T.B.
1982-11-01
This report, the third in a series of reports for RP-1065, describes the final step in the stepwise approach for developing the three-dimensional, nonlinear, fluid-structure interaction methodology to assess the hydroloads on a large PWR during the subcooled portions of a hypothetical LOCA. The final step in the methodology implements enhancements and special modifications to the STEALTH 3D computer program and the WHAMSE 3D computer program. After describing the enhancements, the individual and the coupled computer programs are assessed by comparing calculational results with either analytical solutions or with experimental data. The coupled 3D STEALTH/WHAMSE computer program is then applied to the simulation of HDR Test V31.1 to further assess the program and to investigate the role that fluid-structure interaction plays in the hydrodynamic loading of reactor internals during subcooled blowdown.
NASA Technical Reports Server (NTRS)
Cwik, T.; Jamnejad, V.; Zuffada, C.
1993-01-01
It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.
NASA Astrophysics Data System (ADS)
Cushman, J. H.; Moroni, M.
2002-12-01
Velocity fluctuations over evolving scales of motion, on the scale of observation, often lead to anomalous dispersion of conservative tracers in fluid mechanics studies of turbulence and heterogeneous porous media. Recent theories of anomalous dispersion lead to space-time non-local constitutive models for the flux of concentration, which can adequately model this problem. We review one such model, which has its foundations in non-equilibrium statistical mechanics. The basic premise is that knowledge of the evolution of the self-part of the intermediate scattering function is all that is required to model the phenomena of interest. We derive the basic integro-partial-differential equation this function satisfies and solve the inverse problem to obtain the kernels and use these to describe the wave-vector and frequency dependent dispersion tensor. Subsequently we use this information to study the transition from anomalous to Fickian dispersion. We also make use of the finite size Lyapunov exponent in the description of the dispersive process. Three-camera, three-dimensional, particle -tracking velocimetry experiments are undertaken to study dispersion within a matched-index heterogeneous porous medium. Particle trajectories, mean square displacements, velocity covariance's, intermediate scattering functions, classical dispersion tensors, wave-vector and frequency dependent generalized dispersion tensors and the finite-size Lyapunov exponents are obtained. Comparisons are made in the small frequency and small wave vector limits to obtain the transition from preasymptotic to asymptotic dispersion.
Maker, B.N.
1995-04-14
This report provides a user`s manual for NIKE3D, a fully implicit three-dimensional finite element code for analyzing the finite strain static and dynamic response of inelastic solids, shells, and beams. Spatial discretization is achieved by the use of 8-node solid elements, 2-node truss and beam elements, and 4-node membrane and shell elements. Over twenty constitutive models are available for representing a wide range of elastic, plastic, viscous, and thermally dependent material behavior. Contact-impact algorithms permit gaps, frictional sliding, and mesh discontinuities along material interfaces. Several nonlinear solution strategies are available, including Full-, Modified-, and Quasi-Newton methods. The resulting system of simultaneous linear equations is either solved iteratively by an element-by-element method, or directly by a factorization method, for which case bandwidth minimization is optional. Data may be stored either in or out of core memory to allow for large analyses.
Shurbaji Mozayek, Rami; Allaf, Mirza; B. Abuharb, Mohammad
2016-01-01
Background. Long span is seen in many clinical situations. Treatmentplanning options of these cases are difficult and may require FPD, RPD or ISP. Each option has its own disadvantages, including mechanical problems, patient comfort and cost. This article will evaluate the stress distribution of a different treatment option, which consists of adding a single sup-porting implant to the FPD by using 3D finite element analysis. Methods. Three models, each consisting of 5 units, were created as follows: 1. Tooth Pontic Pontic Pontic Tooth; 2. Tooth Pontic Implant Pontic Tooth; 3. Tooth Pontic Pontic Implant Tooth. An axial force was applied to the prostheses by using 3D finite element method and stresses were evaluated. Results. The maximum stress was found in the prostheses in all the models; the highest stress values in all the shared components of the models were almost similar. Stress in implants was lower in the second model than the third one. Conclusion. Adding a supporting implant in long-span FPD has no advantages while it has the disadvantages of complicating treatment and the complications that may occur to the implant and surrounding bone. PMID:27429723
Shurbaji Mozayek, Rami; Allaf, Mirza; B Abuharb, Mohammad
2016-01-01
Background. Long span is seen in many clinical situations. Treatmentplanning options of these cases are difficult and may require FPD, RPD or ISP. Each option has its own disadvantages, including mechanical problems, patient comfort and cost. This article will evaluate the stress distribution of a different treatment option, which consists of adding a single sup-porting implant to the FPD by using 3D finite element analysis. Methods. Three models, each consisting of 5 units, were created as follows: 1. Tooth Pontic Pontic Pontic Tooth; 2. Tooth Pontic Implant Pontic Tooth; 3. Tooth Pontic Pontic Implant Tooth. An axial force was applied to the prostheses by using 3D finite element method and stresses were evaluated. Results. The maximum stress was found in the prostheses in all the models; the highest stress values in all the shared components of the models were almost similar. Stress in implants was lower in the second model than the third one. Conclusion. Adding a supporting implant in long-span FPD has no advantages while it has the disadvantages of complicating treatment and the complications that may occur to the implant and surrounding bone. PMID:27429723
Baghai-Wadji, Alireza
2015-06-01
The original work for 3-D charge distributions in micro-acoustic devices has been manifestly extended to account for finitely thick busbars. The work has been initiated to create a platform for simulating the electric charge localization and field enhancement at the electrode/busbar gaps depending on the thickness of the metalization in submicrometer geometries. A recipe for the construction of relevant Green's functions has been provided. A universal function (UF) for setting up system matrices in the method-of-moments' implementations has been constructed. Universal functions (moments of Green's functions) are by construction highly smooth and easy to compute. This work also presents a comprehensive completion of earlier work. For the first time, the calculation of the UF for a 3-D problem has been presented in great detail, highlighting the underlying regularization techniques. It is shown that the singular Fourier-type integrals involved can be regularized simultaneously in the near- and far-field. The pinnacle of the work is the detailed demonstration of the property that Hadamard's finite part regularization naturally arises in the construction of UFs. Three lemmata facilitate the understanding of the underlying concepts. PMID:26067048
NASA Astrophysics Data System (ADS)
Voznyuk, I.; Litman, A.; Tortel, H.
2015-08-01
A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database.
Xiao, Dongmin; Ye, Ming; Li, Xinfa; Yang, Lifeng
2015-01-01
Background The aim of this study was to develop and perform the 3D finite element analysis of a femoral head interior supporting device (FHISD). Material/Methods The 3D finite element model was developed to analyze the surface load of femoral head and analyze the stress and strain of the femoral neck, using the normal femoral neck, decompressed bone graft, and FHISD-implanted bone graft models. Results The stress in the normal model concentrated around the femoral calcar, with displacement of 0.3556±0.1294 mm. In the decompressed bone graft model, the stress concentrated on the femur calcar and top and lateral sides of femoral head, with the displacement larger than the normal (0.4163±0.1310 mm). In the FHISD-implanted bone graft model, the stress concentrated on the segment below the lesser trochanter superior to the femur, with smaller displacement than the normal (0.1856±0.0118 mm). Conclusions FHISD could effectively maintain the biomechanical properties of the femoral neck. PMID:26010078
NASA Astrophysics Data System (ADS)
Son, Sang-Kil; Chu, Shih-I.
2008-05-01
We introduce a new computational method on unstructured grids in the three-dimensional (3D) spaces to investigate the electronic structure of polyatomic molecules. The Voronoi-cell finite difference (VFD) method realizes a simple discrete Laplacian operator on unstructured grids based on Voronoi cells and their natural neighbors. The feature of unstructured grids enables us to choose intuitive pictures for an optimal molecular grid system. The new VFD method achieves highly adaptability by the Voronoi-cell diagram and yet simplicity by the finite difference scheme. It has no limitation in local refinement of grids in the vicinity of nuclear positions and provides an explicit expression at each grid without any integration. This method augmented by unstructured molecular grids is suitable for solving the Schr"odinger equation with the realistic 3D Coulomb potentials regardless of symmetry of molecules. For numerical examples, we test accuracies for electronic structures of one-electron polyatomic systems: linear H2^+ and triangular H3^++. We also extend VFD to the density functional theory (DFT) for many-electron polyatomic molecules.
NASA Astrophysics Data System (ADS)
Ronchin, Erika; Masterlark, Timothy; Molist, Joan Martí; Saunders, Steve; Tao, Wei
2013-03-01
Simulating the deformation of active volcanoes is challenging due to inherent mechanical complexities associated with heterogeneous distributions of rheologic properties and irregular geometries associated with the topography and bathymetry. From geologic and tomographic studies we know that geologic bodies naturally have complex 3D shapes. Finite element models (FEMs) are capable of simulating the pressurization of magma intrusions into mechanical domains with arbitrary geometric and geologic complexity. We construct FEMs comprising pressurization (due to magma intrusion) within an assemblage of 3D parts having common mechanical properties for Rabaul Caldera, Papua New Guinea. We use information of material properties distributed on discrete points mainly deduced from topography, geology, seismicity, and tomography of Rabaul Caldera to first create contours of each part and successively to generate each 3D part shape by lofting the volume through the contours. The implementation of Abaqus CAE with Python scripts allows for automated execution of hundreds of commands necessary for the construction of the parts having substantial geometric complexity. The lofted solids are then assembled to form the composite model of Rabaul Caldera, having a geometrically complex loading configuration and distribution of rheologic properties. Comparison between predicted and observed deformation led us to identify multiple deformation sources (0.74 MPa change in pressure in the magma chamber and 0.17 m slip along the ring fault) responsible for the displacements measured at Matupit Island between August 1992 and August 1993.
NASA Astrophysics Data System (ADS)
Bustamante, Miguel D.
2014-11-01
We consider 3D Euler fluids endowed with a discrete symmetry whereby the velocity field is invariant under mirror reflections about a 2D surface known as the ``symmetry plane.'' This type of flow is widely used in numerical simulations of classical/magnetic/quantum turbulence and vortex reconnection. On the 2D symmetry plane, the governing equations are best written in terms of two scalars: vorticity and stretching rate of vorticity. These determine the velocity field on the symmetry plane. However, the governing equations are not closed, because of the contribution of a single pressure term that depends on the full 3D velocity profile. By modelling this pressure term we propose a one-parameter family of sensible models for the flow along the 2D symmetry plane. We apply the method of infinitesimal Lie symmetries and solve the governing equations analytically for the two scalars as functions of time. We show how the value of the model's parameter determines if the analytical solution has a finite-time blowup and obtain explicit formulae for the blowup time. We validate the models by showing that a particular choice of the model's parameter corresponds to a well-known exact solution of 3D Euler equations [Gibbon et al., Physica D 132, 497 (1999)]. We discuss practical applications. Supported by Science Foundation Ireland (SFI) under Grant Number 12/IP/1491.
Nonlinear finite element modeling of dental composite polymerization behavior
NASA Astrophysics Data System (ADS)
Laughlin, Gayle A.
2003-07-01
Polymerization shrinkage has been one of the primary shortcomings preventing the use of resin composites as a universal dental restorative material. This shrinkage of the bonded restoration causes residual stresses in the composite which in turn are transferred to the adhesive interface. The deleterious effects of this stress environment include compromise of the interface itself and the decrease in the mechanical properties of the cured composite. Novel materials which claim to produce less shrinkage have been presented as a new class of restorative materials that could reduce the effects of this problem. One difficulty in assessing the actual in vivo benefits of these new materials is the fact that there is currently no direct way to measure the stress environment at the composite/tooth clinical interface. Computer modeling using finite element analysis (FEA) could provide helpful information regarding the clinical stress performance of dental composites. The purpose of this study was to develop a model that accurately simulates the nonlinear polymerization behavior of light-cured dental composites using a commercial FEA program, which could be accessible for future research. Two phases were needed to accomplish this purpose. First, a data collection phase included volumetric shrinkage, shrinkage stress, tooth analog strain, and dynamic mechanical analysis experiments. Three composites, a standard methacrylate(Z250) and two experimental low stress epoxy-based composites (oxirane and silorane), were tested. The experimental results revealed an intriguing range of polymerization behavior exhibited by the three composites, indicating that the development of a low stress composite is possible. The information gathered from this phase supplied the necessary material input for the computer modeling, and provided empirical validation data for the model solutions. In the second modeling phase, an FEA approach based on a elastic/viscoplastic material model was used to
StrainModeler: A MATHEMATICA™-based program for 3D analysis of finite and progressive strain
NASA Astrophysics Data System (ADS)
Bobillo-Ares, Nilo C.; Aller, Jesús; Bastida, Fernando; Menéndez, Omar; Lisle, Richard J.
2015-05-01
StrainModeler is a program constructed in the MATHEMATICA™ environment that performs 3D progressive strain calculations for lines and planes undergoing any sequence of homogeneous deformations. The main inputs to the system define the initial line or plane to be deformed and the deformation sequence to be applied, including combinations of simple shear, pure shear and volume change. For the deformation of lines, the output of the program is the change of attitude of the initial line, which can be represented by graphics or plotted in an equal-area projection. For the deformation of planes, the program has several outputs: (i) change of attitude of the initial plane; (ii) magnitudes and ratio of the semi-axes of the strain ellipse on the deformed plane; (iii) orientation of the major and minor axes of the strain ellipse on the deformed plane; (iv) orientations of the axial planes of the folds formed on the deformed plane, and (v) area change on the deformed plane. The variation of any of these parameters can be shown against a linear parameter only linked to the number of steps involved in the deformation, as a kind of "time" line, or it can be shown against the variation of a parameter of the strain ellipsoid (e. g.: major axis/minor axis ratio). A sequence of directions can be also visualized as a curve in an equal-area plot. Three applications of the program are presented. In the first, the deformation by simple shear of a plane with any orientation is analyzed. In the second, we explore the formation of recumbent folds in layers with different initial orientations for simple shear and pure shear deformations. In the third, we use StrainModeler to analyze the deformation of a set of folds located in a ductile shear zone in the Variscan Belt of NW Spain.
NASA Technical Reports Server (NTRS)
Sohn, Kiho D.; Ip, Shek-Se P.
1988-01-01
Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.
Moreno, Karen; Wroe, Stephen; Clausen, Philip; McHenry, Colin; D’Amore, Domenic C; Rayfield, Emily J; Cunningham, Eleanor
2008-01-01
The Komodo dragon (Varanus komodoensis) displays a unique hold and pull-feeding technique. Its delicate ‘space-frame’ skull morphology differs greatly from that apparent in most living large prey specialists and is suggestive of a high degree of optimization, wherein use of materials is minimized. Here, using high-resolution finite element modelling based on dissection and in vivo bite and pull data, we present results detailing the mechanical performance of the giant lizard's skull. Unlike most modern predators, V. komodoensis applies minimal input from the jaw muscles when butchering prey. Instead it uses series of actions controlled by postcranial muscles. A particularly interesting feature of the performance of the skull is that it reveals considerably lower overall stress when these additional extrinsic forces are added to those of the jaw adductors. This remarkable reduction in stress in response to additional force is facilitated by both internal and external bone anatomy. Functional correlations obtained from these analyses also provide a solid basis for the interpretation of feeding ecology in extinct species, including dinosaurs and sabre-tooth cats, with which V. komodoensis shares various cranial and dental characteristics. PMID:18510503
Sunbuloglu, Emin
2015-01-01
Complete maxillary dentures are one of the most economic and easy ways of treatment for edentulous patients and are still widely used. However, their survival rate is slightly above three years. It is presumed that the failure reasons are not only due to normal fatigue but also emerge from damage based on unavoidable improper usage. Failure types other than long-term fatigue, such as over-deforming, also influence the effective life span of dentures. A hypothesis is presumed, stating that the premature/unexpected failures may be initiated by impact on dentures, which can be related to dropping them on the ground or other effects such as biting crispy food. Thus, the behavior of a complete maxillary denture under impact loading due to drop on a rigid surface was investigated using the finite element method utilizing explicit time integration and a rate-sensitive elastoplastic material model of polymethylmethacrylate (PMMA). Local permanent deformations have been observed along with an emphasis on frenulum region of the denture, regardless of the point of impact. Contact stresses at the tooth-denture base were also investigated. The spread of energy within the structure via wave propagation is seen to play a critical role in this fact. Stress-wave propagation is also seen to be an important factor that decreases the denture's fatigue life. PMID:24945936
NASA Astrophysics Data System (ADS)
Gholizadeh Doonechaly, N.; Rahman, S. S.
2012-05-01
Simulation of naturally fractured reservoirs offers significant challenges due to the lack of a methodology that can utilize field data. To date several methods have been proposed by authors to characterize naturally fractured reservoirs. Among them is the unfolding/folding method which offers some degree of accuracy in estimating the probability of the existence of fractures in a reservoir. Also there are statistical approaches which integrate all levels of field data to simulate the fracture network. This approach, however, is dependent on the availability of data sources, such as seismic attributes, core descriptions, well logs, etc. which often make it difficult to obtain field wide. In this study a hybrid tectono-stochastic simulation is proposed to characterize a naturally fractured reservoir. A finite element based model is used to simulate the tectonic event of folding and unfolding of a geological structure. A nested neuro-stochastic technique is used to develop the inter-relationship between the data and at the same time it utilizes the sequential Gaussian approach to analyze field data along with fracture probability data. This approach has the ability to overcome commonly experienced discontinuity of the data in both horizontal and vertical directions. This hybrid technique is used to generate a discrete fracture network of a specific Australian gas reservoir, Palm Valley in the Northern Territory. Results of this study have significant benefit in accurately describing fluid flow simulation and well placement for maximal hydrocarbon recovery.
NASA Astrophysics Data System (ADS)
Wu, Guangxi; Yu, Xiong
2015-06-01
Thermoelectric power generator has potential for small-scale and distributed power generation because of its high durability and scalability. It is very important to realize that the transient behavior of thermoelectric modules (TEM) affects a thermoelectric generator's response to dynamic working environments. Traditionally, researchers have used simplified models to describe the behavior of thermoelectric modules. In this paper we propose a comprehensive mathematical model that considers the effect of variations of chemical potential and carrier density, which are ignored by traditional models. Finite element models based on this new model are used to simulate the transient behavior of a thermoelectric module subjected to rapid changes in boundary temperature or working load. Simulation results show that transition times of thermoelectric modules affected by temperature change are much longer than those of modules affected by changes in electrical load resistance. Sudden changes in working temperature cause voltage overshoot of the TEM output, which, however, is not observed in responses to sudden changes of load resistance. Comparisons also show there are significant differences between the behavior of TEM predicted by use of this new comprehensive model and that predicted by use of traditional models, particularly for the high-temperature intrinsic ionization region and the low-temperature weak ionization region. This implies that chemical potential and carrier density variations, which are taken into account by this new model but ignored by traditional models, have major effects on the performance of TEM.
Moreno, Karen; Wroe, Stephen; Clausen, Philip; McHenry, Colin; D'Amore, Domenic C; Rayfield, Emily J; Cunningham, Eleanor
2008-06-01
The Komodo dragon (Varanus komodoensis) displays a unique hold and pull-feeding technique. Its delicate 'space-frame' skull morphology differs greatly from that apparent in most living large prey specialists and is suggestive of a high degree of optimization, wherein use of materials is minimized. Here, using high-resolution finite element modelling based on dissection and in vivo bite and pull data, we present results detailing the mechanical performance of the giant lizard's skull. Unlike most modern predators, V. komodoensis applies minimal input from the jaw muscles when butchering prey. Instead it uses series of actions controlled by postcranial muscles. A particularly interesting feature of the performance of the skull is that it reveals considerably lower overall stress when these additional extrinsic forces are added to those of the jaw adductors. This remarkable reduction in stress in response to additional force is facilitated by both internal and external bone anatomy. Functional correlations obtained from these analyses also provide a solid basis for the interpretation of feeding ecology in extinct species, including dinosaurs and sabre-tooth cats, with which V. komodoensis shares various cranial and dental characteristics. PMID:18510503
NASA Astrophysics Data System (ADS)
Wright, G.; Flyer, N.; Yuen, D. A.; Monnereau, M.; Zhang, S.; Wang, S. M.
2009-05-01
Many numerical methods, such as finite-differences, finite-volume, their yin-yang variants, finite-elements and spectral methods have been employed to study 3-D mantle convection. All have their own strengths, but also serious weaknesses. Spectrally accurate methods do not practically allow for node refinement and often involve cumbersome algebra while finite difference, volume, or element methods are generally low-order, adding excessive numerical diffusion to the model. For the 3-D mantle convection problem, we have introduced a new mesh-free approach, using radial basis functions (RBF). This method has the advantage of being algorithmic simple, spectrally accurate for arbitrary node layouts in multi-dimensions and naturally allows for node-refinement. One virtue of the RBF scheme allows the user to use a simple Cartesian geometry, while implementing the required boundary conditions for the temperature, velocities and stress components on a spherical surface at both the planetary surface and the core-mantle boundary. We have studied time- dependent mantle convection, using both a RBF-pseudospectral code and a code which uses spherical- harmonics in the angular direction and second-order finite volume in the radial direction. We have employed a third code , which uses spherical harmonics and higher-order finite-difference method a la Fornberg in the radial coordinate.We first focus on the onset of time-dependence at Rayleigh number Ra of 70,000. We follow the development of stronger time-dependence to a Ra of one million, using high enough resolution with 120 to 200 points in the radial direction and 128 to 256 spherical harmonics.
Xie, G.; Li, J.
1997-05-01
A new 3D electromagnetic modeling and nonlinear inversion algorithm is presented based on global integral and local differential equations decomposition (GILD). The GILD parallel nonlinear inversion algorithm consists of five parts: (1) the domain is decomposed into subdomain SI and subdomain SII; (2) a new global magnetic integral equation in SI and the local magnetic differential equations IN SII will be used together to obtain the magnetic field in the modeling step; (3) the new global magnetic integral Jacobian equation in SI and the local magnetic differential Jacobian equations in SII will be used together to update the electric conductivity and permittivity from the magnetic field data in the inversion step; (4) the subdomain SII can naturally and uniformly be decomposed into 2{sup n} smaller sub-cubic-domains; the sparse matrix in each sub-cubic-domain can be eliminated separately, in parallel; (5) a new parallel multiple hierarchy substructure algorithm will be used to solve the smaller full matrices in SI, in parallel. The applications of the new 3D parallel GILD EM modeling and nonlinear inversion algorithm and software are: (1) to create high resolution controlled-source electric conductivity and permittivity imaging for interpreting electromagnetic field data acquired from cross hole, surface to borehole, surface to surface, single hole, and multiple holes; (2) to create the magnetotelluric high resolution imaging from the surface impedance and field data. The new GILD parallel nonlinear inversion will be a 3D/2.5D powerful imaging tool for the oil geophysical exploration and environmental remediation and monitoring.
