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.
Simulation of 3D tumor cell growth using nonlinear finite element method.
Dong, Shoubing; Yan, Yannan; Tang, Liqun; Meng, Junping; Jiang, Yi
2016-01-01
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.
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.
3-D Mesh Generation Nonlinear Systems
Christon, M. A.; Dovey, D.; Stillman, D. W.; Hallquist, J. O.; Rainsberger, R. B
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 surface 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.
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.
NASA Astrophysics Data System (ADS)
Weng, W.; Taylor, P. A.
2010-09-01
Based on the early linear and Non-Linear Mixed Spectral Finite-Difference (MSFD and NLMSFD) models, a 3-D non-linear model of planetary boundary-layer flow (NLMSFD-PBL) was developed to study neutral PBL flow over complex terrain. The model assumes upwind or zero-order profiles of mean and turbulence variables about which perturbation quantities are calculated due to the effects of the terrain. In early models, the mean zero-order wind profile was assumed to be a simple logarithmic surface-layer profile and Reynolds stresses were constant throughout the depth of the model domain. This formally limits the applications of model to the surface-layer flow. The new model utilizes the results of early 1-D planetary boundary layer model of Weng and Taylor as the zero-order or upstream profiles of mean and turbulent quantities. The limitations associated with the original MSFD/NLMSFD model (e.g. logarithmic wind profile and constant shear stress layer) are relaxed. The effect of earth's rotation is also included in the model. Model results for planetary boundary-layer flow over complex terrain are discussed, particularly, the flow over Askervein hill - the site of a detailed and much referenced field study of flow over hills in the 1980s. This type of modelling of flow over complex terrain has important applications for wind energy resource assessment and wind farm design.
Stabilized Finite Elements in FUN3D
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Newman, James C.; Karman, Steve L.
2017-01-01
A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.
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.
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.
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.
Parallel 3-D viscoelastic finite difference seismic modelling
NASA Astrophysics Data System (ADS)
Bohlen, Thomas
2002-10-01
Computational power has advanced to a state where we can begin to perform wavefield simulations for realistic (complex) 3-D earth models at frequencies of interest to both seismologists and engineers. On serial platforms, however, 3-D calculations are still limited to small grid sizes and short seismic wave traveltimes. To make use of the efficiency of network computers a parallel 3-D viscoelastic finite difference (FD) code is implemented which allows to distribute the work on several PCs or workstations connected via standard ethernet in an in-house network. By using the portable message passing interface standard (MPI) for the communication between processors, running times can be reduced and grid sizes can be increased significantly. Furthermore, the code shows good performance on massive parallel supercomputers which makes the computation of very large grids feasible. This implementation greatly expands the applicability of the 3-D elastic/viscoelastic finite-difference modelling technique by providing an efficient, portable and practical C-program.
Deep Nonlinear Metric Learning for 3-D Shape Retrieval.
Xie, Jin; Dai, Guoxian; Zhu, Fan; Shao, Ling; Fang, Yi
2016-12-28
Effective 3-D shape retrieval is an important problem in 3-D shape analysis. Recently, feature learning-based shape retrieval methods have been widely studied, where the distance metrics between 3-D shape descriptors are usually hand-crafted. In this paper, motivated by the fact that deep neural network has the good ability to model nonlinearity, we propose to learn an effective nonlinear distance metric between 3-D shape descriptors for retrieval. First, the locality-constrained linear coding method is employed to encode each vertex on the shape and the encoding coefficient histogram is formed as the global 3-D shape descriptor to represent the shape. Then, a novel deep metric network is proposed to learn a nonlinear transformation to map the 3-D shape descriptors to a nonlinear feature space. The proposed deep metric network minimizes a discriminative loss function that can enforce the similarity between a pair of samples from the same class to be small and the similarity between a pair of samples from different classes to be large. Finally, the distance between the outputs of the metric network is used as the similarity for shape retrieval. The proposed method is evaluated on the McGill, SHREC'10 ShapeGoogle, and SHREC'14 Human shape datasets. Experimental results on the three datasets validate the effectiveness of the proposed method.
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.
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.
Finite elements of nonlinear continua.
NASA Technical Reports Server (NTRS)
Oden, J. T.
1972-01-01
The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.
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.
Characteristics Analysis on Various Kinds of Hybrid Stepping Motors Using 3D Finite Element Method
NASA Astrophysics Data System (ADS)
Enomoto, Yuji; Maki, Kohji; Miyata, Kenji; Oonishi, Kazuo; Sakamoto, Masafumi; Abukawa, Toshimi
We have presented a powerful scheme of investigating hybrid stepping motor characteristics by using 3D finite element method. A linear magnetic field analysis is effectively applicable to predict relative performance of several motors in an extremely short computing time. The waveforms of cogging torque by linear and nonlinear analysis resemble each other, while the wave amplitude in the linear analysis is about 2 times larger than one in the nonlinear analysis in the presented example. The overestimation factor of cogging torque is approximately constant for the same material composition.
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 modeling of sliding wear
NASA Astrophysics Data System (ADS)
Buentello Hernandez, Rodolfo G.
Wear is defined as "the removal of material volume through some mechanical process between two surfaces". There are many mechanical situations that can induce wear and each can involve many wear mechanisms. This research focuses on the mechanical wear due to dry sliding between two surfaces. Currently there is a need to identify and compare materials that would endure sliding wear under severe conditions such as high velocities. The high costs associated with the field experimentation of systems subject to high-speed sliding, has prevented the collection of the necessary data required to fully characterize this phenomena. Simulating wear through Finite Elements (FE) would enable its prediction under different scenarios and would reduce experimentation costs. In the aerospace, automotive and weapon industries such a model can aid in material selection, design and/or testing of systems subjected to wear in bearings, gears, brakes, gun barrels, slippers, locomotive wheels, or even rocket test tracks. The 3D wear model presented in this dissertation allows one to reasonably predict high-speed sliding mechanical wear between two materials. The model predictions are reasonable, when compared against those measured on a sled slipper traveling over the Holloman High Speed Tests Track. This slipper traveled a distance of 5,816 meters in 8.14 seconds and reached a maximum velocity of 1,530 m/s.
NASA Astrophysics Data System (ADS)
Kaus, B.; Schmalholz, S.
2006-12-01
Compression of the lithosphere, sedimentary sequences or quartz veins may all result in a folding instability, provided that the effective viscosity contrast between "strong" and "weak" layers is sufficiently large. Whereas this process is relatively well understood in 2D, little is known about the finite amplitude instability in 3D. We perform 3D numerical simulations of viscous single-layer folding to study the growth of the fold amplitude during progressive shortening for different amounts of shortening in the two horizontal directions. We demonstrate that existing, linear theories correctly describe the behavior of the instability for small amplitudes. For larger amplitudes, however, numerical results strongly deviate from the linear theory. Therefore, we present a new nonlinear amplification equation that successfully describes folding up to finite amplitudes. Numerical simulations of folding of an initially horizontal layer, perturbed with random noise, demonstrate that in most cases fold axes form perpendicular to the main shortening direction. Aspect ratios of folds are finite and the patterns are relatively insensitive to the applied background shortening directions. Furthermore, the 3D folding instability reduces the averaged differential stress within the folded ("strong") layer, in agreement with 2D results. This implies that the Christmas-tree approach to represent the strength of the crust and lithosphere may be invalid if folding occurs during the deformation.
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.
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 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.
NASA Astrophysics Data System (ADS)
Kaus, Boris J. P.; Schmalholz, Stefan M.
2006-07-01
Compression of the lithosphere, sedimentary sequences or quartz veins may result in a folding instability. We perform numerical simulations of viscous single-layer folding to study this instability in 3D. It is demonstrated that linear theories correctly describe the instability for small amplitudes. At larger amplitudes, however, the theory breaks down. For these stages we present a new nonlinear amplification equation. Numerical simulations of folding of an initially horizontal layer, perturbed with random noise, demonstrate that in most cases fold axes form perpendicular to the main shortening direction. Aspect ratios of folds are finite and the patterns are relatively insensitive to the applied background shortening directions. Furthermore, the 3D folding instability reduces the averaged differential stress within the folded (``strong'') layer, in agreement with 2D results. This implies that the Christmas-tree approach to represent the strength of the crust and lithosphere may be invalid if folding occurs during the deformation.
A 3D printed electromagnetic nonlinear vibration energy harvester
NASA Astrophysics Data System (ADS)
Constantinou, P.; Roy, S.
2016-09-01
A 3D printed electromagnetic vibration energy harvester is presented. The motion of the device is in-plane with the excitation vibrations, and this is enabled through the exploitation of a leaf isosceles trapezoidal flexural pivot topology. This topology is ideally suited for systems requiring restricted out-of-plane motion and benefits from being fabricated monolithically. This is achieved by 3D printing the topology with materials having a low flexural modulus. The presented system has a nonlinear softening spring response, as a result of designed magnetic force interactions. A discussion of fatigue performance is presented and it is suggested that whilst fabricating, the raster of the suspension element is printed perpendicular to the flexural direction and that the experienced stress is as low as possible during operation, to ensure longevity. A demonstrated power of ˜25 μW at 0.1 g is achieved and 2.9 mW is demonstrated at 1 g. The corresponding bandwidths reach up-to 4.5 Hz. The system’s corresponding power density of ˜0.48 mW cm-3 and normalised power integral density of 11.9 kg m-3 (at 1 g) are comparable to other in-plane systems found in the literature.
TAURUS96. 3-D Finite Element Code Postprocessor
Brown, B.; Hallquist, J.O.; Spelce, T.E.
1993-11-30
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.
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.
Nonlinear 3D MHD verification study: SpeCyl and PIXIE3D codes for RFP and Tokamak plasmas
NASA Astrophysics Data System (ADS)
Bonfiglio, D.; Cappello, S.; Chacon, L.
2010-11-01
A strong emphasis is presently placed in the fusion community on reaching predictive capability of computational models. An essential requirement of such endeavor is the process of assessing the mathematical correctness of computational tools, termed verification [1]. We present here a successful nonlinear cross-benchmark verification study between the 3D nonlinear MHD codes SpeCyl [2] and PIXIE3D [3]. Excellent quantitative agreement is obtained in both 2D and 3D nonlinear visco-resistive dynamics for reversed-field pinch (RFP) and tokamak configurations [4]. RFP dynamics, in particular, lends itself as an ideal non trivial test-bed for 3D nonlinear verification. Perspectives for future application of the fully-implicit parallel code PIXIE3D to RFP physics, in particular to address open issues on RFP helical self-organization, will be provided. [4pt] [1] M. Greenwald, Phys. Plasmas 17, 058101 (2010) [0pt] [2] S. Cappello and D. Biskamp, Nucl. Fusion 36, 571 (1996) [0pt] [3] L. Chac'on, Phys. Plasmas 15, 056103 (2008) [0pt] [4] D. Bonfiglio, L. Chac'on and S. Cappello, Phys. Plasmas 17 (2010)
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
Intersecting D 3 -D3 ' -brane system at finite temperature
NASA Astrophysics Data System (ADS)
Cottrell, William; Hanson, James; Hashimoto, Akikazu; Loveridge, Andrew; Pettengill, Duncan
2017-02-01
We analyze the dynamics of the intersecting D 3 -D3 ' -brane system overlapping in 1 +1 dimensions, in a holographic treatment where N D3 branes are manifested as anti-de Sitter Schwartzschild geometry, and the D3 ' brane is treated as a probe. We extract the thermodynamic equation of state from the set of embedding solutions, and analyze the stability at the perturbative and the nonperturbative level. We review a systematic procedure to resolve local instabilities and multivaluedness in the equations of state based on classic ideas of convexity in the microcanonical ensemble. We then identify a runaway behavior which was not noticed previously for this system.
A detailed 3D finite element analysis of the peeling behaviour of a gecko spatula.
Sauer, Roger A; Holl, Matthias
2013-01-01
This paper presents a detailed finite element analysis of the adhesion of a gecko spatula. The gecko spatulae form the tips of the gecko foot hairs that transfer the adhesional and frictional forces between substrate and foot. The analysis is based on a parameterised description of the 3D geometry of the spatula that only requires 12 parameters. The adhesion is described by a nonlinear computational contact formulation that accounts for the van der Waals interaction between spatula and substrate. The spatula adhesion model is implemented using an enriched contact finite element formulation recently developed by the first author. The finite element model is then used to simulate the peeling behaviour of the gecko spatula under applied vertical and rotational loading for various model parameters. Variations of the material stiffness, adhesional strength and range, stiction, spatula size and spatula inclination are considered to account for the natural variation of spatula properties. The study demonstrates that the spatula can function over a wide range of conditions. The computed pull-off forces are in agreement with experimental results reported in the literature. The study also examines the energy required for the spatula pull-off. The proposed model is ideal to study the influence of substrate roughness on the spatula adhesion, as is finally demonstrated.
3-D Nonlinear Constitutive Modeling Approach for Composite Materials
1992-05-01
material nonlinearities, damage , and interfacial debonding [1]. These nonlinearities must be considered for accurate prediction of strength or stability...the overall nonlinear behavior covers plasticity and damage effects, both of which could have significant impact on structural analysis results...through a user-written material ( UMAT ) subroutine. D Micromechanical Analyse Micromechanical methods and selective experimentation are used to develop an
Modeling electromagnetic rail launchers at speed using 3D finite elements
Rodger, D.; Leonard, P.J.; Eastham, J.F. )
1991-01-01
In this paper a new finite element technique for modelling 3D transient eddy currents in moving conductors is described. This has been implemented in the MEGA software package for 2 and 3D electromagnetic field analysis. The application of the technique to railgun launchers is illustrated.
3-D adaptive nonlinear complex-diffusion despeckling filter.
Rodrigues, Pedro; Bernardes, Rui
2012-12-01
This work aims to improve the process of speckle noise reduction while preserving edges and other relevant features through filter expansion from 2-D to 3-D. Despeckling is very important for data visual inspection and as a preprocessing step for other algorithms, as they are usually notably influenced by speckle noise. To that intent, a 3-D approach is proposed for the adaptive complex-diffusion filter. This 3-D iterative filter was applied to spectral-domain optical coherence tomography medical imaging volumes of the human retina and a quantitative evaluation of the results was performed to allow a demonstration of the better performance of the 3-D over the 2-D filtering and to choose the best total diffusion time. In addition, we propose a fast graphical processing unit parallel implementation so that the filter can be used in a clinical setting.
Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography.
Javaherian, Ashkan; Soleimani, Manuchehr; Moeller, Knut
2015-01-01
This study proposes a method to improve performance of sparse recovery inverse solvers in 3D electrical impedance tomography (3D EIT), especially when the volume under study contains small-sized inclusions, e.g. 3D imaging of breast tumours. Initially, a quadratic regularized inverse solver is applied in a fast manner with a stopping threshold much greater than the optimum. Based on assuming a fixed level of sparsity for the conductivity field, finite elements are then sampled via applying a compressive sensing (CS) algorithm to the rough blurred estimation previously made by the quadratic solver. Finally, a sparse inverse solver is applied solely to the sampled finite elements, with the solution to the CS as its initial guess. The results show the great potential of the proposed CS-based sparse recovery in improving accuracy of sparse solution to the large-size 3D EIT.
A 3D staggered-grid finite difference scheme for poroelastic wave equation
NASA Astrophysics Data System (ADS)
Zhang, Yijie; Gao, Jinghuai
2014-10-01
Three dimensional numerical modeling has been a viable tool for understanding wave propagation in real media. The poroelastic media can better describe the phenomena of hydrocarbon reservoirs than acoustic and elastic media. However, the numerical modeling in 3D poroelastic media demands significantly more computational capacity, including both computational time and memory. In this paper, we present a 3D poroelastic staggered-grid finite difference (SFD) scheme. During the procedure, parallel computing is implemented to reduce the computational time. Parallelization is based on domain decomposition, and communication between processors is performed using message passing interface (MPI). Parallel analysis shows that the parallelized SFD scheme significantly improves the simulation efficiency and 3D decomposition in domain is the most efficient. We also analyze the numerical dispersion and stability condition of the 3D poroelastic SFD method. Numerical results show that the 3D numerical simulation can provide a real description of wave propagation.
Finite element model calibration of a nonlinear perforated plate
NASA Astrophysics Data System (ADS)
Ehrhardt, David A.; Allen, Matthew S.; Beberniss, Timothy J.; Neild, Simon A.
2017-03-01
This paper presents a case study in which the finite element model for a curved circular plate is calibrated to reproduce both the linear and nonlinear dynamic response measured from two nominally identical samples. The linear dynamic response is described with the linear natural frequencies and mode shapes identified with a roving hammer test. Due to the uncertainty in the stiffness characteristics from the manufactured perforations, the linear natural frequencies are used to update the effective modulus of elasticity of the full order finite element model (FEM). The nonlinear dynamic response is described with nonlinear normal modes (NNMs) measured using force appropriation and high speed 3D digital image correlation (3D-DIC). The measured NNMs are used to update the boundary conditions of the full order FEM through comparison with NNMs calculated from a nonlinear reduced order model (NLROM). This comparison revealed that the nonlinear behavior could not be captured without accounting for the small curvature of the plate from manufacturing as confirmed in literature. So, 3D-DIC was also used to identify the initial static curvature of each plate and the resulting curvature was included in the full order FEM. The updated models are then used to understand how the stress distribution changes at large response amplitudes providing a possible explanation of failures observed during testing.
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
3D early embryogenesis image filtering by nonlinear partial differential equations.
Krivá, Z; Mikula, K; Peyriéras, N; Rizzi, B; Sarti, A; Stasová, O
2010-08-01
We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which
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.
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.
Nonlinear Multiscale Modeling of 3D Woven Fiber Composites under Ballistic Loading
2013-07-11
advanced composites like 3D -OWC. On the other hand, a microscale simulation with resolution of individual fiber filament is impractical due to enormous...REPORT Nonlinear Multiscale Modeling of 3D Woven Fiber Composites under Ballistic Loading 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: The objective of...analysis of 3D woven fiber composites under ballistic loading. Since material behavior is determined by its microstructure, it is essential to
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
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.
HEMP 3D -- a finite difference program for calculating elastic-plastic flow
Wilkins, M.L.
1993-05-26
The HEMP 3D program can be used to solve problems in solid mechanics involving dynamic plasticity and time dependent material behavior and problems in gas dynamics. The equations of motion, the conservation equations, and the constitutive relations are solved by finite difference methods following the format of the HEMP computer simulation program formulated in two space dimensions and time. Presented here is an update of the 1975 report on the HEMP 3D numerical technique. The present report includes the sliding surface routines programmed by Robert Gulliford.
An efficient finite-element algorithm for 3D layered complex structure modelling.
Sahalos, J N; Kyriacou, G A; Vafiadis, E
1994-05-01
In this paper an efficient finite-element method (FEM) algorithm for complicated three-dimensional (3D) layered type models has been developed. Its unique feature is that it can handle, with memory requirements within the abilities of a simple PC, arbitrarily shaped 3D elements. This task is achieved by storing only the non-zero coefficients of the sparse FEM system of equations. The algorithm is applied to the solution of the Laplace equation in models with up to 79 layers of trilinear general hexahedron elements. The system of equations is solved with the Gauss-Seidel iterative technique.
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.
3D hierarchical interface-enriched finite element method: Implementation and applications
NASA Astrophysics Data System (ADS)
Soghrati, Soheil; Ahmadian, Hossein
2015-10-01
A hierarchical interface-enriched finite element method (HIFEM) is proposed for the mesh-independent treatment of 3D problems with intricate morphologies. The HIFEM implements a recursive algorithm for creating enrichment functions that capture gradient discontinuities in nonconforming finite elements cut by arbitrary number and configuration of materials interfaces. The method enables the mesh-independent simulation of multiphase problems with materials interfaces that are in close proximity or contact while providing a straightforward general approach for evaluating the enrichments. In this manuscript, we present a detailed discussion on the implementation issues and required computational geometry considerations associated with the HIFEM approximation of thermal and mechanical responses of 3D problems. A convergence study is provided to investigate the accuracy and convergence rate of the HIFEM and compare them with standard FEM benchmark solutions. We will also demonstrate the application of this mesh-independent method for simulating the thermal and mechanical responses of two composite materials systems with complex microstructures.
3D finite-difference modeling algorithm and anomaly features of ZTEM
NASA Astrophysics Data System (ADS)
Wang, Tao; Tan, Han-Dong; Li, Zhi-Qiang; Wang, Kun-Peng; Hu, Zhi-Ming; Zhang, Xing-Dong
2016-09-01
The Z-Axis tipper electromagnetic (ZTEM) technique is based on a frequency-domain airborne electromagnetic system that measures the natural magnetic field. A survey area was divided into several blocks by using the Maxwell's equations, and the magnetic components at the center of each edge of the grid cell are evaluated by applying the staggered-grid finite-difference method. The tipper and its divergence are derived to complete the 3D ZTEM forward modeling algorithm. A synthetic model is then used to compare the responses with those of 2D finite-element forward modeling to verify the accuracy of the algorithm. ZTEM offers high horizontal resolution to both simple and complex distributions of conductivity. This work is the theoretical foundation for the interpretation of ZTEM data and the study of 3D ZTEM inversion.
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.
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.
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.
Finite element 3D reconstruction of the pulmonary acinus imaged by synchrotron X-ray tomography
Tsuda, A.; Filipovic, N.; Haberthür, D.; Dickie, R.; Matsui, Y.; Stampanoni, M.; Schittny, J. C.
2008-01-01
The alveolated structure of the pulmonary acinus plays a vital role in gas exchange function. Three-dimensional (3D) analysis of the parenchymal region is fundamental to understanding this structure-function relationship, but only a limited number of attempts have been conducted in the past because of technical limitations. In this study, we developed a new image processing methodology based on finite element (FE) analysis for accurate 3D structural reconstruction of the gas exchange regions of the lung. Stereologically well characterized rat lung samples (Pediatr Res 53: 72–80, 2003) were imaged using high-resolution synchrotron radiation-based X-ray tomographic microscopy. A stack of 1,024 images (each slice: 1024 × 1024 pixels) with resolution of 1.4 μm3 per voxel were generated. For the development of FE algorithm, regions of interest (ROI), containing ∼7.5 million voxels, were further extracted as a working subunit. 3D FEs were created overlaying the voxel map using a grid-based hexahedral algorithm. A proper threshold value for appropriate segmentation was iteratively determined to match the calculated volume density of tissue to the stereologically determined value (Pediatr Res 53: 72–80, 2003). The resulting 3D FEs are ready to be used for 3D structural analysis as well as for subsequent FE computational analyses like fluid dynamics and skeletonization. PMID:18583378
NASA Astrophysics Data System (ADS)
Shahraeeni, E.; Firoozabadi, A.
2012-12-01
We present a 3D model for fully compositional multi-phase multi-component flow in porous media with species transfer between the phases. Phase properties are modeled with the Peng-Robinson equation of state. Because phase properties may exhibit strong discontinuities, we approximate the mass transport update by the means of discontinuous Galerkin method. Pressure and velocity fields are continuous across the whole domain of solution, which is guaranteed by using the mixed hybrid finite element method. Complexity of the flow necessitates the use of either very fine mesh or higher-order schemes. The use of higher-order finite element methods significantly reduces numerical dispersion and grid orientation effects that plague traditional finite difference methods. We have shown that in 3D the convergence rate of our scheme is twice as first order method and the CPU time may improve up to three orders of magnitude for the same level of accuracy. Our numerical model facilitates accurate simulation of delicate feature of compositional flow like fingering and CO2 injection in complex reservoirs for a broad range of applications, including CO2 sequestration in finite aquifer and water flooded reservoirs with transfer of all species between the phases.
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.
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.
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.
3-D finite element modelling of facial soft tissue and preliminary application in orthodontics.
Chen, Si; Lou, Hangdi; Guo, Liang; Rong, Qiguo; Liu, Yi; Xu, Tian-Min
2012-01-01
Prediction of soft tissue aesthetics is important for achieving an optimal outcome in orthodontic treatment planning. Previously, applicable procedures were mainly restricted to 2-D profile prediction. In this study, a generic 3-D finite element (FE) model of the craniofacial soft and hard tissue was constructed, and individualisation of the generic model based on cone beam CT data and mathematical transformation was investigated. The result indicated that patient-specific 3-D facial FE model including different layers of soft tissue could be obtained through mathematical model transformation. Average deviation between the transformed model and the real reconstructed one was 0.47 ± 0.77 mm and 0.75 ± 0.84 mm in soft and hard tissue, respectively. With boundary condition defined according to treatment plan, such FE model could be used to predict the result of orthodontic treatment on facial soft tissue.
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.
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.
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.
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.
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.
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 problem results are presented.
Parallel 3D Finite Element Particle-in-Cell Simulations with Pic3P
Candel, A.; Kabel, A.; Lee, L.; Li, Z.; Ng, C.; Schussman, G.; Ko, K.; Ben-Zvi, I.; Kewisch, J.; /Brookhaven
2009-06-19
SLAC's Advanced Computations Department (ACD) has developed the parallel 3D Finite Element electromagnetic Particle-In-Cell code Pic3P. Designed for simulations of beam-cavity interactions dominated by space charge effects, Pic3P solves the complete set of Maxwell-Lorentz equations self-consistently and includes space-charge, retardation and boundary effects from first principles. Higher-order Finite Element methods with adaptive refinement on conformal unstructured meshes lead to highly efficient use of computational resources. Massively parallel processing with dynamic load balancing enables large-scale modeling of photoinjectors with unprecedented accuracy, aiding the design and operation of next-generation accelerator facilities. Applications include the LCLS RF gun and the BNL polarized SRF gun.
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
Lee, W; Kim, T-S; Cho, M; Lee, S
2005-01-01
In studying bioelectromagnetic problems, finite element method offers several advantages over other conventional methods such as boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropy. Mesh generation is the first requirement in the finite element analysis and there are many different approaches in mesh generation. However conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes, resulting in numerous elements in the smaller volume regions, thereby increasing computational load and demand. In this work, we present an improved content-adaptive mesh generation scheme that is efficient and fast along with options to change the contents of meshes. For demonstration, mesh models of the head from a volume MRI are presented in 2-D and 3-D.
NASA Astrophysics Data System (ADS)
Aristovich, K. Y.; Khan, S. H.
2010-07-01
Realistic computer modelling of biological objects requires building of very accurate and realistic computer models based on geometric and material data, type, and accuracy of numerical analyses. This paper presents some of the automatic tools and algorithms that were used to build accurate and realistic 3D finite element (FE) model of whole-brain. These models were used to solve the forward problem in magnetic field tomography (MFT) based on Magnetoencephalography (MEG). The forward problem involves modelling and computation of magnetic fields produced by human brain during cognitive processing. The geometric parameters of the model were obtained from accurate Magnetic Resonance Imaging (MRI) data and the material properties - from those obtained from Diffusion Tensor MRI (DTMRI). The 3D FE models of the brain built using this approach has been shown to be very accurate in terms of both geometric and material properties. The model is stored on the computer in Computer-Aided Parametrical Design (CAD) format. This allows the model to be used in a wide a range of methods of analysis, such as finite element method (FEM), Boundary Element Method (BEM), Monte-Carlo Simulations, etc. The generic model building approach presented here could be used for accurate and realistic modelling of human brain and many other biological objects.
Nonlinear Numerical Modeling of Shape Control in IGNITOR in the Presence of 3D Structures
NASA Astrophysics Data System (ADS)
Albanese, R.; Ambrosino, G.; de Tommasi, G.; Pironti, A.; Rubinacci, G.; Villone, F.; Ramogida, G.; Coppi, B.
2014-10-01
IGNITOR is a high field compact machine designed for the investigation of fusion burning plasmas at or close to ignition. The integrated plasma position, shape and current control plays an important role in its safe operation. The analysis of its behavior taking into account nonlinear and 3D effects can be of great interest for assessing its performances. In fact, the system was designed on the basis of an axisymmetric linearized model. To this purpose, we use a computational tool, called CarMa0NL, with the unprecedented capability of simultaneously considering three-dimensional effects of conductors surrounding the plasma and the inherent nonlinearity of the plasma behaviour itself, in the presence of the complex set of circuit equations describing the control system. Preliminary results already lead to the conclusion that the vertical position response is not much influenced by nonlinear and 3D effects, as the vertical stabilization controller is able to ``hide'' the differences in open-loop models. Here we assess the performance of the shape controller, by coupling the nonlinear plasma evolution in the presence of the 3D vessel with ports to the complex circuit dynamics simulating the integrated closed loop control system.
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
Least-squares finite element solution of 3D incompressible Navier-Stokes problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.
1992-01-01
Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.
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.
3-D zebrafish embryo image filtering by nonlinear partial differential equations.
Rizzi, Barbara; Campana, Matteo; Zanella, Cecilia; Melani, Camilo; Cunderlik, Robert; Krivá, Zuzana; Bourgine, Paul; Mikula, Karol; Peyriéras, Nadine; Sarti, Alessandro
2007-01-01
We discuss application of nonlinear PDE based methods to filtering of 3-D confocal images of embryogenesis. We focus on the mean curvature driven and the regularized Perona-Malik equations, where standard as well as newly suggested edge detectors are used. After presenting the related mathematical models, the practical results are given and discussed by visual inspection and quantitatively using the mean Hausdorff distance.
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.
Towards automated 3D finite element modeling of direct fiber reinforced composite dental bridge.
Li, Wei; Swain, Michael V; Li, Qing; Steven, Grant P
2005-07-01
An automated 3D finite element (FE) modeling procedure for direct fiber reinforced dental bridge is established on the basis of computer tomography (CT) scan data. The model presented herein represents a two-unit anterior cantilever bridge that includes a maxillary right incisor as an abutment and a maxillary left incisor as a cantilever pontic bonded by adhesive and reinforced fibers. The study aims at gathering fundamental knowledge for design optimization of this type of innovative composite dental bridges. To promote the automatic level of numerical analysis and computational design of new dental biomaterials, this report pays particular attention to the mathematical modeling, mesh generation, and validation of numerical models. To assess the numerical accuracy and to validate the model established, a convergence test and experimental verification are also presented.
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.
The modelling of VLF Trimpis using both finite element and 3D Born Modelling
NASA Astrophysics Data System (ADS)
Baba, K.; Nunn, D.; Hayakawa, M.
This paper investigates the numerical modelling of VLF Trimpis produced by a D region inhomogeneity on the Great Circle Path. Two different codes are used. The first is a 2D finite element method (FEM) code, whose solutions are valid in the non-Born limit. The second is a 3D model that invokes the Born approximation. The predicted Trimpis from these codes compare closely, thus confirming the validity of both models. The modal scattering matrices have a comparable structure, and indicate strong scattering between the dominant TM modes. Analysis of the scattering matrix from the FEM code delineates the Born regime. For a LIE with a radius of 100kms, the Born approximation becomes invalid at an electron density perturbation of about 8 el/cc.
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.
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
3D finite element model of the diabetic neuropathic foot: a gait analysis driven approach.
Guiotto, Annamaria; Sawacha, Zimi; Guarneri, Gabriella; Avogaro, Angelo; Cobelli, Claudio
2014-09-22
Diabetic foot is an invalidating complication of diabetes that can lead to foot ulcers. Three-dimensional (3D) finite element analysis (FEA) allows characterizing the loads developed in the different anatomical structures of the foot in dynamic conditions. The aim of this study was to develop a subject specific 3D foot FE model (FEM) of a diabetic neuropathic (DNS) and a healthy (HS) subject, whose subject specificity can be found in term of foot geometry and boundary conditions. Kinematics, kinetics and plantar pressure (PP) data were extracted from the gait analysis trials of the two subjects with this purpose. The FEM were developed segmenting bones, cartilage and skin from MRI and drawing a horizontal plate as ground support. Materials properties were adopted from previous literature. FE simulations were run with the kinematics and kinetics data of four different phases of the stance phase of gait (heel strike, loading response, midstance and push off). FEMs were then driven by group gait data of 10 neuropathic and 10 healthy subjects. Model validation focused on agreement between FEM-simulated and experimental PP. The peak values and the total distribution of the pressures were compared for this purpose. Results showed that the models were less robust when driven from group data and underestimated the PP in each foot subarea. In particular in the case of the neuropathic subject's model the mean errors between experimental and simulated data were around the 20% of the peak values. This knowledge is crucial in understanding the aetiology of diabetic foot.
Finite Element Based Anisotropic 3D Inversion of Marine CSEM Data
NASA Astrophysics Data System (ADS)
Chung, Y.; Byun, J.
2015-12-01
In order to interpret three-dimensional (3D) marine controlled-source electromagnetic (MCSEM) data, it is critical to accurately determine electrical anisotropy because ignoring anisotropy can produce misleading artifacts. In this study, we present an inversion method for 3D subsurface imaging in media with an inhomogeneous and anisotropic conductivity distribution. Direct solvers are incorporated both in the forward and inverse problems, For the forward problem, the vector Helmholtz equation for the secondary electric field is discretized on a hexahedral mesh using edge finite elements, then a direct sparse-matrix solver is chosen to effectively reuse its factorization both in the survey simulation and Jacobian computation. The inversion method is formulated as a functional optimization with an objective functional containing terms measuring data misfit and model structure by means of smoothness and anisotropy. These measures are efficiently incorporated through the use of an iteratively reweighted least-squares scheme. The objective functional is minimized by a Gauss-Newton approach using a direct dense-matrix solver. We demonstrate the accuracy and applicability of the algorithm by testing it on synthetic data sets.
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.
3D finite element model of the chinchilla ear for characterizing middle ear functions.
Wang, Xuelin; Gan, Rong Z
2016-10-01
Chinchilla is a commonly used animal model for research of sound transmission through the ear. Experimental measurements of the middle ear transfer function in chinchillas have shown that the middle ear cavity greatly affects the tympanic membrane (TM) and stapes footplate (FP) displacements. However, there is no finite element (FE) model of the chinchilla ear available in the literature to characterize the middle ear functions with the anatomical features of the chinchilla ear. This paper reports a recently completed 3D FE model of the chinchilla ear based on X-ray micro-computed tomography images of a chinchilla bulla. The model consisted of the ear canal, TM, middle ear ossicles and suspensory ligaments, and the middle ear cavity. Two boundary conditions of the middle ear cavity wall were simulated in the model as the rigid structure and the partially flexible surface, and the acoustic-mechanical coupled analysis was conducted with these two conditions to characterize the middle ear function. The model results were compared with experimental measurements reported in the literature including the TM and FP displacements and the middle ear input admittance in chinchilla ear. An application of this model was presented to identify the acoustic role of the middle ear septa-a unique feature of chinchilla middle ear cavity. This study provides the first 3D FE model of the chinchilla ear for characterizing the middle ear functions through the acoustic-mechanical coupled FE analysis.
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.
Comparative Results on 3D Navigation of Quadrotor using two Nonlinear Model based Controllers
NASA Astrophysics Data System (ADS)
Bouzid, Y.; Siguerdidjane, H.; Bestaoui, Y.
2017-01-01
Recently the quadrotors are being increasingly employed in both military and civilian areas where a broad range of nonlinear flight control techniques are successfully implemented. With this advancement, it has become necessary to investigate the efficiency of these flight controllers by studying theirs features and compare their performance. In this paper, the control of Unmanned Aerial Vehicle (UAV) quadrotor, using two different approaches, is presented. The first controller is Nonlinear PID (NLPID) whilst the second one is Nonlinear Internal Model Control (NLIMC) that are used for the stabilization as well as for the 3D trajectory tracking. The numerical simulations have shown satisfactory results using nominal system model or disturbed model for both of them. The obtained results are analyzed with respect to several criteria for the sake of comparison.
Mortezai, Omid; Esmaily, Masomeh; Darvishpour, Hojat
2015-01-01
Objectives: Headgears are among the effective orthodontic appliances to achieve treatment goals. Unilateral molar distal movement is sometimes needed during an orthodontic treatment, which can be achieved by an asymmetric headgear. Different unilateral headgears have been introduced. The main goal of this study was to analyze the force system of unilateral expanded outer bow asymmetric headgears by the finite element method (FEM). Materials and Methods: Six 3D finite element models of a mesiodistal slice of the maxilla containing upper first molars, their periodontal ligaments (PDLs), cancellous bone, cortical bone, and a cervical headgear with expanded outer bow attached to maxillary first molars were designed in SolidWorks 2010 and meshed in ANSYS Workbench ver. 12.1. The models were the same except for the degree of outer bow expansion. The outer bow ends were loaded with 2 N force. The distal driving force and the net moment were evaluated. Results: A decrease in the distalizing force in the normal side molar from 1.69 N to 1.37 N was shown by increasing the degree of unilateral expansion. At the same time, the force increased from 2.19 N to 2.49 N in the expanded side molar. A net moment increasing from 2.26 N.mm to 4.64 N.mm was also shown. Conclusion: Unilateral outer bow expansion can produce different distalizing forces in molars, which increase by increasing the expansion. PMID:26622282
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.
A 3D moving mesh Finite Element Method for two-phase flows
NASA Astrophysics Data System (ADS)
Anjos, G. R.; Borhani, N.; Mangiavacchi, N.; Thome, J. R.
2014-08-01
A 3D ALE Finite Element Method is developed to study two-phase flow phenomena using a new discretization method to compute the surface tension forces. The computational method is based on the Arbitrary Lagrangian-Eulerian formulation (ALE) and the Finite Element Method (FEM), creating a two-phase method with an improved model for the liquid-gas interface. An adaptive mesh update procedure is also proposed for effective management of the mesh to remove, add and repair elements, since the computational mesh nodes move according to the flow. The ALE description explicitly defines the two-phase interface position by a set of interconnected nodes which ensures a sharp representation of the boundary, including the role of the surface tension. The proposed methodology for computing the curvature leads to accurate results with moderate programming effort and computational cost. Static and dynamic tests have been carried out to validate the method and the results have compared well to analytical solutions and experimental results found in the literature, demonstrating that the new proposed methodology provides good accuracy to describe the interfacial forces and bubble dynamics. This paper focuses on the description of the proposed methodology, with particular emphasis on the discretization of the surface tension force, the new remeshing technique, and the validation results. Additionally, a microchannel simulation in complex geometry is presented for two elongated bubbles.
DNS of Sheared Particulate Flows with a 3D Explicit Finite-Difference Scheme
NASA Astrophysics Data System (ADS)
Perrin, Andrew; Hu, Howard
2007-11-01
A 3D explicit finite-difference code for direct simulation of the motion of solid particulates in fluids has been developed, and a periodic boundary condition implemented to study the effective viscosity of suspensions in shear. The code enforces the no-slip condition on the surface of spherical particles in a uniform Cartesian grid with a special particle boundary condition based on matching the Stokes flow solutions next to the particle surface with a numerical solution away from it. The method proceeds by approximating the flow next to the particle surface as a Stokes flow in the particle's local coordinates, which is then matched to the finite difference update in the bulk fluid on a ``cage'' of grid points near the particle surface. (The boundary condition is related to the PHYSALIS method (2003), but modified for explicit schemes and with an iterative process removed.) Advantages of the method include superior accuracy of the scheme on a relatively coarse grid for intermediate particle Reynolds numbers, ease of implementation, and the elimination of the need to track the particle surface. For the sheared suspension, the effects of fluid and solid inertia and solid volume fraction on effective viscosity at moderate particle Reynolds numbers and concentrated suspensions will be discussed.
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.
A 3D discontinuous Galerkin finite-element method for teleseismic modelling.
NASA Astrophysics Data System (ADS)
monteiller, vadim; Beller, Stephen; Nolet, Guust; Operto, Stephane; Virieux, Jean
2014-05-01
The massive development of dense seismic arrays and the rapide increase in computing capacity allow today to consider application of full waveform inversion of teleseismic data for high-resolution lithospheric imaging. We present an hybrid numerical method that allows for the modelling of short period telesismic waves in 3D lithospheric target with the discontinuous Galerkin finite elements method, opennig the possibility to perform waveform inversion of seismograms recorded by dense regional broadband arrays. In order to reduce the computational cost of the forward-problem, we developed a method that relies on multi-core parallel computing and computational-domain reduction. We defined two nested levels for parallelism based on MPI library, which are managed by two MPI communicators. Firstly, we use a domain partitionning strategy, assigning one subdomain to one cpu and, secondly we distribute telesismic sources on different copies of the partitioned domain. However, despite the supercomputer ability, the forward-problem remains expensive for telesismic configuration especially when 3D numerical methods are considered. In order to perform the forward problem in a reasonable amount of time, we reduce the computational domain in which full waveform modelling is performed. We defined a 3D regional domain located below the seismological network that is embeded in a background homogeneous or axisymetric model, in which the seismic wavefield can be computed efficiently. The background wavefield is used to compute the full wavefield in the 3D regional domain using the so-called total-field/scattered-field technique (Alterman & Karal (1968),Taflove & Hagness (2005)), which relies on the decomposition of the wavefield into a background and a scattered wavefields. The computational domain is subdivided intro three subdomains: an outer domain formed by the perfectly-mathed absorbing layers, an intermediate zone in which only the outgoing wavefield scattered by the
A time-space domain stereo finite difference method for 3D scalar wave propagation
NASA Astrophysics Data System (ADS)
Chen, Yushu; Yang, Guangwen; Ma, Xiao; He, Conghui; Song, Guojie
2016-11-01
The time-space domain finite difference methods reduce numerical dispersion effectively by minimizing the error in the joint time-space domain. However, their interpolating coefficients are related with the Courant numbers, leading to significantly extra time costs for loading the coefficients consecutively according to velocity in heterogeneous models. In the present study, we develop a time-space domain stereo finite difference (TSSFD) method for 3D scalar wave equation. The method propagates both the displacements and their gradients simultaneously to keep more information of the wavefields, and minimizes the maximum phase velocity error directly using constant interpolation coefficients for different Courant numbers. We obtain the optimal constant coefficients by combining the truncated Taylor series approximation and the time-space domain optimization, and adjust the coefficients to improve the stability condition. Subsequent investigation shows that the TSSFD can suppress numerical dispersion effectively with high computational efficiency. The maximum phase velocity error of the TSSFD is just 3.09% even with only 2 sampling points per minimum wavelength when the Courant number is 0.4. Numerical experiments show that to generate wavefields with no visible numerical dispersion, the computational efficiency of the TSSFD is 576.9%, 193.5%, 699.0%, and 191.6% of those of the 4th-order and 8th-order Lax-Wendroff correction (LWC) method, the 4th-order staggered grid method (SG), and the 8th-order optimal finite difference method (OFD), respectively. Meanwhile, the TSSFD is compatible to the unsplit convolutional perfectly matched layer (CPML) boundary condition for absorbing artificial boundaries. The efficiency and capability to handle complex velocity models make it an attractive tool in imaging methods such as acoustic reverse time migration (RTM).
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.
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.
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.
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 multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone.
Fan, Lixia; Pei, Shaopeng; Lucas Lu, X; Wang, Liyun
2016-01-01
The transport of fluid, nutrients, and signaling molecules in the bone lacunar-canalicular system (LCS) is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching (FRAP) approach to quantify load-induced fluid and solute transport in the LCS in situ, but the measurements were limited to cortical regions 30-50 μm underneath the periosteum due to the constrains of laser penetration. With this work, we aimed to expand our understanding of load-induced fluid and solute transport in both trabecular and cortical bone using a multiscaled image-based finite element analysis (FEA) approach. An intact murine tibia was first re-constructed from microCT images into a three-dimensional (3D) linear elastic FEA model, and the matrix deformations at various locations were calculated under axial loading. A segment of the above 3D model was then imported to the biphasic poroelasticity analysis platform (FEBio) to predict load-induced fluid pressure fields, and interstitial solute/fluid flows through LCS in both cortical and trabecular regions. Further, secondary flow effects such as the shear stress and/or drag force acting on osteocytes, the presumed mechano-sensors in bone, were derived using the previously developed ultrastructural model of Brinkman flow in the canaliculi. The material properties assumed in the FEA models were validated against previously obtained strain and FRAP transport data measured on the cortical cortex. Our results demonstrated the feasibility of this computational approach in estimating the fluid flux in the LCS and the cellular stimulation forces (shear and drag forces) for osteocytes in any cortical and trabecular bone locations, allowing further studies of how the activation of osteocytes correlates with in vivo functional bone formation. The study provides a promising platform to reveal potential cellular mechanisms underlying the anabolic power of exercises and physical activities in treating
Fortuny, Josep; Marcé-Nogué, Jordi; Konietzko-Meier, Dorota
2017-03-29
The Late Triassic freshwater ecosystems were occupied by different tetrapod groups including large-sized anamniotes, such as metoposaurids. Most members of this group of temnospondyls acquired gigantic sizes (up to 5 m long) with a nearly worldwide distribution. The paleoecology of metoposaurids is controversial; they have been historically considered passive, bottom-dwelling animals, waiting for prey on the bottom of rivers and lakes, or they have been suggested to be active mid-water feeders. The present study aims to expand upon the paleoecological interpretations of these animals using 3D finite element analyses (FEA). Skulls from two taxa, Metoposaurus krasiejowensis, a gigantic taxon from Europe, and Apachesaurus gregorii, a non-gigantic taxon from North America, were analyzed under different biomechanical scenarios. Both 3D models of the skulls were scaled to allow comparisons between them and reveal that the general stress distribution pattern found in both taxa is clearly similar in all scenarios. In light of our results, both previous hypotheses about the paleoecology of these animals can be partly merged: metoposaurids probably were ambush and active predators, but not the top predators of these aquatic environments. The FEA results demonstrate that they were particularly efficient at bilateral biting, and together with their characteristically anteropositioned orbits, optimal for an ambush strategy. Nonetheless, the results also show that these animals were capable of lateral strikes of the head, suggesting active hunting of prey. Regarding the important skull size differences between the taxa analyzed, our results suggest that the size reduction in the North American taxon could be related to drastic environmental changes or the increase of competitors. The size reduction might have helped them expand into new ecological niches, but they likely remained fully aquatic, as are all other metoposaurids.
A multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone
Fan, Lixia; Pei, Shaopeng; Lucas Lu, X; Wang, Liyun
2016-01-01
The transport of fluid, nutrients, and signaling molecules in the bone lacunar–canalicular system (LCS) is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching (FRAP) approach to quantify load-induced fluid and solute transport in the LCS in situ, but the measurements were limited to cortical regions 30–50 μm underneath the periosteum due to the constrains of laser penetration. With this work, we aimed to expand our understanding of load-induced fluid and solute transport in both trabecular and cortical bone using a multiscaled image-based finite element analysis (FEA) approach. An intact murine tibia was first re-constructed from microCT images into a three-dimensional (3D) linear elastic FEA model, and the matrix deformations at various locations were calculated under axial loading. A segment of the above 3D model was then imported to the biphasic poroelasticity analysis platform (FEBio) to predict load-induced fluid pressure fields, and interstitial solute/fluid flows through LCS in both cortical and trabecular regions. Further, secondary flow effects such as the shear stress and/or drag force acting on osteocytes, the presumed mechano-sensors in bone, were derived using the previously developed ultrastructural model of Brinkman flow in the canaliculi. The material properties assumed in the FEA models were validated against previously obtained strain and FRAP transport data measured on the cortical cortex. Our results demonstrated the feasibility of this computational approach in estimating the fluid flux in the LCS and the cellular stimulation forces (shear and drag forces) for osteocytes in any cortical and trabecular bone locations, allowing further studies of how the activation of osteocytes correlates with in vivo functional bone formation. The study provides a promising platform to reveal potential cellular mechanisms underlying the anabolic power of exercises and physical activities in
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
2015-06-25
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 pelvic organ prolapse quantification system (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.
A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling
NASA Astrophysics Data System (ADS)
Ren, Zhengyong; Kalscheuer, Thomas; Greenhalgh, Stewart; Maurer, Hansruedi
2013-08-01
We have developed a novel goal-oriented adaptive mesh refinement approach for finite-element methods to model plane wave electromagnetic (EM) fields in 3-D earth models based on the electric field differential equation. To handle complicated models of arbitrary conductivity, magnetic permeability and dielectric permittivity involving curved boundaries and surface topography, we employ an unstructured grid approach. The electric field is approximated by linear curl-conforming shape functions which guarantee the divergence-free condition of the electric field within each tetrahedron and continuity of the tangential component of the electric field across the interior boundaries. Based on the non-zero residuals of the approximated electric field and the yet to be satisfied boundary conditions of continuity of both the normal component of the total current density and the tangential component of the magnetic field strength across the interior interfaces, three a-posterior error estimators are proposed as a means to drive the goal-oriented adaptive refinement procedure. The first a-posterior error estimator relies on a combination of the residual of the electric field, the discontinuity of the normal component of the total current density and the discontinuity of the tangential component of the magnetic field strength across the interior faces shared by tetrahedra. The second a-posterior error estimator is expressed in terms of the discontinuity of the normal component of the total current density (conduction plus displacement current). The discontinuity of the tangential component of the magnetic field forms the third a-posterior error estimator. Analytical solutions for magnetotelluric (MT) and radiomagnetotelluric (RMT) fields impinging on a homogeneous half-space model are used to test the performances of the newly developed goal-oriented algorithms using the above three a-posterior error estimators. A trapezoidal topographical model, using normally incident EM waves
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.
Nonlinear Conservation Laws and Finite Volume Methods
NASA Astrophysics Data System (ADS)
Leveque, Randall J.
Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References
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
A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems
NASA Astrophysics Data System (ADS)
Zhao, Jing; Vollebregt, Edwin A. H.; Oosterlee, Cornelis W.
2015-05-01
This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, using azimuth angles as variables instead of conventional traction variables. The new variables are scaled by the diagonal of the underlying Jacobian. The fast Fourier transform (FFT) technique accelerates all matrix-vector products encountered, exploiting the matrix' Toeplitz structure. Numerical tests demonstrate a significant reduction of the computational time compared to existing solvers for concentrated contact problems.
A class of finite dimensional optimal nonlinear estimators
NASA Technical Reports Server (NTRS)
Marcus, S. I.; Willsky, A. S.
1974-01-01
Finite dimensional optimal nonlinear state estimators are derived for bilinear systems evolving on nilpotent and solvable Lie groups. These results are extended to other classes of systems involving polynomial nonlinearities. The concepts of exact differentials and path-independent integrals are used to derive optimal finite dimensional estimators for a further class of nonlinear systems.
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.
Plasmonics of 3-D Nanoshell Dimers Using Multipole Expansion and Finite Element Method
Khoury, Christopher G.; Norton, Stephen J.
2013-01-01
The spatial and spectral responses of the plasmonic fields induced in the gap of 3-D Nanoshell Dimers of gold and silver are comprehensively investigated and compared via theory and simulation, using the Multipole Expansion (ME) and the Finite Element Method (FEM) in COMSOL, respectively. The E-field in the dimer gap was evaluated and compared as a function of shell thickness, inter-particle distance, and size. The E-field increased with decreasing shell thickness, decreasing interparticle distance, and increasing size, with the error between the two methods ranging from 1 to 10%, depending on the specific combination of these three variables. This error increases several fold with increasing dimer size, as the quasi-static approximation breaks down. A consistent overestimation of the plasmon’s FWHM and red-shifting of the plasmon peak occurs with FEM, relative to ME, and it increases with decreasing shell thickness and inter-particle distance. The size-effect that arises from surface scattering of electrons is addressed and shown to be especially prominent for thin shells, for which significant damping, broadening and shifting of the plasmon band is observed; the size-effect also affects large nanoshell dimers, depending on their relative shell thickness, but to a lesser extent. This study demonstrates that COMSOL is a promising simulation environment to quantitatively investigate nanoscale electromagnetics for the modeling and designing of Surface Enhanced Raman Scattering (SERS) substrates. PMID:19678677
Efficient finite element modeling of scattering for 2D and 3D problems
NASA Astrophysics Data System (ADS)
Wilcox, Paul D.; Velichko, Alexander
2010-03-01
The scattering of waves by defects is central to ultrasonic NDE and SHM. In general, scattering problems must be modeled using direct numerical methods such as finite elements (FE), which is very computationally demanding. The most efficient way is to only model the scatterer itself and a minimal region of the surrounding host medium, and this was previously demonstrated for 2-dimensional (2D) bulk wave scattering problems in isotropic media. An encircling array of monopole and dipole sources is used to inject an arbitrary wavefront onto the scatterer and the scattered field is monitored by a second encircling array of monitoring points. From this data, the scattered field can be projected out to any point in space. If the incident wave is chosen to be a plane wave incident from a given angle and the scattered field is projected to distant points in the far-field of the scatterer, the far-field scattering or S-matrix may be obtained, which encodes all the available scattering information. In this paper, the technique is generalized to any elastic wave geometry in both 2D and 3D, where the latter can include guided wave scattering problems. A further refinement enables the technique to be employed with free FE meshes of triangular or tetrahedral elements.
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.
Finite element simulation of HIP-process to produce 3d near net shape parts
Zadeh, M.K.
1996-12-31
One of the major problems when producing powder metallurgy parts through hot isostatic pressing (HIP) is the non homogeneous shrinkage of HIP-capsule during the process. This leads to time and cost consuming machining of the HIP parts. In order to reduce the machining to a minimum, one can try to simulate the HIP-process by means of numerical methods. Hereby, the part distortion can be predicted, and hence a new HIP-capsule can be designed in such a way to prevent the distortion partly or even completely. In the following, a finite element method is used, on one hand, to simulate part shrinkage during HIP process; on the other hand a method is integrated in this simulation to optimize the HIP-capsule geometry. For the determination of material dependent parameters, a mixture of theoretical and experimental methods is used. Results of simulation are verified for a complex 3d HIP part out of TiAl6V4.
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.
3D Finite-Difference Modeling of Scattered Teleseismic Wavefields in a Subduction Zone
NASA Astrophysics Data System (ADS)
Morozov, I. B.; Zheng, H.