NASA Technical Reports Server (NTRS)
Ponchak, G. E.; Bushyager, N.; Papapolymerou, J.; Tentzeris, E. M.; Laskar, J.
2002-01-01
Three-dimensional circuits built upon multiple layers of polyimide are required for constructing Si/SiGe monolithic microwave/mm-wave integrated circuits on CMOS (low resistivity) Si wafers. It is expected that these circuits will replace the ones fabricated on GaAs and reduce the overall system cost. However, the closely spaced transmission lines that are required for a high-density circuit environment are susceptible to high levels of cross-coupling, which degrades the overall circuit performance. In this paper, theoretical and experimental results on coupling and ways to reduce it are presented for two types of transmission lines: a) the microstrip line and b) the Finite Ground Coplanar (FGC) line. For microstrip lines it is shown that a fence of metalized via-holes can significantly reduce coupling, especially in the case when both lines are on the same polyimide layer or when the shielding structure extends through several polyimide layers. For closely spaced microstrip lines, coupling is lower for a metal filled trench shield than a via-hole fence. Coupling amongst microstrip lines is dependent on the ratio of line separation to polyimide thickness and is primarily due to magnetic fields. For FGC lines it is shown that they have in general low coupling that can be reduced significantly when there is even a small gap between the ground planes of each line. FGC lines have approximately 8 dB lower coupling than coupled coplanar waveguides (CPW). In addition, forward and backward characteristics of the FGC lines do not resemble those of other transmission lines such as microstrip. Therefore, the coupling mechanism of the FGC lines is different compared to thin film microstrip lines.
Finite time blowup of solutions to the nonlinear Schrödinger equation without gauge invariance
NASA Astrophysics Data System (ADS)
Fujiwara, Kazumasa; Ozawa, Tohru
2016-08-01
A lifespan estimate and a condition of the initial data for finite time blowup for the nonlinear Schrödinger equation are presented from a view point of ordinary differential equation (ODE) mechanism.
NASA Astrophysics Data System (ADS)
Lee, H.; Min, D.; Lim, S.; Yang, J.; Kwon, B.; Yoo, H.
2009-12-01
In a conventional marine seismic data analysis, pressure data have been usually interpreted on the basis of acoustic wave equation. The acoustic wave equation, however, only deals with P-wave propagation, and it cannot correctly describe the wave propagation in acoustic-elastic (fluid-solid) coupled media. Recently, in 4C OBC survey (4-component ocean bottom cable), it is possible to acquire both pressure and 3-component displacements (measured at the sea-bottom). Combining pressure and displacement data allows us to interpret subsurface structures more accurately. In order to accurately simulate wave propagation in fluid-solid coupled media, we need an acoustic-elastic coupled modeling algorithm, which deals with displacements in elastic region and pressure in acoustic region. For waveform inversion and reverse-time migration that require a great number of forward modeling, it is essential to develop an efficient scheme that reduces computing time and computer core memory. In this study, we present a 3D time-domain acoustic-elastic coupled modeling algorithm on the basis of the cell-based finite difference method. The cell-based method has proven to properly describe the free-surface boundary, which indicates that it will also properly describe the fluid-solid interface boundaries. In the acoustic-elastic coupled modeling, we first compose cell-based finite differences individually for the 3D acoustic and elastic media, and then combine the differences using the fluid-solid interface boundary conditions. Considering that the 2D acoustic-elastic coupled modeling algorithm gives numerical solutions comparable to analytic solutions, we expect that the 3D acoustic-elastic coupled modeling will correctly describe wave propagation in the fluid-solid coupled media. We apply our algorithm to 3D horizontal two- and three-layer models. Numerical experiments show that the cell-based coupled modeling algorithm properly describes S- and converted waves as well as P-waves. The
NASA Astrophysics Data System (ADS)
Navon, M. I.; Stefanescu, R.; Fuelberg, H. E.; Marchand, M.
2012-12-01
NASA's launch of the GOES-R Lightning Mapper (GLM) in 2015 will provide continuous, full disc, high resolution total lightning (IC + CG) data. The data will be available at a horizontal resolution of approximately 9 km. Compared to other types of data, the assimilation of lightning data into operational numerical models has received relatively little attention. Previous efforts of lightning assimilation mostly have employed nudging. This paper will describe the implementation of 1D+3D/4D Var assimilation schemes of existing ground-based WTLN (Worldwide Total Lightning Network) lightning observations using non-linear observation operators in the incremental WRFDA system. To mimic the expected output of GLM, the WTLN data were used to generate lightning super-observations characterized by flash rates/81 km2/20 min. A major difficulty associated with variational approaches is the complexity of the observation operator that defines the model equivalent of lightning. We use Convective Available Potential Energy (CAPE) as a proxy between lightning data and model variables. This operator is highly nonlinear. Marecal and Mahfouf (2003) have shown that nonlinearities can prevent direct assimilation of rainfall rates in the ECMWF 4D-VAR (using the incremental formulation proposed by Courtier et al. (1994)) from being successful. Using data from the 2011 Tuscaloosa, AL tornado outbreak, we have proved that the direct assimilation of lightning data into the WRF 3D/4D - Var systems is limited due to this incremental approach. Severe threshold limits must be imposed on the innovation vectors to obtain an improved analysis. We have implemented 1D+3D/4D Var schemes to assimilate lightning observations into the WRF model. Their use avoids innovation vector constrains from preventing the inclusion of a greater number of lightning observations Their use also minimizes the problem that nonlinearities in the moist convective scheme can introduce discontinuities in the cost function
NASA Astrophysics Data System (ADS)
Sun, Yongle; Li, Q. M.; Withers, P. J.
2015-09-01
Realistic simulations are increasingly demanded to clarify the dynamic behaviour of foam materials, because, on one hand, the significant variability (e.g. 20% scatter band) of foam properties and the lack of reliable dynamic test methods for foams bring particular difficulty to accurately evaluate the strain-rate sensitivity in experiments; while on the other hand numerical models based on idealised cell structures (e.g. Kelvin and Voronoi) may not be sufficiently representative to capture the actual structural effect. To overcome these limitations, the strain-rate sensitivity of the compressive and tensile properties of closed-cell aluminium Alporas foam is investigated in this study by means of meso-scale realistic finite element (FE) simulations. The FE modelling method based on X-ray computed tomography (CT) image is introduced first, as well as its applications to foam materials. Then the compression and tension of Alporas foam at a wide variety of applied nominal strain-rates are simulated using FE model constructed from the actual cell geometry obtained from the CT image. The stain-rate sensitivity of compressive strength (collapse stress) and tensile strength (0.2% offset yield point) are evaluated when considering different cell-wall material properties. The numerical results show that the rate dependence of cell-wall material is the main cause of the strain-rate hardening of the compressive and tensile strengths at low and intermediate strain-rates. When the strain-rate is sufficiently high, shock compression is initiated, which significantly enhances the stress at the loading end and has complicated effect on the stress at the supporting end. The plastic tensile wave effect is evident at high strain-rates, but shock tension cannot develop in Alporas foam due to the softening associated with single fracture process zone occurring in tensile response. In all cases the micro inertia of individual cell walls subjected to localised deformation is found to
Exact finite difference schemes for the non-linear unidirectional wave equation
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1985-01-01
Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.
Lovejoy, S.C.; Whirley, R.G.
1990-10-10
This manual describes in detail the solution of ten example problems using the explicit nonlinear finite element code DYNA3D. The sample problems include solid, shell, and beam element types, and a variety of linear and nonlinear material models. For each example, there is first an engineering description of the physical problem to be studied. Next, the analytical techniques incorporated in the model are discussed and key features of DYNA3D are highlighted. INGRID commands used to generate the mesh are listed, and sample plots from the DYNA3D analysis are given. Finally, there is a description of the TAURUS post-processing commands used to generate the plots of the solution. This set of example problems is useful in verifying the installation of DYNA3D on a new computer system. In addition, these documented analyses illustrate the application of DYNA3D to a variety of engineering problems, and thus this manual should be helpful to new analysts getting started with DYNA3D. 7 refs., 56 figs., 9 tabs.
NASA Astrophysics Data System (ADS)
Li, L.; Wang, K.; Li, H.; Eibert, T. F.
2014-11-01
A hybrid higher-order finite element boundary integral (FE-BI) technique is discussed where the higher-order FE matrix elements are computed by a fully analytical procedure and where the gobal matrix assembly is organized by a self-identifying procedure of the local to global transformation. This assembly procedure applys to both, the FE part as well as the BI part of the algorithm. The geometry is meshed into three-dimensional tetrahedra as finite elements and nearly orthogonal hierarchical basis functions are employed. The boundary conditions are implemented in a strong sense such that the boundary values of the volume basis functions are directly utilized within the BI, either for the tangential electric and magnetic fields or for the asssociated equivalent surface current densities by applying a cross product with the unit surface normals. The self-identified method for the global matrix assembly automatically discerns the global order of the basis functions for generating the matrix elements. Higher order basis functions do need more unknowns for each single FE, however, fewer FEs are needed to achieve the same satisfiable accuracy. This improvement provides a lot more flexibility for meshing and allows the mesh size to raise up to λ/3. The performance of the implemented system is evaluated in terms of computation time, accuracy and memory occupation, where excellent results with respect to precision and computation times of large scale simulations are found.
NASA Astrophysics Data System (ADS)
Aristovich, Ekaterina; Khan, Sanowar
2013-06-01
This paper concerns detection of particle concentration (e.g. cholesterol) in conductive media (e.g. human blood) by impedance technique. The technique is based on changes in the impedance measurement across a given conducting medium due to changes in the particle concentration. The impedance is calculated by calculating the current through the conducting media produced by electric field distribution between two electrodes. This is done by modelling and computation of 3D electric fields between the electrodes for known voltages applied between them using the well-known finite element method (FEM). The complexity of such FE models is attributed to particle distribution, their geometric and material parameters, and their shape and size which can be of many orders of magnitude smaller than the overall problem domain under investigation. This paper overcomes this problem by adopting an effective particle coagulation (aggregation) strategy in FE modelling without significantly affecting the accuracy of field computation.
NASA Astrophysics Data System (ADS)
Kajzer, A.; Pozorski, J.; Szewc, K.
2014-08-01
In the paper we present Large-eddy simulation (LES) results of 3D Taylor- Green vortex obtained by the three different computational approaches: Smoothed Particle Hydrodynamics (SPH), Lattice Boltzmann Method (LBM) and Finite Volume Method (FVM). The Smagorinsky model was chosen as a subgrid-scale closure in LES for all considered methods and a selection of spatial resolutions have been investigated. The SPH and LBM computations have been carried out with the use of the in-house codes executed on GPU and compared, for validation purposes, with the FVM results obtained using the open-source CFD software OpenFOAM. A comparative study in terms of one-point statistics and turbulent energy spectra shows a good agreement of LES results for all methods. An analysis of the GPU code efficiency and implementation difficulties has been made. It is shown that both SPH and LBM may offer a significant advantage over mesh-based CFD methods.
Hsu, Sen-Ming; Chang, Hung-Chun
2007-11-26
A full-vectorial finite element method based eigenvalue algorithm is developed to analyze the band structures of two-dimensional (2D) photonic crystals (PCs) with arbitray 3D anisotropy for in-planewave propagations, in which the simple transverse-electric (TE) or transverse-magnetic (TM) modes may not be clearly defined. By taking all the field components into consideration simultaneously without decoupling of the wave modes in 2D PCs into TE and TM modes, a full-vectorial matrix eigenvalue equation, with the square of the wavenumber as the eigenvalue, is derived. We examine the convergence behaviors of this algorithm and analyze 2D PCs with arbitrary anisotropy using this algorithm to demonstrate its correctness and usefulness by explaining the numerical results theoretically. PMID:19550864
NASA Astrophysics Data System (ADS)
Yin, Y.; Hung, S.
2007-12-01
Seismic tomographic imaging has played a key component to unravel the deep processes that caused the surface morphology and rift magmatism in the southwest United States. Several studies used teleseismic body- wave arrivals recorded by the La Ristra experiment, a dense broadband array of 950-km in length deployed during 1999-2001 and run through the Great Plains, the Rio Grande Rift, and the Colorado Plateau, to construct a 2-D tomographic image of the upper mantle structure beneath this linear array (e.g., Gao et al., 2004). However, because of the inevitable smoothing and damping imposed in the tomographic model, the resulting velocity contrast is too weak to explain distinct P and S waveform changes across the array (Song and Helmberger, 2007). In this study, we include all the data from the La Ristra and available nearby arrays and reexamine finite- frequency travel time delays measured by inter-station cross correlation of waveforms at both high- (0.3-2 Hz for P and 0.1-0.5 Hz for S) and low-frequencies (0.03-0.125 Hz for P and 0.03-0.1 Hz for S). Differing from the previous models that rely on classical ray theory and simple grid parameterization, our inversion considers more realistic 3-D sensitivity kernels for relative travel-time delays and a wavelet-based, multi-scale parameterization that enables to yield robust features with spatially-varying resolutions. Our preliminary P-wave model reveals a prominent low-velocity zone extending from near surface to the depth of 300 km beneath the Rio Grande Rift, while the upper mantle which underlies the Great Plains and the Colorado Plateau is seismically fast. We will demonstrate the difference and improvement of 3-D tomographic models through the use of finite-frequency kernels and multi-scale parameterization.
Ausiello, P; Apicella, A; Davidson, C L; Rengo, S
2001-10-01
The combination of diverse materials and complex geometry makes stress distribution analysis in teeth very complicated. Simulation in a computerized model might enable a study of the simultaneous interaction of the many variables. A 3D solid model of a human maxillary premolar was prepared and exported into a 3D-finite element model (FEM). Additionally, a generic class II MOD cavity preparation and restoration was simulated in the FEM model by a proper choice of the mesh volumes. A validation procedure of the FEM model was executed based on a comparison of theoretical calculations and experimental data. Different rigidities were assigned to the adhesive system and restorative materials. Two different stress conditions were simulated: (a) stresses arising from the polymerization shrinkage and (b) stresses resulting from shrinkage stress in combination with vertical occlusal loading. Three different cases were analyzed: a sound tooth, a tooth with a class II MOD cavity, adhesively restored with a high (25 GPa) and one with a low (12.5GPa) elastic modulus composite. The cusp movements induced by polymerization stress and (over)-functional occlusal loading were evaluated. While cusp displacement was higher for the more rigid composites due to the pre-stressing from polymerization shrinkage, cusp movements turned out to be lower for the more flexible composites in case the restored tooth which was stressed by the occlusal loading. This preliminary study by 3D FEA on adhesively restored teeth with a class II MOD cavity indicated that Young's modulus values of the restorative materials play an essential role in the success of the restoration. Premature failure due to stresses arising from polymerization shrinkage and occlusal loading can be prevented by proper selection and combination of materials. PMID:11522306
NASA Astrophysics Data System (ADS)
Han, Daoru; Wang, Pu; He, Xiaoming; Lin, Tao; Wang, Joseph
2016-09-01
Motivated by the need to handle complex boundary conditions efficiently and accurately in particle-in-cell (PIC) simulations, this paper presents a three-dimensional (3D) linear immersed finite element (IFE) method with non-homogeneous flux jump conditions for solving electrostatic field involving complex boundary conditions using structured meshes independent of the interface. This method treats an object boundary as part of the simulation domain and solves the electric field at the boundary as an interface problem. In order to resolve charging on a dielectric surface, a new 3D linear IFE basis function is designed for each interface element to capture the electric field jump on the interface. Numerical experiments are provided to demonstrate the optimal convergence rates in L2 and H1 norms of the IFE solution. This new IFE method is integrated into a PIC method for simulations involving charging of a complex dielectric surface in a plasma. A numerical study of plasma-surface interactions at the lunar terminator is presented to demonstrate the applicability of the new method.
NASA Astrophysics Data System (ADS)
Kohout, B.; Pirinen, J.; Ruiter, N. V.
2012-03-01
The established standard screening method to detect breast cancer is X-ray mammography. However X-ray mammography often has low contrast for tumors located within glandular tissue. A new approach is 3D Ultrasound Computer Tomography (USCT), which is expected to detect small tumors at an early stage. This paper describes the development, improvement and the results of Finite Element Method (FEM) simulations of the Transducer Array System (TAS) used in our 3D USCT. The focus of this work is on researching the influence of meshing and material parameters on the electrical impedance curves. Thereafter, these findings are used to optimize the simulation model. The quality of the simulation was evaluated by comparing simulated impedance characteristics with measured data of the real TAS. The resulting FEM simulation model is a powerful tool to analyze and optimize transducer array systems applied for USCT. With this simulation model, the behavior of TAS for different geometry modifications was researched. It provides a means to understand the acoustical performances inside of any ultrasound transducer represented by its electrical impedance characteristic.
Finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems
NASA Astrophysics Data System (ADS)
Xie, Xue-Jun; Zhang, Xing-Hui; Zhang, Kemei
2016-07-01
This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a ? Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.
Application of variational and Galerkin equations to linear and nonlinear finite element analysis
NASA Technical Reports Server (NTRS)
Yu, Y.-Y.
1974-01-01
The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.
Hoffman, E.L.; Ammerman, D.J.
1995-04-01
A series of tests investigating dynamic pulse buckling of a cylindrical shell under axial impact is compared to several 2D and 3D finite element simulations of the event. The purpose of the work is to investigate the performance of various analysis codes and element types on a problem which is applicable to radioactive material transport packages, and ultimately to develop a benchmark problem to qualify finite element analysis codes for the transport package design industry. Four axial impact tests were performed on 4 in-diameter, 8 in-long, 304 L stainless steel cylinders with a 3/16 in wall thickness. The cylinders were struck by a 597 lb mass with an impact velocity ranging from 42.2 to 45.1 ft/sec. During the impact event, a buckle formed at each end of the cylinder, and one of the two buckles became unstable and collapsed. The instability occurred at the top of the cylinder in three tests and at the bottom in one test. Numerical simulations of the test were performed using the following codes and element types: PRONTO2D with axisymmetric four-node quadrilaterals; PRONTO3D with both four-node shells and eight-node hexahedrons; and ABAQUS/Explicit with axisymmetric two-node shells and four-node quadrilaterals, and 3D four-node shells and eight-node hexahedrons. All of the calculations are compared to the tests with respect to deformed shape and impact load history. As in the tests, the location of the instability is not consistent in all of the calculations. However, the calculations show good agreement with impact load measurements with the exception of an initial load spike which is proven to be the dynamic response of the load cell to the impact. Finally, the PRONIT02D calculation is compared to the tests with respect to strain and acceleration histories. Accelerometer data exhibited good qualitative agreement with the calculations. The strain comparisons show that measurements are very sensitive to gage placement.
Wang, Leimin; Shen, Yi
2015-11-01
This paper is concerned about the finite-time stabilizability and instabilizability for a class of delayed memristive neural networks (DMNNs). Through the design of a new nonlinear controller, algebraic criteria based on M -matrix are established for the finite-time stabilizability of DMNNs, and the upper bound of the settling time for stabilization is estimated. In addition, finite-time instabilizability algebraic criteria are also established by choosing different parameters of the same nonlinear controller. The effectiveness and the superiority of the obtained results are supported by numerical simulations. PMID:26277003
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Cai, X.C.
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
Nonlinear Schwarz-Fas Methods for Unstructured Finite Element Elliptic Problems
Jones, J E; Vassilevski, P S; Woodward, C S
2002-09-30
This paper provides extensions of an element agglomeration AMG method to nonlinear elliptic problems discretized by the finite element method on general unstructured meshes. The method constructs coarse discretization spaces and corresponding coarse nonlinear operators as well as their Jacobians. We introduce both standard (fairly quasi-uniformly coarsened) and non-standard (coarsened away) coarse meshes and respective finite element spaces. We use both kind of spaces in FAS type coarse subspace correction (or Schwarz) algorithms. Their performance is illustrated on a number of model problems. The coarsened away spaces seem to perform better than the standard spaces for problems with nonlinearities in the principal part of the elliptic operator.
Finite-time H∞ filtering for non-linear stochastic systems
NASA Astrophysics Data System (ADS)
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
NASA Technical Reports Server (NTRS)
Davis, D. D., Jr.; Krishnamurthy, T.; Stroud, W. J.; Mccleary, S. L.
1991-01-01
State-of-the-art nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain-displacement relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis.
Cost Considerations in Nonlinear Finite-Element Computing
NASA Technical Reports Server (NTRS)
Utku, S.; Melosh, R. J.; Islam, M.; Salama, M.
1985-01-01
Conference paper discusses computational requirements for finiteelement analysis using quasi-linear approach to nonlinear problems. Paper evaluates computational efficiency of different computer architecturtural types in terms of relative cost and computing time.
SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics
Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.
1999-03-01
This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.
Self-consistent Nonlinear Analysis and 3D Particle-In-Cell Simulation of a W-band Gyro-TWT
NASA Astrophysics Data System (ADS)
Tang, Yong; Luo, Yong; Xu, Yong; Yan, Ran
2014-10-01
The self-consistent nonlinear analysis and CST 3D particle-in-cell (PIC) simulation of a W-band gyrotron traveling wave tube (gyro-TWT) are presented in this paper. Both the simulation results of the two codes are excellent agreement with each other. The gyro-TWT loaded with periodic lossy dielectric in the circuit for suppressing potential spurious oscillations. It is driven by a 70kV, 10A gyrating electron beam with velocity ratio of 1.0. PIC simulation results are: the maximum peak output power of 198kW, statured gain of 62.3dB and efficiency of 28.3% at 92.5GHz. Only the operating mode TE 01 is observed in the CST 3D simulation and the potential competing backward wave oscillations are effectively suppressed. The CST simulation also predicts that the device works stably under the condition of the beam current lower than 14A and B 0 /B g lower than 1.05. The simulated bandwidth with peak power greater than 100kW is 6.8GHz without axial velocity spread, and 4.1GHz with 6% axial velocity spread.
NASA Astrophysics Data System (ADS)
Ghatak, Kamakhya P.
1990-08-01
An attempt is made to study the photoemission :eron 3D quantum well boxes (QWBs) of nonlinear optical materials in the presence of crossed electric and magnetic fields, taking ternary chalcopyrite semiconductors as an example. Consi3ering the anisotropic crystal potential in the Harniltonian, we have formulated the generalized electron energy spectrum taking into account the anisotropies of the 0ther energy band par arne ter s, within the fr sine work of theory. We have then derlved.the photoernission from 3D QWBs of ternary chalCopyrite compounds by using the modified dispersion law under cross field configuration in the said material. It is found, taking 3D QWBs of n-CdGeAs2 as an example, that the photoernission exhibits ladder like dependence with incident photon energy as found in quanturn Hall effect and the corresponding results for three and two-band Kane models together with that of parabolic energy bands have been obtained from the present generalized exjressions as special cases. The photoeinission decreases with increasing magnetic field and decreasing electron concentration respectively. The oscillations in accordance with the present generalized model show up much more significantly and are in agreement with the experimental results as given elsewhere.
Finite-dimensional states and entanglement generation for a nonlinear coupler
Kowalewska-Kudlaszyk, A.; Leonski, W.
2006-04-15
We discuss a system comprising two nonlinear (Kerr-like) oscillators coupled mutually by a nonlinear interaction. The system is excited by an external coherent field that is resonant to the frequency of one of the oscillators. We show that the coupler evolution can be closed within a finite set of n-photon states, analogously as in the nonlinear quantum scissors model. Moreover, for this type of evolution our system can be treated as a Bell-like state generator. Thanks to the nonlinear nature of both oscillators and their internal coupling, these states can be generated even if the system exhibits its energy dissipating nature, contrary to systems with linear couplings.
Blehm, Benjamin H; Devine, Alexus; Staunton, Jack R; Tanner, Kandice
2016-03-01
Variation in matrix elasticity has been shown to determine cell fate in both differentiation and development of malignant phenotype. The tissue microenvironment provides complex biochemical and biophysical signals in part due to the architectural heterogeneities found in extracellular matrices (ECMs). Three dimensional cell cultures can partially mimic in vivo tissue architecture, but to truly understand the role of viscoelasticity on cell fate, we must first determine in vivo tissue mechanical properties to improve in vitro models. We employed Active Microrheology by Optical Trapping InVivo (AMOTIV), using in situ calibration to measure in vivo zebrafish tissue mechanics. Previously used trap calibration methods overestimate complex moduli by ∼ 2-20 fold compared to AMOTIV. Applying differential microscale stresses and strains showed that hyaluronic acid (HA) gels display semi-flexible polymer behavior, while laminin-rich ECM hydrogels display flexible polymer behavior. In contrast, zebrafish tissues displayed different moduli at different stresses, with higher power law exponents at lower stresses, indicating that living tissue has greater stress dependence than the 3D hydrogels examined. To our knowledge, this work is the first vertebrate tissue rheological characterization performed in vivo. Our fundamental observations are important for the development and refinement of in vitro platforms. PMID:26773661
Development of non-linear finite element computer code
NASA Technical Reports Server (NTRS)
Becker, E. B.; Miller, T.
1985-01-01
Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.
Nonlinear finite amplitude torsional vibrations of cantilevers in viscous fluids
NASA Astrophysics Data System (ADS)
Aureli, Matteo; Pagano, Christopher; Porfiri, Maurizio
2012-06-01
In this paper, we study torsional vibrations of cantilever beams undergoing moderately large oscillations within a quiescent viscous fluid. The structure is modeled as an Euler-Bernoulli beam, with thin rectangular cross section, under base excitation. The distributed hydrodynamic loading experienced by the vibrating structure is described through a complex-valued hydrodynamic function which incorporates added mass and fluid damping elicited by moderately large rotations. We conduct a parametric study on the two dimensional computational fluid dynamics of a pitching rigid lamina, representative of a generic beam cross section, to investigate the dependence of the hydrodynamic function on the governing flow parameters. As the frequency and amplitude of the oscillation increase, vortex shedding and convection phenomena increase, thus resulting into nonlinear hydrodynamic damping. We derive a handleable nonlinear correction to the classical hydrodynamic function developed for small amplitude torsional vibrations for use in a reduced order nonlinear modal model and we validate theoretical results against experimental findings.
Choas and instabilities in finite difference approximations to nonlinear differential equations
Cloutman, L. D., LLNL
1998-07-01
The numerical solution of time-dependent ordinary and partial differential equations by finite difference techniques is a common task in computational physics and engineering The rate equations for chemical kinetics in combustion modeling are an important example. They not only are nonlinear, but they tend to be stiff, which makes their solution a challenge for transient problems. We show that one must be very careful how such equations are solved In addition to the danger of large time-marching errors, there can be unphysical chaotic solutions that remain numerically stable for a range of time steps that depends on the particular finite difference method used We point out that the solutions of the finite difference equations converge to those of the differential equations only in the limit as the time step approaches zero for stable and consistent finite difference approximations The chaotic behavior observed for finite time steps in some nonlinear difference equations is unrelated to solutions of the differential equations, but is connected with the onset of numerical instabilities of the finite difference equations This behavior suggests that the use of the theory of chaos in nonlinear iterated maps may be useful in stability anlaysis of finite difference approximations to nonlinear differential equations, providing more stringent time step limits than the formal linear stability analysis that tests only for unbounded solutions This observation implies that apparently stable numerical solutions of nonlinear differential equations by finite difference techniques may in fact be contaminated (if not dominated) by nonphysical chaotic parasitic solutions that degrade the accuracy of the numerical solution We demonstrate this phenomenon with some solutions of the logistic equation and a simple two-dimensional computational fluid dynamics example
Yang, Chun; Tang, Dalin; Atluri, Satya
2011-01-01
Previously, we introduced a computational procedure based on three-dimensional meshless generalized finite difference (MGFD) method and serial magnetic resonance imaging (MRI) data to quantify patient-specific carotid atherosclerotic plaque growth functions and simulate plaque progression. Structure-only models were used in our previous report. In this paper, fluid-stricture interaction (FSI) was added to improve on prediction accuracy. One participating patient was scanned three times (T1, T2, and T3, at intervals of about 18 months) to obtain plaque progression data. Blood flow was assumed to laminar, Newtonian, viscous and incompressible. The Navier-Stokes equations with arbitrary Lagrangian-Eulerian (ALE) formulation were used as the governing equations. Plaque material was assumed to be uniform, homogeneous, isotropic, linear, and nearly incompressible. The linear elastic model was used. The 3D FSI plaque model was discretized and solved using a meshless generalized finite difference (GFD) method. Growth functions with a) morphology alone; b) morphology and plaque wall stress (PWS); morphology and flow shear stress (FSS), and d) morphology, PWS and FSS were introduced to predict future plaque growth based on previous time point data. Starting from the T2 plaque geometry, plaque progression was simulated by solving the FSI model and adjusting plaque geometry using plaque growth functions iteratively until T3 is reached. Numerically simulated plaque progression agreed very well with the target T3 plaque geometry with errors ranging from 8.62%, 7.22%, 5.77% and 4.39%, with the growth function including morphology, plaque wall stress and flow shear stress terms giving the best predictions. Adding flow shear stress term to the growth function improved the prediction error from 7.22% to 4.39%, a 40% improvement. We believe this is the first time 3D plaque progression FSI simulation based on multi-year patient-tracking data was reported. Serial MRI-based progression
On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with a Quadratic Trap
NASA Astrophysics Data System (ADS)
Chen, Xuwen
2013-11-01
We consider the dynamics of the three-dimensional N-body Schrödinger equation in the presence of a quadratic trap. We assume the pair interaction potential is N 3 β-1 V( N β x). We justify the mean-field approximation and offer a rigorous derivation of the three-dimensional cubic nonlinear Schrödinger equation (NLS) with a quadratic trap. We establish the space-time bound conjectured by Klainerman and Machedon (Commun Math Phys 279:169-185, 2008) for by adapting and simplifying an argument in Chen and Pavlović (Annales Henri Poincaré, 2013) which solves the problem for in the absence of a trap.
NASA Astrophysics Data System (ADS)
Hervas, Jaime Rubio; Reyhanoglu, Mahmut; Tang, Hui
2014-12-01
This paper presents a motion tracking and control system for automatically landing Unmanned Aerial Vehicles (UAVs) on an oscillating platform using Laser Radar (LADAR) observations. The system itself is assumed to be mounted on a ship deck. A full nonlinear mathematical model is first introduced for the UAV. The ship motion is characterized by a Fourier transform based method which includes a realistic characterization of the sea waves. LADAR observation models are introduced and an algorithm to process those observations for yielding the relative state between the vessel and the UAV is presented, from which the UAV's state relative to an inertial frame can be obtained and used for feedback purposes. A sliding mode control algorithm is derived for tracking a landing trajectory defined by a set of desired waypoints. An extended Kalman filter (EKF) is proposed to account for process and observation noises in the design of a state estimator. The effectiveness of the control algorithm is illustrated through a simulation example.
Hervas, Jaime Rubio; Tang, Hui; Reyhanoglu, Mahmut
2014-12-10
This paper presents a motion tracking and control system for automatically landing Unmanned Aerial Vehicles (UAVs) on an oscillating platform using Laser Radar (LADAR) observations. The system itself is assumed to be mounted on a ship deck. A full nonlinear mathematical model is first introduced for the UAV. The ship motion is characterized by a Fourier transform based method which includes a realistic characterization of the sea waves. LADAR observation models are introduced and an algorithm to process those observations for yielding the relative state between the vessel and the UAV is presented, from which the UAV's state relative to an inertial frame can be obtained and used for feedback purposes. A sliding mode control algorithm is derived for tracking a landing trajectory defined by a set of desired waypoints. An extended Kalman filter (EKF) is proposed to account for process and observation noises in the design of a state estimator. The effectiveness of the control algorithm is illustrated through a simulation example.
NASA Astrophysics Data System (ADS)
Bernard, R.; Glises, R.; Chamagne, D.; Cuchet, D.; Kauffmann, J. M.
1999-08-01
The aim of this work concerns the development and the validation of a thermal steady state model applied to a permanent magnet direct current motor with commutator. The rated power of the machine is 120 W. Design has been realized thanks to the thermal modulus of the computation software with the finite element method Flux3D. It is shown in this work how it is possible to use only the heat equation to simulate the thermal behaviour of the motor. It implies calculating of new fluid conductivities (considering also all thermal modes) by comparison of calculated and experimental temperatures. To realize these 3D modelizations, it is necessary to know and to locate all the losses of the motor which are considered as thermal sources. The experimental temperatures are given by 40 chromel-alumel thermocouples of 100 μm diameter located in the rotor and the stator of the machine. Numerical computations use Dirichlet boundary layer conditions given by an IR camera. Ce travail concerne le développement et la validation d'un modèle de simulation du comportement thermique tridimensionnel en régime permanent d'un moteur électrique de 120 watt à courant continu, à aimants permanents et à collecteur. Le logiciel est développé à partir du code de calculs par éléments finis Flux3D. L'équation de la chaleur modélise l'ensemble des transferts thermiques du moteur. Cela nécessite de recaler certains paramètres fluides par comparaison des températures simulées et expérimentales. Une séparation détaillée des différentes pertes est nécessaire pour obtenir une bonne précision finale. Un banc d'essais thermiques permet d'obtenir à l'aide de 40 thermocouples (chromel-alumel de 100 μm de diamètre) les températures au stator et au rotor. Une caméra thermographique infrarouge donne les conditions aux limites de Dirichlet nécessaires à la modélisation.
Bayesian Finite Mixtures for Nonlinear Modeling of Educational Data.
ERIC Educational Resources Information Center
Tirri, Henry; And Others
A Bayesian approach for finding latent classes in data is discussed. The approach uses finite mixture models to describe the underlying structure in the data and demonstrate that the possibility of using full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated…
NASA Astrophysics Data System (ADS)
Suzuki, Y.; Geiger, J.
2016-06-01
The impact of the 3D equilibrium response on the plasma edge topology is studied. In Wendelstein 7-X, the island divertor concept is used to assess scenarios for quasi-steady-state operation. However, the boundary islands necessary for the island divertor are strongly susceptible to plasma beta and toroidal current density effects because of the low magnetic shear. The edge magnetic topology for quasi-steady-state operation scenarios is calculated with the HINT-code to study the accompanying changes of the magnetic field structures. Two magnetic configurations have been selected, which had been investigated in self consistent neoclassical transport simulations for low bootstrap current but which use the alternative natural island chains to the standard iota value of 1 (ι b = 5/5, periodicity), namely, at high-iota (ι b = 5/4) and at low-iota (ι b = 5/6). For the high-iota configuration, the boundary islands are robust but the stochasticity around them is enhanced with beta. The addition of toroidal current densities enhances the stochasticity further. The increased stochasticity changes the footprints on in-vessel components with a direct impact on the corresponding heat loads. In the low-iota configuration the boundary islands used for the island divertor are dislocated radially due to the low shear and even show healing effects, i.e. the island width vanishes. In the latter case the plasma changes from divertor to limiter operation. To realize the predicted high-performance quasi-steady-state operation of the transport simulations, further adjustments of the magnetic configuration may be necessary to achieve a proper divertor compatibility of the scenarios.
NASA Astrophysics Data System (ADS)
Kordy, M.; Wannamaker, P.; Maris, V.; Cherkaev, E.; Hill, G.
2016-01-01
We have developed an algorithm, which we call HexMT, for 3-D simulation and inversion of magnetotelluric (MT) responses using deformable hexahedral finite elements that permit incorporation of topography. Direct solvers parallelized on symmetric multiprocessor (SMP), single-chassis workstations with large RAM are used throughout, including the forward solution, parameter Jacobians and model parameter update. In Part I, the forward simulator and Jacobian calculations are presented. We use first-order edge elements to represent the secondary electric field (E), yielding accuracy O(h) for E and its curl (magnetic field). For very low frequencies or small material admittivities, the E-field requires divergence correction. With the help of Hodge decomposition, the correction may be applied in one step after the forward solution is calculated. This allows accurate E-field solutions in dielectric air. The system matrix factorization and source vector solutions are computed using the MKL PARDISO library, which shows good scalability through 24 processor cores. The factorized matrix is used to calculate the forward response as well as the Jacobians of electromagnetic (EM) field and MT responses using the reciprocity theorem. Comparison with other codes demonstrates accuracy of our forward calculations. We consider a popular conductive/resistive double brick structure, several synthetic topographic models and the natural topography of Mount Erebus in Antarctica. In particular, the ability of finite elements to represent smooth topographic slopes permits accurate simulation of refraction of EM waves normal to the slopes at high frequencies. Run-time tests of the parallelized algorithm indicate that for meshes as large as 176 × 176 × 70 elements, MT forward responses and Jacobians can be calculated in ˜1.5 hr per frequency. Together with an efficient inversion parameter step described in Part II, MT inversion problems of 200-300 stations are computable with total run times
Ma, J; Wittek, A; Singh, S; Joldes, G; Washio, T; Chinzei, K; Miller, K
2010-12-01
In this paper, the accuracy of non-linear finite element computations in application to surgical simulation was evaluated by comparing the experiment and modelling of indentation of the human brain phantom. The evaluation was realised by comparing forces acting on the indenter and the deformation of the brain phantom. The deformation of the brain phantom was measured by tracking 3D motions of X-ray opaque markers, placed within the brain phantom using a custom-built bi-plane X-ray image intensifier system. The model was implemented using the ABAQUS(TM) finite element solver. Realistic geometry obtained from magnetic resonance images and specific constitutive properties determined through compression tests were used in the model. The model accurately predicted the indentation force-displacement relations and marker displacements. Good agreement between modelling and experimental results verifies the reliability of the finite element modelling techniques used in this study and confirms the predictive power of these techniques in surgical simulation. PMID:21153973
Finite-time consensus of time-varying nonlinear multi-agent systems
NASA Astrophysics Data System (ADS)
Liu, Qingrong; Liang, Zhishan
2016-08-01
This paper investigates the problem of leader-follower finite-time consensus for a class of time-varying nonlinear multi-agent systems. The dynamics of each agent is assumed to be represented by a strict feedback nonlinear system, where nonlinearities satisfy Lipschitz growth conditions with time-varying gains. The main design procedure is outlined as follows. First, it is shown that the leader-follower consensus problem is equivalent to a conventional control problem of multi-variable high-dimension systems. Second, by introducing a state transformation, the control problem is converted into the construction problem of two dynamic equations. Third, based on the Lyapunov stability theorem, the global finite-time stability of the closed-loop control system is proved, and the finite-time consensus of the concerned multi-agent systems is thus guaranteed. An example is given to verify the effectiveness of the proposed consensus protocol algorithm.
Large spatial, temporal, and algorithmic adaptivity for implicit nonlinear finite element analysis
Engelmann, B.E.; Whirley, R.G.
1992-07-30
The development of effective solution strategies to solve the global nonlinear equations which arise in implicit finite element analysis has been the subject of much research in recent years. Robust algorithms are needed to handle the complex nonlinearities that arise in many implicit finite element applications such as metalforming process simulation. The authors experience indicates that robustness can best be achieved through adaptive solution strategies. In the course of their research, this adaptivity and flexibility has been refined into a production tool through the development of a solution control language called ISLAND. This paper discusses aspects of adaptive solution strategies including iterative procedures to solve the global equations and remeshing techniques to extend the domain of Lagrangian methods. Examples using the newly developed ISLAND language are presented to illustrate the advantages of embedding temporal, algorithmic, and spatial adaptivity in a modem implicit nonlinear finite element analysis code.
Dynamic topology and flux rope evolution during non-linear tearing of 3D null point current sheets
Wyper, P. F. Pontin, D. I.
2014-10-15
In this work, the dynamic magnetic field within a tearing-unstable three-dimensional current sheet about a magnetic null point is described in detail. We focus on the evolution of the magnetic null points and flux ropes that are formed during the tearing process. Generally, we find that both magnetic structures are created prolifically within the layer and are non-trivially related. We examine how nulls are created and annihilated during bifurcation processes, and describe how they evolve within the current layer. The type of null bifurcation first observed is associated with the formation of pairs of flux ropes within the current layer. We also find that new nulls form within these flux ropes, both following internal reconnection and as adjacent flux ropes interact. The flux ropes exhibit a complex evolution, driven by a combination of ideal kinking and their interaction with the outflow jets from the main layer. The finite size of the unstable layer also allows us to consider the wider effects of flux rope generation. We find that the unstable current layer acts as a source of torsional magnetohydrodynamic waves and dynamic braiding of magnetic fields. The implications of these results to several areas of heliophysics are discussed.
NASA Astrophysics Data System (ADS)
Liang, Xiaofeng; Chen, Yun; Tian, Xiaobo; Chen, Yongshun John; Ni, James; Gallegos, Andrea; Klemperer, Simon L.; Wang, Minling; Xu, Tao; Sun, Changqing; Si, Shaokun; Lan, Haiqiang; Teng, Jiwen
2016-06-01
We perform a finite-frequency tomographic inversion to image 3D velocity structures beneath southern and central Tibet using teleseismic body-wave data recorded by the TIBET-31N passive seismic array as well as waveforms from previous temporary seismic arrays. High-velocity bodies dip ∼40° northward beneath the Himalaya and the Lhasa Terrane. We interpret these high-velocity anomalies as subducting Indian Continental Lithosphere (ICL). The ICL appears to extend further north in central Tibet than in eastern Tibet, reaching 350 km depth at ∼31°N along 85°E but at ∼30°N along 91°E. Low P- and S-wave velocity anomalies extend from the lower crust to ≥180 km depth beneath the Tangra Yum Co Rift, Yadong-Gulu Rift, and the Cona Rift, suggesting that rifting in southern Tibet may involve the entire lithosphere. The anomaly beneath Tangra Yum Co Rift extends down to about 180 km, whereas the anomalies west of the Yadong-Gulu Rift and east of the Cona Rift extend to more than 300 km depth. The low-velocity upper mantle west of the Yadong-Gulu Rift extends furthest north and appears to connect with the extensive upper-mantle low-velocity region beneath central Tibet. Thus the northward-subducting Indian Plate is fragmented along north-south breaks that permit or induce asthenospheric upwellings indistinguishable from the upper mantle of northern Tibet.
NASA Astrophysics Data System (ADS)
Ichimura, Tsuyoshi; Agata, Ryoichiro; Hori, Takane; Hirahara, Kazuro; Hashimoto, Chihiro; Hori, Muneo; Fukahata, Yukitoshi
2016-07-01
As a result of the accumulation of high-resolution observation data, 3-D high-fidelity crustal structure data for large domains are becoming available. However, it has been difficult to use such data to perform elastic/viscoelastic crustal deformation analyses in large domains with quality assurance of the numerical simulation that guarantees convergence of the numerical solution with respect to the discretization size because the costs of analysis are significantly high. This paper proposes a method of constructing a high-fidelity crustal structure finite element (FE) model using high-fidelity crustal structure data and fast FE analysis to reduce the costs of analysis (based on automatic FE model generation for parallel computation, OpenMP/MPI hybrid parallel computation on distributed memory computers, a geometric multigrid, variable preconditioning and multiple precision arithmetic). Using the proposed methods, we construct 10 billion degree-of-freedom high-fidelity crustal structure FE models for the entire Japan, and conduct elastic/viscoelastic crustal deformation analysis using this model with enough high accuracy of the numerical simulation.