2005-12-01
For a teleseismic array targeting subducting crust in a zone of active subduction, scattering from the zone underlying the trench result in subhorizontally-propagating waves that could be difficult to distinguish from converted P- and S- wave backscattered from the surface. Because back-scattered modes often provide the most spectacular images of subducting slabs, it is important to understand their differences from the arrivals scattered from the trench zone. To investigate the detailed teleseismic wavefield in a subduction zone environment, we performed a full-waveform, 3-D visco-elastic finite-difference modeling of teleseismic wave propagation using a Beowulf cluster. The synthetics show strong scattering from the trench zone, dominated by the mantle and crustal P-waves propagating at 6.2-8.1.km/s and slower. These scattered waves occupy the same time and moveout intervals as the backscattered modes, and also have similar amplitudes. Although their amplitude decay characters are different, with the uncertainties in the velocity and density structure of the subduction zone, unambiguous distinguishing of these modes appears difficult. However, under minimal assumptions (in particular, without invoking slab dehydration), recent observations of receiver function amplitudes decreasing away from the trench favor the interpretation of trench-zone scattering.
NASA Astrophysics Data System (ADS)
Tang, Peipei; Wang, Chengjing; Dai, Xiaoxia
2016-04-01
In this paper, we propose a majorized Newton-CG augmented Lagrangian-based finite element method for 3D elastic frictionless contact problems. In this scheme, we discretize the restoration problem via the finite element method and reformulate it to a constrained optimization problem. Then we apply the majorized Newton-CG augmented Lagrangian method to solve the optimization problem, which is very suitable for the ill-conditioned case. Numerical results demonstrate that the proposed method is a very efficient algorithm for various large-scale 3D restorations of geological models, especially for the restoration of geological models with complicated faults.
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.
NASA Astrophysics Data System (ADS)
Wang, Ren H.
1991-02-01
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.
Non-linear tearing of 3D null point current sheets
Wyper, P. F. Pontin, D. I.
2014-08-15
The manner in which the rate of magnetic reconnection scales with the Lundquist number in realistic three-dimensional (3D) geometries is still an unsolved problem. It has been demonstrated that in 2D rapid non-linear tearing allows the reconnection rate to become almost independent of the Lundquist number (the “plasmoid instability”). Here, we present the first study of an analogous instability in a fully 3D geometry, defined by a magnetic null point. The 3D null current layer is found to be susceptible to an analogous instability but is marginally more stable than an equivalent 2D Sweet-Parker-like layer. Tearing of the sheet creates a thin boundary layer around the separatrix surface, contained within a flux envelope with a hyperbolic structure that mimics a spine-fan topology. Efficient mixing of flux between the two topological domains occurs as the flux rope structures created during the tearing process evolve within this envelope. This leads to a substantial increase in the rate of reconnection between the two domains.
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.
Wakefield Simulation of CLIC PETS Structure Using Parallel 3D Finite Element Time-Domain Solver T3P
Candel, A.; Kabel, A.; Lee, L.; Li, Z.; Ng, C.; Schussman, G.; Ko, K.; Syratchev, I.; /CERN
2009-06-19
In recent years, SLAC's Advanced Computations Department (ACD) has developed the parallel 3D Finite Element electromagnetic time-domain code T3P. Higher-order Finite Element methods on conformal unstructured meshes and massively parallel processing allow unprecedented simulation accuracy for wakefield computations and simulations of transient effects in realistic accelerator structures. Applications include simulation of wakefield damping in the Compact Linear Collider (CLIC) power extraction and transfer structure (PETS).
3-D Finite-Difference Modeling of Earthquakes in the City of Rome, Italy
NASA Astrophysics Data System (ADS)
Akinci, A.; Olsen, K. B.; Rovelli, A.; Marra, F.; Malagnini, L.
2002-12-01
The goal of this study is to estimate 3-D amplification effects from regional and local earthquakes in the city of Rome. Mainly, two distinct seismogenic districts may affect the city of Rome: the (1) Alban Hills region, located about 25 km from downtown Rome, and (2) the Central Apennines, located 80-100 km from Rome where the most recent event occurred on January 13, 1915 (M=6.8) which was felt in Rome with a VII degree intensity. To address the seismic hazard in Rome from such sources we have simulated 0-1 Hz viscoelastic wave propagation in a three-dimensional model of the Tiber Valley, Rome, for an M5.5 scenario earthquake (1 Hz) in the seismogenic area of Alban Hills about 25 km from downtown Rome and an M7.0 earthquake (0.5 Hz) about 100 km east of the valley using a fourth-order staggered-grid finite-difference method. We used a basin model (~ 6 km by 6 km by 0.050 km) which includes sediments with shear-wave velocities as low as 250 m/s in the Tiber River sediments, constrained by more than 3000 borehole measurements. We have also estimated the amplification of the 3D model due to a 1-Hz vertically-incident planar SH wave. Our results suggest that the strongest ground motion amplification in Rome is restricted to the Holocene alluvial areas with a significant concentration close to the edges of the Tiber River valley, in agreement with the results by Tertulliani and Riguzzi (1995). In particular, the fill deposits in the Tiber River generate amplification by up to a factor of 2 with respect to the surrounding volcanics, largest near the contact between the alluvial sediments and the surrounding volcanic deposits for the incident plane wave source. We find 1-Hz peak ground velocities of up to 30 cm/sec for the M5.5, Alban Hills earthquake, largest near the northwestern edges of the Tiber River. The largest 0.5-Hz peak velocity is 24 cm/s for the M7.0 earthquake with extended durations up to about 1 min. The lower maximum frequency for this scenario is
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
Poroelastic Wave Propagation With a 3D Velocity-Stress-Pressure Finite-Difference Algorithm
NASA Astrophysics Data System (ADS)
Aldridge, D. F.; Symons, N. P.; Bartel, L. C.
2004-12-01
Seismic wave propagation within a three-dimensional, heterogeneous, isotropic poroelastic medium is numerically simulated with an explicit, time-domain, finite-difference algorithm. A system of thirteen, coupled, first-order, partial differential equations is solved for the particle velocity vector components, the stress tensor components, and the pressure associated with solid and fluid constituents of the two-phase continuum. These thirteen dependent variables are stored on staggered temporal and spatial grids, analogous to the scheme utilized for solution of the conventional velocity-stress system of isotropic elastodynamics. Centered finite-difference operators possess 2nd-order accuracy in time and 4th-order accuracy in space. Seismological utility is enhanced by an optional stress-free boundary condition applied on a horizontal plane representing the earth's surface. Absorbing boundary conditions are imposed on the flanks of the 3D spatial grid via a simple wavefield amplitude taper approach. A massively parallel computational implementation, utilizing the spatial domain decomposition strategy, allows investigation of large-scale earth models and/or broadband wave propagation within reasonable execution times. Initial algorithm testing indicates that a point force density and/or moment density source activated within a poroelastic medium generates diverging fast and slow P waves (and possibly an S-wave)in accord with Biot theory. Solid and fluid particle velocities are in-phase for the fast P-wave, whereas they are out-of-phase for the slow P-wave. Conversions between all wave types occur during reflection and transmission at interfaces. Thus, although the slow P-wave is regarded as difficult to detect experimentally, its presence is strongly manifest within the complex of waves generated at a lithologic or fluid boundary. Very fine spatial and temporal gridding are required for high-fidelity representation of the slow P-wave, without inducing excessive
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...
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.
Toroidal Rotation and 3D Nonlinear Dynamics in the Peeling-Ballooning Model of ELMs
NASA Astrophysics Data System (ADS)
Snyder, P. B.
2004-11-01
Maximizing the height of the edge transport barrier (or ``pedestal'') while maintaining acceptably small edge localized modes (ELMs) is a critical issue for tokamak performance. The peeling-ballooning model proposes that intermediate wavelength MHD instabilities are responsible for ELMs and impose constraints on the pedestal. Recent studies of linear peeling-ballooning stability have found encouraging agreement with observations [e.g. 1]. To allow more detailed prediction of mode characteristics, including eventually predictions of the ELM energy loss and its deposition, we consider effects of sheared toroidal rotation, as well as 3D nonlinear dynamics. An eigenmode formulation for toroidal rotation shear is developed and incorporated into the framework of the ELITE stability code [2], resolving the low rotation discontinuity in previous high-n results. Rotation shear is found to impact the structure of peeling-ballooning modes, causing radial narrowing and mode shearing. The calculated mode frequency is found to agree with observed rotation in the edge region in the early stages of the ELM crash. Nonlinear studies with the 3D BOUT and NIMROD codes reveal detailed characteristics of the early evolution of these edge instabilities, including the impact of non-ideal effects. The expected linear growth phase is followed by a fast crash event in which poloidally narrow, filamentary structures propagate radially outward from the pedestal region, closely resembling observed ELM events. Comparisons with ELM observations will be discussed. \\vspace0.25em [1] P.B. Snyder et al., Nucl. Fusion 44, 320 (2004); P.B. Snyder et al., Phys. Plasmas 9, 2037 (2002). [2] H.R. Wilson et al., Phys. Plasmas 9, 1277 (2002).
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
Low-Velocity Impact Response and Finite Element Analysis of Four-Step 3-D Braided Composites
NASA Astrophysics Data System (ADS)
Sun, Baozhong; Zhang, Yan; Gu, Bohong
2013-08-01
The low-velocity impact characters of 3-D braided carbon/epoxy composites were investigated from experimental and finite element simulation approaches. The quasi-static tests were carried out at a constant velocity of 2 mm/min on MTS 810.23 material tester system to obtain the indentation load-displacement curves and indentation damages. The low-velocity tests were conducted at the velocities from 1 m/s to 6 m/s (corresponding to the impact energy from 3.22 J to 116 J) on Instron Dynatup 9250 impact tester. The peak force, energy for peak force, time to peak force, and total energy absorption were obtained to determine the impact responses of 3-D braided composites. A unit cell model was established according to the microstructure of 3-D braided composites to derive the constitutive equation. Based on the model, a user-defined material subroutine (VUMAT) has been compiled by FORTRAN and connected with commercial finite element code ABAQUS/Explicit to calculate the impact damage. The unit cell model successfully predicted the impact response of 3-D braided composites. Furthermore, the stress wave propagation and failure mechanisms have been revealed from the finite element simulation results and ultimate damage morphologies of specimens.
NASA Astrophysics Data System (ADS)
Bustamante, Miguel D.
2011-06-01
We prove by an explicit construction that solutions to incompressible 3D Euler equations defined in the periodic cube Ω=[0 can be mapped bijectively to a new system of equations whose solutions are globally regular. We establish that the usual Beale-Kato-Majda criterion for finite-time singularity (or blowup) of a solution to the 3D Euler system is equivalent to a condition on the corresponding regular solution of the new system. In the hypothetical case of Euler finite-time singularity, we provide an explicit formula for the blowup time in terms of the regular solution of the new system. The new system is amenable to being integrated numerically using similar methods as in Euler equations. We propose a method to simulate numerically the new regular system and describe how to use this to draw robust and reliable conclusions on the finite-time singularity problem of Euler equations, based on the conservation of quantities directly related to energy and circulation. The method of mapping to a regular system can be extended to any fluid equation that admits a Beale-Kato-Majda type of theorem, e.g. 3D Navier-Stokes, 2D and 3D magnetohydrodynamics, and 1D inviscid Burgers. We discuss briefly the case of 2D ideal magnetohydrodynamics. In order to illustrate the usefulness of the mapping, we provide a thorough comparison of the analytical solution versus the numerical solution in the case of 1D inviscid Burgers equation.
Geramy, Allahyar; Shahroudi, Atefe Saffar
2014-01-01
Objective: Several appliances have been used for palatal expansion for treatment of posterior cross bite. The purpose of this study was to evaluate the stress induced in the apical and crestal alveolar bone and the pattern of tooth displacement following expansion via removable expansion plates or fixed-banded palatal expander using the finite element method (FEM) analysis. Materials and Methods: Two 3D FEM models were designed from a mesio-distal slice of the maxilla containing the upper first molars, their periodontium and alveolar bone. Two palatal expanders (removable and fixed) were modeled. The models were designed in SolidWorks 2006 and then transferred to ANSYS Workbench. The appliance halves were displaced 0.1 mm laterally. The von Mises stress in the apical, crestal, and PDL areas and also the vertical displacement of the cusps (palatal and buccal) was were evaluated. Results: The total PDL stress was 0.40003 MPa in the removable appliance (RA) model and 4.88e-2 MPa in the fixed appliance (FA) model and the apical stress was 9.9e-2 and 1.17e-2 MPa, respectively. The crestal stress was 2.99e-1 MPa in RA and 7.62e-2 MPa in the FA. The stress in the cortical bone crest was 0.30327 and 7.9244e-2 MPa for RA and FA, respectively and 3.7271 and 7.4373e-2 MPa in crestal area of spongy bone, respectively. The vertical displacement of the buccal cusp and palatal cusp was 1.64e-2 and 5.90e-2 mm in RA and 1.05e-4 and 1.7e-4 mm in FA, respectively. Conclusion: The overall stress as well as apical and crestal stress in periodontium of anchor teeth was higher in RA than FA; RA elicited higher stress in both cortical and spongy bone. The vertical displacement of molar cusps was more in removable than fixed palatal expander model. PMID:24910679
NASA Astrophysics Data System (ADS)
Sladen, A.; Monteiller, V.
2014-12-01
Most large earthquakes are generated in subduction zones. To study the complexity of these events, teleseismic body waves offer many advantages over other types of data: they allow to study both the temporal and spatial evolution of slip during the rupture, they don't depend on the presence of nearby land and they allow to study earthquakes regardless of their location. Since the development of teleseismic finite-fault inversion in the 1980th, teleseismic body waves have been simulated using 1D velocity models to take into account propagation effects at the source. Yet, subduction zones are known to be highly heterogeneous: they are characterized by curved and dipping structures, strong seismic velocity contrasts, strong variations of topography and height of the water column. The main reason for relying on a 1D approximation is the computational cost of 3D simulations. And while forward simulations of teleseismic waves in a 3D Earth are only starting to be tractable on modern computers at the frequency range of interest (0.1Hz or shorter), finite-fault source studies require a large number of these simulations. In this work, we present a new and efficient approach to compute 3D teleseismic body waves, in which the full 3D propagation is only computed in a regional domain using discontinuous Galerkin finite-element method, while the rest of the seismic wave field is propagated in a background axisymmetric Earth. The regional and global wave fields are matched using the so-called Total-Field/Scattered-Field technique. This new simulation approach allows us to study the waveform complexities resulting from 3D propagation and investigate how they could improve the resolution and reduce the non-uniqueness of finite-fault inversions.
Giannoula, Alexia; Cobbold, Richard; Bezerianos, Anastasios
2014-02-01
A modulated acoustic radiation force, produced by two confocal tone-burst ultrasound beams of slightly different frequencies (i.e. 2.0 MHz ± Δf/2, where Δf is the difference frequency), can be used to remotely generate modulated low-frequency (Δf ≤ 500 Hz) shear waves in attenuating media. By appropriately selecting the duration of the two beams, the energy of the generated shear waves can be concentrated around the difference frequency (i.e., Δf ± Δf/2). In this manner, neither their amplitude nor their phase information is distorted by frequency-dependent effects, thereby, enabling a more accurate reconstruction of the viscoelastic properties. Assuming a Voigt viscoelastic model, this paper describes the use of a finite-element-method model to simulate three-dimensional (3-D) shear-wave propagation in viscoelastic media containing a spherical inclusion. Nonlinear propagation is assumed for the two ultrasound beams, so that higher harmonics are developed in the force and shear spectrum. Finally, an inverse reconstruction algorithm is used to extract 3-D maps of the local shear modulus and viscosity from the simulated shear-displacement fields based on the fundamental and second-harmonic component. The quality of the reconstructed maps is evaluated using the contrast between the inclusion and the background and the contrast-to-noise ratio (CNR). It is shown that the shear modulus can be accurately reconstructed based on the fundamental component, such that the observed contrast deviates from the true contrast by a root-mean-square-error (RMSE) of only 0.38 and the CNR is greater than 30 dB. If the second-harmonic component is used, the RMSE becomes 1.54 and the corresponding CNR decreases by approximately 10-15 dB. The reconstructed shear viscosity maps based on the second harmonic are shown to be of higher quality than those based on the fundamental. The effects of noise are also investigated and a fusion operation between the two spectral components is
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.
Reddy, A.V.; Kothe, D.B.; Lam, K.L.
1997-06-01
The Los Alamos National Laboratory (LANL) is currently developing a new casting simulation tool (known as Telluride) that employs robust, high-resolution finite volume algorithms for incompressible fluid flow, volume tracking of interfaces, and solidification physics on three-dimensional (3-D) unstructured meshes. Their finite volume algorithms are based on colocated cell-centered schemes that are formally second order in time and space. The flow algorithm is a 3-D extension of recent work on projection method solutions of the Navier-Stokes (NS) equations. Their volume tracking algorithm can accurately track topologically complex interfaces by approximating the interface geometry as piecewise planar. Coupled to their fluid flow algorithm is a comprehensive binary alloy solidification model that incorporates macroscopic descriptions of heat transfer, solute redistribution, and melt convection as well as a microscopic description of segregation. The finite volume algorithms, which are efficient, parallel, and robust, can yield high-fidelity solutions on a variety of meshes, ranging from those that are structured orthogonal to fully unstructured (finite element). The authors discuss key computer science issues that have enabled them to efficiently parallelize their unstructured mesh algorithms on both distributed and shared memory computing platforms. These include their functionally object-oriented use of Fortran 90 and new parallel libraries for gather/scatter functions (PGSLib) and solutions of linear systems of equations (JTpack90). Examples of their current capabilities are illustrated with simulations of mold filling and solidification of complex 3-D components currently being poured in LANL foundries.
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.
NASA Astrophysics Data System (ADS)
Zhang, Huiming; Zhang, Min; Yuan, Weijia
2017-02-01
An efficient three dimensional (3D) finite element method numerical model is proposed for superconducting coated conductors. The model is based on the T-A formulation and can be used to tackle 3D computational challenges for superconductors with high aspect ratios. By assuming a sheet approximation for the conductors, the model can speed up the computational process. The model has been validated by established analytical solutions. Two examples with complex geometries, which can hardly be simulated by the 2D model, are given. The model could be used to characterise and design large-scale applications using superconducting coated conductors, such as high field magnets and other electrical devices.
NASA Astrophysics Data System (ADS)
Xie, Yifan; Wu, Jichun; Nan, Tongchao; Xue, Yuqun; Xie, Chunhong; Ji, Haifeng
2017-03-01
In this paper, an efficient triple-grid multiscale finite element method (ETMSFEM) is proposed for 3D groundwater simulation in heterogeneous porous media. The main idea of this method is to employ new 3D linear base functions and the domain decomposition technique to solve the local reduced elliptical problem, thereby simplifying the base function construction process and improving the efficiency. Furthermore, by using the ETMSFEM base functions, this method can solve Darcy's equation with high efficiency to obtain a continuous velocity field. Therefore, this method can considerably reduce the computational cost of solving for heads and velocities, which is crucial for large-scale 3D groundwater simulations. In the application section, we present numerical examples to compare the ETMSFEM with several classical methods to demonstrate its efficiency and effectiveness.
Application of the Finite Orbit Width Version of the CQL3D Code to Transport of Fast Ions
NASA Astrophysics Data System (ADS)
Petrov, Yu. V.; Harvey, R. W.
2016-10-01
The CQL3D bounce-averaged Fokker-Planck (FP) code now includes the ``fully'' neoclassical version in which the diffusion and advection processes are averaged over actual drift orbits, rather than using a 1st-order expansion. Incorporation of Finite-Orbit-Width (FOW) effects results in neoclassical radial transport caused by collisions, RF wave heating and by toroidal electric field (radial pinch). We apply the CQL3D-full-FOW code to study the thermalization and radial transport of high-energy particles, such as alpha-particles produced by fusion in ITER or deuterons from NBI in NSTX, under effect of their interaction with auxiliary RF waves. A particular attention is given to visualization of transport in 3D space of velocity +major-radius coordinates. Supported by USDOE Grants FC02-01ER54649, FG02-04ER54744, and SC0006614.
1992-03-01
COSATI CODES 18 SuBJECT TERMS (Continue on reverse if necessary and identify by block number) FIELD GROUP SUB-GROlP Underwater Explosion 19. ABSTRACT...Continue on reverse if necessary and dentify by block number) Nonlinear 3-D Dynamic Analysis Code (VEC/DYNA3D) has been interfaced with Underwater...whipping mode. Large plastic strains occurred at the center of the cylinder on the reverse side to the explosive and near the ends of the cylinder on
Nonlinear Optical Macroscopic Assessment of 3-D Corneal Collagen Organization and Axial Biomechanics
Winkler, Moritz; Chai, Dongyul; Kriling, Shelsea; Nien, Chyong Jy; Brown, Donald J.; Jester, Bryan; Juhasz, Tibor
2011-01-01
Purpose. To characterize and quantify the collagen fiber (lamellar) organization of human corneas in three dimensions by using nonlinear optical high-resolution macroscopy (NLO-HRMac) and to correlate these findings with mechanical data obtained by indentation testing of corneal flaps. Methods. Twelve corneas from 10 donors were studied. Vibratome sections, 200 μm thick, from five donor eyes were cut along the vertical meridian from limbus to limbus (arc length, 12 mm). Backscattered second harmonic–generated (SHG) NLO signals from these sections were collected as a series of overlapping 3-D images, which were concatenated to form a single 3-D mosaic (pixel resolution: 0.44 μm lateral, 2 μm axial). Collagen fiber intertwining was quantified by determining branching point density as a function of stromal depth. Mechanical testing was performed on corneal flaps from seven additional eyes. Corneas were cut into three layers (anterior, middle, and posterior) using a femtosecond surgical laser system and underwent indentation testing to determine the elastic modulus for each layer. Results. The 3-D reconstructions revealed complex collagen fiber branching patterns in the anterior cornea, with fibers extending from the anterior limiting lamina (ALL, Bowman's layer), intertwining with deeper fibers and reinserting back to the ALL, forming bow spring–like structures. Measured branching-point density was four times higher in the anterior third of the cornea than in the posterior third and decreased logarithmically with increasing distance from the ALL. Indentation testing showed an eightfold increase in elastic modulus in the anterior stroma. Conclusions. The axial gradient in lamellar intertwining appears to be associated with an axial gradient in the effective elastic modulus of the cornea, suggesting that collagen fiber intertwining and formation of bow spring–like structures provide structural support similar to cross-beams in bridges and large-scale structures
Nonlinear static and dynamic finite element analysis of an eccentrically loaded graphite-epoxy beam
NASA Technical Reports Server (NTRS)
Fasanella, Edwin L.; Jackson, Karen E.; Jones, Lisa E.
1991-01-01
The Dynamic Crash Analysis of Structures (DYCAT) and NIKE3D nonlinear finite element codes were used to model the static and implulsive response of an eccentrically loaded graphite-epoxy beam. A 48-ply unidirectional composite beam was tested under an eccentric axial compressive load until failure. This loading configuration was chosen to highlight the capabilities of two finite element codes for modeling a highly nonlinear, large deflection structural problem which has an exact solution. These codes are currently used to perform dynamic analyses of aircraft structures under impact loads to study crashworthiness and energy absorbing capabilities. Both beam and plate element models were developed to compare with the experimental data using the DYCAST and NIKE3D codes.
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.
NASA Astrophysics Data System (ADS)
Vaidyanathan, S.
2014-06-01
This paper proposes a eight-term 3-D polynomial chaotic system with three quadratic nonlinearities and describes its properties. The maximal Lyapunov exponent (MLE) of the proposed 3-D chaotic system is obtained as L 1 = 6.5294. Next, new results are derived for the global chaos synchronization of the identical eight-term 3-D chaotic systems with unknown system parameters using adaptive control. Lyapunov stability theory has been applied for establishing the adaptive synchronization results. Numerical simulations are shown using MATLAB to describe the main results derived in this paper.
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.
Parallel Finite Element Solution of 3D Rayleigh-Benard-Marangoni Flows
NASA Technical Reports Server (NTRS)
Carey, G. F.; McLay, R.; Bicken, G.; Barth, B.; Pehlivanov, A.
1999-01-01
A domain decomposition strategy and parallel gradient-type iterative solution scheme have been developed and implemented for computation of complex 3D viscous flow problems involving heat transfer and surface tension effects. Details of the implementation issues are described together with associated performance and scalability studies. Representative Rayleigh-Benard and microgravity Marangoni flow calculations and performance results on the Cray T3D and T3E are presented. The work is currently being extended to tightly-coupled parallel "Beowulf-type" PC clusters and we present some preliminary performance results on this platform. We also describe progress on related work on hierarchic data extraction for visualization.
1992-09-01
the 3D isoparametric family of elements, and using a Total Lagrangian formulation and implicit integration of the global equations of motion. The...to be observed. NLDFEP, a NonLinear Dynamic Finite Element Program, is designed around the I three dimensional isoparametric family of elements...implemented in NLDFEP are the 8 and 20 node bricks. The program is structured so that additional elements, such as the 27 node brick or another family of
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.
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.
Nonlinear 3-D simulation of high-intensity focused ultrasound therapy in the Kidney.
Suomi, Visa; Jaros, Jiri; Treeby, Bradley; Cleveland, Robin
2016-08-01
Kidney cancer is a severe disease which can be treated non-invasively using high-intensity focused ultrasound (HIFU) therapy. However, tissue in front of the transducer and the deep location of kidney can cause significant losses to the efficiency of the treatment. The effect of attenuation, refraction and reflection due to different tissue types on HIFU therapy of the kidney was studied using a nonlinear ultrasound simulation model. The geometry of the tissue was derived from a computed tomography (CT) dataset of a patient which had been segmented for water, bone, soft tissue, fat and kidney. The combined effect of inhomogeneous attenuation and soundspeed was found to result in an 11.0 dB drop in spatial peak-temporal average (SPTA) intensity in the kidney compared to pure water. The simulation without refraction effects showed a 6.3 dB decrease indicating that both attenuation and refraction contribute to the loss in focal intensity. The losses due to reflections at soft tissue interfaces were less than 0.1 dB. Focal point shifting due to refraction effects resulted in -1.3, 2.6 and 1.3 mm displacements in x-, y- and z-directions respectively. Furthermore, focal point splitting into several smaller subvolumes was observed. The total volume of the secondary focal points was approximately 46% of the largest primary focal point. This could potentially lead to undesired heating outside the target location and longer therapy times.
Nonlinear evolution of 3D-inertial Alfvén wave and turbulent spectra in Auroral region
NASA Astrophysics Data System (ADS)
Rinawa, M. L.; Modi, K. V.; Sharma, R. P.
2014-10-01
In the present paper, we have investigated nonlinear interaction of three dimensional (3D) inertial Alfvén wave and perpendicularly propagating magnetosonic wave for low β-plasma ( β≪ m e / m i ). We have developed the set of dimensionless equations in the presence of ponderomotive nonlinearity due to 3D-inertial Alfvén wave in the dynamics of perpendicularly propagating magnetosonic wave. Stability analysis and numerical simulation has been carried out to study the effect of nonlinear coupling on the formation of localized structures and turbulent spectra, applicable to auroral region. The results reveal that the localized structures become more and more complex as the nonlinear interaction progresses. Further, we have studied the turbulent spectrum which follows spectral index (˜ k -3.57) at smaller scales. Relevance of the obtained results has been shown with the observations received by various spacecrafts like FAST, Hawkeye and Heos 2.
Bounds on nonlinear motion for a finite time
Warnock, R.L.; Ruth, R.D.
1989-06-01
Recent improvements in numerical methods to compute canonical transformations make it feasible to set interesting bounds on the motion of nonlinear Hamiltonian systems over a finite interval of time. 7 refs.
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.
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.
Simulation of suspension flow of finite-size spherical particles in a 3D square channel
NASA Astrophysics Data System (ADS)
Gao, Hui; Wang, Lian-Ping
2008-11-01
Suspension flow of finite-size particles in a turbulent gas is of importance to many engineering applications and natural phenomena. As a first step, the present work focuses on the motion and hydrodynamic interaction of finite-size particles in the absence of background carrier-fluid turbulence. The major challenge for an accurate simulation is twofold: an efficient implementation of no-slip boundary conditions on the moving particle surface and an accurate representation of short-range lubrication effects that typically are not resolved numerically. A Navier-Stokes based hybrid approach (i.e., Physalis) developed by Prosperetti and co-workers is employed to solve the suspension flows of a pair of finite-size, freely-moving particles at finite particle Reynolds numbers. A lubrication force representation, designed by Ladd, involving particle relative location and velocity, is incorporated to capture the short-range interactions between particles. The accuracy of the representation and its compatibility with the flow simulation will be examined. A mesoscopic lattice Boltzmann equation (LBE) approach is also used to simulate the same problem for cross validation. Specific implementation issues will be addressed. Comparison with available numerical data will also be discussed.
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 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.
Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials
NASA Astrophysics Data System (ADS)
Huang, Yunqing; Li, Jichun; Yang, Wei; Sun, Shuyu
2011-09-01
Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell's equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis.
Static & Dynamic Response of 3D Solids
Lin, Jerry
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.
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.
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
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
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 a 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.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
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
NASA Astrophysics Data System (ADS)
Shoji, Noritaka; Hirata, Katsuhiro; Ueyama, Kenji; Hashimoto, Eiichiro; Takagi, Takahiro
Recently, linear oscillatory actuators have been used in a wide range of applications because of their advantages, such as high efficiency, simple structure, and easy control. Small linear oscillatory actuators are expected to be used in haptic devices and the vibration system of mobile phones. In this paper, we propose a new structure of a small linear oscillatory actuator. The static and dynamic characteristics of the actuator are calculated by the 3-D finite element method. The effectiveness of this method is shown by the comparison of the calculated results with the experimental results.
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
NASA Astrophysics Data System (ADS)
Cai, Hongzhu; Hu, Xiangyun; Li, Jianhui; Endo, Masashi; Xiong, Bin
2017-02-01
We solve the 3D controlled-source electromagnetic (CSEM) problem using the edge-based finite element method. The modeling domain is discretized using unstructured tetrahedral mesh. We adopt the total field formulation for the quasi-static variant of Maxwell's equation and the computation cost to calculate the primary field can be saved. We adopt a new boundary condition which approximate the total field on the boundary by the primary field corresponding to the layered earth approximation of the complicated conductivity model. The primary field on the modeling boundary is calculated using fast Hankel transform. By using this new type of boundary condition, the computation cost can be reduced significantly and the modeling accuracy can be improved. We consider that the conductivity can be anisotropic. We solve the finite element system of equations using a parallelized multifrontal solver which works efficiently for multiple source and large scale electromagnetic modeling.
PROGRESS IN THE PEELING-BALLOONING MODEL OF ELMS: TOROIDAL ROTATION AND 3D NONLINEAR DYNAMICS
SNYDER,P.B; WILSON,H.R; XU,X.Q; WEBSTER,A.J
2004-06-01
Understanding the physics of the H-Mode pedestal and edge localized modes (ELMs) is very important to next-step fusion devices for two primary reasons: (1) The pressure at the top of the edge barrier (''pedestal height'') strongly impacts global confinement and fusion performance, and (2) large ELMs lead to localized transient heat loads on material surfaces that may constrain component lifetimes. The development of the peeling-ballooning model has shed light on these issues by positing a mechanism for ELM onset and constraints on the pedestal height. The mechanism involves instability of ideal coupled ''peeling-ballooning'' modes driven by the sharp pressure gradient and consequent large bootstrap current in the H-mode edge. It was first investigated in the local, high-n limit [1], and later quantified for non-local, finite-n modes in general toroidal geometry [2,3]. Important aspects are that a range of wavelengths may potentially be unstable, with intermediate n's (n {approx} 3-30) generally limiting in high performance regimes, and that stability bounds are strongly sensitive to shape [Fig l(a)], and to collisionality (i.e. temperature and density) [4] through the bootstrap current. The development of efficient MHD stability codes such as ELITE [3,2] and MISHKA [5] has allowed detailed quantification of peeling-ballooning stability bounds (e.g. [6]) and extensive and largely successful comparisons with observation (e.g. [2,6-9]). These previous calculations are ideal, static, and linear. Here we extend this work to incorporate the impact of sheared toroidal rotation, and the non-ideal, nonlinear dynamics which must be studied to quantify ELM size and heat deposition on material surfaces.
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.
Finite Element Treatment of Vortex States in 3D Cubic Superconductors in a Tilted Magnetic Field
NASA Astrophysics Data System (ADS)
Peng, Lin; Cai, Chuanbing
2017-03-01
The time-dependent Ginzburg-Landau equations have been solved numerically by a finite element analysis for superconducting samples with a cubic shape in a tilted magnetic field. We obtain different vortex patterns as a function of the external magnetic field. With a magnetic field not parallel to the x- or y-axis, the vortices attempt to change their orientation accordingly. Our analysis of the corresponding changes in the magnetic response in different directions can provide information not only about vorticity but also about the three-dimensional vortex arrangement, even about the very subtle changes for the superconducting samples with a cubic shape in a tilted magnetic field.
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.
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.
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.
Splinting effect on posterior implants under various loading modes: a 3D finite element analysis.
Hauchard, Erwan; Fournier, Benjamin Philippe; Jacq, Romain; Bouton, Antoine; Pierrisnard, Laurent; Naveau, Adrien
2011-09-01
This three-dimensional finite element study compared stresses, intensities and displacements of three mandibular posterior implants restored with cemented crowns (two molars and a premolar in straight line), splinted versus non-splinted. Hundred newton occlusal loads were vertically or horizontally applied, either on one single crown or on all of them. Maximal stresses and implants displacements were higher under horizontal loading. Splinting major effects appeared under single horizontal load with a decrease in stresses (34-49%) and displacements (16-19%) of the loaded crown. Splinting seems more appropriate for implant-supported restorations submitted to frequent single horizontal or oblique loads than vertical ones.
Visualization methods for high-resolution, transient, 3-D, finite element situations
Christon, M.A.
1995-01-10
Scientific visualization is the process whereby numerical data is transformed into a visual form to augment the process of discovery and understanding. Visualizing the data generated by large-scale, transient, three-dimensional finite element simulations poses many challenges due to geometric complexity, the presence of multiple materials and multiple element types, and the inherent unstructured nature of the meshes. In this paper, the direct use of finite element data structures, nodal assembly procedures, and element interpolants for volumetric adaptive surface extraction, surface rendering, vector grids and particle tracing is discussed. A brief description of a {open_quotes}direct-to-disk{close_quotes} animation system is presented, and case studies which demonstrate the use of isosurfaces, vector plots, cutting planes, reference surfaces and particle tracing are then discussed in the context of several case studies for transient incompressible viscous flow, and acoustic fluid-structure interaction simulations. An overview of the implications of massively parallel computers on visualization is presented to highlight the issues in parallel visualization methodology, algorithms. data locality and the ultimate requirements for temporary and archival data storage and network bandwidth.
3-D geoelectrical modelling using finite-difference: a new boundary conditions improvement
NASA Astrophysics Data System (ADS)
Maineult, A.; Schott, J.-J.; Ardiot, A.
2003-04-01
Geoelectrical prospecting is a well-known and frequently used method for quantitative and non-destructive subsurface exploration until depths of a few hundreds metres. Thus archeological objects can be efficiently detected as their resistivities often contrast with those of the surrounding media. Nevertheless using the geoelectrical prospecting method has long been restricted due to inhability to model correctly arbitrarily-shaped structures. The one-dimensional modelling and inversion have long been classical, but are of no interest for the majority of field data, since the natural distribution of resistivity is rarely homogeneous or tabular. Since the 1970's some authors developed discrete methods in order to solve the two and three-dimensional problem, using mathematical tools such as finite-element or finite-difference. The finite-difference approach is quite simple, easily understandable and programmable. Since the work of Dey and Morrison (1979), this approach has become quite popular. Nevertheless, one of its major drawbacks is the difficulty to establish satisfying boundary conditions. Recently Lowry et al. (1989) and Zhao and Yedlin (1996) suggested some refinements on the improvement of the boundary problem. We propose a new betterment, based on the splitting of the potential into two terms, the potential due to a reference tabular medium and a secondary potential caused by a disturbance of this medium. The surface response of a tabular medium has long been known (see for example Koefoed 1979). Here we developed the analytical solution for the electrical tabular potential everywhere in the medium, in order to establish more satisfying boundary conditions. The response of the perturbation, that is to say the object of interest, is then solved using volume-difference and preconditioned conjugate gradient. Finally the grid is refined one or more times in the perturbed domain in order to ameliorate the precision. This method of modelling is easy to implement
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.
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.
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.
3-D finite element cyclic symmetric and contact stress analysis for a complete gear train
NASA Astrophysics Data System (ADS)
Yin, Zeyong; Xu, Youliang; Gao, Xiangqun; Wei, Gang
1992-10-01
A complete gear train of a reduction gearbox is the object of finite element stress analysis. One of the basic segments of the complete gear train is taken as the computational model in the light of the cyclic symmetry of the gear train; meanwhile, the contact transmission forces between the corresponding meshed teeth are considered in the analysis of the model. For simplicity, the corresponding meshed lines are used instead of the actual contact surfaces. Both torque and centrifugal loads are involved in the analysis. The stresses in all the parts of a complete gear train can be determined by one analysis. The computed results show that the contact force on a meshed tooth is correlative not only to the length of the meshed line, but also to its position. It is shown that the neglect of the stress resulted from centrifugal load is inappropriate to a high speed gear train.
A 3D finite-volume scheme for the Euler equations on adaptive tetrahedral grids
Vijayan, P.; Kallinderis, Y. )
1994-08-01
The paper describes the development and application of a new Euler solver for adaptive tetrahedral grids. Spatial discretization uses a finite-volume, node-based scheme that is of central-differencing type. A second-order Taylor series expansion is employed to march the solution in time according to the Lax-Wendroff approach. Special upwind-like smoothing operators for unstructured grids are developed for shock-capturing, as well as for suppression of solution oscillations. The scheme is formulated so that all operations are edge-based, which reduces the computational effort significantly. An adaptive grid algorithm is employed in order to resolve local flow features. This is achieved by dividing the tetrahedral cells locally, guided by a flow feature detection algorithm. Application cases include transonic flow around the ONERA M6 wing and transonic flow past a transport aircraft configuration. Comparisons with experimental data evaluate accuracy of the developed adaptive solver. 31 refs., 33 figs.
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
Stress distribution on external hexagon implant system using 3d finite element analysis.
Segundo, Regênio M H; Oshima, Hugo M S; Silva, Isaac N L; Júnior, Luis H B; Mota, Eduardo G; Coelho, Luiz F B
2007-01-01
The aim of this study was to compare and evaluate strain distribution on dental implant, abutment, screw and crown virtual models in the posterior region. The analysis was performed by means of a 3D virtual model developed by the PRO-ENGINEER System (PRO-ENGINEER, PTC, Needham, MA, USA ) with an external butt joint (3i Implant Innovations, Palm Beach, Florida), square headed Gold Tite abutment retainer screw (3i Implant Innovations, Palm Beach, Florida), STA abutment (3i Implant Innovations, Palm Beach, Florida), metal infrastructure of Ag-Pd alloy and feldspatic ceramic. The standard load was 382N at 15 degree angle to the implant axis, applied at 6 mm from the implant center at different observation points on the implant-screw set. The data showed that on the implant virtual model, the highest strain concentration was found at the interface between the implant platform and the abutment, and in the middle point of the 1st screw thread internal diameter on the load application side.
Vestige of T = 0 jamming transition at finite temperature in 3D
NASA Astrophysics Data System (ADS)
Caswell, Thomas; Gardel, Margaret; Nagel, Sidney; Zhang, Zexin; Yodh, Arjun
2012-02-01
When a random packing of spheres at T = 0 is compressed to the jamming transition, the system becomes rigid and the first peak of the pair-correlation function, g(r), diverges [1]. We study the manifestation of this signature and the associated particle dynamics when the temperature, T, is no longer negligible. To this end, we employ a three-dimensional packing of monodisperse, micron-size, colloids made from n-isopropyl acrylimide (NIPAM). NIPAM particles change size and hence the packing fraction of the system in response to environmental temperature. Thus by changing sample temperature we can probe all packing fractions of interest using a single sample. These particles are compressible so the system can reach packing fractions and configurations inaccessible to hard colloids. We observe a vestige of the T = 0 divergence as a maximum in the first peak of g(r) versus packing fraction coincident with dynamical arrest of the particles. The general features in 3D are in agreement with a previous study in a two-dimensional bi-disperse NIPAM system [2]. We report the dependence of g(r) and particle motion on packing fraction. [1] C. S. O'Hern, et al., Phys. Rev. E 68, 011306 (2003). [2] Z. Zhang, N. Xu, et al., Nature 459, 230 (2009).
3D Finite Element Electrical Model of Larval Zebrafish ECG Signals.
Crowcombe, James; Dhillon, Sundeep Singh; Hurst, Rhiannon Mary; Egginton, Stuart; Müller, Ferenc; Sík, Attila; Tarte, Edward
2016-01-01
Assessment of heart function in zebrafish larvae using electrocardiography (ECG) is a potentially useful tool in developing cardiac treatments and the assessment of drug therapies. In order to better understand how a measured ECG waveform is related to the structure of the heart, its position within the larva and the position of the electrodes, a 3D model of a 3 days post fertilisation (dpf) larval zebrafish was developed to simulate cardiac electrical activity and investigate the voltage distribution throughout the body. The geometry consisted of two main components; the zebrafish body was modelled as a homogeneous volume, while the heart was split into five distinct regions (sinoatrial region, atrial wall, atrioventricular band, ventricular wall and heart chambers). Similarly, the electrical model consisted of two parts with the body described by Laplace's equation and the heart using a bidomain ionic model based upon the Fitzhugh-Nagumo equations. Each region of the heart was differentiated by action potential (AP) parameters and activation wave conduction velocities, which were fitted and scaled based on previously published experimental results. ECG measurements in vivo at different electrode recording positions were then compared to the model results. The model was able to simulate action potentials, wave propagation and all the major features (P wave, R wave, T wave) of the ECG, as well as polarity of the peaks observed at each position. This model was based upon our current understanding of the structure of the normal zebrafish larval heart. Further development would enable us to incorporate features associated with the diseased heart and hence assist in the interpretation of larval zebrafish ECGs in these conditions.
3D Finite Element Electrical Model of Larval Zebrafish ECG Signals
Crowcombe, James; Dhillon, Sundeep Singh; Hurst, Rhiannon Mary; Egginton, Stuart; Müller, Ferenc; Sík, Attila; Tarte, Edward
2016-01-01
Assessment of heart function in zebrafish larvae using electrocardiography (ECG) is a potentially useful tool in developing cardiac treatments and the assessment of drug therapies. In order to better understand how a measured ECG waveform is related to the structure of the heart, its position within the larva and the position of the electrodes, a 3D model of a 3 days post fertilisation (dpf) larval zebrafish was developed to simulate cardiac electrical activity and investigate the voltage distribution throughout the body. The geometry consisted of two main components; the zebrafish body was modelled as a homogeneous volume, while the heart was split into five distinct regions (sinoatrial region, atrial wall, atrioventricular band, ventricular wall and heart chambers). Similarly, the electrical model consisted of two parts with the body described by Laplace’s equation and the heart using a bidomain ionic model based upon the Fitzhugh-Nagumo equations. Each region of the heart was differentiated by action potential (AP) parameters and activation wave conduction velocities, which were fitted and scaled based on previously published experimental results. ECG measurements in vivo at different electrode recording positions were then compared to the model results. The model was able to simulate action potentials, wave propagation and all the major features (P wave, R wave, T wave) of the ECG, as well as polarity of the peaks observed at each position. This model was based upon our current understanding of the structure of the normal zebrafish larval heart. Further development would enable us to incorporate features associated with the diseased heart and hence assist in the interpretation of larval zebrafish ECGs in these conditions. PMID:27824910
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
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.
NASA Astrophysics Data System (ADS)
Moortgat, Joachim; Amooie, Mohammad Amin; Soltanian, Mohamad Reza
2016-10-01
We present a new implicit higher-order finite element (FE) approach to efficiently model compressible multicomponent fluid flow on unstructured grids and in fractured porous subsurface formations. The scheme is sequential implicit: pressures and fluxes are updated with an implicit Mixed Hybrid Finite Element (MHFE) method, and the transport of each species is approximated with an implicit second-order Discontinuous Galerkin (DG) FE method. Discrete fractures are incorporated with a cross-flow equilibrium approach. This is the first investigation of all-implicit higher-order MHFE-DG for unstructured triangular, quadrilateral (2D), and hexahedral (3D) grids and discrete fractures. A lowest-order implicit finite volume (FV) transport update is also developed for the same grid types. The implicit methods are compared to an Implicit-Pressure-Explicit-Composition (IMPEC) scheme. For fractured domains, the unconditionally stable implicit transport update is shown to increase computational efficiency by orders of magnitude as compared to IMPEC, which has a time-step constraint proportional to the pore volume of discrete fracture grid cells. However, when lowest-order Euler time-discretizations are used, numerical errors increase linearly with the larger implicit time-steps, resulting in high numerical dispersion. Second-order Crank-Nicolson implicit MHFE-DG and MHFE-FV are therefore presented as well. Convergence analyses show twice the convergence rate for the DG methods as compared to FV, resulting in two to three orders of magnitude higher computational efficiency. Numerical experiments demonstrate the efficiency and robustness in modeling compressible multicomponent flow on irregular and fractured 2D and 3D grids, even in the presence of fingering instabilities.
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.
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.
C1 finite elements on non-tensor-product 2d and 3d manifolds
Nguyen, Thien; Karčiauskas, Kęstutis; Peters, Jörg
2015-01-01
Geometrically continuous (Gk) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are Ck also for non-tensor-product layout. This paper describes and analyzes one such concrete C1 geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed G1 surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Remarkably, for Poisson’s equation on the disk using interior vertices of valence 3 and symmetric layout, we observe O(h3) convergence in the L∞ norm for this family of elements. Numerical experiments confirm the elements to be effective for solving the trivariate Poisson equation on the solid cylinder, deformations thereof (a turbine blade), modeling and computing geodesics on smooth free-form surfaces via the heat equation, for solving the biharmonic equation on the disk and for Koiter-type thin-shell analysis. PMID:26594070
2D and 3D Non-planar Dynamic Rupture by a Finite Volume Method
NASA Astrophysics Data System (ADS)
Benjemaa, M.; Glinsky-Olivier, N.; Cruz-Atienza, V. M.; Virieux, J.; Piperno, S.; Lanteri, S.
2006-12-01
Understanding the physics of the rupture process requires very sophisticated and accurate tools in which both the geometry of the fault surface and realistic frictional behaviours could interact during rupture propagation. New formulations have been recently proposed for modelling the dynamic shear rupture of non-planar faults (Ando et al., 2004; Cruz-Atienza &Virieux, 2004; Huang &Costanzo, 2004) providing highly accurate field estimates nearby the crack edges at the expanse of a simple medium description or high computational cost. We propose a new method based on the finite volume formulation to model the dynamic rupture propagation of non-planar faults. After proper transformations of the velocity-stress elastodynamic system of partial differential equations following an explicit conservative law, we construct an unstructured time-domain numerical formulation of the crack problem. As a result, arbitrary non-planar faults can be explicitly represented without extra computational cost. The analysis of the total discrete energy through the fault surface leads us to the specification of dynamic rupture boundary conditions which insure the correct discrete energy time variation and, therefore, the system stability. These boundary conditions are set on stress fluxes and not on stress values, which makes the fracture to have no thickness. Different shapes of cracks are analysed. We present an example of a bidimensional non-planar spontaneous fault growth in heterogeneous media as well as preliminary results of a highly efficient extension to the three dimensional rupture model based on the standard MPI.
C(1) finite elements on non-tensor-product 2d and 3d manifolds.
Nguyen, Thien; Karčiauskas, Kęstutis; Peters, Jörg
2016-01-01
Geometrically continuous (G(k) ) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are C(k) also for non-tensor-product layout. This paper describes and analyzes one such concrete C(1) geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed G(1) surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Remarkably, for Poisson's equation on the disk using interior vertices of valence 3 and symmetric layout, we observe O(h(3)) convergence in the L(∞) norm for this family of elements. Numerical experiments confirm the elements to be effective for solving the trivariate Poisson equation on the solid cylinder, deformations thereof (a turbine blade), modeling and computing geodesics on smooth free-form surfaces via the heat equation, for solving the biharmonic equation on the disk and for Koiter-type thin-shell analysis.
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.
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.
A σ-coordinate model for 3D free-surface flows using an unstructured finite-volume technique
NASA Astrophysics Data System (ADS)
Uh Zapata, Miguel
2016-11-01
The aim of this work is to develop a numerical solution of three-dimensional free-surface flows using a σ-coordinate model, a projection method and an unstructured finite-volume technique. The coordinate transformation is used in order to overcome difficulties arising from free surface elevation and irregular geometry. The projection method consists to combine the momentum and continuity equations in order to establish a Poisson-type equation for the non-hydrostatic pressure. A cell-centered finite volume method with a triangular mesh in the horizontal direction is used to simulate the flows with free-surfaces, in which the average values of conserved variables are stored at the centre of each element. A parallel algorithm is also presented for the finite volume discretization of the 3D Navier-Stokes equations. The proposed parallel method is formulated by using a multi-color SOR method, a block domain decomposition and interprocessor data communication techniques with Message Passing Interface. The model has been validated by several benchmarks which numerical simulations are in good agreement with the corresponding analytical and existing experimental results.
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.
Nonlinear finite element analysis: An alternative formulation
NASA Technical Reports Server (NTRS)
Merazzi, S.; Stehlin, P.
1980-01-01
A geometrical nonlinear analysis based on an alternative definition of strain is presented. Expressions for strain are obtained by computing the change in length of the base vectors in the curvilinear element coordinate system. The isoparametric element formulation is assumed in the global Cartesian coordinate system. The approach is based on the minimization of the strain energy, and the resulting nonlinear equations are solved by the modified Newton method. Integration of the first and second variation of the strain energy is performed numerically in the case of two and three dimensional elements. Application is made to a simple long cantilever beam.
A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations
NASA Technical Reports Server (NTRS)
Liu, Yen; Kwak, Dochan (Technical Monitor)
1995-01-01
A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind
NIKE3D96. Static & Dynamic Response of 3D Solids
Maker, B.; Hallquist, J.O.; Ferencz, R.M.
1991-02-01
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Giasin, Khaled; Ayvar-Soberanis, Sabino; French, Toby; Phadnis, Vaibhav
2017-02-01
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.
3D finite element model for writing long-period fiber gratings by CO2 laser radiation.
Coelho, João M P; Nespereira, Marta; Abreu, Manuel; Rebordão, José
2013-08-12
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.
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
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.
VLF Trimpi modelling on the path NWC-Dunedin using both finite element and 3D Born modelling
NASA Astrophysics Data System (ADS)
Nunn, D.; Hayakawa, K. B. M.
1998-10-01
This paper investigates the numerical modelling of VLF Trimpis, produced by a D region inhomogeneity on the great circle path. Two different codes are used to model Trimpis on the path NWC-Dunedin. The first is a 2D Finite Element Method Code (FEM), whose solutions are rigorous and valid in the strong scattering or non-Born limit. The second code is a 3D model that invokes the Born approximation. The predicted Trimpis from these codes compare very closely, thus confirming the validity of both models. The modal scattering matrices for both codes are analysed in some detail and are found to have a comparable structure. They indicate strong scattering between the dominant TM modes. Analysis of the scattering matrix from the FEM code shows that departure from linear Born behaviour occurs when the inhomogeneity has a horizontal scale size of about 100 km and a maximum electron density enhancement at 75 km altitude of about 6 electrons.
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.
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.
NASA Astrophysics Data System (ADS)
Wang, Min; Chen, Yi-Feng; Ma, Guo-Wei; Zhou, Jia-Qing; Zhou, Chuang-Bing
2016-10-01
This study investigates the impacts of surface roughness on the nonlinear fluid flow through three-dimensional (3D) self-affine rock fractures, whose original surface roughness is decomposed into primary roughness (i.e. the large-scale waviness of the fracture morphology) and secondary roughness (i.e. the small-scale unevenness) with a wavelet analysis technique. A 3D Lattice Boltzmann method (LBM) is adopted to predict the flow physics in rock fractures numerically created with and without consideration of the secondary roughness, respectively. The simulation results show that the primary roughness mostly controls the pressure distribution and fracture flow paths at a large scale, whereas the secondary roughness determines the nonlinear properties of the fluid flow at a local scale. As the pressure gradient increases, the secondary roughness enhances the local complexity of velocity distribution by generating and expanding the eddy flow and back flow regions in the vicinity of asperities. It was found that the Forchheimer's law characterizes well the nonlinear flow behavior in fractures of varying roughness. The inertial effects induced by the primary roughness differ only marginally in fractures with the roughness exponent varying from 0.5 to 0.8, and it is the secondary roughness that significantly enhances the nonlinear flow and leads to earlier onset of nonlinearity. Further examined were the effects of surface roughness on the transmissivity, hydraulic aperture and the tortuosity of flow paths, demonstrating again the dominant role of the secondary roughness, especially for the apparent transmissivity and the equivalent hydraulic aperture at high pressure gradient or high Reynolds number. The results may enhance our understanding of the role of surface roughness in the nonlinear flow behaviors in natural rock fractures.