NASA Astrophysics Data System (ADS)
Wang, Xiaowei; Gong, Jianming; Zhao, Yanping; Wang, Yanfei
2015-05-01
This study used ABAQUS finite element (FE) software to investigate the residual stress distributions of P92 welded pipes in both the as-weld and post weld heat treated (PWHT) condition. Sequential coupling quasi-static thermo-mechanical in conjunction with moving double ellipsoidal heat source and an element add/remove technique to simulate deposition of new weld material, are combined in the 3D FE analysis. To validate the simulation results, the residual stresses in axial direction at the surface of pipe were measured by X-ray diffraction technique and compared with the results of FE analysis. Detailed characteristic distributions of the residual stresses are discussed. Results show that the FE model can predict the residual stress distributions satisfactorily. Highest residual stresses on the outer surface are found in the last weld bead to be deposited. And the highest tensile residual stress for the full welded section take place in heat affected zone (HAZ) near the middle thickness. Larger residual sstress can be found around the welding start point along the pipe circumference. Comparison of heat treated specimen and untreated specimen illustrates that PWHT has a strong effect on the residual stress field.
NASA Astrophysics Data System (ADS)
Luo, Jiao; Wu, Bin; Li, Miao-Quan
2012-02-01
The physically-based internal state variable (ISV) models were used to describe the changes of dislocation density, grain size, and flow stress in the high temperature deformation of titanium alloys in this study. The constants of the present models could be identified based on experimental results, which were conducted at deformation temperatures ranging from 1093 K to 1303 K, height reductions ranging from 20% to 60%, and the strain rates of 0.001, 0.01, 0.1, 1.0, and 10.0 s-1. The physically-based internal state variable models were implemented into the commercial finite element (FE) code. Then, a three-dimensional (3D) FE simulation system coupling of deformation, heat transfer, and microstructure evolution was developed for the blade forging of Ti-6Al-4V alloy. FE analysis was carried out to simulate the microstructure evolution in the blade forging of Ti-6Al-4V alloy. Finally, the blade forging tests of Ti-6Al-4V alloy were performed to validate the results of FE simulation. According to the tensile tests, it is seen that the mechanical properties, such as tensile strength and elongation, satisfy the application requirements well. The maximum and minimum differences between the calculated and experimental grain size of primary α phase are 11.71% and 4.23%, respectively. Thus, the industrial trials show a good agreement with FE simulation of blade forging.
Brummund, Martin; Brailovski, Vladimir; Facchinello, Yann; Petit, Yvan; Mac-Thiong, Jean-Marc
2015-08-01
Monolithic superelastic-elastoplastic spinal rods (MSER) are promising candidates to provide (i) dynamic stabilisation in spinal segments prone to mechanical stress concentration and adjacent segment disease and (ii) to provide fusion-ready stabilization in spinal segments at risk of implant failure. However, the stiffness distributions along the rod's longitudinal axis that best meet clinical requirements remain unknown. The present study is part of a mixed numerical experimental research project and aims at the implementation of a 3D finite element model of the porcine lumbar spine to study the role of MSER material properties and stiffness distributions on the intradiscal pressure distribution in the adjacent segment. In this paper, preliminary intradiscal pressure predictions obtained at one functional spinal unit are presented. Due to a lack of porcine material property data, these predictions were obtained on the basis of uncalibrated human vertebral disc data which were taken from the literature. The results indicate that human annulus and nucleus data predict experimental porcine in vivo and in vitro data reasonably well for the compressive forces of varying magnitudes. PMID:26736412
Finite difference time domain calculation of transients in antennas with nonlinear loads
NASA Technical Reports Server (NTRS)
Luebbers, Raymond J.; Beggs, John H.; Kunz, Karl S.; Chamberlin, Kent
1991-01-01
In this paper transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm. PMID:25277626
NASA Astrophysics Data System (ADS)
Padmanabhan, R.; Oliveira, M. C.; Baptista, A. J.; Alves, J. L.; Menezes, L. F.
2007-05-01
Springback phenomenon associated with the elastic properties of sheet metals makes the design of forming dies a complex task. Thus, to develop consistent algorithms for springback compensation an accurate prediction of the amount of springback is mandatory. The numerical simulation using the finite element method is consensually the only feasible method to predict springback. However, springback prediction is a very complicated task and highly sensitive to various numerical parameters of finite elements (FE), such as: type, order, integration scheme, shape and size, as well the time integration formulae and the unloading strategy. All these numerical parameters make numerical simulation of springback more sensitive to numerical tolerances than the forming operation. In case of an unconstrained cylindrical bending, the in-plane to thickness FE size ratio is more relevant than the number of FE layers through-thickness, for the numerical prediction of final stress and strain states, variables of paramount importance for an accurate springback prediction. The aim of the present work is to evaluate the influence of the refinement of a 3-D FE mesh, namely the in-plane mesh refinement and the number of through-thickness FE layers, in springback prediction. The selected example corresponds to the first stage of the "Numisheet'05 Benchmark♯3", which consists basically in the sheet forming of a channel section in an industrial-scale channel draw die. The physical drawbeads are accurately taken into account in the numerical model in order to accurately reproduce its influence during the forming process simulation. FEM simulations were carried out with the in-house code DD3IMP. Solid finite elements were used. They are recommended for accuracy in FE springback simulation when the ratio between the tool radius and blank thickness is lower than 5-6. In the selected example the drawbead radius is 4.0 mm. The influence of the FE mesh refinement in springback prediction is
Material nonlinear analysis via mixed-iterative finite element method
NASA Technical Reports Server (NTRS)
Sutjahjo, Edhi; Chamis, Christos C.
1992-01-01
The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Muravyov, Alexander A.
2002-01-01
Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.
PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual
NASA Technical Reports Server (NTRS)
Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.
1977-01-01
The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.
NASA Technical Reports Server (NTRS)
Muravyov, Alexander A.
1999-01-01
In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.
Breakdown of nonlinear elasticity in amorphous solids at finite temperatures
NASA Astrophysics Data System (ADS)
Procaccia, Itamar; Rainone, Corrado; Shor, Carmel A. B. Z.; Singh, Murari
2016-06-01
It is known [H. G. E. Hentschel et al., Phys. Rev. E 83, 061101 (2011), 10.1103/PhysRevE.83.061101] that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus, which exists, none of the higher order coefficients exist in the thermodynamic limit. Here we show that the same phenomenon persists up to temperatures comparable to that of the glass transition. The zero-temperature mechanism due to the prevalence of dangerous plastic modes of the Hessian matrix is replaced by anomalous stress fluctuations that lead to the divergence of the variances of the higher order elastic coefficients. The conclusion is that in amorphous solids elasticity can never be decoupled from plasticity: the nonlinear response is very substantially plastic.
Optimization of a finite difference method for nonlinear wave equations
NASA Astrophysics Data System (ADS)
Chen, Miaochao
2013-07-01
Wave equations have important fluid dynamics background, which are extensively used in many fields, such as aviation, meteorology, maritime, water conservancy, etc. This paper is devoted to the explicit difference method for nonlinear wave equations. Firstly, a three-level and explicit difference scheme is derived. It is shown that the explicit difference scheme is uniquely solvable and convergent. Moreover, a numerical experiment is conducted to illustrate the theoretical results of the presented method.
CUERVO: A finite element computer program for nonlinear scalar transport problems
Sirman, M.B.; Gartling, D.K.
1995-11-01
CUERVO is a finite element code that is designed for the solution of multi-dimensional field problems described by a general nonlinear, advection-diffusion equation. The code is also applicable to field problems described by diffusion, Poisson or Laplace equations. The finite element formulation and the associated numerical methods used in CUERVO are outlined here; detailed instructions for use of the code are also presented. Example problems are provided to illustrate the use of the code.
Linear vs nonlinear and infinite vs finite: An interpretation of chaos
Protopopescu, V.
1990-10-01
An example of a linear infinite-dimensional system is presented that exhibits deterministic chaos and thus challenges the presumably unquestionable connection between chaos and nonlinearity. Via this example, the roles of, and relationships between, linearity, nonlinearity, infinity and finiteness in the occurrence of chaos are investigated. The analysis of these complementary but related aspects leads to: a new interpretation of chaos as the manifestation of incompressible and thus incompressible information and a conjecture about the nonexistence of operationally accessible linear systems.
Andrianov, I.V.; Danishevsky, V.V.
1994-12-31
Asymptotic approaches for nonlinear dynamics of continual system are developed well for the infinite in spatial variables. For the systems with finite sizes we have an infinite number of resonance, and Poincare-Lighthill-Go method does riot work. Using of averaging procedure or method of multiple scales leads to the infinite systems of nonlinear algebraic or ordinary differential equations systems and then using truncation method. which does not gives possibility to obtain all important properties of the solutions.
Taylor, Z A; Cheng, M; Ourselin, S
2008-05-01
The use of biomechanical modelling, especially in conjunction with finite element analysis, has become common in many areas of medical image analysis and surgical simulation. Clinical employment of such techniques is hindered by conflicting requirements for high fidelity in the modelling approach, and fast solution speeds. We report the development of techniques for high-speed nonlinear finite element analysis for surgical simulation. We use a fully nonlinear total Lagrangian explicit finite element formulation which offers significant computational advantages for soft tissue simulation. However, the key contribution of the work is the presentation of a fast graphics processing unit (GPU) solution scheme for the finite element equations. To the best of our knowledge, this represents the first GPU implementation of a nonlinear finite element solver. We show that the present explicit finite element scheme is well suited to solution via highly parallel graphics hardware, and that even a midrange GPU allows significant solution speed gains (up to 16.8 x) compared with equivalent CPU implementations. For the models tested the scheme allows real-time solution of models with up to 16,000 tetrahedral elements. The use of GPUs for such purposes offers a cost-effective high-performance alternative to expensive multi-CPU machines, and may have important applications in medical image analysis and surgical simulation. PMID:18450538
NASA Astrophysics Data System (ADS)
Wawerzinek, B.; Ritter, J. R. R.; Roy, C.
2013-08-01
We analyse travel times of shear waves, which were recorded at the MAGNUS network, to determine the 3D shear wave velocity (vS) structure underneath Southern Scandinavia. The travel time residuals are corrected for the known crustal structure of Southern Norway and weighted to account for data quality and pick uncertainties. The resulting residual pattern of subvertically incident waves is very uniform and simple. It shows delayed arrivals underneath Southern Norway compared to fast arrivals underneath the Oslo Graben and the Baltic Shield. The 3D upper mantle vS structure underneath the station network is determined by performing non-linear travel time tomography. As expected from the residual pattern the resulting tomographic model shows a simple and continuous vS perturbation pattern: a negative vS anomaly is visible underneath Southern Norway relative to the Baltic Shield in the east with a contrast of up to 4% vS and a sharp W-E dipping transition zone. Reconstruction tests reveal besides vertical smearing a good lateral reconstruction of the dipping vS transition zone and suggest that a deep-seated anomaly at 330-410 km depth is real and not an inversion artefact. The upper part of the reduced vS anomaly underneath Southern Norway (down to 250 km depth) might be due to an increase in lithospheric thickness from the Caledonian Southern Scandes in the west towards the Proterozoic Baltic Shield in Sweden in the east. The deeper-seated negative vS anomaly (330-410 km depth) could be caused by a temperature anomaly possibly combined with effects due to fluids or hydrous minerals. The determined simple 3D vS structure underneath Southern Scandinavia indicates that mantle processes might influence and contribute to a Neogene uplift of Southern Norway.
NASA Astrophysics Data System (ADS)
Jheng, Y.; Hung, S.; Zhou, Y.; Chang, Y.
2012-12-01
Surface wave travel-time tomography has been widely used as a powerful strategy to image shear wave velocity structure of the Earth's crust and upper mantle, providing comparable information other than body wave tomography. Traditionally, lateral variations of dispersive phase velocities are first obtained at multiple frequencies and then used to invert for shear wave velocity with 1-D depth-dependent sensitivity kernels. However, this approach runs short on considering the directional- and depth-dependence of scattering while surface wave propagating through laterally heterogeneous Earth. To refrain from these shortcomings, we here provide a fully 3-D finite-frequency method based on the Born scattering theory formulated with surface wave mode summation, and apply it to regional fundamental Rayleigh wave travel-time tomography in central Tibet. Our data were collected from Project Hi-CLIMB, which deployed an N-S trending linear array of over 100 broadband seismic stations with a large aperture of 800 km and very dense spacing of ~3-8 km across the Lhasa and Qiangtang terranes during 2004-2005. We follow a standard procedure of ambient noise cross correlation to extract empirical Green's functions of fundamental Rayleigh waves at 10-33 s between station pairs. A multi-taper method is employed to measure the phase differences as a function of period between observed and synthetic Rayleigh waves as well as the corresponding sensitivity kernels for the measured phase delays to 3-D shear wave velocity perturbations in a spherically-symmetric model suitable for central Tibet. A wavelet-based, multi-scale parameterization is invoked in the tomographic inversion to deal with the intrinsically multi-scale nature of unevenly distributed data and resolve the structure with data-adaptive spectral and spatial resolutions. The preliminary result shows that to the north of the Banggong-Nujiang suture (BNS), the crustal shear wave velocity beneath the Qiangtang terrane is
Flynn, Cormac; Taberner, Andrew; Nielsen, Poul
2011-02-01
The complex mechanical properties of skin have been the subject of much study in recent years. Several experimental methods developed to measure the mechanical properties of skin in vivo, such as suction or torsion, are unable to measure skin's anisotropic characteristics. An experiment characterising the mechanical properties of in vivo human skin using a novel force-sensitive micro-robot is presented. The micro-robot applied in-plane deformations to the anterior forearm and the posterior upper arm. The behaviour of the skin in each area is highly nonlinear, anisotropic, and viscoelastic. The response of the upper arm skin is very dependent on the orientation of the arm. A finite element model consisting of an Ogden strain energy function and quasi-linear viscoelasticity was developed to simulate the experiments. An orthogonal initial stress field, representing the in vivo skin tension, was used as an additional model parameter. The model simulated the experiments accurately with an error-of-fit of 17.5% for the anterior lower forearm area, 6.5% for the anterior upper forearm and 9.3% for the posterior upper arm. The maximum in vivo tension in each area determined by the model was 6.2 Nm(-1) in the anterior lower forearm, 11.4 Nm(-1) in anterior upper forearm and 5.6 Nm(-1) in the posterior upper arm. The results also show that a finite element model with a neo-Hookean strain energy function cannot simulate the experiments with the same accuracy. PMID:20429025
Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures
NASA Technical Reports Server (NTRS)
Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.
2011-01-01
Detailed two-dimensional finite element analyses of the cross-sections of a model CVI (chemical vapor infiltrated) SiC/SiC (silicon carbide fiber in a silicon carbide matrix) ceramic matrix composites are performed. High resolution images of the cross-section of this composite material are generated using serial sectioning of the test specimens. These images are then used to develop very detailed finite element models of the cross-sections using the public domain software OOF2 (Object Oriented Analysis of Material Microstructures). Examination of these images shows that these microstructures have significant variability and irregularity. How these variabilities manifest themselves in the variability in effective properties as well as the stress distribution, damage initiation and damage progression is the overall objective of this work. Results indicate that even though the macroscopic stress-strain behavior of various sections analyzed is very similar, each section has a very distinct damage pattern when subjected to in-plane tensile loads and this damage pattern seems to follow the unique architectural and microstructural details of the analyzed sections.
Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures
NASA Technical Reports Server (NTRS)
Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.
2012-01-01
A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.
Test-Analysis Correlation and Finite Element Model Updating for Nonlinear Transient Dynamics
Hemez, F.M.; Doebling, S.W.
1999-02-08
This research aims at formulating criteria for measuring the correlation between test data and finite element results for nonlinear, transient dynamics. After reviewing the linear case and illustrating the limitations of modal-based updating when it is applied to nonlinear experimental data, simple time-domain, test-analysis correlation metrics are proposed. Two implementations are compared: the conventional least-squares technique and the Principal Component Decomposition that correlates subspaces rather than individual time-domain responses. Illustrations and discussions are provided using the LANL 8-DOF system, an experimental testbed for validating nonlinear data correlation and model updating techniques.
Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma
NASA Technical Reports Server (NTRS)
Osherovich, V. A.; Farrugia, C. J.; Burlaga, L. F.
1995-01-01
In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a polytropic relationship and reduce the set of ideal MHD equations to a single, second-order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue -- a one-dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index gamma and a dimensionless quantity kappa the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and gamma. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for gamma greater than 1 and all values of kappa, only oscillations are possible. For gamma less than 1, however, both oscillations and expansion are allowed. For gamma less than 1 and kappa below a critical value, the energy of the nonlinear oscillator determines whether the flux rope will oscillate or expand to infinity. For gamma less than 1 and kappa above critical, however, only expansion occurs. Thus by increasing kappa while keeping gamma fixed (less than 1), a phase transition occurs at kappa = kappa(sub critical) and the oscillatory mode disappears. We illustrate the above theoretical considerations by the example of a flux rope of constant field line twist evolving self-similarly. For this example, we present the full numerical MHD solution. In an appendix to the paper we catalogue all possible evolutions when (1) either the magnetic field or (2) the gas pressure decreases monotonically toward the axis. We find that in these cases
NASA Astrophysics Data System (ADS)
Lollino, Piernicola; Fazio, Nunzio Luciano; Vennari, Carmela; Parise, Mario
2015-04-01
In December 2013 a large landslide occurred along a clay slope located at the south-western outskirts of the Montescaglioso village (Basilicata, Southern Italy) as a consequence of intense and prolonged rainfalls that presumably caused a significant increment of the pore water pressures in the slope. The slope is formed of stiff clays belonging to the formation of the Subappennine Blue Clays, which are over-consolidated and characterized by medium plasticity. According to aerial photos dating back to 1950s, the slope was already affected by previous landslide processes, so that the examined landslide process can be classified as an occasional reactivation according to the well-known classification of Cruden & Varnes (1996). Also, during the last decades several man-made actions in the area resulted in strong changes in the original water surface network that could have played some role in the slope reactivation. Based on displacement data, obtained from a monitoring system installed few days after the phenomenon, and still in function, at present the landslide does not show relevant signs of activity. Preliminary 2-D and 3-D finite element analyses have been carried out to investigate the factors that controlled the mechanism of reactivation of the landslide. The numerical model has been setup based on the available topographical, geological and geomorphological information, the geotechnical properties of the involved soils and the information concerning the piezometric regime in the slope. The results indicate that the mobilized shear strength of the clays ranges between the typical post-peak and residual values for this type of material and confirmed that the strong increment of the pore water pressures in the slope induced by the exceptional rainfalls occurred in the previous days can be identified as the main triggering factor of the reactivation.
Baillie, D; St Aubin, J; Fallone, B; Steciw, S
2014-06-15
Purpose: To design a new compact S-band linac waveguide capable of producing a 10 MV x-ray beam, while maintaining the length (27.5 cm) of current 6 MV waveguides. This will allow higher x-ray energies to be used in our linac-MRI systems with the same footprint. Methods: Finite element software COMSOL Multiphysics was used to design an accelerator cavity matching one published in an experiment breakdown study, to ensure that our modeled cavities do not exceed the threshold electric fields published. This cavity was used as the basis for designing an accelerator waveguide, where each cavity of the full waveguide was tuned to resonate at 2.997 GHz by adjusting the cavity diameter. The RF field solution within the waveguide was calculated, and together with an electron-gun phase space generated using Opera3D/SCALA, were input into electron tracking software PARMELA to compute the electron phase space striking the x-ray target. This target phase space was then used in BEAM Monte Carlo simulations to generate percent depth doses curves for this new linac, which were then used to re-optimize the waveguide geometry. Results: The shunt impedance, Q-factor, and peak-to-mean electric field ratio were matched to those published for the breakdown study to within 0.1% error. After tuning the full waveguide, the peak surface fields are calculated to be 207 MV/m, 13% below the breakdown threshold, and a d-max depth of 2.42 cm, a D10/20 value of 1.59, compared to 2.45 cm and 1.59, respectively, for the simulated Varian 10 MV linac and brehmsstrahlung production efficiency 20% lower than a simulated Varian 10 MV linac. Conclusion: This work demonstrates the design of a functional 27.5 cm waveguide producing 10 MV photons with characteristics similar to a Varian 10 MV linac.
Ghasemi, Ehsan; Abedian, Alireza; Iranmanesh, Pedram; Khazaei, Saber
2015-01-01
Background: Osseointegration of dental implants is influenced by many biomechanical factors that may be related to stress distribution. The aim of this study was to evaluate the effect of type of luting agent on stress distribution in the bone surrounding implants, which support a three-unit fixed dental prosthesis (FDP) using finite element (FE) analysis. Materials and Methods: A 3D FE model of a three-unit FDP was designed replacing the maxillary first molar with maxillary second premolar and second molar as the abutments using CATIA V5R18 software and analyzed with ABAQUS/CAE 6.6 version. The model was consisted of 465108 nodes and 86296 elements and the luting agent thickness was considered 25 μm. Three load conditions were applied on eight points in each functional cusp in horizontal (57.0 N), vertical (200.0 N) and oblique (400.0 N, θ = 120°) directions. Five different luting agents were evaluated. All materials were assumed to be linear elastic, homogeneous, time independent and isotropic. Results: For all luting agent types, the stress distribution pattern in the cortical bone, connectors, implant and abutment regions was almost uniform among the three loads. Furthermore, the maximum von Mises stress of the cortical bone was at the palatal side of second premolar. Likewise, the maximum von Mises stress in the connector region was in the top and bottom of this part. Conclusion: Luting agents transfer the load to cortical bone and different types of luting agents do not affect the pattern of load transfer. PMID:25709676
Boukazouha, F; Poulin-Vittrant, G; Tran-Huu-Hue, L P; Bavencoffe, M; Boubenider, F; Rguiti, M; Lethiecq, M
2015-07-01
This article is dedicated to the study of Piezoelectric Transformers (PTs), which offer promising solutions to the increasing need for integrated power electronics modules within autonomous systems. The advantages offered by such transformers include: immunity to electromagnetic disturbances; ease of miniaturisation for example, using conventional micro fabrication processes; and enhanced performance in terms of voltage gain and power efficiency. Central to the adequate description of such transformers is the need for complex analytical modeling tools, especially if one is attempting to include combined contributions due to (i) mechanical phenomena owing to the different propagation modes which differ at the primary and secondary sides of the PT; and (ii) electrical phenomena such as the voltage gain and power efficiency, which depend on the electrical load. The present work demonstrates an original one-dimensional (1D) analytical model, dedicated to a Rosen-type PT and simulation results are successively compared against that of a three-dimensional (3D) Finite Element Analysis (COMSOL Multiphysics software) and experimental results. The Rosen-type PT studied here is based on a single layer soft PZT (P191) with corresponding dimensions 18 mm × 3 mm × 1.5 mm, which operated at the second harmonic of 176 kHz. Detailed simulational and experimental results show that the presented 1D model predicts experimental measurements to within less than 10% error of the voltage gain at the second and third resonance frequency modes. Adjustment of the analytical model parameters is found to decrease errors relative to experimental voltage gain to within 1%, whilst a 2.5% error on the output admittance magnitude at the second resonance mode were obtained. Relying on the unique assumption of one-dimensionality, the present analytical model appears as a useful tool for Rosen-type PT design and behavior understanding. PMID:25753623
NASA Astrophysics Data System (ADS)
Wang, Shuai; Wang, Yu; Zi, Yanyang; He, Zhengjia
2015-12-01
A generalized and efficient model for rotating anisotropic rotor-bearing systems is presented in this paper with full considerations of the system's anisotropy in stiffness, inertia and damping. Based on the 3D finite element model and the model order reduction method, the effects of anisotropy in shaft and bearings on the forced response and whirling of anisotropic rotor-bearing systems are systematically investigated. First, the coefficients of journal bearings are transformed from the fixed frame to the rotating one. Due to the anisotropy in shaft and bearings, the motion is governed by differential equations with periodically time-variant coefficients. Then, a free-interface complex component mode synthesis (CMS) method is employed to generate efficient reduced-order models (ROM) for the periodically time-variant systems. In order to solve the obtained equations, a variant of Hill's method for systems with multiple harmonic excitations is developed. Four dimensionless parameters are defined to quantify the types and levels of anisotropy of bearings. Finally, the effects of the four types of anisotropy on the forced response and whirl orbits are studied. Numerical results show that the anisotropy of bearings in stiffness splits the sole resonant peak into two isolated ones, but the anisotropy of bearings in damping coefficients mainly affect the response amplitudes. Moreover, the whirl orbits become much more complex when the shaft and bearings are both anisotropic. In addition, the cross-coupling stiffness coefficients of bearings significantly affect the dynamic behaviors of the systems and cannot be neglected, though they are often much smaller than the principle stiffness terms.