Verri, Fellippo Ramos; Cruz, Ronaldo Silva; Lemos, Cleidiel Aparecido Araújo; de Souza Batista, Victor Eduardo; Almeida, Daniel Augusto Faria; Verri, Ana Caroline Gonçales; Pellizzer, Eduardo Piza
2017-02-01
The aim of study was to evaluate the stress distribution in implant-supported prostheses and peri-implant bone using internal hexagon (IH) implants in the premaxillary area, varying surgical techniques (conventional, bicortical and bicortical in association with nasal floor elevation), and loading directions (0°, 30° and 60°) by three-dimensional (3D) finite element analysis. Three models were designed with Invesalius, Rhinoceros 3D and Solidworks software. Each model contained a bone block of the premaxillary area including an implant (IH, Ø4 × 10 mm) supporting a metal-ceramic crown. 178 N was applied in different inclinations (0°, 30°, 60°). The results were analyzed by von Mises, maximum principal stress, microstrain and displacement maps including ANOVA statistical test for some situations. Von Mises maps of implant, screws and abutment showed increase of stress concentration as increased loading inclination. Bicortical techniques showed reduction in implant apical area and in the head of fixation screws. Bicortical techniques showed slight increase stress in cortical bone in the maximum principal stress and microstrain maps under 60° loading. No differences in bone tissue regarding surgical techniques were observed. As conclusion, non-axial loads increased stress concentration in all maps. Bicortical techniques showed lower stress for implant and screw; however, there was slightly higher stress on cortical bone only under loads of higher inclinations (60°).
NASA Astrophysics Data System (ADS)
Bravo, Agustín; Barham, Richard; Ruiz, Mariano; López, Juan Manuel; De Arcas, Guillermo; Alonso, Jesus
2012-12-01
In part I, the feasibility of using three-dimensional (3D) finite elements (FEs) to model the acoustic behaviour of the IEC 60318-1 artificial ear was studied and the numerical approach compared with classical lumped elements modelling. It was shown that by using a more complex acoustic model that took account of thermo-viscous effects, geometric shapes and dimensions, it was possible to develop a realistic model. This model then had clear advantages in comparison with the models based on equivalent circuits using lumped parameters. In fact results from FE modelling produce a better understanding about the physical phenomena produced inside ear simulator couplers, facilitating spatial and temporal visualization of the sound fields produced. The objective of this study (part II) is to extend the investigation by validating the numerical calculations against measurements on an ear simulator conforming to IEC 60318-1. For this purpose, an appropriate commercially available device is taken and a complete 3D FE model developed for it. The numerical model is based on key dimensional data obtained with a non-destructive x-ray inspection technique. Measurements of the acoustic transfer impedance have been carried out on the same device at a national measurement institute using the method embodied in IEC 60318-1. Having accounted for the actual device dimensions, the thermo-viscous effects inside narrow slots and holes and environmental conditions, the results of the numerical modelling were found to be in good agreement with the measured values.
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.
Scaling/LER study of Si GAA nanowire FET using 3D finite element Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Elmessary, Muhammad A.; Nagy, Daniel; Aldegunde, Manuel; Seoane, Natalia; Indalecio, Guillermo; Lindberg, Jari; Dettmer, Wulf; Perić, Djordje; García-Loureiro, Antonio J.; Kalna, Karol
2017-02-01
3D Finite Element (FE) Monte Carlo (MC) simulation toolbox incorporating 2D Schrödinger equation quantum corrections is employed to simulate ID-VG characteristics of a 22 nm gate length gate-all-around (GAA) Si nanowire (NW) FET demonstrating an excellent agreement against experimental data at both low and high drain biases. We then scale the Si GAA NW according to the ITRS specifications to a gate length of 10 nm predicting that the NW FET will deliver the required on-current of above 1 mA/ μ m and a superior electrostatic integrity with a nearly ideal sub-threshold slope of 68 mV/dec and a DIBL of 39 mV/V. In addition, we use a calibrated 3D FE quantum corrected drift-diffusion (DD) toolbox to investigate the effects of NW line-edge roughness (LER) induced variability on the sub-threshold characteristics (threshold voltage (VT), OFF-current (IOFF), sub-threshold slope (SS) and drain-induced-barrier-lowering (DIBL)) for the 22 nm and 10 nm gate length GAA NW FETs at low and high drain biases. We simulate variability with two LER correlation lengths (CL = 20 nm and 10 nm) and three root mean square values (RMS = 0.6, 0.7 and 0.85 nm).
Finite-difference and finite-volume methods for nonlinear standing ultrasonic waves in fluid media.
Vanhille, C; Conde, C; Campos-Pozuelo, C
2004-04-01
In the framework of the application of high-power ultrasonics in industrial processing in fluid media, the mathematical prediction of the acoustical parameters inside resonators should improve the development of practical systems. This can be achieved by the use of numerical tools able to treat the nonlinear acoustics involved in these phenomena. In particular, effects like nonlinear distortion and nonlinear attenuation are fundamental in applications. In this paper, three one-dimensional numerical models in the time domain for calculating the nonlinear acoustic field inside a one-dimensional resonant cavity are presented and compared. They are based on the finite-difference and the finite-volume methods. These different algorithms solve the differential equations, from the linear up to the strongly nonlinear case (including weak shock). Some physical results obtained from the modelling of ultrasonic waves and a comparison of the efficiency of the different algorithms are presented.
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.
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.
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)
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.
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.
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
A fully-neoclassical finite-orbit-width version of the CQL3D Fokker-Planck code
NASA Astrophysics Data System (ADS)
Petrov, Yu V.; Harvey, R. W.
2016-11-01
The time-dependent bounce-averaged CQL3D flux-conservative finite-difference Fokker-Planck equation (FPE) solver has been upgraded to include finite-orbit-width (FOW) capabilities which are necessary for an accurate description of neoclassical transport, losses to the walls, and transfer of particles, momentum, and heat to the scrape-off layer. The FOW modifications are implemented in the formulation of the neutral beam source, collision operator, RF quasilinear diffusion operator, and in synthetic particle diagnostics. The collisional neoclassical radial transport appears naturally in the FOW version due to the orbit-averaging of local collision coefficients coupled with transformation coefficients from local (R, Z) coordinates along each guiding-center orbit to the corresponding midplane computational coordinates, where the FPE is solved. In a similar way, the local quasilinear RF diffusion terms give rise to additional radial transport of orbits. We note that the neoclassical results are obtained for ‘full’ orbits, not dependent on a common small orbit-width approximation. Results of validation tests for the FOW version are also presented.
Visualization of high-density 3D graphs using nonlinear visual space transformations
NASA Astrophysics Data System (ADS)
Hao, Ming C.; Dayal, Umeshwar; Garg, Pankaj; Machiraju, Vijay
2002-03-01
The real world data distribution is seldom uniform. Clutter and sparsity commonly occur in visualization. Often, clutter results in overplotting, in which certain data items are not visible because other data items occlude them. Sparsity results in the inefficient use of the available display space. Common mechanisms to overcome this include reducing the amount of information displayed or using multiple representations with a varying amount of detail. This paper describes out experiments on Non-Linear Visual Space Transformations (NLVST). NLVST encompasses several innovative techniques: (1) employing a histogram for calculating the density of data distribution; (2) mapping the raw data values to a non-linear scale for stretching a high-density area; (3) tightening the sparse area to save the display space; (4) employing different color ranges of values on a non-linear scale according to the local density. We have applied NLVST to several web applications: market basket analysis, transactions observation, and IT search behavior analysis.
Measuring nonlinear stresses generated by defects in 3D colloidal crystals
NASA Astrophysics Data System (ADS)
Lin, Neil Y. C.; Bierbaum, Matthew; Schall, Peter; Sethna, James P.; Cohen, Itai
2016-11-01
The mechanical, structural and functional properties of crystals are determined by their defects, and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect density rises to levels routinely found in real-world materials, transport is governed by local stresses that are predominantly nonlinear. Such stress fields however, cannot be measured using conventional bulk and local measurement techniques. Here, we report direct and spatially resolved experimental measurements of the nonlinear stresses surrounding colloidal crystalline defect cores, and show that the stresses at vacancy cores generate attractive interactions between them. We also directly visualize the softening of crystalline regions surrounding dislocation cores, and find that stress fluctuations in quiescent polycrystals are uniformly distributed rather than localized at grain boundaries, as is the case in strained atomic polycrystals. Nonlinear stress measurements have important implications for strain hardening, yield and fatigue.
Jackson, Alicia R; Huang, Chun-Yuh C; Brown, Mark D; Gu, Wei Yong
2011-09-01
The intervertebral disc (IVD) receives important nutrients, such as glucose, from surrounding blood vessels. Poor nutritional supply is believed to play a key role in disc degeneration. Several investigators have presented finite element models of the IVD to investigate disc nutrition; however, none has predicted nutrient levels and cell viability in the disc with a realistic 3D geometry and tissue properties coupled to mechanical deformation. Understanding how degeneration and loading affect nutrition and cell viability is necessary for elucidating the mechanisms of disc degeneration and low back pain. The objective of this study was to analyze the effects of disc degeneration and static deformation on glucose distributions and cell viability in the IVD using finite element analysis. A realistic 3D finite element model of the IVD was developed based on mechano-electrochemical mixture theory. In the model, the cellular metabolic activities and viability were related to nutrient concentrations, and transport properties of nutrients were dependent on tissue deformation. The effects of disc degeneration and mechanical compression on glucose concentrations and cell density distributions in the IVD were investigated. To examine effects of disc degeneration, tissue properties were altered to reflect those of degenerated tissue, including reduced water content, fixed charge density, height, and endplate permeability. Two mechanical loading conditions were also investigated: a reference (undeformed) case and a 10% static deformation case. In general, nutrient levels decreased moving away from the nutritional supply at the disc periphery. Minimum glucose levels were at the interface between the nucleus and annulus regions of the disc. Deformation caused a 6.2% decrease in the minimum glucose concentration in the normal IVD, while degeneration resulted in an 80% decrease. Although cell density was not affected in the undeformed normal disc, there was a decrease in cell
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 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.
Finite area method for nonlinear conical flows
NASA Technical Reports Server (NTRS)
Sritharan, S. S.; Seebass, A. R.
1982-01-01
A fully conservative finite area method for the computation of steady inviscid flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell and a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is desymmetrized by adding appropriate artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigations.
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.
Probabilistic finite elements for transient analysis in nonlinear continua
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.; Mani, A.
1985-01-01
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
Sayed, Ahmed; Layne, Ginger; Abraham, Jame; Mukdadi, Osama M
2014-07-01
The goal of the study described here was to introduce new methods for the classification and visualization of human breast tumors using 3-D ultrasound elastography. A tumor's type, shape and size are key features that can help the physician to decide the sort and extent of necessary treatment. In this work, tumor type, being either benign or malignant, was classified non-invasively for nine volunteer patients. The classification was based on estimating four parameters that reflect the tumor's non-linear biomechanical behavior, under multi-compression levels. Tumor prognosis using non-linear elastography was confirmed with biopsy as a gold standard. Three tissue classification parameters were found to be statistically significant with a p-value < 0.05, whereas the fourth non-linear parameter was highly significant, having a p-value < 0.001. Furthermore, each breast tumor's shape and size were estimated in vivo using 3-D elastography, and were enhanced using interactive segmentation. Segmentation with level sets was used to isolate the stiff tumor from the surrounding soft tissue. Segmentation also provided a reliable means to estimate tumors volumes. Four volumetric strains were investigated: the traditional normal axial strain, the first principal strain, von Mises strain and maximum shear strain. It was noted that these strains can provide varying degrees of boundary enhancement to the stiff tumor in the constructed elastograms. The enhanced boundary improved the performance of the segmentation process. In summary, the proposed methods can be employed as a 3-D non-invasive tool for characterization of breast tumors, and may provide early prognosis with minimal pain, as well as diminish the risk of late-stage breast cancer.
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.
Identifiability of 3D attributed scattering features from sparse nonlinear apertures
NASA Astrophysics Data System (ADS)
Jackson, Julie Ann; Moses, Randolph L.
2007-04-01
Attributed scattering feature models have shown potential in aiding automatic target recognition and scene visualization from radar scattering measurements. Attributed scattering features capture physical scattering geometry, including the non-isotropic response of target scattering over wide angles, that is not discerned from traditional point scatter models. In this paper, we study the identifiability of canonical scattering primitives from complex phase history data collected over sparse nonlinear apertures that have both azimuth and elevation diversity. We study six canonical shapes: a flat plate, dihedral, trihedral, cylinder, top-hat, and sphere, and three flight path scenarios: a monostatic linear path, a monostatic nonlinear path, and a bistatic case with a fixed transmitter and a nonlinear receiver flight path. We modify existing scattering models to account for nonzero object radius and to scale peak scattering intensities to equate to radar cross section. Similarities in some canonical scattering responses lead to confusion among multiple shapes when considering only model fit errors. We present additional model discriminators including polarization consistency between the model and the observed feature and consistency of estimated object size with radar cross section. We demonstrate that flight path diversity and combinations of model discriminators increases identifiability of canonical shapes.
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
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.
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
Nonlinear Synchronization for Automatic Learning of 3D Pose Variability in Human Motion Sequences
NASA Astrophysics Data System (ADS)
Mozerov, M.; Rius, I.; Roca, X.; González, J.
2009-12-01
A dense matching algorithm that solves the problem of synchronizing prerecorded human motion sequences, which show different speeds and accelerations, is proposed. The approach is based on minimization of MRF energy and solves the problem by using Dynamic Programming. Additionally, an optimal sequence is automatically selected from the input dataset to be a time-scale pattern for all other sequences. The paper utilizes an action specific model which automatically learns the variability of 3D human postures observed in a set of training sequences. The model is trained using the public CMU motion capture dataset for the walking action, and a mean walking performance is automatically learnt. Additionally, statistics about the observed variability of the postures and motion direction are also computed at each time step. The synchronized motion sequences are used to learn a model of human motion for action recognition and full-body tracking purposes.
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.
NASA Astrophysics Data System (ADS)
Krebs, I.; Jardin, S. C.; Günter, S.; Lackner, K.; Hoelzl, M.; Ferraro, N.
2016-10-01
We use the finite element 3D MHD code M3D-C1 to study large-scale instabilities in the center of tokamak plasmas. It has been shown that in 3D MHD simulations of plasmas with a flat central q 1 , an ideal interchange instability can develop that keeps the current density from peaking despite central heating. The instability yields a (m = 1 , n = 1) perturbation of the core plasma, i.a. a helical flow that flattens the central current density by (1) flattening the temperature profile and (2) combining with the perturbed magnetic field to generate a negative loop voltage through a dynamo effect. This might explain the ``flux-pumping'' effect observed in hybrid discharges. We study in which parameter range the two effects are strong enough to prevent sawtoothing. We describe a new regime of quasi-stationary oscillating states and analyze cases in between the stationary and the cycling regime in which the sawtooth behaviour is modified by the current flattening mechanisms. To connect to experimental observations, we have set up simulations starting with a scenario comparable to the current ramp-up phase.
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.
Majumder, Santanu; Roychowdhury, Amit; Pal, Subrata
2009-07-22
Injuries due to backward fall apart from sideways fall are a major health problem, particularly among the aged populations. The objectives of this study was to evaluate the responses to changing body configurations (angle between the trunk and impacting floor as 0 degrees, 15 degrees, 45 degrees and 80 degrees) during backward fall, based on a previously developed CT-scan-derived 3D non-linear and non-homogeneous finite element (FE) model of pelvis-femur-soft tissue complex with simplified biomechanical representation of the whole body. Under constant impact energy, these FE models evaluated the pelvic injury situations on the basis of peak impact force (7.64-16.74 kN) and peak principal compressive strain (more than 1.5%), consistent with the clinically observed injuries (sacral insufficiency, coccydynia). Also the change in location of peak strain and increase in peak impact force for changing configurations from 0 degrees to 80 degrees indicated the effect of whole body inertia during backward fall. It was also concluded that the inclusion of sacro-iliac and acetabular cartilages in the above FE models will further reduce above findings marginally (9.2% for 15 degrees fall). These quantifications would also be helpful for a better design and development of safety structures such as safety floor for the nursing home or home for the aged persons.
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
NASA Astrophysics Data System (ADS)
Kwak, Chang-Seob; Kim, Hong-Kyu; Kim, Tae-Hoon; Lee, Se-Hee
2017-01-01
A systematic numerical method for analyzing a 3D moving vacuum arc was proposed and tested in this research by using a transverse magnetic field (TMF) contact. The analysis was carried out by employing the finite element method and the experimental energy equation defined by Gundlach's formula. In the literature, the vacuum interrupter has been widely applied to medium-voltage switching circuits. TMF-type contacts use the Lorentz force density to move a high-temperature arc so as to prevent the contacts from being melted and damaged. The material erosion caused by the arc on the electrode's surface is an important process that results in the interruptive capabilities of these vacuum interrupters. In a classical arc model, to move the vacuum arc, it is required that the magneto-hydrodynamics be analyzed in the arc region at each step. However, with this approach convergence is difficult, resulting in a very time-consuming. Therefore, we propose a new technique to predict the behaviors of vacuum arc between two electrodes. This new approach adopts the experimental arc voltage equation between two electrodes defined by Gundlach's formula. We verify our proposed model by comparing its results with the arcing behaviors obtained from earlier experiments.
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)
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.
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.
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.
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.
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.
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.
A natural flow wing design employing 3-D nonlinear analysis applied at supersonic speeds
NASA Technical Reports Server (NTRS)
Bauer, Steven X. S.; Wood, Richard M.; Brown, S. Melissa
1989-01-01
A wing-design study has been conducted on a 65-deg-swept leading-edge delta wing in which a near-conical geometry was employed to take advantage of the naturally occurring conical flow which arises over such a wing in a supersonic flow field. Three-dimensional nonlinear analysis methods were used in the study. In preliminary design, wing planform, design conditions, and near-conical concept were derived and a baseline standard wing (conventional airfoil distribution) and a baseline near-conical wing were chosen. During the initial analysis, a full-potential solver was employed to determine the aerodynamic characteristics of the baseline standard delta wing and the near-conical delta wing. Modifications due to airfoil thickness, leading-edge radius, and camber were then applied to the baseline near-conical wing. The final design employed a Euler solver to analyze the best wing configurations found in the initial design, and to extend this study to develop a more refined wing. Benefits due to each modification are discussed, and a final natural flow wing geometry is chosen and its aerodynamic characteristics are compared with the baseline wings.
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.
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.
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.
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…
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.
NASA Astrophysics Data System (ADS)
Kawabe, H.; Kamae, K.
2005-12-01
There is high possibility of the occurrence of the Tonankai and Nankai earthquakes which are capable of causing immense damage. During these huge earthquakes, long period ground motions may strike mega-cities Osaka and Nagoya located inside the Osaka and Nobi basins in which there are many long period and low damping structures (such as tall buildings and oil tanks). It is very important for the earthquake disaster mitigation to predict long period strong ground motions of the future Tonankai and Nankai earthquakes that are capable of exciting long-period strong ground motions over a wide area. In this study, we tried to predict long-period ground motions of the future Tonankai and Nankai earthquakes using 3D finite difference method. We construct a three-dimensional underground structure model including not only the basins but also propagation field from the source to the basins. Resultantly, we can point out that the predominant periods of pseudo-velocity response spectra change basin by basin. Long period ground motions with periods of 5 to 8 second are predominant in the Osaka basin, 3 to 6 second in the Nobi basin and 2 to 5 second in the Kyoto basin. These characteristics of the long-period ground motions are related with the thicknesses of the sediments of the basins. The duration of long period ground motions inside the basin are more than 5 minutes. These results are very useful for the earthquake disaster mitigation of long period structures such as tall buildings and oil tanks.
NASA Astrophysics Data System (ADS)
Perrin, A.; Hu, H.
2006-11-01
We have extended previous work on an 2D explicit finite-difference code for direct simulation of the motion of solid particles in a fluid to 3D. It is challenging to enforce the no-slip condition on the surface of spherical particles in a uniform Cartesian grid. We have implemented a treatment of the boundary condition similar to that in the PHYSALIS method of Takagi et. al. (2003), which is based on matching the Stokes flow solutions next to the particle surface with a numerical solution away from it. The original PHYSALIS method was developed for implicit flow solvers, and required an iterative process to match the Stokes flow solutions with the numerical solution. However, it was easily adapted to work with the present explicit scheme, and found to be more efficient since no iterative process is required in the matching. The method proceeds by approximating the flow next to the particle surface as a Stokes flow in the particle’s local coordinates, which is then matched to the numerically computed external flow on a ``cage'' of grid points near the particle surface. Advantages of the method include superior accuracy of the scheme on a relatively coarse grid for intermediate Reynolds numbers, ease of implementation, and the elimination of the need to track the particle surface. Several examples are presented, including flow over a stationary sphere in a square tube, sedimentation of a particle, and dropping, kissing, and tumbling of two particles. This research is supported by a GAANN fellowship from the U.S. Dept. of Education.
Maurel, N; Diop, A; Grimberg, J
2005-09-01
In order to help to understand the loosening phenomenon around glenoïd prostheses, a 3D finite element model of a previously tested implanted scapula has been developed. The construction of the model was done using CT scans of the tested scapula. Different bone material properties were tested and shell elements or 8 nodes hexaedric elements were used to model the cortical bone. Surface contact elements were introduced on one hand between the bone and the lower part of the plate of the implant, and on the other, between the loading metallic ball and the upper surface of the implant. The results of the model were compared with those issued from in vitro experiments carried out on the same scapula. The evaluation of the model was done for nine cases of loading of 500 N distributed on the implant, in terms of strains (principal strains of six spots around peripheral cortex of the glenoïd) and displacement of four points positioned on the implant. The best configuration of the model presented here, fits with experiments for most of the strains (difference lower than 150microdef) but it seems to be still too stiff (mainly in the lower part). Nevertheless, we want, in this paper, to underline the importance of doing a multiparametric validation for such a model. Indeed, some models can give correct results for one case of loading but bad results for another kind of loading, some others can give good results for one kind of compared parameters (like strains for instance) but bad results for the other one (like displacements).
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.
NASA Astrophysics Data System (ADS)
Balkaya, Çağlayan; Ekinci, Yunus Levent; Göktürkler, Gökhan; Turan, Seçil
2017-01-01
3D non-linear inversion of total field magnetic anomalies caused by vertical-sided prismatic bodies has been achieved by differential evolution (DE), which is one of the population-based evolutionary algorithms. We have demonstrated the efficiency of the algorithm on both synthetic and field magnetic anomalies by estimating horizontal distances from the origin in both north and east directions, depths to the top and bottom of the bodies, inclination and declination angles of the magnetization, and intensity of magnetization of the causative bodies. In the synthetic anomaly case, we have considered both noise-free and noisy data sets due to two vertical-sided prismatic bodies in a non-magnetic medium. For the field case, airborne magnetic anomalies originated from intrusive granitoids at the eastern part of the Biga Peninsula (NW Turkey) which is composed of various kinds of sedimentary, metamorphic and igneous rocks, have been inverted and interpreted. Since the granitoids are the outcropped rocks in the field, the estimations for the top depths of two prisms representing the magnetic bodies were excluded during inversion studies. Estimated bottom depths are in good agreement with the ones obtained by a different approach based on 3D modelling of pseudogravity anomalies. Accuracy of the estimated parameters from both cases has been also investigated via probability density functions. Based on the tests in the present study, it can be concluded that DE is a useful tool for the parameter estimation of source bodies using magnetic anomalies.
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.
Finite element methods for the nonlinear motion of flexible aircraft
NASA Astrophysics Data System (ADS)
Yang, Victor P.
Conventional strategies in aeroelasticity and flight dynamics for studying aircraft involve making broad assumptions based more on analytical or computational convenience rather than on physical reality. Typically in aeroelastic analyses, the study of the interaction between aircraft flexibility and aerodynamic forces, the aircraft or structural component in question is constrained in a way that is not representative of realistic flight conditions. In flight dynamics, the study of the maneuvering of aircraft, it is common to consider the vehicle as perfectly rigid. In both disciplines it is well known that such contrivances can produce incorrect results. To address these shortcomings, a finite element formulation is developed for analyzing the dynamics of flexible aircraft undergoing arbitrarily large rotation and translation. The formulation is derived in a set of body-attached axes, a frame of reference conducive to analyzing the motion and control of aircraft, and considers the structure as a whole. Several implementation issues are addressed and mitigated, including finite element interpolating functions, the use of eigenvectors as the basis for nonlinear deformation, inclusion of geometrically nonlinear effects in the strain energy, and enforcement of kinematic constraints. Numerical examples illustrate the capabilities of the latter two aspects, and a free-flying aeroelastic model problem demonstrates the overall potential of the proposed formulation. The development is approached in a general way so that the methodology can be applied to any structure that may be modeled by finite elements.
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.
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.
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
2016-02-29
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.
Tang, Shu-Wei; Feng, Jing-Dong; Qiu, Yong-Qing; Sun, Hao; Wang, Feng-Di; Chang, Ying-Fei; Wang, Rong-Shun
2010-11-15
Electronic structures and nonlinear optical properties of two highly deformed halofullerenes C(3v) C(60)F(18) and D(3d) C(60)Cl(30) have been systematically studied by means of density functional theory. The large energy gaps (3.62 and 2.61 eV) between the highest occupied and lowest unoccupied molecular orbitals (HOMOs and LUMOs) and the strong aromatic character (with nucleus-independent chemical shifts varying from -15.08 to -23.71 ppm) of C(60)F(18) and C(60)Cl(30) indicate their high stabilities. Further investigations of electronic property show that C(60)F(18) and C(60)Cl(30) could be excellent electron acceptors for potential photonic/photovoltaic applications in consequence of their large vertical electron affinities. The density of states and frontier molecular orbitals are also calculated, which present that HOMOs and LUMOs are mainly distributed in the tortoise shell subunit of C(60)F(18) and the aromatic [18] trannulene ring of C(60)Cl(30), and the influence from halogen atoms is secondary. In addition, the static linear polarizability
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.
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.
NASA Astrophysics Data System (ADS)
Nardon, E.; Fil, A.; Hoelzl, M.; Huijsmans, G.; contributors, JET
2017-01-01
3D non-linear MHD simulations of a D 2 massive gas injection (MGI) triggered disruption in JET with the JOREK code provide results which are qualitatively consistent with experimental observations and shed light on the physics at play. In particular, it is observed that the gas destabilizes a large m/n = 2/1 tearing mode, with the island O-point coinciding with the gas deposition region, by enhancing the plasma resistivity via cooling. When the 2/1 island gets so large that its inner side reaches the q = 3/2 surface, a 3/2 tearing mode grows. Simulations suggest that this is due to a steepening of the current profile right inside q = 3/2. Magnetic field stochastization over a large fraction of the minor radius as well as the growth of higher n modes ensue rapidly, leading to the thermal quench (TQ). The role of the 1/1 internal kink mode is discussed. An I p spike at the TQ is obtained in the simulations but with a smaller amplitude than in the experiment. Possible reasons are discussed.
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
Nonlinear harmonic generation in finite amplitude black hole oscillations
NASA Astrophysics Data System (ADS)
Papadopoulos, Philippos
2002-04-01
The nonlinear generation of harmonics in gravitational perturbations of black holes is explored using numerical relativity based on an ingoing light-cone framework. Localized, finite, perturbations of an isolated black hole are parametrized by amplitude and angular harmonic form. The response of the black hole spacetime is monitored and its harmonic content analyzed to identify the strength of the nonlinear generation of harmonics as a function of the initial data amplitude. It is found that overwhelmingly the black hole responds at the harmonic mode perturbed, even for spacetimes with 10% of the black hole mass radiated. The coefficients for down and up scattering in harmonic space are computed for a range of couplings. Down scattering, leading to smoothing out of angular structure, is found to be equally as or more efficient than the up scatterings that would lead to increased rippling. The details of this nonlinear balance may form the quantitative mechanism by which black holes avoid fission even for arbitrary strong distortions.