NASA Astrophysics Data System (ADS)
Arjunan, A.; Wang, C. J.; Yahiaoui, K.; Mynors, D. J.; Morgan, T.; Nguyen, V. B.; English, M.
2014-11-01
Building standards incorporating quantitative acoustical criteria to ensure adequate sound insulation are now being implemented. Engineers are making great efforts to design acoustically efficient double-wall structures. Accordingly, efficient simulation models to predict the acoustic insulation of double-leaf wall structures are needed. This paper presents the development of a numerical tool that can predict the frequency dependent sound reduction index R of stud based double-leaf walls at one-third-octave band frequency range. A fully vibro-acoustic 3D model consisting of two rooms partitioned using a double-leaf wall, considering the structure and acoustic fluid coupling incorporating the existing fluid and structural solvers are presented. The validity of the finite element (FE) model is assessed by comparison with experimental test results carried out in a certified laboratory. Accurate representation of the structural damping matrix to effectively predict the R values are studied. The possibilities of minimising the simulation time using a frequency dependent mesh model was also investigated. The FEA model presented in this work is capable of predicting the weighted sound reduction index Rw along with A-weighted pink noise C and A-weighted urban noise Ctr within an error of 1 dB. The model developed can also be used to analyse the acoustically induced frequency dependent geometrical behaviour of the double-leaf wall components to optimise them for best acoustic performance. The FE modelling procedure reported in this paper can be extended to other building components undergoing fluid-structure interaction (FSI) to evaluate their acoustic insulation.
COYOTE: a finite-element computer program for nonlinear heat-conduction problems
Gartling, D.K.
1982-10-01
COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program.
Nonlinear wave propagation using three different finite difference schemes (category 2 application)
NASA Technical Reports Server (NTRS)
Pope, D. Stuart; Hardin, J. C.
1995-01-01
Three common finite difference schemes are used to examine the computation of one-dimensional nonlinear wave propagation. The schemes are studied for their responses to numerical parameters such as time step selection, boundary condition implementation, and discretization of governing equations. The performance of the schemes is compared and various numerical phenomena peculiar to each is discussed.
A hybrid symbolic/finite-element algorithm for solving nonlinear optimal control problems
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1991-01-01
The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.
Finite difference time domain calculation of transients in antennas with nonlinear loads
NASA Technical Reports Server (NTRS)
Luebbers, Raymond J.; Beggs, John H.; Kunz, Karl S.; Chamberlin, Kent
1991-01-01
Determining transient electromagnetic fields in antennas with nonlinear loads is a challenging problem. Typical methods used involve calculating frequency domain parameters at a large number of different frequencies, then applying Fourier transform methods plus nonlinear equation solution techniques. If the antenna is simple enough so that the open circuit time domain voltage can be determined independently of the effects of the nonlinear load on the antennas current, time stepping methods can be applied in a straightforward way. Here, transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain (FDTD) methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case, the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets, including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.
NASA Astrophysics Data System (ADS)
Boehm, Holger F.; Link, Thomas M.; Monetti, Roberto A.; Mueller, Dirk; Rummeny, Ernst J.; Raeth, Christoph W.
2005-04-01
Osteoporosis is a metabolic bone disease leading to de-mineralization and increased risk of fracture. The two major factors that determine the biomechanical competence of bone are the degree of mineralization and the micro-architectural integrity. Today, modern imaging modalities (high resolution MRI, micro-CT) are capable of depicting structural details of trabecular bone tissue. From the image data, structural properties obtained by quantitative measures are analysed with respect to the presence of osteoporotic fractures of the spine (in-vivo) or correlated with biomechanical strength as derived from destructive testing (in-vitro). Fairly well established are linear structural measures in 2D that are originally adopted from standard histo-morphometry. Recently, non-linear techniques in 2D and 3D based on the scaling index method (SIM), the standard Hough transform (SHT), and the Minkowski Functionals (MF) have been introduced, which show excellent performance in predicting bone strength and fracture risk. However, little is known about the performance of the various parameters with respect to monitoring structural changes due to progression of osteoporosis or as a result of medical treatment. In this contribution, we generate models of trabecular bone with pre-defined structural properties which are exposed to simulated osteoclastic activity. We apply linear and non-linear texture measures to the models and analyse their performance with respect to detecting architectural changes. This study demonstrates, that the texture measures are capable of monitoring structural changes of complex model data. The diagnostic potential varies for the different parameters and is found to depend on the topological composition of the model and initial "bone density". In our models, non-linear texture measures tend to react more sensitively to small structural changes than linear measures. Best performance is observed for the 3rd and 4th Minkowski Functionals and for the scaling
Large scale nonlinear numerical optimal control for finite element models of flexible structures
NASA Technical Reports Server (NTRS)
Shoemaker, Christine A.; Liao, Li-Zhi
1990-01-01
This paper discusses the development of large scale numerical optimal control algorithms for nonlinear systems and their application to finite element models of structures. This work is based on our expansion of the optimal control algorithm (DDP) in the following steps: improvement of convergence for initial policies in non-convex regions, development of a numerically accurate penalty function method approach for constrained DDP problems, and parallel processing on supercomputers. The expanded constrained DDP algorithm was applied to the control of a four-bay, two dimensional truss with 12 soft members, which generates geometric nonlinearities. Using an explicit finite element model to describe the structural system requires 32 state variables and 10,000 time steps. Our numerical results indicate that for constrained or unconstrained structural problems with nonlinear dynamics, the results obtained by our expanded constrained DDP are significantly better than those obtained using linear-quadratic feedback control.
Shestakov, A I; Milovich, J L; Noy, A
2002-03-01
The nonlinear Poisson-Boltzmann (PB) equation is solved using Newton-Krylov iterations coupled with pseudo-transient continuation. The PB potential is used to compute the electrostatic energy and evaluate the force on a user-specified contour. The PB solver is embedded in a existing, 3D, massively parallel, unstructured-grid, finite element code. Either Dirichlet or mixed boundary conditions are allowed. The latter specifies surface charges, approximates far-field conditions, or linearizes conditions "regulating" the surface charge. Stability and robustness are proved using results for backward Euler differencing of diffusion equations. Potentials and energies of charged spheres and plates are computed and results compared to analysis. An approximation to the potential of the nonlinear, spherical charge is derived by combining two analytic formulae. The potential and force due to a conical probe interacting with a flat plate are computed for two types of boundary conditions: constant potential and constant charge. The second case is compared with direct force measurements by chemical force microscopy. The problem is highly nonlinear-surface potentials of the linear and nonlinear PB equations differ by over an order of magnitude. Comparison of the simulated and experimentally measured forces shows that approximately half of the surface carboxylic acid groups, of density 1/(0.2 nm2), ionize in the electrolyte implying surface charges of 0.4 C/m2, surface potentials of 0.27 V, and a force of 0.6 nN when the probe and plate are 8.7 nm apart. PMID:16290441
Nonlinear stress analysis of titanium implants by finite element method.
Nagasawa, Sakae; Hayano, Keigo; Niino, Tooru; Yamakura, Kazunori; Yoshida, Takamitsu; Mizoguchi, Toshihide; Terashima, Nobuyosi; Tamura, Kaoru; Ito, Michio; Yagasaki, Hiroshi; Kubota, Osamu; Yoshimura, Masayuki
2008-07-01
With use of dental implants on the rise, there is also a tandem increase in the number of implant fracture reports. To the end of investigating the stress occurring in implants, elasticity and plasticity analyses were performed using the finite element method. The following results were obtained: (1) With one-piece type of implants of 3.3 mm diameter, elasticity analysis showed that after applying 500 N in a 45-degree direction, stress exceeding 500 MPa which is the proof stress of grade 4 pure titanium - occurred. This suggested the possibility of fatigue destruction due to abnormal occlusal force, such as during bruxism. (2) With two-piece type of implants that can tolerate vertical loading of 5,000 N, plasticity analysis suggested the possibility of screw area fracture after applying 500 N in a 45-degree direction. (3) On the combined use of an abutment and a fixture from different manufacturers, fracture destruction of even Ti-6Al-4V, which has a high degree of strength, was predicted. PMID:18833779
Research of carbon composite material for nonlinear finite element method
NASA Astrophysics Data System (ADS)
Kim, Jung Ho; Garg, Mohit; Kim, Ji Hoon
2011-11-01
Works on the absorption of collision energy in the structural members are carried out widely with various material and cross-sections. And, with ever increasing safety concerns, they are presently applied in various fields including railroad trains, air crafts and automobiles. In addition to this, problem of lighting structural members became important subject by control of exhaust gas emission, fuel economy and energy efficiency. CFRP(Carbon Fiber Reinforced Plastics) usually is applying the two primary structural members because of different result each design parameter as like stacking thickness, stacking angle, moisture absorption ect. We have to secure the data for applying primary structural members. But it always happens to test design parameters each for securing the data. So, it has much more money and time. We can reduce the money and the time, if can ensure the CFRP material properties each design parameters. In this study, we experiment the coupon test each tension, compression and shear using CFRP prepreg sheet and simulate non-linear analyze at the sources - test result, Caron longitudinal modulus and matrix poisson's ratio using GENOAMQC is specialized at Composite analysis. And then we predict the result that specimen manufacture changing stacking angle and experiment in such a way of test method using GENOA-MCQ.
Research of carbon composite material for nonlinear finite element method
NASA Astrophysics Data System (ADS)
Kim, Jung Ho; Garg, Mohit; Kim, Ji Hoon
2012-04-01
Works on the absorption of collision energy in the structural members are carried out widely with various material and cross-sections. And, with ever increasing safety concerns, they are presently applied in various fields including railroad trains, air crafts and automobiles. In addition to this, problem of lighting structural members became important subject by control of exhaust gas emission, fuel economy and energy efficiency. CFRP(Carbon Fiber Reinforced Plastics) usually is applying the two primary structural members because of different result each design parameter as like stacking thickness, stacking angle, moisture absorption ect. We have to secure the data for applying primary structural members. But it always happens to test design parameters each for securing the data. So, it has much more money and time. We can reduce the money and the time, if can ensure the CFRP material properties each design parameters. In this study, we experiment the coupon test each tension, compression and shear using CFRP prepreg sheet and simulate non-linear analyze at the sources - test result, Caron longitudinal modulus and matrix poisson's ratio using GENOAMQC is specialized at Composite analysis. And then we predict the result that specimen manufacture changing stacking angle and experiment in such a way of test method using GENOA-MCQ.
Multiple-mode nonlinear free and forced vibrations of beams using finite element method
NASA Technical Reports Server (NTRS)
Mei, Chuh; Decha-Umphai, Kamolphan
1987-01-01
Multiple-mode nonlinear free and forced vibration of a beam is analyzed by the finite element method. The geometric nonlinearity is investigated. Inplane displacement and inertia (IDI) are also considered in the formulation. Harmonic force matrix is derived and explained. Nonlinear free vibration can be simply treated as a special case of the general forced vibration by setting the harmonic force matrix equal to zero. The effect of the higher modes is more pronouced for the clamped supported beam than the simply supported one. Beams without IDI yield more effect of the higher modes than the one with IDI. The effects of IDI are to reduce nonlinearity. For beams with end supports restrained from axial movement (immovable cases), only the hardening type nonlinearity is observed. However, beams of small slenderness ratio (L/R = 20) with movable end supports, the softening type nonlinearity is found. The concentrated force case yields a more severe response than the uniformly distributed force case. Finite element results are in good agreement with the solution of simple elliptic response, harmonic balance method, and Runge-Kutte method and experiment.
Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction
NASA Astrophysics Data System (ADS)
Upadrashta, Deepesh; Yang, Yaowen
2015-04-01
Piezoelectric energy harvesting from ambient vibrations is a potential technology for powering wireless sensors and low power electronic devices. The conventional linear harvesters suffer from narrow operational bandwidth. Many attempts have been made especially using the magnetic interaction to broaden the bandwidth of harvesters. The finite element (FE) modeling has been used only for analyzing the linear harvesters in the literature. The main difficulties in extending the FE modeling to analyze the nonlinear harvesters involving magnetic interaction are developing the mesh needed for magnetic interaction in dynamic problems and the high demand on computational resource needed for solving the coupled electrical-mechanical-magnetic problem. In this paper, an innovative method is proposed to model the magnetic interaction without inclusion of the magnetic module. The magnetic force is modeled using the nonlinear spring element available in ANSYS finite element analysis (FEA) package, thus simplifying the simulation of nonlinear piezoelectric energy harvesters as an electromechanically coupled problem. Firstly, an FE model of a monostable nonlinear harvester with cantilever configuration is developed and the results are validated with predictions from the theoretical model. Later, the proposed technique of FE modeling is extended to a complex 2-degree of freedom nonlinear energy harvester for which an accurate analytical model is difficult to derive. The performance predictions from FEA are compared with the experimental results. It is concluded that the proposed modeling technique is able to accurately analyze the behavior of nonlinear harvesters with magnetic interaction.
Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan
2016-01-01
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740
NASA Technical Reports Server (NTRS)
Lyell, M. J.; Zhang, L.
1994-01-01
The aspects of nonlinear behavior of a finite length liquid column is investigated with an emphasis on bridge dynamics. The primary objectives are to determine the nonlinear corrections to the interface shape of a naturally oscillating finite length liquid column and to determine the nonlinear corrections to the oscillation frequencies for various modes of oscillation. Application of the Lindstedt-Poincare expansion in conjunction with the domain perturbation techniques results in an hierarchical system of equations.
Huang, Huajun; Xiang, Chunling; Zeng, Canjun; Ouyang, Hanbin; Wong, Kelvin Kian Loong; Huang, Wenhua
2015-12-01
We improved the geometrical modeling procedure for fast and accurate reconstruction of orthopedic structures. This procedure consists of medical image segmentation, three-dimensional geometrical reconstruction, and assignment of material properties. The patient-specific orthopedic structures reconstructed by this improved procedure can be used in the virtual surgical planning, 3D printing of real orthopedic structures and finite element analysis. A conventional modeling consists of: image segmentation, geometrical reconstruction, mesh generation, and assignment of material properties. The present study modified the conventional method to enhance software operating procedures. Patient's CT images of different bones were acquired and subsequently reconstructed to give models. The reconstruction procedures were three-dimensional image segmentation, modification of the edge length and quantity of meshes, and the assignment of material properties according to the intensity of gravy value. We compared the performance of our procedures to the conventional procedures modeling in terms of software operating time, success rate and mesh quality. Our proposed framework has the following improvements in the geometrical modeling: (1) processing time: (femur: 87.16 ± 5.90 %; pelvis: 80.16 ± 7.67 %; thoracic vertebra: 17.81 ± 4.36 %; P < 0.05); (2) least volume reduction (femur: 0.26 ± 0.06 %; pelvis: 0.70 ± 0.47, thoracic vertebra: 3.70 ± 1.75 %; P < 0.01) and (3) mesh quality in terms of aspect ratio (femur: 8.00 ± 7.38 %; pelvis: 17.70 ± 9.82 %; thoracic vertebra: 13.93 ± 9.79 %; P < 0.05) and maximum angle (femur: 4.90 ± 5.28 %; pelvis: 17.20 ± 19.29 %; thoracic vertebra: 3.86 ± 3.82 %; P < 0.05). Our proposed patient-specific geometrical modeling requires less operating time and workload, but the orthopedic structures were generated at a higher rate of success as compared with the conventional method. It is expected to benefit the surgical planning of orthopedic
NASA Astrophysics Data System (ADS)
Zeumann, Stefanie; Hampel, Andrea
2015-04-01
Subduction of aseismic oceanic ridges causes considerable deformation of the forearc region. To investigate the role of ridge orientation relative to the margin and convergence direction on the style of forearc deformation, we developed a series of 3D finite-elemente models, in which a rigid oceanic plate carrying the model ridge subducts beneath a deformable forearc wedge. Experiments were carried out for angles of 30°, 60° and 90° between the ridge axis and the trench and for different convergence directions. In the experiments, in which the ridge axis is parallel to the convergence direction, the ridge is stationary; in all other experiments, the ridge migrates along the margin and thus affects different regions of the forearc. Our results show that the ridge indents and uplifts the forearc in all models. For obliquely subducting ridges the displacement and strain fields become highly asymmetric regardless if the ridge is stationary or migrates along the forearc. Only if the ridge is stationary and oriented perpendicular to the margin, the deformation is symmetric relative to the ridge axis. Stationary ridges show uplift only above the ridge tip, whereas a migrating ridge causes a wave of uplift above the leading flank of the ridge followed by subsidence above the trailing flank. Horizontal strain components show domains of both extension and shortening, with extension occurring above the ridge tip and shortening above the ridge flanks. To compare our results with natural case studies, we computed additional models reflecting the setting of the stationary Cocos Ridge subducting beneath southern Costa Rica and of the Nazca Ridge, which migrates along the Peruvian margin. The results of these adjusted models are in good agreement with field observations. For the model of the Cocos Ridge the highest degree of shortening occurs normal to the margin, which coincides with the location of a thrust belt in the forearc of Costa Rica with its maximum shortening inboard
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer. PMID
Ghosh, Sanjoy; Parashar, Tulasi N.
2015-04-15
The local k-space ratio of linear and nonlinear accelerations associated with a variety of initial conditions undergoing steady relaxation is investigated for the Hall–finite-Larmor-radius magnetohydrodynamics (MHD) system in the presence of a mean magnetic field. Building on a related study (Paper I) where it was shown that discrepancies exist between describing the global and local characterizations of the pure MHD system with mean magnetic field, we find regions of the Fourier space that are consistently dominated by linear acceleration and other regions that are consistently dominated by nonlinear acceleration, independent of the overall system's description as linear, weakly nonlinear, or turbulent. In general, dynamics within a certain angular range of the mean magnetic field direction are predominantly linear, while dynamics adjacent the Hall scales along the field-parallel direction and dynamics adjacent the finite Larmor radius scales in the field-perpendicular direction can become strongly nonlinear. The nonlinear influences are particularly significant as the plasma beta increases from unity to higher values.
Gartling, D.K.; Hogan, R.E.
1994-10-01
The theoretical and numerical background for the finite element computer program, COYOTE II, is presented in detail. COYOTE II is designed for the multi-dimensional analysis of nonlinear heat conduction problems and other types of diffusion problems. A general description of the boundary value problems treated by the program is presented. The finite element formulation and the associated numerical methods used in COYOTE II are also outlined. Instructions for use of the code are documented in SAND94-1179; examples of problems analyzed with the code are provided in SAND94-1180.
A general purpose nonlinear rigid body mass finite element for application to rotary wing dynamics
NASA Technical Reports Server (NTRS)
Hamilton, B. K.; Straub, F. K.; Ruzicka, G. C.
1991-01-01
The Second Generation Comprehensive Helicopter Analysis System employs the present formulation of the general-purpose nonlinear rigid body mass finite element, which represents the hub masses, blade tip masses, and pendulum vibration absorbers. The rigid body mass element has six degrees of freedom, and accounts for gravitational as well as dynamic effects. A consequence of deriving the element's equations from various physical principles is that, prior to the transformation which couples the rigid body mass element to the rotor blade finite element, the forces obtained for each element are fundamentally different; this is true notwithstanding the degrees-of-freedom of each element are parameterized using the same coordinates.
Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling
NASA Astrophysics Data System (ADS)
Komarov, Maxim; Pikovsky, Arkady
2015-08-01
We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles and disappears in the thermodynamic limit. For all considered setups, which include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.
Nonlinear Comparison of High-Order and Optimized Finite-Difference Schemes
NASA Technical Reports Server (NTRS)
Hixon, R.
1998-01-01
The effect of reducing the formal order of accuracy of a finite-difference scheme in order to optimize its high-frequency performance is investigated using the I-D nonlinear unsteady inviscid Burgers'equation. It is found that the benefits of optimization do carry over into nonlinear applications. Both explicit and compact schemes are compared to Tam and Webb's explicit 7-point Dispersion Relation Preserving scheme as well as a Spectral-like compact scheme derived following Lele's work. Results are given for the absolute and L2 errors as a function of time.