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)
Levin, David; Dey, Damini; Slomka, Piotr
2005-04-01
We have implemented two hardware accelerated Thin Plate Spline (TPS) warping algorithms. The first algorithm is a hardware-software approach (HW-TPS) that uses OpenGL Vertex Shaders to perform a grid warp. The second is a Graphics Processor based approach (GPU-TPS) that uses the OpenGL Shading Language to perform all warping calculations on the GPU. Comparison with a software TPS algorithm was used to gauge the speed and quality of both hardware algorithms. Quality was analyzed visually and using the Sum of Absolute Difference (SAD) similarity metric. Warping was performed using 92 user-defined displacement vectors for 512x512x173 serial lung CT studies, matching normal-breathing and deep-inspiration scans. On a Xeon 2.2 Ghz machine with an ATI Radeon 9800XT GPU the GPU-TPS required 26.1 seconds to perform a per-voxel warp compared to 148.2 seconds for the software algorithm. The HW-TPS needed 1.63 seconds to warp the same study while the GPU-TPS required 1.94 seconds and the software grid transform required 22.8 seconds. The SAD values calculated between the outputs of each algorithm and the target CT volume were 15.2%, 15.4% and 15.5% for the HW-TPS, GPU-TPS and both software algorithms respectively. The computing power of ubiquitous 3D graphics cards can be exploited in medical image processing to provide order of magnitude acceleration of nonlinear warping algorithms without sacrificing output quality.
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
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.
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.
Finite bandwidth, nonlinear convective flow in a mushy layer
NASA Astrophysics Data System (ADS)
Riahi, D. N.
2017-04-01
Finite amplitude convection with a continuous finite bandwidth of modes in a horizontal mushy layer during the solidification of binary alloys is investigated. We analyze the nonlinear convection for values of the Rayleigh number close to its critical value by using multiple scales and perturbation techniques. Applying a combined temporal and spatial evolution approach, we determine a set of three coupled differential equations for the amplitude functions of the convective modes. A large number of new subcritical or supercritical stable solutions to these equations in the form of steady rolls and hexagons with different horizontal length scales are detected. We find, in particular, that depending on the parameter values and on the magnitude and direction of the wave number vectors for the amplitude functions, hexagons with down-flow or up-flow at the cells’ centers or rolls can be stable. Rolls or hexagons with longer horizontal wave length can be stable at higher amplitudes, and there are cases where hexagons are unstable for any value of the Rayleigh number, while rolls are stable only for the values of the Rayleigh number beyond some value. We also detected new stable and irregular flow patterns with two different horizontal scales in the form of superposition of either two sets of hexagons or two sets of inclined rolls.
NASA Astrophysics Data System (ADS)
Balusu, K.; Huang, H.
2017-04-01
A combined dislocation fan-finite element (DF-FE) method is presented for efficient and accurate simulation of dislocation nodal forces in 3D elastically anisotropic crystals with dislocations intersecting the free surfaces. The finite domain problem is decomposed into half-spaces with singular traction stresses, an infinite domain, and a finite domain with non-singular traction stresses. As such, the singular and non-singular parts of the traction stresses are addressed separately; the dislocation fan (DF) method is introduced to balance the singular traction stresses in the half-spaces while the finite element method (FEM) is employed to enforce the non-singular boundary conditions. The accuracy and efficiency of the DF method is demonstrated using a simple isotropic test case, by comparing it with the analytical solution as well as the FEM solution. The DF-FE method is subsequently used for calculating the dislocation nodal forces in a finite elastically anisotropic crystal, which produces dislocation nodal forces that converge rapidly with increasing mesh resolutions. In comparison, the FEM solution fails to converge, especially for nodes closer to the surfaces.
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.
NASA Astrophysics Data System (ADS)
Soudah, Eduardo; Rossi, Riccardo; Idelsohn, Sergio; Oñate, Eugenio
2014-10-01
A reduced-order model for an efficient analysis of cardiovascular hemodynamics problems using multiscale approach is presented in this work. Starting from a patient-specific computational mesh obtained by medical imaging techniques, an analysis methodology based on a two-step automatic procedure is proposed. First a coupled 1D-3D Finite Element Simulation is performed and the results are used to adjust a reduced-order model of the 3D patient-specific area of interest. Then, this reduced-order model is coupled with the 1D model. In this way, three-dimensional effects are accounted for in the 1D model in a cost effective manner, allowing fast computation under different scenarios. The methodology proposed is validated using a patient-specific aortic coarctation model under rest and non-rest conditions.
2015-08-01
primarily concerned with the results of a three-dimensional elasto– plastic finite element contact analysis of a typical aluminium fatigue test coupon...determine the nonlinear three-dimensional elasto–plastic contact stress distributions around a circular hole in an aluminium plate that is fitted...Australian Air Force (RAAF) airframes. An aluminium -alloy fatigue test coupon (see Figure 1) has been designed and applied in support of the validation of
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.
Chen, Luyun; Ashton-Miller, James A.; DeLancey, John O.L.
2009-01-01
Objectives To develop a 3D computer model of the anterior vaginal wall and its supports, validate that model, and then use it to determine the combinations of muscle and connective tissue impairments that result in cystocele formation, as observed on dynamic magnetic resonance imaging (MRI). Methods A subject-specific 3D model of the anterior vaginal wall and its supports was developed based on MRI geometry from a healthy nulliparous woman. It included simplified representations of the anterior vaginal wall, levator muscle, cardinal and uterosacral ligaments, arcus tendineus fascia pelvis and levator ani, paravaginal attachments, and the posterior compartment. This model was then imported into ABAQUS™ and tissue properties were assigned from the literature. An iterative process was used to refine anatomical assumptions until convergence was obtained between model behavior under increases of abdominal pressure up to 168 cmH2O and deformations observed on dynamic MRI. Results Cystocele size was sensitive to abdominal pressure and impairment of connective tissue and muscle. Larger cystocele formed in the presence of impairments in muscular and apical connective tissue support compared to either support element alone. Apical impairment resulted in a larger cystocele than paravaginal impairment. Levator ani muscle impairment caused a larger urogenital hiatus size, longer length of the distal vagina exposed to a pressure differential, larger apical descent and resulted in a larger cystocele size. Conclusions Development of a cystocele requires a levator muscle impairment, an increase in abdominal pressure, and apical and paravaginal support defects. PMID:19481208
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.
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. During the pulse buckling tests, a buckle formed at each end of the cylinder, and one of the two buckles became unstable and collapsed. Numerical simulations of the test were performed using PRONTO, a Sandia developed transient dynamics analysis code, and ABAQUS/Explicit with both shell and continuum elements. The calculations are compared to the tests with respect to deformed shape and impact load history.
González-Lluch, Carmen; Pérez-González, Antonio; Sancho-Bru, Joaquín L; Rodríguez-Cervantes, Pablo-Jesús
2014-08-01
Many studies have investigated the effect of different parameters of the endodontically restored tooth on its final strength, using in vitro tests and model simulations. However, the differences in the experimental set-up or modelling conditions and the limited number of parameters studied in each case prevent us from obtaining clear conclusions about the relative importance of each parameter. In this study, a validated 3D biomechanical model of the restored tooth was used for an exhaustive sensitivity analysis. The individual influence of 20 different parameters on the mechanical performance of an endodontic restoration with prefabricated posts was studied. The results bring up the remarkable importance of the loading angle on the final restoration strength. Flexural loads are more critical than compressive or tensile loads. Young's modulus of the post and its length and diameter are the most influential parameters for strength, whereas other parameters such as ferrule geometry or core and crown characteristics are less significant.
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.
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.
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.
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.
Ramos Verri, Fellippo; Santiago Junior, Joel Ferreira; de Faria Almeida, Daniel Augusto; de Oliveira, Guilherme Bérgamo Brandão; de Souza Batista, Victor Eduardo; Marques Honório, Heitor; Noritomi, Pedro Yoshito; Pellizzer, Eduardo Piza
2015-01-02
The study of short implants is relevant to the biomechanics of dental implants, and research on crown increase has implications for the daily clinic. The aim of this study was to analyze the biomechanical interactions of a singular implant-supported prosthesis of different crown heights under vertical and oblique force, using the 3-D finite element method. Six 3-D models were designed with Invesalius 3.0, Rhinoceros 3D 4.0, and Solidworks 2010 software. Each model was constructed with a mandibular segment of bone block, including an implant supporting a screwed metal-ceramic crown. The crown height was set at 10, 12.5, and 15 mm. The applied force was 200 N (axial) and 100 N (oblique). We performed an ANOVA statistical test and Tukey tests; p<0.05 was considered statistically significant. The increase of crown height did not influence the stress distribution on screw prosthetic (p>0.05) under axial load. However, crown heights of 12.5 and 15 mm caused statistically significant damage to the stress distribution of screws and to the cortical bone (p<0.001) under oblique load. High crown to implant (C/I) ratio harmed microstrain distribution on bone tissue under axial and oblique loads (p<0.001). Crown increase was a possible deleterious factor to the screws and to the different regions of bone tissue.
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.
Superplastic forming using NIKE3D
Puso, M.
1996-12-04
The superplastic forming process requires careful control of strain rates in order to avoid strain localizations. A load scheduler was developed and implemented into the nonlinear finite element code NIKE3D to provide strain rate control during forming simulation and process schedule output. Often the sheets being formed in SPF are very thin such that less expensive membrane elements can be used as opposed to shell elements. A large strain membrane element was implemented into NIKE3D to assist in SPF process modeling.
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.
Adaptive superposition of finite element meshes in linear and nonlinear dynamic analysis
NASA Astrophysics Data System (ADS)
Yue, Zhihua
2005-11-01
The numerical analysis of transient phenomena in solids, for instance, wave propagation and structural dynamics, is a very important and active area of study in engineering. Despite the current evolutionary state of modern computer hardware, practical analysis of large scale, nonlinear transient problems requires the use of adaptive methods where computational resources are locally allocated according to the interpolation requirements of the solution form. Adaptive analysis of transient problems involves obtaining solutions at many different time steps, each of which requires a sequence of adaptive meshes. Therefore, the execution speed of the adaptive algorithm is of paramount importance. In addition, transient problems require that the solution must be passed from one adaptive mesh to the next adaptive mesh with a bare minimum of solution-transfer error since this form of error compromises the initial conditions used for the next time step. A new adaptive finite element procedure (s-adaptive) is developed in this study for modeling transient phenomena in both linear elastic solids and nonlinear elastic solids caused by progressive damage. The adaptive procedure automatically updates the time step size and the spatial mesh discretization in transient analysis, achieving the accuracy and the efficiency requirements simultaneously. The novel feature of the s-adaptive procedure is the original use of finite element mesh superposition to produce spatial refinement in transient problems. The use of mesh superposition enables the s-adaptive procedure to completely avoid the need for cumbersome multipoint constraint algorithms and mesh generators, which makes the s-adaptive procedure extremely fast. Moreover, the use of mesh superposition enables the s-adaptive procedure to minimize the solution-transfer error. In a series of different solid mechanics problem types including 2-D and 3-D linear elastic quasi-static problems, 2-D material nonlinear quasi-static problems
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.
Shestakov, A I; Milovich, J L; Noy, A
2000-12-27
The nonlinear Poisson-Boltzmann (PB) equation is solved using Pseudo Transient Continuation. The PB solver is constructed by modifying the nonlinear diffusion module of a 3D, massively parallel, unstructured-grid, finite element, radiation-hydrodynamics code. The solver also computes the electrostatic energy and evaluates the force on a user-specified contour. Either Dirichlet or mixed boundary conditions are allowed. The latter specifies surface charges, approximates far-field conditions, or linearizes conditions ''regulating'' the surface charge. The code may be run in either Cartesian, cylindrical, or spherical coordinates. The potential and force due to a conical probe interacting with a flat plate is computed and the result compared with direct force measurements by chemical force microscopy.
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.
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
2008-01-01
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
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.
Calibration of 3D ALE finite element model from experiments on friction stir welding of lap joints
NASA Astrophysics Data System (ADS)
Fourment, Lionel; Gastebois, Sabrina; Dubourg, Laurent
2016-10-01
In order to support the design of such a complex process like Friction Stir Welding (FSW) for the aeronautic industry, numerical simulation software requires (1) developing an efficient and accurate Finite Element (F.E.) formulation that allows predicting welding defects, (2) properly modeling the thermo-mechanical complexity of the FSW process and (3) calibrating the F.E. model from accurate measurements from FSW experiments. This work uses a parallel ALE formulation developed in the Forge® F.E. code to model the different possible defects (flashes and worm holes), while pin and shoulder threads are modeled by a new friction law at the tool / material interface. FSW experiments require using a complex tool with scroll on shoulder, which is instrumented for providing sensitive thermal data close to the joint. Calibration of unknown material thermal coefficients, constitutive equations parameters and friction model from measured forces, torques and temperatures is carried out using two F.E. models, Eulerian and ALE, to reach a satisfactory agreement assessed by the proper sensitivity of the simulation to process parameters.
Lee, W H; Kim, T S; Kim, Andrew T; Lee, S Y
2008-01-01
Realistic finite element (FE) head models have been successfully applied to bioelectromagnetic problems due to a realistic representation of arbitrary head geometry with inclusion of anisotropic material properties. In this paper, we propose a new automatic FE mesh generation scheme to generate a diffusion tensor MRI (DT-MRI) white matter anisotropy content-adaptive FE head model. We term this kind of mesh as wMesh. With this meshing technique, the anisotropic electrical conductivities derived from DT-MRIs can be best incorporated into the model. The influence of the white matter anisotropy on the EEG forward solutions has been studied via our wMesh head models. The scalp potentials computed from the anisotropic wMesh models against those of the isotropic models have been compared. The results describe that there are substantial changes in the scalp electrical potentials between the isotropic and anisotropic models, indicating that the inclusion of the white matter anisotropy is critical for accurate computation of E/MEG forward and inverse solutions. This fully automatic anisotropy-adaptive wMesh meshing scheme could be useful for modeling of individual-specific FE head models with better incorporation of the white matter anisotropic property towards bioelectromagnetic imaging.
NASA Astrophysics Data System (ADS)
Bertolesi, Elisa; Milani, Gabriele; Casolo, Siro
2016-12-01
A simple homogenized rigid body and spring model (HRBSM) is presented and applied for the non-linear dynamic analysis of 3D masonry structures. The approach, previously developed by the authors for the modeling of in-plane loaded walls is herein extended to real 3D buildings subjected to in- and out-of-plane deformation modes. The elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. At a structural level, the non-linear analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM) by means of which both in and out of plane mechanisms are allowed. All the simulations here presented are performed using the commercial software Abaqus. In order to validate the proposed model for the analyses of full scale structures subjected to seismic actions, two different examples are critically discussed, namely a church façade and an in-scale masonry building, both subjected to dynamic excitation. The results obtained are compared with experimental or numerical results available in literature.
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.
NASA Astrophysics Data System (ADS)
Belashov, V. Yu.; Belashova, E. S.
2016-11-01
On the basis of the model of the three-dimensional (3D) generalized Kadomtsev-Petviashvili equation for magnetic field h = B / B the formation, stability, and dynamics of 3D soliton-like structures, such as the beams of fast magnetosonic (FMS) waves generated in ionospheric and magnetospheric plasma at a low-frequency branch of oscillations when β = 4 πnT/ B 2 ≪ 1 and β > 1, are studied. The study takes into account the highest dispersion correction determined by values of the plasma parameters and the angle θ = ( B, k), which plays a key role in the FMS beam propagation at those angles to the magnetic field that are close to π/2. The stability of multidimensional solutions is studied by an investigation of the Hamiltonian boundness under its deformations on the basis of solving of the corresponding variational problem. The evolution and dynamics of the 3D FMS wave beam are studied by the numerical integration of equations with the use of specially developed methods. The results can be interpreted in terms of the self-focusing phenomenon, as the formation of a stationary beam and the scattering and self-focusing of the solitary beam of FMS waves. These cases were studied with a detailed investigation of all evolutionary stages of the 3D FMS wave beams in the ionospheric and magnetospheric plasma.
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
Chen, Wen-Ming; Park, Jaeyoung; Park, Seung-Bum; Shim, Victor Phyau-Wui; Lee, Taeyong
2012-06-26
The functions of the gastrocnemius-soleus (G-S) complex and other plantar flexor muscles are to stabilize and control major bony joints, as well as to provide primary coordination of the foot during the stance phase of gait. Geometric positioning of the foot and transferring of plantar loads can be adversely affected when muscular control is abnormal (e.g., equinus contracture). Although manipulation of the G-S muscle complex by surgical intervention (e.g., tendo-Achilles lengthening) is believed to be effective in restoring normal plantar load transfer in the foot, there is lack of quantitative data supporting that notion. Thus, the objective of this study is to formulate a three-dimensional musculoskeletal finite element model of the foot to quantify the precise role of the G-S complex in terms of biomechanical response of the foot. The model established corresponds to a muscle-demanding posture during heel rise, with simulated activation of major extrinsic plantar flexors. In the baseline (reference) case, required muscle forces were determined from what would be necessary to generate the targeted resultant ground reaction forces. The predicted plantar load transfer through the forefoot plantar surface, as indicated by plantar pressure distribution, was verified by comparison with experimental observations. This baseline model served as a reference for subsequent parametric analysis, where muscle forces applied by the G-S complex were decreased in a step-wise manner. Adaptive changes of the foot mechanism, in terms of internal joint configurations and plantar stress distributions, in response to altered muscular loads were analyzed. Movements of the ankle and metatarsophalangeal joints, as well as forefoot plantar pressure peaks and pressure distribution under the metatarsal heads (MTHs), were all found to be extremely sensitive to reduction in the muscle load in the G-S complex. A 40% reduction in G-S muscle stabilization can result in dorsal-directed rotations
Parameter sampling and metamodel generation for nonlinear finite element simulations
Cundy, A. L.; Schultze, J. F.; Hemez, F. M.; Doebling, S. W.; Hylok, J. E.; Bingham, D.
2002-01-01
This research addresses the problem of analyzing the nonlinear transient response of a structural dynamics simulation. A threaded joint assembly's response to impulse loading has been studied. Twelve parameters relating to the input level, preloads of the joint and friction between components are thought to influence the acceleration response of the structure. Due to the high cost of physical testing and large amount of computation time to run numerical models a fastrunning metamodel is being developed. In this case, a metamodel is a statistically developed surrogate to the physics-based finite element model and can be evaluated in minutes on a single processor desktop computer. An unreasonable number of runs is required (312>500,000) to generate a three level full factorial design with 12 parameters for metamodel creation. Some manner of down-selecting or variable screening is needed in order to determine which of the parameters most affect the response and should be retained in subsequent models. A comparision of screening methods to general sensitivity analysis was conducted. A significant effects methodology, which involves a design of experiments technique has been examined. In this method, all parameters were first included in the model and then eliminated on the basis of statistical contributions associated with each parameter. Bayesian variable screening techniques, in which probabilities of effects are generated and updated, have also been explored, Encouraging results have been obtained, as the two methods yield similar sets of statistically significant parameters. Both methods have been compared to general sensitivity analysis (GSA). The resulting compact metamodel can then be explored at more levels to appropriately capture the underlying physics of the threaded assembly with a much smaller set of simulations.
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)
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.
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.
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.
Crashdynamics with DYNA3D: Capabilities and research directions
NASA Technical Reports Server (NTRS)
Whirley, Robert G.; Engelmann, Bruce E.
1993-01-01
The application of the explicit nonlinear finite element analysis code DYNA3D to crashworthiness problems is discussed. Emphasized in the first part of this work are the most important capabilities of an explicit code for crashworthiness analyses. The areas with significant research promise for the computational simulation of crash events are then addressed.
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.
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.
High-contrast step-index waveguides in borate nonlinear laser crystals by 3D laser writing.
Rodenas, Airan; Kar, Ajoy K
2011-08-29
We report the ultrafast fabrication of high-contrast step-index channel waveguides in Nd(3+):YCa(4)O(BO(3))(3) borate laser crystals by means of 3D direct laser writing. Guiding up to 3.4 μm wavelength is demonstrated for the first time in a laser written crystalline waveguide. Modeling the measured fundamental modes at the wavelengths of 1.9 µm and 3.4 µm allowed us to estimate the high laser-induced refractive index increments (index contrasts) to be 0.010 (0.59%), and 0.005 (0.29%), respectively. Confocal µ-Raman spectral imaging of the waveguides cross-sections confirmed that the cores have very well defined step profiles, and that the increase in the refractive index can be linked to the localized creation of permanent intrinsic defects. These results indicate that this crystalline waveguides are a potential candidate for the development of 3D active waveguide circuits, due to the laser and electro-optic properties of rare earth doped borate crystals.
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.
NASA Astrophysics Data System (ADS)
Zhai, Jun-Yong
2014-03-01
This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.
Nonlinear dynamics of planetary gears using analytical and finite element models
NASA Astrophysics Data System (ADS)
Ambarisha, Vijaya Kumar; Parker, Robert G.
2007-05-01
Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.
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.
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.
Shi, Dufang; Wang, Fang; Wang, Dongmei; Li, Xiaoqin; Wang, Qiugen
2014-06-01
The anterior part of the sacroiliac joint (SIJ) is a synovial joint, with little gliding and rotary movement between the contact surfaces of SIJ during locomotion. Due to its complex structure, especially when considering the surrounding ligaments, it is difficult to construct an accurate three-dimensional (3-D) finite element model for the human pelvis. Most of the pelvic models in the previous studies were simplified with either SIJ fusing together or without the sacral bone. However, the influence of those simplifications on the load transmission in human pelvis has not been studied, so the reliability of those studies remains unclear. In this study, two 3-D pelvic models were constructed: an SIJ fusing model and an SIJ contacting model. In the SIJ fusing model, the SIJ interfaces were fused together. In the SIJ contacting model, the SIJ interfaces were just in contact with each other without fusion. Compared with the SIJ contacting model, the SIJ fusing model have smaller movements in the SIJ. The stress distribution area in the SIJ fusing model on sacroiliac cartilages was also different. Those differences contributed to the decline of tensile force in the SIJ surrounding ligaments and the re-distribution of stress in the pelvic bones. In addition, the SIJ fusing model was far less sensitive to the increase in modulus of the sacroiliac cartilages, and decrease in stiffness of the ligaments surrounding the SIJ. The presence of synovia in the SIJ had greater influence on the load transmission in the human pelvic system. Therefore, the effect of the presence of synovia should not be neglected when the biomechanical behavior of human pelvis is being studied, especially for those studies related to clinical applications.
2013-01-01
Background Stress shielding in the cemented hip prosthesis occurs due to the mismatching in the mechanical properties of metallic stem and bone. This mismatching in properties is considered as one of the main reasons for implant loosening. Therefore, a new stem material in orthopedic surgery is still required. In the present study, 3D finite element modeling is used for evaluating the artificial hip joint stem that is made of Function Graded (FG) material in terms of joint stress distributions and stem length. Method 3D finite element models of different stems made of two types of FG materials and traditional stems made of Cobalt Chromium alloy (CoCrMo) and Titanium alloy (Ti) were developed using the ANSYS Code. The effects on the total artificial hip joint stresses (Shear stress and Von Mises stresses at bone cement, Von Mises stresses at bone and stem) due to using the proposed FG materials stems were investigated. The effects on the total artificial hip joint system stresses due to using different stem lengths were investigated. Results Using FG stem (with low stiffness at stem distal end and high stiffness at its proximal end) resulted in a significant reduction in shear stress at the bone cement/stem interface. Also, the Von Mises stresses at the bone cement and stem decrease significantly when using FG material instead of CoCrMo and Ti alloy. The stresses’ distribution along the bone cement length when using FG material was found to be more uniform along the whole bone cement compared with other stem materials. These more uniform stresses will help in the reduction of the artificial hip joint loosening rate and improve its short and long term performance. Conclusion FE results showed that using FG stem increases the resultant stresses at the femur bone (reduces stress shielding) compared to metallic stem. The results showed that the stem length has significant effects on the resultant shear and Von Mises stresses at bone, stem and bone cement for all types
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.
A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation.
Bou Matar, Olivier; Guerder, Pierre-Yves; Li, YiFeng; Vandewoestyne, Bart; Van Den Abeele, Koen
2012-05-01
A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb's problem and plane wave nonlinear propagation.
NASA Astrophysics Data System (ADS)
Boehm, Holger F.; Link, Thomas M.; Monetti, Roberto A.; Mueller, Dirk; Rummeny, Ernst J.; Newitt, David; Majumdar, Sharmila; Raeth, Christoph W.
2004-05-01
Multi-dimensional convex objects can be characterized with respect to shape, structure, and the connectivity of their components using a set of morphological descriptors known as the Minkowski functionals. In a 3D Euclidian space, these correspond to volume, surface area, mean integral curvature, and the Euler-Poincaré characteristic. We introduce the Minkowski functionals to medical image processing for the morphological analysis of trabecular bone tissue. In the context of osteoporosis-a metabolic disorder leading to a weakening of bone due to deterioration of micro-architecture-the structure of bone increasingly gains attention in the quantification of bone quality. The trabecular architecture of healthy cancellous bone consists of a complex 3D system of inter-connected mineralised elements whereas in osteoporosis the micro-structure is dominated by gaps and disconnections. At present, the standard parameter for diagnosis and assessment of fracture risk in osteoporosis is the bone mineral density (BMD) - a bulk measure of mineralisation irrespective of structural texture characteristics. With the development of modern imaging modalities (high resolution MRI, micro-CT) with spatial resolutions allowing to depict individual trabeculae bone micro-architecture has successfully been analysed using linear, 2- dimensional structural measures adopted from standard histo-morphometry. The preliminary results of our study demonstrate that due to the complex - i.e. the non-linear - network of trabecular bone structures non-linear measures in 3D are superior to linear ones in predicting mechanical properties of trabecular bone from structural information extracted from high resolution MR image data.
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
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.
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.
Nonlinear modes in finite-dimensional PT-symmetric systems.
Zezyulin, D A; Konotop, V V
2012-05-25
By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear properties of the systems undergo significant changes. On an example of an array of four waveguides described by the discrete nonlinear Schrödinger equation with dissipation and gain, we show that the equivalence of the underlying linear spectra does not imply similarity of the structure or stability of the nonlinear modes in the arrays. Even the existence of one-parametric families of nonlinear modes is not guaranteed by the PT symmetry of a newly obtained system. In addition, the stability is not directly related to the PT symmetry: stable nonlinear modes exist even when the spectrum of the linear array is not purely real. We use a graph representation of PT-symmetric networks allowing for a simple illustration of linearly equivalent networks and indicating their possible experimental design.