Adaptation of a program for nonlinear finite element analysis to the CDC STAR 100 computer
NASA Technical Reports Server (NTRS)
Pifko, A. B.; Ogilvie, P. L.
1978-01-01
The conversion of a nonlinear finite element program to the CDC STAR 100 pipeline computer is discussed. The program called DYCAST was developed for the crash simulation of structures. Initial results with the STAR 100 computer indicated that significant gains in computation time are possible for operations on gloval arrays. However, for element level computations that do not lend themselves easily to long vector processing, the STAR 100 was slower than comparable scalar computers. On this basis it is concluded that in order for pipeline computers to impact the economic feasibility of large nonlinear analyses it is absolutely essential that algorithms be devised to improve the efficiency of element level computations.
A new nonlinear finite volume scheme preserving positivity for diffusion equations
NASA Astrophysics Data System (ADS)
Sheng, Zhiqiang; Yuan, Guangwei
2016-06-01
In this paper we present a new nonlinear finite volume scheme preserving positivity for diffusion equations. The main feature of the scheme is the assumption that the values of auxiliary unknowns are nonnegative is avoided. Two nonnegative parameters are introduced to define a new nonlinear two-point flux, in which one point is the cell-center and the other is the midpoint of cell-edge. The final flux on the edge is obtained by the continuity of normal flux. Numerical results show that the accuracy of both solution and flux for our new scheme is superior to that of some existing monotone schemes.
A fast algorithm for nonlinear finite element analysis using equivalent magnetization current
NASA Astrophysics Data System (ADS)
Lee, Joon-Ho; Park, Il-Han; Kim, Dong-Hun; Lee, Ki-Sik
2002-05-01
A fast algorithm for iterative nonlinear finite element analysis is presented in this paper. The algorithm replaces updated permeability by an equivalent magnetization current and moves it to the source current term. Once the initial system matrix is decomposed in the LU form, the iterative procedure involves the trivial step of back-substitution from the LU form. Consequently, the computation time for the nonlinear analysis is greatly reduced. A numerical model of a cylindrical conductor enclosed with saturable iron is tested to validate the proposed algorithm. Numerical results are compared with those obtained using conventional Newton-Raphson algorithm in respect to accuracy and computational time.
MAGNUS-3D: Accelerator magnet calculations in 3-dimensions
NASA Astrophysics Data System (ADS)
Pissanetzky, S.
1988-12-01
MAGNUS-3D is a professional finite element code for nonlinear magnetic engineering. MAGNUS-3D can solve numerically any general problem of linear or nonlinear magnetostatics in three dimensions. The problem is formulated in a domain with Dirichlet, Neumann or periodic boundary conditions, that can contain any combination of conductors of any shape in space, nonlinear magnetic materials with magnetic properties specified by magnetization tables, and nonlinear permanent magnets with any given demagnetization curve. MAGNUS-3D uses the two-scalar-potentials formulation of Magnetostatics and the finite element method, has an automatic 3D mesh generator, and advanced post-processing features that include graphics on a variety of supported devices, tabulation, and calculation of design quantities required in Magnetic Engineering. MAGNUS-3D is a general purpose 3D code, but it has been extensively used for accelerator work and many special features required for accelerator engineering have been incorporated into the code. One of such features is the calculation of field harmonic coefficients averaged in the direction of the beam, so important for the design of magnet ends. Another feature is its ability to calculate line integrals of any field component along the direction of the beam, or plot the field as a function of the z coordinate. MAGNUS-3D has found applications to the design of accelerator magnets and spectrometers, steering magnets, wigglers and undulators for free electron lasers, microtrons and magnets for synchrotron light sources, as well as magnets for NMR and medical applications, recording heads and various magnetic devices. There are three more programs closely associated with MAGNUS-3D. MAGNUS-GKS is the graphical postprocessor for the package; it supports a numer of output devices, including color vector or bit map devices. WIRE is an independent program that can calculate the field produced by any configuration of electric conductors in space, at any
Finite element nonlinear flutter and fatigue life of 2-D panels with temperature effects
NASA Technical Reports Server (NTRS)
Mei, Chuh; Xue, David Y.
1991-01-01
A frequency domain method for two-dimensional nonlinear panel flutter with thermal effects obtained from a consistent finite element formulation is presented. The von Karman nonlinear strain-displacement relation is used to account for large deflections, and the quasi-steady first-order piston theory is employed for aerodynamic loading. The finite element frequency domain results are compared with analytical time domain solutions. In a limit-cycle motion, the panel frequency and stress can be determined, thus fatigue life can be predicted. The influence of temperature and dynamic pressure on panel fatigue life is presented. An endurance dynamic pressure can be established at a given temperature from the present method.
Finite element modelling of non-linear magnetic circuits using Cosmic NASTRAN
NASA Technical Reports Server (NTRS)
Sheerer, T. J.
1986-01-01
The general purpose Finite Element Program COSMIC NASTRAN currently has the ability to model magnetic circuits with constant permeablilities. An approach was developed which, through small modifications to the program, allows modelling of non-linear magnetic devices including soft magnetic materials, permanent magnets and coils. Use of the NASTRAN code resulted in output which can be used for subsequent mechanical analysis using a variation of the same computer model. Test problems were found to produce theoretically verifiable results.
Jammazi, Chaker
2009-03-05
The paper gives Lyapunov type sufficient conditions for partial finite-time and asymptotic stability in which some state variables converge to zero while the rest converge to constant values that possibly depend on the initial conditions. The paper then presents partially asymptotically stabilizing controllers for many nonlinear control systems for which continuous asymptotically stabilizing (in the usual sense) controllers are known not to exist.
Properties of finite difference models of non-linear conservative oscillators
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1988-01-01
Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.
Hou, Gary Y.; Luo, Jianwen; Marquet, Fabrice; Maleke, Caroline; Vappou, Jonathan; Konofagou, Elisa E.
2014-01-01
Harmonic Motion Imaging for Focused Ultrasound (HMIFU) is a novel high-intensity focused ultrasound (HIFU) therapy monitoring method with feasibilities demonstrated in vitro, ex vivo and in vivo. Its principle is based on Amplitude-modulated (AM) - Harmonic Motion Imaging (HMI), an oscillatory radiation force used for imaging the tissue mechanical response during thermal ablation. In this study, a theoretical framework of HMIFU is presented, comprising a customized nonlinear wave propagation model, a finite-element (FE) analysis module, and an image-formation model. The objective of this study is to develop such a framework in order to 1) assess the fundamental performance of HMIFU in detecting HIFU lesions based on the change in tissue apparent elasticity, i.e., the increasing Young's modulus, and the HIFU lesion size with respect to the HIFU exposure time and 2) validate the simulation findings ex vivo. The same HMI and HMIFU parameters as in the experimental studies were used, i.e., 4.5-MHz HIFU frequency and 25 Hz AM frequency. For a lesion-to-background Young's modulus ratio of 3, 6, and 9, the FE and estimated HMI displacement ratios were equal to 1.83, 3.69, 5.39 and 1.65, 3.19, 4.59, respectively. In experiments, the HMI displacement followed a similar increasing trend of 1.19, 1.28, and 1.78 at 10-s, 20-s, and 30-s HIFU exposure, respectively. In addition, moderate agreement in lesion size growth was also found in both simulations (16.2, 73.1 and 334.7 mm2) and experiments (26.2, 94.2 and 206.2 mm2). Therefore, the feasibility of HMIFU for HIFU lesion detection based on the underlying tissue elasticity changes was verified through the developed theoretical framework, i.e., validation of the fundamental performance of the HMIFU system for lesion detection, localization and quantification, was demonstrated both theoretically and ex vivo. PMID:22036637
Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint
Wang, Q.; Sprague, M. A.; Jonkman, J.; Johnson, N.
2014-01-01
This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context of LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.
Geometrically non-linear vibration of spinning structures by finite element method
NASA Astrophysics Data System (ADS)
Leung, A. Y. T.; Fung, T. C.
1990-05-01
The geometrically non-linear steady state vibration of spinning structures is studied. Full flap-lag-torsional gyroscopic coupling effects are considered. The non-linearity arises mainly from the non-linear axial strain-displacement relation. The equations of motion are derived from Lagrangian equations. Spatial discretization is achieved by the finite element method and steady state nodal displacements are expanded into Fourier series. The harmonic balance method gives a set of non-linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns. The non-linear algebraic equations are solved by a Newtonian algorithm iteratively. The importance of the conditions of completeness and balanceability in choosing the number of harmonic terms to be used is discussed. General frame structures with arbitrary orientation in a rotating frame can be investigated by the present method. Rotating blades and shafts are treated as special cases. Examples of a rotating ring with different orientations are given. The non-linear amplitude-frequency relation can be constructed parametrically.
Distributed robust finite-time nonlinear consensus protocols for multi-agent systems
NASA Astrophysics Data System (ADS)
Zuo, Zongyu; Tie, Lin
2016-04-01
This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.
NASA Astrophysics Data System (ADS)
Bouklas, Nikolaos; Landis, Chad M.; Huang, Rui
2015-06-01
Hydrogels are capable of coupled mass transport and large deformation in response to external stimuli. In this paper, a nonlinear, transient finite element formulation is presented for initial boundary value problems associated with swelling and deformation of hydrogels, based on a nonlinear continuum theory that is consistent with classical theory of linear poroelasticity. A mixed finite element method is implemented with implicit time integration. The incompressible or nearly incompressible behavior at the initial stage imposes a constraint to the finite element discretization in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for stability of the mixed method, similar to linear poroelasticity as well as incompressible elasticity and Stokes flow; failure to choose an appropriate discretization would result in locking and numerical oscillations in transient analysis. To demonstrate the numerical method, two problems of practical interests are considered: constrained swelling and flat-punch indentation of hydrogel layers. Constrained swelling may lead to instantaneous surface instability for a soft hydrogel in a good solvent, which can be regulated by assuming a stiff surface layer. Indentation relaxation of hydrogels is simulated beyond the linear regime under plane strain conditions, in comparison with two elastic limits for the instantaneous and equilibrium states. The effects of Poisson's ratio and loading rate are discussed. It is concluded that the present finite element method is robust and can be extended to study other transient phenomena in hydrogels.
Finite dimensional approximation of a class of constrained nonlinear optimal control problems
NASA Technical Reports Server (NTRS)
Gunzburger, Max D.; Hou, L. S.
1994-01-01
An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.
Dynamic Analysis of Flexible Slider-Crank Mechanisms with Non-Linear Finite Element Method
NASA Astrophysics Data System (ADS)
CHEN, J.-S.; HUANG, C.-L.
2001-09-01
Previous research in finite element formulation of flexible mechanisms usually neglected high order terms in the strain-energy function. In particular, the quartic term of the displacement gradient is always neglected due to the common belief that it is not important in the dynamic analysis. In this paper, we show that this physical intuition is not always valid. By retaining all the high order terms in the strain-energy function the equations of motion naturally become non-linear, which can then be solved by the Newmark method. In the low-speed range it is found that the dynamic responses predicted by non-linear and linear approaches indeed make no significant difference. However, when the rotation speed increases up to about one-fifth of the fundamental bending natural frequency of the connecting rod, simplified approaches begin to incur noticeable error. Specifically, for a connecting rod with a slenderness ratio of 0·01 the conventional simplified approaches overestimate the vibration amplitude almost 10-fold when the rotation speed is comparable to the fundamental natural frequency of the connecting rod. Therefore, non-linear finite element formulation taking into account the complete non-linear strain is needed in analyzing high-speed flexible mechnisms with slender links.
NASA Astrophysics Data System (ADS)
Nanda, Namita; Bandyopadhyay, J. N.
2009-08-01
The nonlinear transient response of composite shells with/without cutouts and initial geometric imperfection is investigated using the finite element method. The present formulation considers doubly curved shells incorporating von Kármán type nonlinear strains into the first order shear deformation theory. The analysis is carried out using quadratic C0 eight-noded isoparametric element. The governing nonlinear equations are solved by using the Newmark average acceleration method in the time integration in conjunction with modified Newton-Raphson iteration scheme. The validity of the model is demonstrated by comparing the present results with those available in the literature. Parametric studies are carried out varying the radius of curvature to width ratio and amplitude of initial geometric imperfection of laminated composite cylindrical, spherical and hyperbolic paraboloid shells with/without cutouts.
Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems
D'Aguanno, G.; Mattiucci, N.; Larciprete, M. C.; Belardini, A.; Fazio, E.; Centini, M.; Sibilia, C.; Bloemer, M. J.; Buganov, O.
2010-01-15
We have investigated and experimentally demonstrated the applicability of the Bloch vector for one-dimensional, nonlinear, finite, dissipative systems. The case studied is the second harmonic generation from metallodielectric multilayer filters. In particular, we have applied the Bloch vector analysis to Ag/Ta{sub 2}O{sub 5} thin-film multilayer samples and shown the importance of the phase matching calculated through the Bloch vector. The nonlinear coefficients extracted from experimental results are consistent with previous studies. Nowadays, metal-based nanostructures play a fundamental role in nonlinear nanophotonics and nanoplasmonics. Our results clearly suggest that even in these forefront fields the Bloch vector continues to play an essential role.
Characterizing two-timescale nonlinear dynamics using finite-time Lyapunov exponents and subspaces
NASA Astrophysics Data System (ADS)
Mease, K. D.; Topcu, U.; Aykutluğ, E.; Maggia, M.
2016-07-01
Finite-time Lyapunov exponents and subspaces are used to define and diagnose boundary-layer type, two-timescale behavior in the tangent linear dynamics and to determine the associated manifold structure in the flow of a finite-dimensional nonlinear autonomous dynamical system. Two-timescale behavior is characterized by a slow-fast splitting of the tangent bundle for a state space region. The slow-fast splitting is defined using finite-time Lyapunov exponents and vectors, guided by the asymptotic theory of partially hyperbolic sets, with important modifications for the finite-time case; for example, finite-time Lyapunov analysis relies more heavily on the Lyapunov vectors due to their relatively fast convergence compared to that of the corresponding exponents. The splitting is used to characterize and locate points approximately on normally hyperbolic center manifolds via tangency conditions for the vector field. Determining manifolds from tangent bundle structure is more generally applicable than approaches, such as the singular perturbation method, that require special normal forms or other a priori knowledge. The use, features, and accuracy of the approach are illustrated via several detailed examples.
Hoffman, E.L.; Ammerman, D.J.
1993-08-01
A series of tests investigating dynamic pulse buckling of a cylindrical shell under axial impact is compared to several finite element simulations of the event. The purpose of the study is to compare the performance of the various analysis codes and element types with respect to a problem which is applicable to radioactive material transport packages, and ultimately to develop a benchmark problem to qualify finite element analysis codes for the transport package design industry.
NASA Technical Reports Server (NTRS)
Przekop, Adam; Wu, Hsi-Yung T.; Shaw, Peter
2014-01-01
The Environmentally Responsible Aviation Project aims to develop aircraft technologies enabling significant fuel burn and community noise reductions. Small incremental changes to the conventional metallic alloy-based 'tube and wing' configuration are not sufficient to achieve the desired metrics. One of the airframe concepts that might dramatically improve aircraft performance is a composite-based hybrid wing body configuration. Such a concept, however, presents inherent challenges stemming from, among other factors, the necessity to transfer wing loads through the entire center fuselage section which accommodates a pressurized cabin confined by flat or nearly flat panels. This paper discusses a nonlinear finite element analysis of a large-scale test article being developed to demonstrate that the Pultruded Rod Stitched Efficient Unitized Structure concept can meet these challenging demands of the next generation airframes. There are specific reasons why geometrically nonlinear analysis may be warranted for the hybrid wing body flat panel structure. In general, for sufficiently high internal pressure and/or mechanical loading, energy related to the in-plane strain may become significant relative to the bending strain energy, particularly in thin-walled areas such as the minimum gage skin extensively used in the structure under analysis. To account for this effect, a geometrically nonlinear strain-displacement relationship is needed to properly couple large out-of-plane and in-plane deformations. Depending on the loading, this nonlinear coupling mechanism manifests itself in a distinct manner in compression- and tension-dominated sections of the structure. Under significant compression, nonlinear analysis is needed to accurately predict loss of stability and postbuckled deformation. Under significant tension, the nonlinear effects account for suppression of the out-of-plane deformation due to in-plane stretching. By comparing the present results with the previously
NASA Astrophysics Data System (ADS)
Yamasaki, Tadashi; Houseman, Gregory; Hamling, Ian; Postek, Elek
2010-05-01
We have developed a new parallelized 3-D numerical code, OREGANO_VE, for the solution of the general visco-elastic problem in a rectangular block domain. The mechanical equilibrium equation is solved using the finite element method for a (non-)linear Maxwell visco-elastic rheology. Time-dependent displacement and/or traction boundary conditions can be applied. Matrix assembly is based on a tetrahedral element defined by 4 vertex nodes and 6 nodes located at the midpoints of the edges, and within which displacement is described by a quadratic interpolation function. For evaluating viscoelastic relaxation, an explicit time-stepping algorithm (Zienkiewicz and Cormeau, Int. J. Num. Meth. Eng., 8, 821-845, 1974) is employed. We test the accurate implementation of the OREGANO_VE by comparing numerical and analytic (or semi-analytic half-space) solutions to different problems in a range of applications: (1) equilibration of stress in a constant density layer after gravity is switched on at t = 0 tests the implementation of spatially variable viscosity and non-Newtonian viscosity; (2) displacement of the welded interface between two blocks of differing viscosity tests the implementation of viscosity discontinuities, (3) displacement of the upper surface of a layer under applied normal load tests the implementation of time-dependent surface tractions (4) visco-elastic response to dyke intrusion (compared with the solution in a half-space) tests the implementation of all aspects. In each case, the accuracy of the code is validated subject to use of a sufficiently small time step, providing assurance that the OREGANO_VE code can be applied to a range of visco-elastic relaxation processes in three dimensions, including post-seismic deformation and post-glacial uplift. The OREGANO_VE code includes a capability for representation of prescribed fault slip on an internal fault. The surface displacement associated with large earthquakes can be detected by some geodetic observations
NASA Astrophysics Data System (ADS)
Otis, Collin; Ferrero, Pietro; Candler, Graham; Givi, Peyman
2013-11-01
The scalar filtered mass density function (SFMDF) methodology is implemented into the computer code US3D. This is an unstructured Eulerian finite volume hydrodynamic solver and has proven very effective for simulation of compressible turbulent flows. The resulting SFMDF-US3D code is employed for large eddy simulation (LES) on unstructured meshes. Simulations are conducted of subsonic and supersonic flows under non-reacting and reacting conditions. The consistency and the accuracy of the simulated results are assessed along with appraisal of the overall performance of the methodology. The SFMDF-US3D is now capable of simulating high speed flows in complex configurations.
NASA Technical Reports Server (NTRS)
Oden, J. T.
1976-01-01
Some results of studies of convergence and accuracy of finite element approximations of certain nonlinear problems encountered in finite elasticity are presented. A general technique for obtaining error bounds is also described together with an existence theorem. Numerical results obtained by solving a representative problem are also included.
3-D Cavern Enlargement Analyses
EHGARTNER, BRIAN L.; SOBOLIK, STEVEN R.
2002-03-01
Three-dimensional finite element analyses simulate the mechanical response of enlarging existing caverns at the Strategic Petroleum Reserve (SPR). The caverns are located in Gulf Coast salt domes and are enlarged by leaching during oil drawdowns as fresh water is injected to displace the crude oil from the caverns. The current criteria adopted by the SPR limits cavern usage to 5 drawdowns (leaches). As a base case, 5 leaches were modeled over a 25 year period to roughly double the volume of a 19 cavern field. Thirteen additional leaches where then simulated until caverns approached coalescence. The cavern field approximated the geometries and geologic properties found at the West Hackberry site. This enabled comparisons are data collected over nearly 20 years to analysis predictions. The analyses closely predicted the measured surface subsidence and cavern closure rates as inferred from historic well head pressures. This provided the necessary assurance that the model displacements, strains, and stresses are accurate. However, the cavern field has not yet experienced the large scale drawdowns being simulated. Should they occur in the future, code predictions should be validated with actual field behavior at that time. The simulations were performed using JAS3D, a three dimensional finite element analysis code for nonlinear quasi-static solids. The results examine the impacts of leaching and cavern workovers, where internal cavern pressures are reduced, on surface subsidence, well integrity, and cavern stability. The results suggest that the current limit of 5 oil drawdowns may be extended with some mitigative action required on the wells and later on to surface structure due to subsidence strains. The predicted stress state in the salt shows damage to start occurring after 15 drawdowns with significant failure occurring at the 16th drawdown, well beyond the current limit of 5 drawdowns.
Nonlinear bend stiffener analysis using a simple formulation and finite element method
NASA Astrophysics Data System (ADS)
Tong, Dong Jin; Low, Ying Min; Sheehan, John M.
2011-12-01
Flexible marine risers are commonly used in deepwater floating systems. Bend stiffeners are designed to protect flexible risers against excessive bending at the connection with the hull. The structure is usually analyzed as a cantilever beam subjected to an inclined point load. As deflections are large and the bend stiffener material exhibits nonlinear stress-strain characteristics, geometric and material nonlinearities are important considerations. A new approach has been developed to solve this nonlinear problem. Its main advantage is its simplicity; in fact the present method can be easily implemented on a spreadsheet. Finite element analysis using ABAQUS is performed to validate the method. Solid elements are used for the bend stiffener and flexible pipe. To simulate the near inextensibility of flexible risers, a simple and original idea of using truss elements is proposed. Through a set of validation studies, the present method is found to be in a good agreement with the finite element analysis. Further, parametric studies are performed by using both methods to identify the key parameters and phenomena that are most critical in design. The most important finding is that the common practice of neglecting the internal steel sleeve in the bend stiffener analysis is non-conservative and therefore needs to be reassessed.
A Finite Mixture of Nonlinear Random Coefficient Models for Continuous Repeated Measures Data.
Kohli, Nidhi; Harring, Jeffrey R; Zopluoglu, Cengiz
2016-09-01
Nonlinear random coefficient models (NRCMs) for continuous longitudinal data are often used for examining individual behaviors that display nonlinear patterns of development (or growth) over time in measured variables. As an extension of this model, this study considers the finite mixture of NRCMs that combine features of NRCMs with the idea of finite mixture (or latent class) models. The efficacy of this model is that it allows the integration of intrinsically nonlinear functions where the data come from a mixture of two or more unobserved subpopulations, thus allowing the simultaneous investigation of intra-individual (within-person) variability, inter-individual (between-person) variability, and subpopulation heterogeneity. Effectiveness of this model to work under real data analytic conditions was examined by executing a Monte Carlo simulation study. The simulation study was carried out using an R routine specifically developed for the purpose of this study. The R routine used maximum likelihood with the expectation-maximization algorithm. The design of the study mimicked the output obtained from running a two-class mixture model on task completion data. PMID:25925010
NASA Astrophysics Data System (ADS)
Wang, Dongwei
Recent research and development of adaptive materials, smart structures and structronic systems have opened a new era to aerospace and structural engineering. Effective control of these intelligent structures and systems using piezoelectric materials can enhance operation precision, accuracy and reliability. This research is to investigate the dynamics, vibration sensing and control of the geometrically nonlinear distributed piezothermoelastic structures subjected to the combined mechanical, electrical, and thermal excitations by the finite element method. Based on the layerwise constant shear angle theory, the curved hexahedral and triangular piezothermoelastic shell elements are proposed. The generic finite element formulations for vibration sensing and control analysis of nonlinear piezothermoelastic shell structures are derived based on the total Lagrangian virtual work principle. Dynamic system equations, equations of electric potential outputs, and feedback control forces are derived and discussed. The modified Newton-Raphson method is used for efficient dynamic analysis of the nonlinear piezothermoelastic structural systems. Different control algorithms are implemented. The feedback control forces generated from the distributed actuator can effectively enhance system damping and suppress system vibration via proper feedback control techniques. Comprehensive case studies are performed to evaluate the accuracy of the newly developed piezothermoelastic shell elements and to validate the finite element code. Dynamics and vibration sensing/control of nonlinear piezothermoelastic beam and plate systems are analyzed. Distributed piezoelectric films placed on the beam and plate structures respectively serving as sensor and actuators are discussed. The effect of geometric nonlinearity is to stiffen the beam and plate structures and the control effect becomes worse when geometric nonlinearity becomes significant. It shows that negative velocity control scheme is
NASA Technical Reports Server (NTRS)
Bartels, Robert E.; Scott, Robert C.; Allen, Timothy J.; Sexton, Bradley W.
2015-01-01
Considerable attention has been given in recent years to the design of highly flexible aircraft. The results of numerous studies demonstrate the significant performance benefits of strut-braced wing (SBW) and trussbraced wing (TBW) configurations. Critical aspects of the TBW configuration are its larger aspect ratio, wing span and thinner wings. These aspects increase the importance of considering fluid/structure and control system coupling. This paper presents high-fidelity Navier-Stokes simulations of the dynamic response of the flexible Boeing Subsonic Ultra Green Aircraft Research (SUGAR) truss-braced wing wind-tunnel model. The latest version of the SUGAR TBW finite element model (FEM), v.20, is used in the present simulations. Limit cycle oscillations (LCOs) of the TBW wing/strut/nacelle are simulated at angle-of-attack (AoA) values of -1, 0 and +1 degree. The modal data derived from nonlinear static aeroelastic MSC.Nastran solutions are used at AoAs of -1 and +1 degrees. The LCO amplitude is observed to be dependent on AoA. LCO amplitudes at -1 degree are larger than those at +1 degree. The LCO amplitude at zero degrees is larger than either -1 or +1 degrees. These results correlate well with both wind-tunnel data and the behavior observed in previous studies using linear aerodynamics. The LCO onset at zero degrees AoA has also been computed using unloaded v.20 FEM modes. While the v.20 model increases the dynamic pressure at which LCO onset is observed, it is found that the LCO onset at and above Mach 0.82 is much different than that produced by an earlier version of the FEM, v. 19.
Input-output finite-time stabilisation of nonlinear stochastic system with missing measurements
NASA Astrophysics Data System (ADS)
Song, Jun; Niu, Yugang; Jia, Tinggang
2016-09-01
This paper considers the problem of the input-output finite-time stabilisation for a class of nonlinear stochastic system with state-dependent noise. The phenomenon of the missing measurements may occur when state signals are transmitted via communication networks. An estimating method is proposed to compensate the lost state information. And then, a compensator-based controller is designed to ensure the input-output finite-time stochastic stability (IO-FTSS) of the closed-loop system. Some parameters-dependent sufficient conditions are derived and the corresponding solving approach is given. Finally, numerical simulations are provided to demonstrate the feasibility and effectiveness of the developed IO-FTSS scheme.
A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation
Banks, J W; Hittinger, J A
2009-11-24
Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.
NASA Astrophysics Data System (ADS)
Wang, Yajun; Liu, Yang; Li, Hong; Wang, Jinfeng
2016-03-01
In this article, a Galerkin finite element method combined with second-order time discrete scheme for finding the numerical solution of nonlinear time fractional Cable equation is studied and discussed. At time t_{k-α/2} , a second-order two step scheme with α -parameter is proposed to approximate the first-order derivative, and a weighted discrete scheme covering second-order approximation is used to approximate the Riemann-Liouville fractional derivative, where the approximate order is higher than the obtained results by the L1-approximation with order (2-α in the existing references. For the spatial direction, Galerkin finite element approximation is presented. The stability of scheme and the rate of convergence in L^2 -norm with O(Δ t^2+(1+Δ t^{-α})h^{m+1}) are derived in detail. Moreover, some numerical tests are shown to support our theoretical results.
Xu, Hao; Jagannathan, Sarangapani
2015-03-01
The stochastic optimal control of nonlinear networked control systems (NNCSs) using neuro-dynamic programming (NDP) over a finite time horizon is a challenging problem due to terminal constraints, system uncertainties, and unknown network imperfections, such as network-induced delays and packet losses. Since the traditional iteration or time-based infinite horizon NDP schemes are unsuitable for NNCS with terminal constraints, a novel time-based NDP scheme is developed to solve finite horizon optimal control of NNCS by mitigating the above-mentioned challenges. First, an online neural network (NN) identifier is introduced to approximate the control coefficient matrix that is subsequently utilized in conjunction with the critic and actor NNs to determine a time-based stochastic optimal control input over finite horizon in a forward-in-time and online manner. Eventually, Lyapunov theory is used to show that all closed-loop signals and NN weights are uniformly ultimately bounded with ultimate bounds being a function of initial conditions and final time. Moreover, the approximated control input converges close to optimal value within finite time. The simulation results are included to show the effectiveness of the proposed scheme. PMID:25720004
A three-dimensional robust nonlinear terminal guidance law with ISS finite-time convergence
NASA Astrophysics Data System (ADS)
Li, Guilin; Ji, Haibo
2016-05-01
This paper presents a novel three-dimensional nonlinear terminal guidance law with finite-time convergence for intercepting manoeuvring targets. Different from the usual method of decoupling the missile-target relative motion into two-dimensional planes, this law is designed via using the coupled dynamics. The guidance law is derived based on the theory of finite-time input-to-state stability (ISS), which needs no assumption of the linearisation and the estimation of target accelerations. Under this law, the line-of-sight angular rates can be stabilised to a small domain of convergence around zero in finite time. The convergence rate and convergence domain can be adjusted by changing the guidance parameters. First, a sufficient condition on finite-time ISS of the guidance system is given, and is subsequently used to design the guidance law. Finally, simulation results are provided to show that the proposed guidance law possesses fast convergence rate and strong robustness to target manoeuvres.
The solution of non-linear hyperbolic equation systems by the finite element method
NASA Technical Reports Server (NTRS)
Loehner, R.; Morgan, K.; Zienkiewicz, O. C.
1984-01-01
A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.
NASA Technical Reports Server (NTRS)
Schroeter, Jens; Wunsch, Carl
1986-01-01
The paper studies with finite difference nonlinear circulation models the uncertainties in interesting flow properties, such as western boundary current transport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies. Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.
A non-linear finite-element model of the newborn ear canal
Qi, Li; Liu, Hengjin; Lutfy, Justyn; Funnell, W. Robert J.; Daniel, Sam J.
2010-01-01
We present a three-dimensional non-linear finite-element model of a 22-day-old newborn ear canal. The geometry is based on a clinical X-ray CT scan. A non-linear hyperelastic constitutive law is applied to model large deformations. The Young’s modulus of the soft tissue is found to have a significant effect on the ear-canal volume change, which ranges from approximately 27% to 75% over the static-pressure range of ±3 kPa. The effects of Poisson’s ratio and of the ratio C10:C01 in the hyperelastic model are found to be small. The volume changes do not reach a plateau at high pressures, which implies that the newborn ear-canal wall would not be rigid in tympanometric measurements. The displacements and volume changes calculated from the model are compared with available experimental data. PMID:17225406
Nonlinear damping of a finite amplitude whistler wave due to modified two stream instability
Saito, Shinji; Nariyuki, Yasuhiro; Umeda, Takayuki
2015-07-15
A two-dimensional, fully kinetic, particle-in-cell simulation is used to investigate the nonlinear development of a parallel propagating finite amplitude whistler wave (parent wave) with a wavelength longer than an ion inertial length. The cross field current of the parent wave generates short-scale whistler waves propagating highly oblique directions to the ambient magnetic field through the modified two-stream instability (MTSI) which scatters electrons and ions parallel and perpendicular to the magnetic field, respectively. The parent wave is largely damped during a time comparable to the wave period. The MTSI-driven damping process is proposed as a cause of nonlinear dissipation of kinetic turbulence in the solar wind.
On nonlinear finite element analysis in single-, multi- and parallel-processors
NASA Technical Reports Server (NTRS)
Utku, S.; Melosh, R.; Islam, M.; Salama, M.
1982-01-01
Numerical solution of nonlinear equilibrium problems of structures by means of Newton-Raphson type iterations is reviewed. Each step of the iteration is shown to correspond to the solution of a linear problem, therefore the feasibility of the finite element method for nonlinear analysis is established. Organization and flow of data for various types of digital computers, such as single-processor/single-level memory, single-processor/two-level-memory, vector-processor/two-level-memory, and parallel-processors, with and without sub-structuring (i.e. partitioning) are given. The effect of the relative costs of computation, memory and data transfer on substructuring is shown. The idea of assigning comparable size substructures to parallel processors is exploited. Under Cholesky type factorization schemes, the efficiency of parallel processing is shown to decrease due to the occasional shared data, just as that due to the shared facilities.
Comparison of Finite Element Non-Linear Beam Random Response with Experimental Results
NASA Astrophysics Data System (ADS)
Chen, R. R.; Mei, C.; Wolfe, HF
1996-09-01
A finite element formulation combined with the equivalent linearization technique and normal mode method is developed for the non-linear random response of beams subjected to acoustic and thermal loads applied simultaneously. To validate the present formulation and solution procedure, results are compared with the classical continuum solution and the Fokker-Planck-Kolmogorov equation solution. Comparison is also made with experimental data for a pre-stretched clamped beam. Random responses of thermally buckled simply supported beam, clamped beam and simply supported-clamped beam are presented. The comparison of the present simultaneously loaded response with the existing sequentially loaded results shows a significant difference between them.
NASA Astrophysics Data System (ADS)
Chen, Ruixi; Mei, Chuh
1993-04-01
A finite element formulation combined with the equivalent linearization technique and the normal mode method is developed for the study of nonlinear random response of beams subjected to simultaneously applied acoustic and thermal loads. Examples include thermally buckled random response of simply supported beam, clamped-clamped beam and simply supported-clamped beam. To compare and validate the present formulation, results are compared with the solutions from existing sequential load method, and significant difference has been found. Results by classical continuum solution and the solution of Fokker-Planck-Kolmogorov equation are also derived and obtained for comparison.
Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
NASA Astrophysics Data System (ADS)
Li, Changpin; Yi, Qian; Chen, An
2016-07-01
In this article, finite difference methods with non-uniform meshes for solving nonlinear fractional differential equations are presented, where the non-equidistant stepsize is non-decreasing. The rectangle formula and trapezoid formula are proposed based on the non-uniform meshes. Combining the above two methods, we then establish the predictor-corrector scheme. The error and stability analysis are carefully investigated. At last, numerical examples are carried out to verify the theoretical analysis. Besides, the comparisons between non-uniform and uniform meshes are given, where the non-uniform meshes show the better performance when dealing with the less smooth problems.
NASA Technical Reports Server (NTRS)
Padovan, Joe
1987-01-01
In a three-part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modeled by fractional integrodifferential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating, as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator.
Simulation of Aircraft Landing Gears with a Nonlinear Dynamic Finite Element Code
NASA Technical Reports Server (NTRS)
Lyle, Karen H.; Jackson, Karen E.; Fasanella, Edwin L.
2000-01-01
Recent advances in computational speed have made aircraft and spacecraft crash simulations using an explicit, nonlinear, transient-dynamic, finite element analysis code more feasible. This paper describes the development of a simple landing gear model, which accurately simulates the energy absorbed by the gear without adding substantial complexity to the model. For a crash model, the landing gear response is approximated with a spring where the force applied to the fuselage is computed in a user-written subroutine. Helicopter crash simulations using this approach are compared with previously acquired experimental data from a full-scale crash test of a composite helicopter.
NASA Technical Reports Server (NTRS)
Jameson, A.
1976-01-01
A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.
NASA Astrophysics Data System (ADS)
Abbas, Ibrahim A.; Youssef, Hamdy M.
2012-07-01
In this article, a general finite element method (FEM) is proposed to analyze transient phenomena in a thermoelastic model in the context of the theory of generalized thermoelasticity with one relaxation time. The exact solution of the nonlinear model of the thermal shock problem of a generalized thermoelastic half-space of temperature-dependent materials exists only for very special and simple initial- and boundary problems. In view of calculating general problems, a numerical solution technique is to be used. For this reason, the FEM is chosen. The results for the temperature increment, the stress components, and the displacement component are illustrated graphically with some comparisons.
High Order Finite Volume Nonlinear Schemes for the Boltzmann Transport Equation
Bihari, B L; Brown, P N
2005-03-29
The authors apply the nonlinear WENO (Weighted Essentially Nonoscillatory) scheme to the spatial discretization of the Boltzmann Transport Equation modeling linear particle transport. The method is a finite volume scheme which ensures not only conservation, but also provides for a more natural handling of boundary conditions, material properties and source terms, as well as an easier parallel implementation and post processing. It is nonlinear in the sense that the stencil depends on the solution at each time step or iteration level. By biasing the gradient calculation towards the stencil with smaller derivatives, the scheme eliminates the Gibb's phenomenon with oscillations of size O(1) and reduces them to O(h{sup r}), where h is the mesh size and r is the order of accuracy. The current implementation is three-dimensional, generalized for unequally spaced meshes, fully parallelized, and up to fifth order accurate (WENO5) in space. For unsteady problems, the resulting nonlinear spatial discretization yields a set of ODE's in time, which in turn is solved via high order implicit time-stepping with error control. For the steady-state case, they need to solve the non-linear system, typically by Newton-Krylov iterations. There are several numerical examples presented to demonstrate the accuracy, non-oscillatory nature and efficiency of these high order methods, in comparison with other fixed-stencil schemes.
NASA Astrophysics Data System (ADS)
Astroza, Rodrigo; Ebrahimian, Hamed; Conte, Joel P.
2015-03-01
This paper describes a novel framework that combines advanced mechanics-based nonlinear (hysteretic) finite element (FE) models and stochastic filtering techniques to estimate unknown time-invariant parameters of nonlinear inelastic material models used in the FE model. Using input-output data recorded during earthquake events, the proposed framework updates the nonlinear FE model of the structure. The updated FE model can be directly used for damage identification and further used for damage prognosis. To update the unknown time-invariant parameters of the FE model, two alternative stochastic filtering methods are used: the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A three-dimensional, 5-story, 2-by-1 bay reinforced concrete (RC) frame is used to verify the proposed framework. The RC frame is modeled using fiber-section displacement-based beam-column elements with distributed plasticity and is subjected to the ground motion recorded at the Sylmar station during the 1994 Northridge earthquake. The results indicate that the proposed framework accurately estimate the unknown material parameters of the nonlinear FE model. The UKF outperforms the EKF when the relative root-mean-square error of the recorded responses are compared. In addition, the results suggest that the convergence of the estimate of modeling parameters is smoother and faster when the UKF is utilized.
Langerman, M.A.
1990-09-01
Steady-state modeling considerations for simulating the in situ vitrification (ISV) process are documented based upon the finite element numerical approach. Recommendations regarding boundary condition specifications and mesh discretization are presented. The effects of several parameters on the ISV process response are calculated and the results discussed. The parameters investigated include: (1) electrode depth, (2) ambient temperature, (3) supplied current, (4) electrical conductivity, (5) electrode separation, and (6) soil/waste characterization. 13 refs., 29 figs., 1 tab.
Not Available
1984-10-01
STEALTH is a family of computer codes that can be used to calculate a variety of physical processes in which the dynamic behavior of a continuum is involved. The version of STEALTH described in this volume is designed for calculations of fluid-structure interaction. This version of the program consists of a hydrodynamic version of STEALTH which has been coupled to a finite-element code, WHAMSE. STEALTH computes the transient response of the fluid continuum, while WHAMSE computes the transient response of shell and beam structures under external fluid loadings. The coupling between STEALTH and WHAMSE is performed during each cycle or step of a calculation. Separate calculations of fluid response and structure response are avoided, thereby giving a more accurate model of the dynamic coupling between fluid and structure. This volume provides the theoretical background, the finite-difference equations, the finite-element equations, a discussion of several sample problems, a listing of the input decks for the sample problems, a programmer's manual and a description of the input records for the STEALTH/WHAMSE computer program.
Orozco, Gustavo A; Smith, Joshua H; García, José J
2014-10-01
A previously proposed finite element model that considers geometric and material nonlinearities and the free boundary problems that occur at the catheter tip and in the annular zone around the lateral surface of the catheter was revised and was used to fit a power-law formula to predict backflow length during infusions into brain tissue. Compared to a closed-form solution based on linear elasticity, the power-law formula for compliant materials predicted a substantial lower influence of the shear modulus and catheter radius on the backflow length, whereas the corresponding influence for stiffer materials was more consistent with the closed-form solution. The finite element model predicted decreases of the backflow length for reduction of the shear modulus for highly compliant materials (shear modulus less than 500 Pa) due to the increased area of infusion and the high fluid fraction near the infusion cavity that greatly increased the surface area available for fluid transfer and reduced the hydraulic resistance toward the tissue. These results show the importance of taking into account the material and geometrical nonlinearities that arise near the infusion surface as well as the change of hydraulic conductivity with strain for a proper characterization of backflow length during flow-controlled infusions into the brain. PMID:25154980
NASA Astrophysics Data System (ADS)
Zeqiri, Bajram; Cook, Ashley; Rétat, Lise; Civale, John; ter Haar, Gail
2015-04-01
The acoustic nonlinearity parameter, B/A, is an important parameter which defines the way a propagating finite amplitude acoustic wave progressively distorts when travelling through any medium. One measurement technique used to determine its value is the finite amplitude insertion substitution (FAIS) method which has been applied to a range of liquid, tissue and tissue-like media. Importantly, in terms of the achievable measurement uncertainties, it is a relative technique. This paper presents a detailed study of the method, employing a number of novel features. The first of these is the use of a large area membrane hydrophone (30 mm aperture) which is used to record the plane-wave component of the acoustic field. This reduces the influence of diffraction on measurements, enabling studies to be carried out within the transducer near-field, with the interrogating transducer, test cell and detector positioned close to one another, an attribute which assists in controlling errors arising from nonlinear distortion in any intervening water path. The second feature is the development of a model which estimates the influence of finite-amplitude distortion as the acoustic wave travels from the rear surface of the test cell to the detector. It is demonstrated that this can lead to a significant systematic error in B/A measurement whose magnitude and direction depends on the acoustic property contrast between the test material and the water-filled equivalent cell. Good qualitative agreement between the model and experiment is reported. B/A measurements are reported undertaken at (20 ± 0.5) °C for two fluids commonly employed as reference materials within the technical literature: Corn Oil and Ethylene Glycol. Samples of an IEC standardised agar-based tissue-mimicking material were also measured. A systematic assessment of measurement uncertainties is presented giving expanded uncertainties in the range ±7% to ±14%, expressed at a confidence level close to 95
Nonlinear finite beta saturation of the drift cyclotron loss cone instability
Ferraro, R.D.
1984-01-01
The nonlinear saturation of a single Drift Cyclotron Loss Cone mode is considered in the case of a mirror confined finite {beta} plasma. The instability is modeled in slab geometry with the local approximation made. Using a variation of the Bogoliubov technique, analytic expressions are derived for the time asymptotic distribution function, electrostatic potential, and vector potential. The saturation amplitude and frequency shift are determined as functions of the fractional increase of the density above its threshold value. Freedom is retained in the equilibrium ion velocity space distribution function so that the effect of a partially filled loss cone may be investigated. A term neglected in a previous low {beta} application of this technique to the DCLC is found to affect the saturation results. In a collisionless, lossless model, the effect of a partially filled loss cone on the saturation amplitude and density, density gradient space stability boundary is demonstrated. A delta function equilibrium velocity space distribution is found to have only large amplitude saturated states. The nonlinear shift in the electrostatic potential is found to be negligibly small in this model, and the nonlinear shift in the vector potential is found to be just that needed to restore particle-field pressure balance. A second model is employed which takes into account plasma losses through a simple Krook type collision term in the Boltzman equation. Ion losses are assumed to be dominated by electron drag into the loss cone and the electron losses are modeled by the classical expression derived by Pastukhov.
ORMDIN: a finite element program for two-dimensional nonlinear inverse heat conduction analysis
Bass, B.R.; Drake, J.B.; Ott, L.J.