Majumder, Santanu; Roychowdhury, Amit; Pal, Subrata
2007-12-01
Hip fractures due to sideways falls are a worldwide health problem, especially among the elderly population. The objective of this study was to simulate a real life sideways fall leading to hip fracture. To achieve this a computed tomography (CT) scan based three-dimensional (3D) finite element (FE) model of the pelvis-femur complex was developed using a wide range of mechanical properties in the bone of the complex. For impact absorption through large deformation, surrounding soft tissue was also included in the FE model from CT scan data. To incorporate the inertia effect, the whole body was represented by a spring-mass-dashpot system. For trochanteric soft tissue thickness of 14 mm, body weight of 77.47 kg and average hip impact velocity of 3.17 m/s, this detailed FE model could approximately simulate a sideways fall configuration and examine femoral fracture situation. At the contact surface, the peak impact load was 8331 N. In spite of the presence of 14 mm thick trochanteric soft tissue, within the trochanteric zone the most compressive peak principal strain was 3.5% which exceeds ultimate compressive strain. The modeled trochanteric fracture was consistent with clinical findings and with the findings of previous studies. Further, this detailed FE model may be used to find the effect of trochanteric soft tissue thickness variations on peak impact force, peak strain in sideways fall, and to simulate automobile side impact and backward fall situations.
Shin, Joo-Hee; Kim, Jong-Eun; Kim, Jee-Hwan; Lee, Won-Chang; Shin, Sang-Wan
2017-01-01
The aim of this study was to evaluate the biomechanical behavior and long-term safety of high performance polymer PEKK as an intraradicular dental post-core material through comparative finite element analysis (FEA) with other conventional post-core materials. A 3D FEA model of a maxillary central incisor was constructed. A cyclic loading force of 50 N was applied at an angle of 45° to the longitudinal axis of the tooth at the palatal surface of the crown. For comparison with traditionally used post-core materials, three materials (gold, fiberglass, and PEKK) were simulated to determine their post-core properties. PEKK, with a lower elastic modulus than root dentin, showed comparably high failure resistance and a more favorable stress distribution than conventional post-core material. However, the PEKK post-core system showed a higher probability of debonding and crown failure under long-term cyclic loading than the metal or fiberglass post-core systems. PMID:28386547
NASA Astrophysics Data System (ADS)
Tan, E.; Choi, E.; Lavier, L. L.; Calo, V. M.
2013-12-01
Many tectonic problems treat the lithosphere as a compressible elastic material, which can also flow viscously or break in a brittle fashion depending on the stress level applied and the temperature conditions. We present a flexible methodology to address the resulting complex material response, which imposes severe challenges on the discretization and rheological models used. This robust, adaptive, multidimensional, finite element method solves the momentum balance and the heat equation in Lagrangian form with unstructured simplicial mesh (triangles in 2D and tetrahedra in 3D). The mesh locking problem is avoided by using averaged volumetric strain rate to update the stress. The solver uses contingent mesh adaptivity in places where shear strain is focused (localization) during remeshing. A simple scheme of mesh coarsening is employed to prevent tiny elements during remeshing. Lagrangian markers are used to track multiple compositions of rocks. The code is parallelized via OpenMP with graph coloring. We detail the solver and verify it in a number of benchmark problems against analytic and numerical solutions from the literature.
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.
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.
The nonlinear modified equation approach to analyzing finite difference schemes
NASA Technical Reports Server (NTRS)
Klopfer, G. H.; Mcrae, D. S.
1981-01-01
The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.
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.
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…
A composite Chebyshev finite difference method for nonlinear optimal control problems
NASA Astrophysics Data System (ADS)
Marzban, H. R.; Hoseini, S. M.
2013-06-01
In this paper, a composite Chebyshev finite difference method is introduced and is successfully employed for solving nonlinear optimal control problems. The proposed method is an extension of the Chebyshev finite difference scheme. This method can be regarded as a non-uniform finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well-known Chebyshev-Gauss-Lobatto points. The convergence of the method is established. The nice properties of hybrid functions are then used to convert the nonlinear optimal control problem into a nonlinear mathematical programming one that can be solved efficiently by a globally convergent algorithm. The validity and applicability of the proposed method are demonstrated through some numerical examples. The method is simple, easy to implement and yields very accurate results.
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.
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.
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.
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.
Nonlinear finite element analysis of solids and structures. Volume 1: Essentials
Crisfield, M.A.
1991-12-31
This book is written for the practicing engineer. It is an attempt to bring together various strands of work on nonlinear finite elements. The developments in the book are related to computer applications; there are a number of Fortran listings, and many flow charts, for solving parts of nonlinear finite element problems. (Floppy disks with the Fortran source and data files are available from the publisher). This book takes an engineering rather than a mathematical approach to nonlinear finite elements. The first three chapters deal with truss elements. The author introduces basic concepts of nonlinear finite element analysis for simple truss systems with one degree of freedom. The solution schemes considered include an incremental (Euler), an iterative (Newton-Raphson), and a combined incremental and iteration approach (full or modified Newton-Raphson or the initial stress method). In chapter 2, the author introduces the shallow truss theory of chapter 1 to derive the finite element equations for a shallow truss slement with four degrees of freedom. A set of Fortran subroutines is given to solve simple bar-spring problems; some flowcharts are also provided. This chapter also contains data and solutions from a number of bar-spring problems.
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.
A modal method for finite amplitude, nonlinear sloshing
NASA Astrophysics Data System (ADS)
Shankar, P. N.; Kidambi, R.
2002-10-01
A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefficients in the expansions of the interface and the potential. The effects of capillarity are included in the formulation. The simplicity, generality and power of the method are exhibited not only by recovering the earlier results obtained, for example, by Penney and Price [1], Tadjbakhsh and Keller [2] and Faltinsen et al [3], but also by obtaining new and interesting results of the effects of capillarity and shallow depth, which would be difficult to obtain otherwise. For example, it is found that for the initial interface profile considered here, parasitic capillary waves, borne by the higher number wave modes, are generated for moderate capillarity but disappear for larger values of the parameter. The method can be extended to other simple geometries.
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.
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)
Letellier, C.; Aguirre, L. A.; Maquet, J.; Lefebvre, B.
2003-05-01
This paper investigates nonlinear wave-wave interactions in a system that describes a modified decay instability and consists of three Langmuir and one ion-sound waves. As a means to establish that the underlying dynamics exists in a 3D space and that it is of the Lorenz-type, both continuous and discrete-time multivariable global models were obtained from data. These data were obtained from a 10D dynamical system that describes the modified decay instability obtained from Zakharov’s equations which characterise Langmuir turbulence. This 10D model is equivariant under a continuous rotation symmetry and a discrete order-2 rotation symmetry. When the continuous rotation symmetry is modded out, that is, when the dynamics are represented with the continuous rotation symmetry removed under a local diffeomorphism, it is shown that a 3D system may describe the underlying dynamics. For certain parameter values, the models, obtained using global modelling techniques from three time series from the 10D dynamics with the continuous rotation symmetry modded out, generate attractors which are topologically equivalent. These models can be simulated easily and, due to their simplicity, are amenable for analysis of the original dynamics after symmetries have been modded out. Moreover, it is shown that all of these attractors are topologically equivalent to an attractor generated by the well-known Lorenz system.
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.
Chieruzzi, Manila; Pagano, Stefano; Cianetti, Stefano; Lombardo, Guido; Kenny, José M; Torre, Luigi
2017-05-01
The aim of this work was to evaluate the stress distribution inside endodontically treated teeth restored with different posts (glass fibre, carbon fibre and steel posts) under different loading conditions by using a 3D-finite element analysis. The effect of masticatory and impact forces on teeth with different degrees of bone loss was analysed. The model consists of: dentine, post, cement, gutta-percha, core and crown. Four simulations were conducted with two static forces (170N horizontal and 100N oblique) and two sections constrained: 1mm (alveolar bone position in a normal periodontium) and 6mm (middle of root) below the crown. Von Mises and the principal stresses were evaluated and analysed with a 3-way ANOVA and Tukey test (α=0.05) and the effect of fibre percentage analysed. Significant differences were found among the stress values for all conditions (p<0.05). Impact load was always responsible for the most critical situation especially when the bone loss was more evident. The system with steel posts showed the highest principal stresses at the post-cement interface with horizontal load and top constraints (compressive stress of 121MPa and tensile stress of 115MPa). The use of glass posts provides a more homogeneous behaviour of the system with lower stresses. Higher fibre percentages gave higher stress in the posts. Moreover, larger bone losses are responsible for important increase in stress. Thus, this work demonstrated that periodontal disease has an important role in the success of tooth restoration after endodontic therapy, influencing the choice of post material and depth.
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
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.
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)
Moczo, Peter; Kristek, Jozef; Galis, Martin; Chaljub, Emmanuel; Etienne, Vincent
2011-12-01
We analyse 13 3-D numerical time-domain explicit schemes for modelling seismic wave propagation and earthquake motion for their behaviour with a varying P-wave to S-wave speed ratio (VP/VS). The second-order schemes include three finite-difference, three finite-element and one discontinuous-Galerkin schemes. The fourth-order schemes include three finite-difference and two spectral-element schemes. All schemes are second-order in time. We assume a uniform cubic grid/mesh and present all schemes in a unified form. We assume plane S-wave propagation in an unbounded homogeneous isotropic elastic medium. We define relative local errors of the schemes in amplitude and the vector difference in one time step and normalize them for a unit time. We also define the equivalent spatial sampling ratio as a ratio at which the maximum relative error is equal to the reference maximum error. We present results of the extensive numerical analysis. We theoretically (i) show how a numerical scheme sees the P and S waves if the VP/VS ratio increases, (ii) show the structure of the errors in amplitude and the vector difference and (iii) compare the schemes in terms of the truncation errors of the discrete approximations to the second mixed and non-mixed spatial derivatives. We find that four of the tested schemes have errors in amplitude almost independent on the VP/VS ratio. The homogeneity of the approximations to the second mixed and non-mixed spatial derivatives in terms of the coefficients of the leading terms of their truncation errors as well as the absolute values of the coefficients are key factors for the behaviour of the schemes with increasing VP/VS ratio. The dependence of the errors in the vector difference on the VP/VS ratio should be accounted for by a proper (sufficiently dense) spatial sampling.
2015-08-01
information systems (GIS) software. A smaller 6.25 square kilometer area around the Southern Methodist University was extracted from the larger...area and analyzed using an acoustic finite- difference time-domain (FDTD) code. The procedures to model the area using GIS software, extract required...create directories. .................................................. 127 Figure 8.4. Choose section cut to extract data
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.
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.
NASA Astrophysics Data System (ADS)
Jiang, Zhongzheng; Zhao, Wenwen; Chen, Weifang
2016-11-01
Non-equilibrium effects play a vital role in high-speed and rarefied gas flows and the accurate simulation of these flow regimes are far beyond the capability of near-local-equilibrium Navier-Stokes-Fourier equations. Eu proposed generalized hydrodynamic equations which are consistent with the laws of irreversible thermodynamics to solve this problem. Based on Eu's generalized hydrodynamics equations, a computation model, namely the nonlinear coupled constitutive relations (NCCR), was developed by R.S. Myong and applied successfully to one-dimensional shock wave structure and two-dimensional rarefied flows. In this paper, finite volume schemes, including LU-SGS time advance scheme, MUSCL interpolation and AUSMPW+ scheme, are firstly adopted to investigate NCCR model's validity and potential in three-dimensional complex hypersonic rarefied gas flows. Moreover, in order to solve the computational stability problems in 3D complex flows, a modified solution is developed for the NCCR model. Finally, the modified solution is tested for a slip complex flow over a 3D hollow cylinder-flare configuration. The numerical results show that the NCCR model by the modified solution yields good solutions in better agreement with the DSMC results and experimental data than NSF equations, and imply NCCR model's great potential capability in further application.
Discrete- and finite-bandwidth-frequency distributions in nonlinear stability applications
NASA Astrophysics Data System (ADS)
Kuehl, Joseph J.
2017-02-01
A new "wave packet" formulation of the parabolized stability equations method is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening, and results in disturbance representation more consistent with the experiment than traditional formulations. A Mach 6 flared-cone example is presented.
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.
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 Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.
1986-01-01
A Taylor-Galerkin finite element method for solving large, nonlinear thermal-structural problems is presented. The algorithm is formulated for coupled transient and uncoupled quasistatic thermal-structural problems. Vectorizing strategies ensure computational efficiency. Two applications demonstrate the validity of the approach for analyzing transient and quasistatic thermal-structural problems.
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
NASA Astrophysics Data System (ADS)
Singh, Gajbir; Venkateswara Rao, G.; Iyengar, N. G. R.
1995-03-01
The influence of finite amplitudes on the free flexural vibration response of moderately thick laminated plates is investigated. For this purpose, a simple higher order theory involving only four unknowns and satisfying the stress free conditions at the top and bottom surface of the composite plate is proposed. The proposed theory eliminates the use of shear correction factors which are otherwise required in Mindlin's plate theory. A rectangular four-node[formula]continuous finite element is developed based on this theory. The non-linear finite element equations are reduced to two non-linear ordinary differential equations governing the response of positive and negative deflection cycles. Direct numerical integration method is then employed to obtain the periods or non-linear frequencies. The finite element developed and the direct numerical integration method employed are validated for the case of isotropic rectangular plates. It is found that unsymmetrically laminated rectangular plates with hinged-hinged edge conditions oscillate with different amplitudes in the positive and negative deflection cycles. Furthermore, such plates would oscillate with a frequency less than the fundamental frequency for finite small amplitudes of oscillation. It is shown that this behaviour is strongly influenced by the boundary conditions. Results are presented for many configurations of composite plates.
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.
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
An approach for verification of finite-element analysis in nonlinear elasticity under large strains
NASA Astrophysics Data System (ADS)
Zingerman, K. M.; Vershinin, A. V.; Levin, V. A.
2016-11-01
An approach to verification of finite-element calculations of stress-strain state of nonlinear elastic bodies under large deformations is suggested. The problems that may be reduced to one-dimensional ones using a semi-inverse method are taken as test problems. An example of such a test problem is the Lame problem for a cylinder. Generally, this problem for compressible hyperelastic materials has no exact analytical solution, but it can be reduced to a boundary value problem for an ordinary second-order nonlinear differential equation, and in some cases - to the Cauchy problem. A numerical solution of this problem can be used as a test one for finite element calculations carried out in three-dimensional statement. Some results of such verification (finite element calculations were performed using the Fidesys CAE-system) are presented.
Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan
2016-01-01
In this wIn 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.ork, we explore finite
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.
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 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.
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
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.
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.
Characterization of the nonlinear propagation of diffracting, finite amplitude ultrasonic fields
NASA Astrophysics Data System (ADS)
Wallace, Kirk Dennis
The scope of this thesis is to investigate the nonlinear physics fundamental to the progressive distortion of a bounded finite amplitude ultrasonic beam. Emphasis is placed on the experimental characterization of the spatial dependence in harmonic frequency content for a finite amplitude ultrasonic field generated by a narrowband bounded source. Asymptotic forms of the Burgers equation are considered to facilitate analysis of finite amplitude measurements (Fubini solution) and simulation of strongly shocked waveforms (Fay solution). The impact of the Kramers-Kronig dispersion relationship on shock wave evolution in media with frequency dependent power law attenuation is demonstrated. A numerical simulation tool incorporating the complete form of the nonlinear Burgers equation into a linear angular spectrum description of the three dimensional ultrasonic field is developed and presented. Experimental validation of the numerical simulation tool is achieved through comparison with a series of detailed hydrophone measurements of the finite amplitude ultrasonic field generated by a clinical echocardiographic imaging system. Once validated, the simulation tool is used to assist the design and motivation of experimental measurements of intrinsic acoustic parameters in liquid mixtures. A novel experimental technique is utilized to determine both nonlinear and linear acoustic parameters in mixtures of isopropyl alcohol and water.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-01-01
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
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.
Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Vismara, S. O.; Ricci, S.; Bellini, M.; Trittoni, L.
2016-06-01
The objective of the present paper is to describe a procedure to identify and model the non-linear behaviour of structural elements. The procedure herein applied can be divided into two main steps: the system identification and the finite element model updating. The application of the restoring force surface method as a strategy to characterize and identify localized non-linearities has been investigated. This method, which works in the time domain, has been chosen because it has `built-in' characterization capabilities, it allows a direct non-parametric identification of non-linear single-degree-of-freedom systems and it can easily deal with sine-sweep excitations. Two different application examples are reported. At first, a numerical test case has been carried out to investigate the modelling techniques in the case of non-linear behaviour based on the presence of a free-play in the model. The second example concerns the flap of the Intermediate eXperimental Vehicle that successfully completed its 100-min mission on 11 February 2015. The flap was developed under the responsibility of Thales Alenia Space Italia, the prime contractor, which provided the experimental data needed to accomplish the investigation. The procedure here presented has been applied to the results of modal testing performed on the article. Once the non-linear parameters were identified, they were used to update the finite element model in order to prove its capability of predicting the flap behaviour for different load levels.
Hoffelner, J; Landes, H; Kaltenbacher, M; Lerch, R
2001-05-01
A recently developed finite element method (FEM) for the numerical simulation of nonlinear sound wave propagation in thermoviscous fluids is presented. Based on the nonlinear wave equation as derived by Kuznetsov, typical effects associated with nonlinear acoustics, such as generation of higher harmonics and dissipation resulting from the propagation of a finite amplitude wave through a thermoviscous medium, are covered. An efficient time-stepping algorithm based on a modification of the standard Newmark method is used for solving the non-linear semidiscrete equation system. The method is verified by comparison with the well-known Fubini and Fay solutions for plane wave problems, where good agreement is found. As a practical application, a high intensity focused ultrasound (HIFU) source is considered. Impedance simulations of the piezoelectric transducer and the complete HIFU source loaded with air and water are performed and compared with measured data. Measurements of radiated low and high amplitude pressure pulses are compared with corresponding simulation results. The obtained good agreement demonstrates validity and applicability of the nonlinear FEM.
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
Hou, Gary Y; Luo, Jianwen; Marquet, Fabrice; Maleke, Caroline; Vappou, Jonathan; Konofagou, Elisa E
2011-12-01
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 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 and 5.39 and 1.65, 3.19 and 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 found in both simulations (16.2, 73.1 and 334.7 mm(2)) and experiments (26.2, 94.2 and 206.2 mm(2)). 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.
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.
NASA Astrophysics Data System (ADS)
Pérez-Aparicio, José L.; Sosa, Horacio
2004-06-01
Magnetostriction is a phenomenon observed in all ferromagnetic materials. It couples elastic, electric, magnetic and in some situations also thermal fields and is of great industrial interest for use in sensors, actuators, adaptive or functional structures, robotics, transducers and MEMS. In this work, the governing equations of the three-field problem (i.e., the interactions of elastic, electric and magnetic effects) are formulated in three dimensions, accounting for non-linear (through magnetic body forces represented by the Maxwell tensor) and dynamic effects, and with constitutive equations resembling those of piezoelectricity. Through manipulation of Maxwell equations it is possible to find suitable expressions for developing the numerical weak, Galerkin and matrix forms in a natural way, including seven residuals (one for each nodal degree of freedom) and non-symmetric tangent, 'capacity' and mass consistent matrices. Simple backward Euler and central difference schemes can be used for the time domain integration. The only assumption made in this work for simplification is that the time variation of electric induction is negligible. This is justified by the relatively low frequencies ({\\ll }1 GHz) under which magnetostrictive materials usually work. The principal feature of the equations is the use of a magnetic potential (without much physical meaning) that allows a complete 'displacement' finite element formulation: all elastic, electric and magnetic nodal unknowns are zero derivatives. This allows the algorithm to be treated in a standard way, and important effects such as eddy currents can be obtained naturally. The formulation is implemented in the research finite element code FEAP. Although seven degrees of freedom per node is computer expensive to solve (especially for 3D problems), the current trend in the performance of computers, even personal ones, makes it worthwhile to build complete finite elements following the well-established (in mechanics
Error estimations of mixed finite element methods for nonlinear problems of shallow shell theory
NASA Astrophysics Data System (ADS)
Karchevsky, M.
2016-11-01
The variational formulations of problems of equilibrium of a shallow shell in the framework of the geometrically and physically nonlinear theory by boundary conditions of different main types, including non-classical, are considered. Necessary and sufficient conditions for their solvability are derived. Mixed finite element methods for the approximate solutions to these problems based on the use of second derivatives of the bending as auxiliary variables are proposed. Estimations of accuracy of approximate solutions are established.
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.
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.
A Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis
NASA Technical Reports Server (NTRS)
Thornton, Earl A.; Dechaumphai, Pramote
1985-01-01
A Taylor-Galerkin finite element solution algorithm for transient nonlinear thermal-structural analysis of large, complex structural problems subjected to rapidly applied thermal-structural loads is described. The two-step Taylor-Galerkin algorithm is an application of an algorithm recently developed for problems in compressible fluid dynamics. The element integrals that appear in the algorithm can be evaluated in closed form for two and three dimensional elements.
Finite Dimensional Approximation of a Class of Constrained Nonlinear Optimal Control Problems
1994-03-01
property for Schr ~ dinger Hanxiltonians, Helvetica Physiea Acta, 52 (1979), pp. 655-670. [13) V. GIRAULT AND P. RAVIART, Finite Element Methods for Navier...involves the von Kirma.n plate equations of nonlinear elasticity, the second the Ginzburg-Landau equations of superconductivity, and the third the...Navier-Stokes equations for incompressible, viscous flows. ’This research was supported by the National Aeronautics and Space Administration under NASA
NASA Astrophysics Data System (ADS)
Su, Zhan; Zhang, Qingling; Ai, Jun; Sun, Xin
2015-01-01
For nonlinear descriptor systems, this paper presents an approach to obtain a fuzzy controller with guaranteed finite-time stability and finite-time boundedness with non-zero initial state, which outperforms some recent work and additionally provides a precision estimation of model approximation. We prove necessary and sufficient conditions of finite-time stability and finite-time boundedness with non-zero initial state for nonlinear descriptor systems. Using Takagi-Sugeno fuzzy dynamic models and proposed sufficient conditions, we define fuzzy sets and use linear matrix inequalities to satisfy differential linear matrix inequalities. A simulation confirms efficiency and precision of the given method.
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.
Finite-Time State Estimation for Coupled Markovian Neural Networks With Sensor Nonlinearities.
Wang, Zhuo; Xu, Yong; Lu, Renquan; Peng, Hui
2017-03-01
This paper investigates the issue of finite-time state estimation for coupled Markovian neural networks subject to sensor nonlinearities, where the Markov chain with partially unknown transition probabilities is considered. A Luenberger-type state estimator is proposed based on incomplete measurements, and the estimation error system is derived by using the Kronecker product. By using the Lyapunov method, sufficient conditions are established, which guarantee that the estimation error system is stochastically finite-time bounded and stochastically finite-time stable, respectively. Then, the estimator gains are obtained via solving a set of coupled linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed new design method.
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)
Fisher, Aaron C.
We have developed a mixed Vector Finite Element Method (VFEM) for Maxwell's equations with third order polarization terms. The method allows for discretization of complicated device geometries with arbitrary order representations of the B and E fields, and up to 4th order accurate time discretization. Additionally we have implemented a series of computational optimizations that significantly increase the scale of simulations that can be performed with this method. Among these optimizations is a new generalized mass lumping method that we developed which reduces the computational cost of the finite element system solve by a factor of 10x. In this dissertation we will present the Vector Finite Element Method, and the computational optimizations that we employed. Additionally, we will present a series of analyses and simulations that were performed to validate the method. Finally, we will present some production runs using this method, including nonlinear mode mixing in waveguides and supercontinuum generation in a photonic crystal fiber.
NASA Astrophysics Data System (ADS)
Brünig, M.
The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the rate-independent finite strain analysis of solids undergoing large elastic-plastic deformations. The formulation relies on the introduction of a mixed-variant metric transformation tensor which will be multiplicatively decomposed into a plastic and an elastic part. This leads to the definition of an appropriate logarithmic strain measure whose rate is shown to be additively decomposed into elastic and plastic strain rate tensors. The mixed-variant logarithmic elastic strain tensor provides a basis for the definition of a local isotropic hyperelastic stress response in the elastic-plastic solid. Additionally, the plastic material behavior is assumed to be governed by a generalized J2 yield criterion and rate-independent isochoric plastic strain rates are computed using an associated flow rule. On the numerical side, the computation of the logarithmic strain tensors is based on 1st and higher order Padé approximations. Estimates of the stress and strain histories are obtained via a highly stable and accurate explicit scalar integration procedure which employs a plastic predictor followed by an elastic corrector step. The development of a consistent elastic-plastic tangent operator as well as its implementation into a nonlinear finite element program will also be discussed. Finally, the numerical solution of finite strain elastic-plastic problems is presented to demonstrate the efficiency of the algorithm.
Kooijman, Gerben; Ouweltjes, Okke
2009-04-01
A lumped element electroacoustic model for a synthetic jet actuator is presented. The model includes the nonlinear flow resistance associated with flow separation and employs a finite difference scheme in the time domain. As opposed to more common analytical frequency domain electroacoustic models, in which the nonlinear resistance can only be considered as a constant, it allows the calculation of higher harmonics, i.e., distortion components, generated as a result of this nonlinear resistance. Model calculations for the time-averaged momentum flux of the synthetic jet as well as the radiated sound power spectrum are compared to experimental results for various configurations. It is shown that a significantly improved prediction of the momentum flux-and thus flow velocity-of the jet is obtained when including the nonlinear resistance. Here, the current model performs slightly better than an analytical model. For the power spectrum of radiated sound, a reasonable agreement is obtained when assuming a plausible slight asymmetry in the nonlinear resistance. However, results suggest that loudspeaker nonlinearities play a significant role as well in the generation of the first few higher harmonics.
Optimal finite-thrust spacecraft trajectories using direct transcription and nonlinear programming
NASA Astrophysics Data System (ADS)
Enright, Paul James
1991-08-01
A class of methods for the numerical solution of optimal control problems is analyzed and applied to the optimization of finite-thrust spacecraft trajectories. These methods use discrete approximations to the state and control histories, and a discretization of the equations of motion to derive a mathematical programming problem which approximates the optimal control problem, and which is solved numerically. This conversion is referred to as transcription. Recent advances in nonlinear programming, however, have made it feasible to solve the original heavily-constrained nonlinear programming problem, which is referred to as the direct transcription of the optimal control problem. This method is referred to as direct transcription and nonlinear programming. A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables and enforces the equations of motion via a collocation procedure, resulting in a nonlinear programming problem, which is solved numerically. This method is identified as being of the general class of direct transcription methods described above. Also, a new direct transcription method which discretizes the equations of motion using a parallel-shooting approach is developed. Both methods are applied to thrust-limited spacecraft trajectory problems, including finite-thrust transfer, rendezvous, and orbit insertion, a low-thrust escape, and a low-thrust Earth-moon transfer.
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.
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 Astrophysics Data System (ADS)
Li, J. H.; Zhu, Z. Q.; Liu, S. C.; Zeng, S. H.