1980-12-01
The calculation of the surface temperature and surface heat flux from measured temperature transients at one or more interior points of a body is identified in the literature as the inverse heat conduction problem. Heretofore, analytical and computational methods of treating this problem have been limited to one-dimensional nonlinear or two-dimensional linear material models. This report presents, to the authors' knowledge, the first inverse solution technique applicable to the two-dimensional nonlinear model with temperature-dependent thermophysical properties. This technique, representing an extension of the one-dimensional formulation previously developed by one of the authors, utilizes a finite element heat conduction model and a generalization of Beck's one-dimensional nonlinear estimation procedure. A digital computer program ORMDIN (Oak Ridge Multi-Dimensional INverse) is developed from the formulation and applied to the cross section of a composite cylinder with temperature-dependent material properties. Results are presented to demonstrate that the inverse formulation is capable of successfully treating experimental data. An important feature of the method is that small time steps are permitted while avoiding severe oscillations or numerical instabilities due to experimental errors in measured data.
Real-time nonlinear finite element analysis for surgical simulation using graphics processing units.
Taylor, Zeike A; Cheng, Mario; Ourselin, Sébastien
2007-01-01
Clinical employment of biomechanical modelling techniques in areas of medical image analysis and surgical simulation is often hindered by conflicting requirements for high fidelity in the modelling approach and high solution speeds. We report the development of techniques for high-speed nonlinear finite element (FE) analysis for surgical simulation. We employ a previously developed nonlinear total Lagrangian explicit FE formulation which offers significant computational advantages for soft tissue simulation. However, the key contribution of the work is the presentation of a fast graphics processing unit (GPU) solution scheme for the FE equations. To the best of our knowledge this represents the first GPU implementation of a nonlinear FE solver. We show that the present explicit FE scheme is well-suited to solution via highly parallel graphics hardware, and that even a midrange GPU allows significant solution speed gains (up to 16.4x) compared with equivalent CPU implementations. For the models tested the scheme allows real-time solution of models with up to 16000 tetrahedral elements. The use of GPUs for such purposes offers a cost-effective high-performance alternative to expensive multi-CPU machines, and may have important applications in medical image analysis and surgical simulation. PMID:18051120
NASA Astrophysics Data System (ADS)
Abudaram, Yaakov Jack
This work is concerned with a new method to apply consistent and known pretension to silicone rubber membranes intended for micro air vehicles as well as an understanding in the science of developed pre-tension in membranes constrained by 2- D and 3-D frames and structures. Pre-tension has a marked effect on the static and dynamic response of membrane wings and controls the overall deflections, as such control and measurement of the membrane pre-tension is important. Two different 2-D frame geometries were fabricated to evaluate the technique. For open-cell frames, the pretension was not uniform, whereas it was for closed-cell frames. Results show developed full-field stress and strain fields as a function of membrane attachment temperature and frame geometry along with experimental iterations to prove repeatability. The membranes can be stretched to a specific pretension according to the temperature at which it adheres to frames. Strain fields in membranes attached to 3-D frames at various temperatures are modeled through FEA utilizing Abaqus to be able to predict the developed membrane deformations, stresses, and strains. Rigid frames with various curvatures are built via appropriate molds and then adhered to silicone rubber membranes and elevated to various temperatures to achieve different pre-strains for experimental validation. Additional experiments are conducted for more complex frame geometries involving both convex and concave topologies embedded within frames. Results are then compared with the Abaqus outputs to validate the accuracy of the FEA model. Highly compliant wings have been used for MAV platforms, where the wing structure is determined by some combination of carbon fiber composites and a membrane skin, adhered in between the layers of composite material. Another new technique of attaching membranes firmly on wing structures is introduced, which involves the application of a technology known as corona treatment coupled with another method of
NASA Astrophysics Data System (ADS)
Valdrè, Giovanni; Moro, Daniele
2008-10-01
The investigation of the nanoscale distribution of electrostatic forces on material surfaces is of paramount importance for the development of nanotechnology, since these confined forces govern many physical processes on which a large number of technological applications are based. For instance, electric force microscopy (EFM) and micro-electro-mechanical-systems (MEMS) are technologies based on an electrostatic interaction between a cantilever and a specimen. In the present work we report on a 3D finite element analysis of the electrostatic deflection of cantilevers for electric and Kelvin force microscopy. A commercial triangular shaped cantilever with a symmetric pyramidal tip was modelled. In addition, the cantilever was modified by a focused ion beam (FIB) in order to reduce its parasitic electrostatic force, and its behaviour was studied by computation analysis. 3D modelling of the electrostatic deflection was realized by using a multiphysics finite element analysis software and it was applied to the real geometry of the cantilevers and probes obtained by using basic CAD tools. The results of the modelling are in good agreement with experimental data.
Valdrè, Giovanni; Moro, Daniele
2008-10-01
This paper deals with an application of 3D finite element analysis to the electrostatic interaction between (i) a commercial rectangular shaped cantilever (with an integrated anisotropic pyramidal tip) and a conductive sample, when a voltage difference is applied between them, and (ii) a focused ion beam (FIB) modified cantilever in order to realize a probe with reduced parasitic electrostatic force. The 3D modelling of their electrostatic deflection was realized by using multiphysics finite element analysis software and applied to the real geometry of the cantilevers and probes as used in conventional electric and Kelvin force microscopy to evaluate the contribution of the various part of a cantilever to the total force, and derive practical criteria to optimize the probe performances. We report also on the simulation of electrostatic shielding of nanometric features, in order to quantitatively evaluate an alternative way of reducing the systematic error caused by the cantilever-to-sample capacitive coupling. Finally, a quantitative comparison between the performances of rectangular and triangular cantilevers (part I of this work) is reported. PMID:21832618
Valdrè, Giovanni; Moro, Daniele
2008-10-01
The investigation of the nanoscale distribution of electrostatic forces on material surfaces is of paramount importance for the development of nanotechnology, since these confined forces govern many physical processes on which a large number of technological applications are based. For instance, electric force microscopy (EFM) and micro-electro-mechanical-systems (MEMS) are technologies based on an electrostatic interaction between a cantilever and a specimen. In the present work we report on a 3D finite element analysis of the electrostatic deflection of cantilevers for electric and Kelvin force microscopy. A commercial triangular shaped cantilever with a symmetric pyramidal tip was modelled. In addition, the cantilever was modified by a focused ion beam (FIB) in order to reduce its parasitic electrostatic force, and its behaviour was studied by computation analysis. 3D modelling of the electrostatic deflection was realized by using a multiphysics finite element analysis software and it was applied to the real geometry of the cantilevers and probes obtained by using basic CAD tools. The results of the modelling are in good agreement with experimental data. PMID:21832617
NASA Astrophysics Data System (ADS)
Skarlatoudis, A. A.; Papazachos, C. B.; Theodoulidis, N.; Kristek, J.; Moczo, P.
2010-07-01
The site effects of seismic motion in the metropolitan area of the city of Thessaloniki (Northern Greece) are investigated using a 3-D finite-difference modelling approach. Three different seismic scenarios are assumed with two different focal mechanisms for each one. Standard spectral ratios (SSR) are calculated from 3-D synthetics and compared with the ratios from the recorded motion, as well as ratios obtained from 1-D and 2-D modelling by other researchers. The average SSR curves from the six scenarios are in good agreement with the empirical ones, whereas the SSR results from 3-D modelling are different from those from 1-D modelling, exhibiting higher fundamental frequencies and larger amplification amplitudes, in much better agreement with observed SSR ratios. Comparisons of Fourier amplitude spectra obtained for various scenarios for the broader area of Thessaloniki show considerable dependence of the site effects on the source properties (position, depth and fault-plane solution), as well as on the local structure.
NASA Astrophysics Data System (ADS)
Kang, Yu-Bong; Jung, Duk-Young; Tanaka, Masatoshi; Yoshino, Nobuyuki; Tsutsumi, Sadami; Ikeuchi, Ken
Whiplash injuries are most common disorders in rear-end car accidents, while the injury mechanism is yet unknown. Many numerical and experimental approaches have conducted to investigate the cervical behaviors with solely two-dimensional analyses in the sagittal plane. In real accidents, however, as impacts may affect several directions, the cervical behaviors should be evaluated three-dimensionally. Therefore, we evaluated the cervical behaviors under assumption of the posterior-oblique impacts depending on the impact angles with 3-D FE analysis. In addition, we analyzed the stresses occurred in the facet joints considering the relationship with a whiplash disorders. The cervical behaviors showed complex motion combined with axial torsion and lateral bending. The bending angle peaked in the impact at the angle of 15°, and the peak compressive and shear stress on the facet cartilage at C6-C7 increased by 11% and 14%. In the impact at the angle of 30°, the torsion angle peaked at C2-C3, the peak shear stress in the facet cartilage increased by 27%. It showed that the torsion and lateral bending affected the cervical behaviors, and caused the increase of peak stresses on the soft tissues. It is assumed as one of important causes of whiplash injury.
Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D.
2014-01-01
The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique. PMID:24527060
Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D
2014-01-01
The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique. PMID:24527060
2009-06-29
JAS3D is a three-dimensional finite element program originally designed to solve Lagrangian quasistatic non-linear mechanics problems, and subsequently extended to include both implicit and explicit dynamics. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. Innovative multilevel nonlinear iterative methods are used to solve the equations. A wide variety of material constitutive models are available, and contact interface logic is implemented. Two Lagrangian uniform-strain elements are available: an eighth-node hexahedronmore » for solids and a four-node quadrilateral for shells. Both use hourglass stiffness to control zero-energy modes. In addition, a version of the hexahedron is available with uniform pressure and a deviatoric response scalable from the mean response of the original element up to a fully-integrated response. Bodies under analysis may be loaded by surface pressures and concentrated forces, specified displacements, or body forces from gravity, steady-state transport, or thermal expansion.« less
3D Elastic Wavefield Tomography
NASA Astrophysics Data System (ADS)
Guasch, L.; Warner, M.; Stekl, I.; Umpleby, A.; Shah, N.
2010-12-01
Wavefield tomography, or waveform inversion, aims to extract the maximum information from seismic data by matching trace by trace the response of the solid earth to seismic waves using numerical modelling tools. Its first formulation dates from the early 80's, when Albert Tarantola developed a solid theoretical basis that is still used today with little change. Due to computational limitations, the application of the method to 3D problems has been unaffordable until a few years ago, and then only under the acoustic approximation. Although acoustic wavefield tomography is widely used, a complete solution of the seismic inversion problem requires that we account properly for the physics of wave propagation, and so must include elastic effects. We have developed a 3D tomographic wavefield inversion code that incorporates the full elastic wave equation. The bottle neck of the different implementations is the forward modelling algorithm that generates the synthetic data to be compared with the field seismograms as well as the backpropagation of the residuals needed to form the direction update of the model parameters. Furthermore, one or two extra modelling runs are needed in order to calculate the step-length. Our approach uses a FD scheme explicit time-stepping by finite differences that are 4th order in space and 2nd order in time, which is a 3D version of the one developed by Jean Virieux in 1986. We chose the time domain because an explicit time scheme is much less demanding in terms of memory than its frequency domain analogue, although the discussion of wich domain is more efficient still remains open. We calculate the parameter gradients for Vp and Vs by correlating the normal and shear stress wavefields respectively. A straightforward application would lead to the storage of the wavefield at all grid points at each time-step. We tackled this problem using two different approaches. The first one makes better use of resources for small models of dimension equal
Ozan, Oguz; Ramoglu, Serhat
2015-06-01
Implant-supported overdentures with self-aligning attachment systems are preferred to improve the stability and retention of complete dentures. The positioning of the implant attachments is a very important aspect of two-implant overdentures in obtaining better stress distribution. Therefore, the objective of this study was to compare two different attachment systems in a two-implant overdenture by evaluating the stress distributions in peri-implant bone and stresses on the attachments with positioning at different height levels using the 3D FEA method. Six models with ball attachments and 6 models with locator attachments-totaling 12 models (including 2 controls)-with the left implant positioned unilaterally at different height levels were subjected to 3 loading conditions (anterior, right posterior, and left posterior). Data for Von Misses stresses were produced numerically, color coded, and compared among the models for attachments and peri-implant cortical bone. The configurations in which implants presented 3 mm height differences in the bone level showed the most successful results in the peri-implant bone. When stresses on the attachments were compared, greater stress values were obtained from the ball attachments. As a conclusion, the configurations with a considerable (3 mm) height difference between quadrants of the mandible in the anterior segment showed the most successful results in the peri-implant bone. On the contrary, peak stress values around the implant observed from the models with less (1 mm) bone height difference may require leveling of the bone during surgery. However, these findings should be corroborated with clinical studies. PMID:24471769
Sanchez, R.
2012-07-01
Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self adjoint angular flux (SAAF) form of the transport equation and use a post processing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a formal derivation of the boundary conditions for the SAAF. (authors)
Richard Sanchez; Cristian Rabiti; Yaqi Wang
2013-11-01
Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self-adjoint angular flux (SAAF) form of the transport equation and use a postprocessing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a novel formal derivation of the boundary conditions for the SAAF.
NASA Technical Reports Server (NTRS)
Watson, Brian C.; Kamat, Manohar P.
1992-01-01
Concurrent computing environments provide the means to achieve very high performance for finite element analysis of systems, provided the algorithms take advantage of multiple processors. The authors have examined several algorithms for both linear and nonlinear finite element analysis. The performance of these algorithms on an Alliant FX/80 parallel supercomputer has been studied. For single load case linear analysis, the optimal solution algorithm is strongly problem dependent. For multiple load cases or nonlinear analysis through a modified Newton-Raphson method, decomposition algorithms are shown to have a decided advantage over element-by-element preconditioned conjugate gradient algorithms.
Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E
2013-12-01
In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. PMID:23850847
A finite element method for the statistics of non-linear random vibration
NASA Astrophysics Data System (ADS)
Langley, R. S.
1985-07-01
The transitional probability density function for the random response of a certain class of non-linear system satisfies the Fokker-Planck-Kolmogorov equation. This paper concerns the numerical solution of the stationary form of this equation, yielding the stationary probability density function of response. The weighted residual statement for the problem is integrated by parts to yield the weak form of the equations, which are then solved by the finite element method. The method is applied to a Duffing oscillator and good agreement is found with the exact result, and the method is compared favourably with a Galerkin solution method given by Bhandari and Sherrer [1]. Also, the method is applied to the ship rolling problem and good agreement is found with an approximate analytical result due to Roberts [2].
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Peters, Jeanne M.
1989-01-01
A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric and antisymmetric response vectors (modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (1) mixed (or primitive variable) formulation with independent shape functions for the different fields; (2) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response; and (3) two level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers.
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Peters, Jeanne M.
1989-01-01
A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric and antisymmetric response vectors (modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (1) mixed (or primitive variable) formulation with independent shape functions for the different fields; (2) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response; and (3) two level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers.
Effects of finite-precision arithmetic on interior-point methods for nonlinear programming.
Wright, S. J.; Mathematics and Computer Science
2001-10-23
We show that the effects of finite-precision arithmetic in forming and solving the linear system that arises at each iteration of primal-dual interior-point algorithms for nonlinear programming are benign, provided that the iterates satisfy centrality and feasibility conditions of the type usually associated with path-following methods. When we replace the standard assumption that the active constraint gradients are independent by the weaker Mangasarian--Fromovitz constraint qualification, rapid convergence usually is attainable, even when cancellation and roundoff errors occur during the calculations. In deriving our main results, we prove a key technical result about the size of the exact primal-dual step. This result can be used to modify existing analysis of primal-dual interior-point methods for convex programming, making it possible to extend the superlinear local convergence results to the nonconvex case.
Leng, Wei; Ju, Lili; Gunzburger, Max; Price, Stephen; Ringler, Todd
2012-01-01
The numerical modeling of glacier and ice sheet evolution is a subject of growing interest, in part because of the potential for models to inform estimates of global sea level change. This paper focuses on the development of a numerical model that determines the velocity and pressure fields within an ice sheet. Our numerical model features a high-fidelity mathematical model involving the nonlinear Stokes system and combinations of no-sliding and sliding basal boundary conditions, high-order accurate finite element discretizations based on variable resolution grids, and highly scalable parallel solution strategies, all of which contribute to a numerical model that can achieve accurate velocity and pressure approximations in a highly efficient manner. We demonstrate the accuracy and efficiency of our model by analytical solution tests, established ice sheet benchmark experiments, and comparisons with other well-established ice sheet models.
Stevenson, Thomas; Doschak, Michael
2014-01-01
The aim of this animal study was to develop a model of orthodontic tooth movement using a microimplant as a TSAD in rodents. A finite element model of the TSAD in alveolar bone was built using μCT images of rat maxilla to determine the von Mises stresses and displacement in the alveolar bone surrounding the TSAD. For in vivo validation of the FE model, Sprague-Dawley rats (n = 25) were used and a Stryker 1.2 × 3 mm microimplant was inserted in the right maxilla and used to protract the right first permanent molar using a NiTi closed coil spring. Tooth movement measurements were taken at baseline, 4 and 8 weeks. At 8 weeks, animals were euthanized and tissues were analyzed by histology and EPMA. FE modeling showed maximum von Mises stress of 45 Mpa near the apex of TSAD but the average von Mises stress was under 25 Mpa. Appreciable tooth movement of 0.62 ± 0.04 mm at 4 weeks and 1.99 ± 0.14 mm at 8 weeks was obtained. Histological and EPMA results demonstrated no active bone remodeling around the TSAD at 8 weeks depicting good secondary stability. This study provided evidence that protracted tooth movement is achieved in small animals using TSADs. PMID:25295060
NASA Astrophysics Data System (ADS)
Gibert, Mathieu; Klein, Simon; Bodenschatz, Eberhard
2012-11-01
We report a novel experimental technique that measures simultaneously in three dimensions the trajectories, the translation, and the rotation of finite size inertial particles together with the turbulent flow. The flow field is analyzed by tracking the temporal evolution of small fluorescent tracer particles. The inertial particles consist of a super-absorbent polymer that renders them index and density matched with water and thus invisible. The particles are marked by inserting at various locations tracer particles into the polymer. Translation and rotation, as well as the flow field around the particle are recovered dynamically from the analysis of the marker and tracer particle trajectories. We apply this technique to study the dynamics of inertial particles much larger in size (Rp / η ~ 100) than the Kolmogorov length scale η in a von Kármán swirling water flow (Rλ ~ 400). We show, using the mixed (particle/fluid) Eulerian second order velocity structure function, that the interaction zone between the particle and the flow develops in a spherical shell of width 2Rp around the particle of radius Rp. This we interpret as an indication of a wake induced by the particle. (http://arxiv.org/abs/1205.2181) This work was funded generously by the Max Planck Society and the Marie Curie Fellowship, Program PEOPLE - Call FP7-PEOPLE-IEF-2008 Proposal No 237521. Support from COST Action MP0806 is kindly acknowledged.
NASA Astrophysics Data System (ADS)
Klein, Simon; Gibert, Mathieu; Bérut, Antoine; Bodenschatz, Eberhard
2013-02-01
We report a novel experimental technique that measures simultaneously in three dimensions the trajectories, the translation and the rotation of finite-size inertial particles together with the turbulent flow. The flow field is analyzed by tracking the temporal evolution of small fluorescent tracer particles. The inertial particles consist of a super-absorbent polymer that renders them index and density matched with water and thus invisible. The particles are marked by inserting at various locations tracer particles into the polymer. Translation and rotation, as well as the flow field around the particle are recovered dynamically from the analysis of the marker and tracer particle trajectories. We apply this technique to study the dynamics of inertial particles much larger in size (Rp/η ≈ 100) than the Kolmogorov length scale η in a von Kármán swirling water flow (Rλ ≈ 400). We show, using the mixed (particle/fluid) Eulerian second-order velocity structure function, that the interaction zone between the particle and the flow develops in a spherical shell of width 2Rp around the particle of radius Rp. This we interpret as an indication of a wake induced by the particle. This measurement technique has many additional advantages that will make it useful to address other problems such as particle collisions, dynamics of non-spherical solid objects, or even of wet granular matter.
Fernandez, M; House, M; Jambawalikar, S; Zork, N; Vink, J; Wapner, R; Myers, K
2016-01-01
Preterm birth is a strong contributor to perinatal mortality, and preterm infants that survive are at risk for long-term morbidities. During most of pregnancy, appropriate mechanical function of the cervix is required to maintain the developing fetus in utero. Premature cervical softening and subsequent cervical shortening are hypothesized to cause preterm birth. Presently, there is a lack of understanding of the structural and material factors that influence the mechanical function of the cervix during pregnancy. In this study we build finite element models of the pregnant uterus, cervix, and fetal membrane based on magnetic resonance imagining data in order to examine the mechanical function of the cervix under the physiologic loading conditions of pregnancy. We calculate the mechanical loading state of the cervix for two pregnant patients: 22 weeks gestational age with a normal cervical length and 28 weeks with a short cervix. We investigate the influence of (1) anatomical geometry, (2) cervical material properties, and (3) fetal membrane material properties, including its adhesion properties, on the mechanical loading state of the cervix under physiologically relevant intrauterine pressures. Our study demonstrates that membrane-uterus interaction, cervical material modeling, and membrane mechanical properties are factors that must be deliberately and carefully handled in order to construct a high quality mechanical simulation of pregnancy. PMID:25970655
Mansoor, K; Maley, M; Demir, Z; Hoffman, F
2001-08-08
Lawrence Livermore National Laboratory (LLNL) is a large Superfund site in California that is implementing an extensive ground water remediation program. The site is underlain by a thick sequence of heterogeneous alluvial sediments. Defining ground-water flow pathways in this complex geologic setting is difficult. To better evaluate these pathways, a deterministic approach was applied to define hydrostratigraphic units (HSUS) on the basis of identifiable hydraulic behavior and contaminant migration trends. The conceptual model based on this approach indicates that groundwater flow and contaminant transport occurs within packages of sediments bounded by thin, low-permeability confining layers. To aid in the development of the remediation program, a three-dimensional finite-element model was developed for two of the HSUS at LLNL. The primary objectives of this model are to test the conceptual model with a numerical model, and provide well field management support for the large ground-water remediation system. The model was successfully calibrated to 12 years of ground water flow and contaminant transport data. These results confirm that the thin, low-permeability confining layers within the heterogeneous alluvial sediments are the dominant hydraulic control to flow and transport. This calibrated model is currently being applied to better manage the large site-wide ground water extraction system by optimizing the location of new extraction wells, managing pumping rates for extraction wells, and providing performance estimates for long-term planning and budgeting.