2011-12-01
Based on the principle of abnormal field algorithms, Helmholtz equations for electromagnetic field have been deduced. We made the electric field Helmholtz equation the governing equation, and derived the corresponding system of vector finite element method equations using the Galerkin method. For solving the governing equation using the vector finite element method, we divided the computing domain into homogenous brick elements, and used Whitney-type vector basis functions. After obtaining the electric field's anomaly field in the Laplace domain using the vector finite element method, we used the Gaver-Stehfest algorithm to transform the electric field's anomaly field to the time domain, and obtained the impulse response of magnetic field's anomaly field through the Faraday law of electromagnetic induction. By comparing 1D analytic solutions of quasi-H-type geoelectric models, the accuracy of the vector finite element method is tested. For the low resistivity brick geoelectric model, the plot shape of electromotive force computed using the vector finite element method coincides with that of the integral equation method and finite difference in time domain solutions.
1986-04-30
TenCate , who is supported by ONR Contract NOOO I 4-84-K-0574, in the completion of work on pure tones that interact in higher order modes of a...rectangular duct.26 Through collaboration with TenCate , Lind has acquired experience with the same experimental apparatus that he will use beginning I June...34 J. Acoust. Soc. " .. Am. 65.1127-1133(1979). 36. J. A TenCate and K F. Hamilton, "Dispersive nonlinear wave interactions in a rectangular duct," In
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
Finite element simulation of non-linear acoustic generation in a horn loudspeaker
NASA Astrophysics Data System (ADS)
Tsuchiya, T.; Kagawa, Y.; Doi, M.; Tsuji, T.
2003-10-01
The loudspeaker is an electro-acoustic device for sound reproduction which requires the distortion as small as possible. The distortion may arise from the magnetic non-linearity of the york, the uneven magnetic field distribution, the mechanical non-linearity at the diaphragm suspension and the acoustic non-linearity due to the high sound pressure and velocity in the duct-radiation system. A horn is sometimes provided in front of the vibrating diaphragm radiator, which plays an important role to increase the efficiency by matching the acoustic impedance between the radiator and the ambient medium. The horn is in many cases folded twice or three times to shorten the length, which further degrades the reproduction quality. The sound intensity and velocity are apt to attain very high in the small cross-sectional area in the throat and in the folded regions, which may cause the distortion due to the non-linear effect of the medium. The present paper is to investigate the frequency characteristics of the loudspeaker numerically evaluating the generation of the harmonics and sub-harmonics. An axisymmetric folded horn is considered for which the wave equation with the non-linear term retained is solved by the finite element method. The solution is made in time domain in which the sound pressure calculated at the opening end of the horn is Fourier-transformed to the frequency domain to evaluate the distortion, while the wave marching in the horn is visualized.
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 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.
Finite-dimensional constrained fuzzy control for a class of nonlinear distributed process systems.
Wu, Huai-Ning; Li, Han-Xiong
2007-10-01
This correspondence studies the problem of finite-dimensional constrained fuzzy control for a class of systems described by nonlinear parabolic partial differential equations (PDEs). Initially, Galerkin's method is applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, a systematic modeling procedure is given to construct exactly a Takagi-Sugeno (T-S) fuzzy model for the finite-dimensional ODE system under state constraints. Then, based on the T-S fuzzy model, a sufficient condition for the existence of a stabilizing fuzzy controller is derived, which guarantees that the state constraints are satisfied and provides an upper bound on the quadratic performance function for the finite-dimensional slow system. The resulting fuzzy controllers can also guarantee the exponential stability of the closed-loop PDE system. Moreover, a local optimization algorithm based on the linear matrix inequalities is proposed to compute the feedback gain matrices of a suboptimal fuzzy controller in the sense of minimizing the quadratic performance bound. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.
A semi-Lagrangian finite difference WENO scheme for scalar nonlinear conservation laws
NASA Astrophysics Data System (ADS)
Huang, Chieh-Sen; Arbogast, Todd; Hung, Chen-Hui
2016-10-01
For a nonlinear scalar conservation law in one-space dimension, we develop a locally conservative semi-Lagrangian finite difference scheme based on weighted essentially non-oscillatory reconstructions (SL-WENO). This scheme has the advantages of both WENO and semi-Lagrangian schemes. It is a locally mass conservative finite difference scheme, it is formally high-order accurate in space, it has small time truncation error, and it is essentially non-oscillatory. The scheme is nearly free of a CFL time step stability restriction for linear problems, and it has a relaxed CFL condition for nonlinear problems. The scheme can be considered as an extension of the SL-WENO scheme of Qiu and Shu (2011) [2] developed for linear problems. The new scheme is based on a standard sliding average formulation with the flux function defined using WENO reconstructions of (semi-Lagrangian) characteristic tracings of grid points. To handle nonlinear problems, we use an approximate, locally frozen trace velocity and a flux correction step. A special two-stage WENO reconstruction procedure is developed that is biased to the upstream direction. A Strang splitting algorithm is used for higher-dimensional problems. Numerical results are provided to illustrate the performance of the scheme and verify its formal accuracy. Included are applications to the Vlasov-Poisson and guiding-center models of plasma flow.
Hou, Huazhou; Zhang, Qingling
2016-11-01
In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method.
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.
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.
Global finite-time stabilisation of a class of switched nonlinear systems
NASA Astrophysics Data System (ADS)
Liang, Ying-Jiu; Ma, Ruicheng; Wang, Min; Fu, Jun
2015-12-01
This paper is concerned with the global finite-time stabilisation problem for a class of switched nonlinear systems under arbitrary switchings. All subsystems of the studied switched system under consideration are in lower triangular form. Based on the adding one power integrator technique, both a class of non-Lipschitz continuous state feedback controllers and a common Lyapunov function are simultaneously constructed such that the closed-loop switched system is global finite-time stable under arbitrary switchings. In the controller design process, a common coordinate transformation of all subsystems is exploited to avoid using individual coordinate transformations for subsystems. Finally, two examples are given to show the effectiveness of the proposed method.
A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy
NASA Astrophysics Data System (ADS)
Viebahn, Nils; Pimenta, Paulo M.; Schröder, Jörg
2016-11-01
This work presents a simple finite element implementation of a geometrically exact and fully nonlinear Kirchhoff-Love shell model. Thus, the kinematics are based on a deformation gradient written in terms of the first- and second-order derivatives of the displacements. The resulting finite element formulation provides C^1 -continuity using a penalty approach, which penalizes the kinking at the edges of neighboring elements. This approach enables the application of well-known C^0 -continuous interpolations for the displacements, which leads to a simple finite element formulation, where the only unknowns are the nodal displacements. On the basis of polyconvex strain energy functions, the numerical framework for the simulation of isotropic and anisotropic thin shells is presented. A consistent plane stress condition is incorporated at the constitutive level of the model. A triangular finite element, with a quadratic interpolation for the displacements and a one-point integration for the enforcement of the C^1 -continuity at the element interfaces leads to a robust shell element. Due to the simple nature of the element, even complex geometries can be meshed easily, which include folded and branched shells. The reliability and flexibility of the element formulation is shown in a couple of numerical examples, including also time dependent boundary value problems. A plane reference configuration is assumed for the shell mid-surface, but initially curved shells can be accomplished if one regards the initial configuration as a stress-free deformed state from the plane position, as done in previous works.
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.
Nonlinear, Local Kinetic Damping of Finite-Size Plasma Waves Relevant to Stimulated Raman Scattering
NASA Astrophysics Data System (ADS)
Mori, Warren; Fahlen, Jay; Winjum, Benjamin; Grismayer, Thomas; Decyk, Viktor
2009-11-01
Computer simulations of stimulated Raman scattering (SRS) indicate that the instability is bursty in time and space, leading to finite-size plasma waves in both the longitudinal and transverse directions. Using particle-in-cell (PIC) simulations with an external, ponderomotive impulse driver, we present the results of detailed study of the nonlinear behavior of finite-sized plasma waves in order to better understand the long-time behavior of SRS reflectivities. In one dimension, we present recently published results (Fahlen et al., PRL 102, 245002 (2009)) showing that finite-length plasma waves erode from the rear edge as new resonant particles enter and locally damp the packet. In multiple dimensions, recent results show that finite-width plasma waves localize about their axis due primarily to local, kinetic damping at the edges. The simulations are performed using a 1D and 2D electrostatic PIC code, and also using a 2D Darwin PIC code. This work was supported by DOE under Grant Nos. DE-FG52-03-NA00065, DE-FG52-06NA26195, and DE-FG02-03ER54721.
A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy
NASA Astrophysics Data System (ADS)
Viebahn, Nils; Pimenta, Paulo M.; Schröder, Jörg
2017-02-01
This work presents a simple finite element implementation of a geometrically exact and fully nonlinear Kirchhoff-Love shell model. Thus, the kinematics are based on a deformation gradient written in terms of the first- and second-order derivatives of the displacements. The resulting finite element formulation provides C^1-continuity using a penalty approach, which penalizes the kinking at the edges of neighboring elements. This approach enables the application of well-known C^0-continuous interpolations for the displacements, which leads to a simple finite element formulation, where the only unknowns are the nodal displacements. On the basis of polyconvex strain energy functions, the numerical framework for the simulation of isotropic and anisotropic thin shells is presented. A consistent plane stress condition is incorporated at the constitutive level of the model. A triangular finite element, with a quadratic interpolation for the displacements and a one-point integration for the enforcement of the C^1-continuity at the element interfaces leads to a robust shell element. Due to the simple nature of the element, even complex geometries can be meshed easily, which include folded and branched shells. The reliability and flexibility of the element formulation is shown in a couple of numerical examples, including also time dependent boundary value problems. A plane reference configuration is assumed for the shell mid-surface, but initially curved shells can be accomplished if one regards the initial configuration as a stress-free deformed state from the plane position, as done in previous works.
2015-07-01
circular hole in an aluminium plate fitted with a titanium fastener that were computed using two-dimensional finite element contact analysis. By...used to validate the contact stress distributions associated with a circular hole in an aluminium plate fitted with a titanium fastener that were...fatigue life and aircraft structural integrity management of RAAF airframes. An aluminium coupon has been previously designed in support of the
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.
NASA Astrophysics Data System (ADS)
Germaneau, A.; Peyruseigt, F.; Mistou, S.; Doumalin, P.; Dupré, J.-C.
2010-06-01
On Airbus aircraft, spherical plain bearings are used on many components; in particular to link engine to pylon or pylon to wing. Design of bearings is based on contact pressure distribution on spherical surfaces. To determine this distribution, a 3D analysis of the mechanical behaviour of aeronautical plain bearing is presented in this paper. A numerical model has been built and validated from a comparison with 3D experimental measurements of kinematic components. For that, digital volume correlation (DVC) coupled with optical scanning tomography (OST) is employed to study the mechanical response of a plain bearing model made in epoxy resin. Experimental results have been compared with the ones obtained from the simulated model. This comparison enables us to study the influence of various boundary conditions to build the FE model. Some factors have been highlighted like the fitting behaviour which can radically change contact pressure distribution. This work shows the contribution of a representative mechanical environment to study precisely mechanical response of aeronautical plain bearings.
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.
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.
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.
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.
Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
NASA Astrophysics Data System (ADS)
Yang, Z.; Yuan, Z.; Nie, Y.; Wang, J.; Zhu, X.; Liu, F.
2017-02-01
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.
Nonlinear, three-dimensional finite-element analysis of air-cooled gas turbine blades
NASA Technical Reports Server (NTRS)
Kaufman, A.; Gaugler, R. E.
1980-01-01
Cyclic stress-strain states in cooled turbine blades were calculated for a simulated mission of an advanced-technology commercial aircraft engine. The MARC, nonlinear, finite-element computer program was used for the analysis of impingement-cooled airfoils, with and without leading-edge film cooling. Creep was the predominant damage mode (ignoring hot corrosion), particularly artund film-cooling holes. Radially angled holes exhibited less creep than holes with axes normal to the surface. Beam-theory analyses of all-impingement-cooled airfoils gave fair agreement with MARC results for initial creep.
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)
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.
NASA Astrophysics Data System (ADS)
Hamim, Salah Uddin Ahmed
Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost.
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)
Mohd Nor, M. K.; Ma'at, N.; Kamarudin, K. A.; Ismail, A. E.
2016-11-01
The constitutive models adopted to represent dynamic plastic behaviour are of great importance in the current design and analysis of forming processes. Many have studied this topic, leading to results in various technologies involving analytical, experimental and computational methods. Despite of this current status, it is generally agreed that there is still a need for improved constitutive models. There are still many issues relating to algorithm implementation of the proposed constitutive model in the selected code to represent the proposed formulation. Using this motivation, the implementation of a new constitutive model into the LLNL-DYNA3D code to predict the deformation behaviour of commercial aluminium alloys is discussed concisely in this paper. The paper initially explains the background and the basic structure of the LLNL-DYNA3D code. This is followed by a discussion on the constitutive models that have been chosen as the starting point for this work. The initial stage of this implementation work is then discussed in order to allow all the required material data and the deformation gradient tensor F to be read and initialised for the main analysis. Later, the key section of this implementation is discussed, which mainly relates to subroutine f3dm93 including equation of state (EOS) implementation. The implementation of the elastic-plastic part with isotropic plastic hardening, which establishes the relationship between stress and strain with respect to the isoclinic configuration Ω¯ i in the new deviatoric plane, is then presented before the implemented algorithm is validated against Plate Impact test data of the Aluminium Alloy 7010. A good agreement is obtained in each test.
Moulin, Céline; Glière, Alain; Barbier, Daniel; Joucla, Sebastien; Yvert, Blaise; Mailley, Pascal; Guillemaud, Régis
2008-02-01
A transient finite-element model has been developed to simulate an extracellular action potential recording in a tissue slice by a planar microelectrode array. The thin-film approximation of the active neuron membrane allows the simulation within single finite-element software of the intracellular and extracellular potential fields. In comparison with a compartmental neuron model, it is shown that the thin-film approximation-based model is able to properly represent the neuron bioelectrical behavior in terms of transmembrane current and potential. Moreover, the model is able to simulate extracellular action potential recordings with properties similar to those observed in biological experiments. It is demonstrated that an ideal measurement system model can be used to represent the recording microelectrode, provided that the electronic recording system adapts to the electrode-tissue interface impedance. By comparing it with a point source approximated neuron, it is also shown that the neuron three-dimensional volume should be taken into account to simulate the extracellular action potential recording. Finally, the influence of the electrode size on the signal amplitude is evaluated. This parameter, together with the microelectrode noise, should be taken into account in order to optimize future microelectrode designs in terms of the signal-to-noise ratio.
Fracture prediction for the proximal femur using finite element models: Part II--Nonlinear analysis.
Lotz, J C; Cheal, E J; Hayes, W C
1991-11-01
In Part I we reported the results of linear finite element models of the proximal femur generated using geometric and constitutive data collected with quantitative computed tomography. These models demonstrated excellent agreement with in vitro studies when used to predict ultimate failure loads. In Part II, we report our extension of those finite element models to include nonlinear behavior of the trabecular and cortical bone. A highly nonlinear material law, originally designed for representing concrete, was used for trabecular bone, while a bilinear material law was used for cortical bone. We found excellent agreement between the model predictions and in vitro fracture data for both the onset of bone yielding and bone fracture. For bone yielding, the model predictions were within 2 percent for a load which simulated one-legged stance and 1 percent for a load which simulated a fall. For bone fracture, the model predictions were within 1 percent and 17 percent, respectively. The models also demonstrated different fracture mechanisms for the two different loading configurations. For one-legged stance, failure within the primary compressive trabeculae at the subcapital region occurred first, leading to load transfer and, ultimately, failure of the surrounding cortical shell. However, for a fall, failure of the cortical and trabecular bone occurred simultaneously within the intertrochanteric region. These results support our previous findings that the strength of the subcapital region is primarily due to trabecular bone whereas the strength of the intertrochanteric region is primarily due to cortical bone.
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.
Moerman, Kevin M; van Vijven, Marc; Solis, Leandro R; van Haaften, Eline E; Loenen, Arjan C Y; Mushahwar, Vivian K; Oomens, Cees W J
2017-04-01
Pressure ulcers are a type of local soft tissue injury due to sustained mechanical loading and remain a common issue in patient care. People with spinal cord injury (SCI) are especially at risk of pressure ulcers due to impaired mobility and sensory perception. The development of load improving support structures relies on realistic tissue load evaluation e.g. using finite element analysis (FEA). FEA requires realistic subject-specific mechanical properties and geometries. This study focuses on the effect of geometry. MRI is used for the creation of geometrically accurate models of the human buttock for three able-bodied volunteers and three volunteers with SCI. The effect of geometry on observed internal tissue deformations for each subject is studied by comparing FEA findings for equivalent loading conditions. The large variations found between subjects confirms the importance of subject-specific FEA.
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.
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.
Miranda, Pedro C; Hallett, Mark; Basser, Peter J
2003-09-01
We investigate the effect of tissue heterogeneity and anisotropy on the electric field and current density distribution induced in the brain during magnetic stimulation. Validation of the finite-element (FE) calculations in a homogeneous isotropic sphere showed that the magnitude of the total electric field can be calculated to within an error of approximately 5% in the region of interest, even in the presence of a significant surface charge contribution. We used a high conductivity inclusion within a sphere of lower conductivity to simulate a lesion due to an infarct. Its effect is to increase the electric field induced in the surrounding low conductivity region. This boost is greatest in the vicinity of interfaces that lie perpendicular to the current flow. For physiological values of the conductivity distribution, it can reach a factor of 1.6 and extend many millimeters from the interface. We also show that anisotropy can significantly alter the electric field and current density distributions. Either heterogeneity or anisotropy can introduce a radial electric field component, not present in a homogeneous isotropic conductor. Heterogeneity and anisotropy are predicted to significantly affect the distribution of the electric field induced in the brain. It is, therefore, expected that anatomically faithful FE models of individual brains which incorporate conductivity tensor data derived from diffusion tensor measurements, will provide a better understanding of the location of possible stimulation sites in the brain.
NASA Astrophysics Data System (ADS)
Mountris, K. A.; Bert, J.; Noailly, J.; Rodriguez Aguilera, A.; Valeri, A.; Pradier, O.; Schick, U.; Promayon, E.; Gonzalez Ballester, M. A.; Troccaz, J.; Visvikis, D.
2017-03-01
Prostate volume changes due to edema occurrence during transperineal permanent brachytherapy should be taken under consideration to ensure optimal dose delivery. Available edema models, based on prostate volume observations, face several limitations. Therefore, patient-specific models need to be developed to accurately account for the impact of edema. In this study we present a biomechanical model developed to reproduce edema resolution patterns documented in the literature. Using the biphasic mixture theory and finite element analysis, the proposed model takes into consideration the mechanical properties of the pubic area tissues in the evolution of prostate edema. The model’s computed deformations are incorporated in a Monte Carlo simulation to investigate their effect on post-operative dosimetry. The comparison of Day1 and Day30 dosimetry results demonstrates the capability of the proposed model for patient-specific dosimetry improvements, considering the edema dynamics. The proposed model shows excellent ability to reproduce previously described edema resolution patterns and was validated based on previous findings. According to our results, for a prostate volume increase of 10–20% the Day30 urethra D10 dose metric is higher by 4.2%–10.5% compared to the Day1 value. The introduction of the edema dynamics in Day30 dosimetry shows a significant global dose overestimation identified on the conventional static Day30 dosimetry. In conclusion, the proposed edema biomechanical model can improve the treatment planning of transperineal permanent brachytherapy accounting for post-implant dose alterations during the planning procedure.
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.
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.
Kaipatur, Neelambar; Wu, Yuchin; Adeeb, Samer; Stevenson, Thomas; Major, Paul; 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.
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.
NASA Astrophysics Data System (ADS)
Qi, Wenhai; Gao, Xianwen
2016-01-01
This paper focuses on the problem of finite-time H∞ control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity. By employing an appropriate Lyapunov function and some appropriate free-weighting matrices, a state feedback controller is designed to ensure H∞ finite-time boundedness of the resulting closed-loop system that contains time-varying delay, admissible external disturbance, It ?-type stochastic disturbance and nonlinearity. All the proposed conditions are established in the form of linear matrix inequalities. Finally, an example is given to demonstrate the validity of the main results.
NASA Astrophysics Data System (ADS)
Martinez, J.; Belahcen, A.; Detoni, J. G.
2016-01-01
This paper presents a coupled Finite Element Model in order to study the vibrations in induction motors under steady-state. The model utilizes a weak coupling strategy between both magnetic and elastodynamic fields on the structure. Firstly, the problem solves the magnetic vector potential in an axial cut and secondly the former solution is coupled to a three dimensional model of the stator. The coupling is performed using projection based algorithms between the computed magnetic solution and the three-dimensional mesh. The three-dimensional model of the stator includes both end-windings and end-shields in order to give a realistic picture of the motor. The present model is validated using two steps. Firstly, a modal analysis hammer test is used to validate the material characteristic of this complex structure and secondly an array of accelerometer sensors is used in order to study the rotating waves using multi-dimensional spectral techniques. The analysis of the radial vibrations presented in this paper firstly concludes that slot harmonic components are visible when the motor is loaded. Secondly, the multidimensional spectrum presents the most relevant mechanical waves on the stator such as the ones produced by the space harmonics or the saturation of the iron core. The direct retrieval of the wave-number in a multi-dimensional spectrum is able to show the internal current distribution in a non-intrusive way. Experimental results for healthy induction motors are showing mechanical imbalances in a multi-dimensional spectrum in a more straightforward form.
NASA Astrophysics Data System (ADS)
Chang, Y.; Hung, S.; Kuo, B.; Kuochen, H.
2012-12-01
Taiwan is one of the archetypical places for studying the active orogenic process in the world, where the Luzon arc has obliquely collided into the southwest China continental margin since 5 Ma ago. Because of the lack of convincing evidence for the structure in the lithospheric mantle and at even greater depths, several competing models have been proposed for the Taiwan mountain-building process. With the deployment of ocean-bottom seismometers (OBSs) on the seafloor around Taiwan from the TAIGER (TAiwan Integrated GEodynamic Research) and IES seismic experiments, the aperture of the seismic network is greatly extended to improve the depth resolution of tomographic imaging, which is critical to illuminate the nature of the arc-continent collision and accretion in Taiwan. In this study, we use relative travel-time residuals between a collection of teleseismic body wave arrivals to tomographically image the velocity structure beneath Taiwan. In addition to those from common distant earthquakes observed across an array of stations, we take advantage of dense seismicity in the vicinity of Taiwan and the source and receiver reciprocity to augment the data coverage from clustered earthquakes recorded by global stations. As waveforms are dependent of source mechanisms, we carry out the cluster analysis to group the phase arrivals with similar waveforms into clusters and simultaneously determine relative travel-time anomalies in the same cluster accurately by a cross correlation method. The combination of these two datasets would particularly enhance the resolvability of the tomographic models offshore of eastern Taiwan, where the two subduction systems of opposite polarity are taking place and have primarily shaped the present tectonic framework of Taiwan. On the other hand, our inversion adopts an innovation that invokes wavelet-based, multi-scale parameterization and finite-frequency theory. Not only does this approach make full use of frequency-dependent travel
NASA Astrophysics Data System (ADS)
Pletinckx, D.
2011-09-01
The current 3D hype creates a lot of interest in 3D. People go to 3D movies, but are we ready to use 3D in our homes, in our offices, in our communication? Are we ready to deliver real 3D to a general public and use interactive 3D in a meaningful way to enjoy, learn, communicate? The CARARE project is realising this for the moment in the domain of monuments and archaeology, so that real 3D of archaeological sites and European monuments will be available to the general public by 2012. There are several aspects to this endeavour. First of all is the technical aspect of flawlessly delivering 3D content over all platforms and operating systems, without installing software. We have currently a working solution in PDF, but HTML5 will probably be the future. Secondly, there is still little knowledge on how to create 3D learning objects, 3D tourist information or 3D scholarly communication. We are still in a prototype phase when it comes to integrate 3D objects in physical or virtual museums. Nevertheless, Europeana has a tremendous potential as a multi-facetted virtual museum. Finally, 3D has a large potential to act as a hub of information, linking to related 2D imagery, texts, video, sound. We describe how to create such rich, explorable 3D objects that can be used intuitively by the generic Europeana user and what metadata is needed to support the semantic linking.
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.
Richins, W.D.; Miller, G.K.
1995-12-01
Large displacement, non-linear finite element analyses were performed to evaluate a swaging process used to fabricate connections between plates in the fuel elements for a test reactor at the Idaho National Engineering Laboratory. The force required to pull the fuel plate from the connection is referred to as the strength of the connection. Assurance that the integrity of the connections is maintained through reactor operation is provided by establishing a minimum acceptance requirement for this strength. Analysis results were used to assess the sensitivity of the strength of the swaged connections to variations in several manufacturing process parameters. The predicted strengths correlated well with results from tests where sample swaged connections were loaded to failure. Results from these investigations were used to assess the adequacy and need for various fabrication, testing, and quality control requirements.
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.
Non-linear rotation-free shell finite-element models for aortic heart valves.
Gilmanov, Anvar; Stolarski, Henryk; Sotiropoulos, Fotis
2017-01-04
Hyperelastic material models have been incorporated in the rotation-free, large deformation, shell finite element (FE) formulation of (Stolarski et al., 2013) and applied to dynamic simulations of aortic heart valve. Two models used in the past in analysis of such problem i.e. the Saint-Venant and May-Newmann-Yin (MNY) material models have been considered and compared. Uniaxial tests for those constitutive equations were performed to verify the formulation and implementation of the models. The issue of leaflets interactions during the closing of the heart valve at the end of systole is considered. The critical role of using non-linear anisotropic model for proper dynamic response of the heart valve especially during the closing phase is demonstrated quantitatively. This work contributes an efficient FE framework for simulating biological tissues and paves the way for high-fidelity flow structure interaction simulations of native and bioprosthetic aortic heart valves.
Finite interval tracking algorithm for nonlinear multi-agent systems with communication delays
NASA Astrophysics Data System (ADS)
Dong, Lijing; Chai, Senchun; Zhang, Baihai; Li, Xiangshun; Kiong Nguang, Sing
2016-11-01
We propose an iterative learning control (ILC) tracking strategy to solve the tracking problem of multi-agent systems with nonlinear dynamics and time-varying communication delays. The distributed tracking strategy, in which each tracking agent only utilises its own and neighbours' information, enables the tracking agents successfully track a maneuvering target in a finite time interval although with presence of time delays. Compared with the existing related work, the quantitative relationship between the boundary of tracking errors and the estimation of time delays is derived. Furthermore, in many practical control problems, identical initialisation condition may not be satisfied, which is called initial-shift problem. Hence, a forgetting factor is introduced to deal with that problem. It is proved that the presented results are effective via conducting numerical examples.
Vu, Cung Khac; Nihei, Kurt Toshimi; Johnson, Paul A.; Guyer, Robert A.; Ten Cate, James A.; Le Bas, Pierre-Yves; Larmat, Carene S.
2016-06-07
A system and method of characterizing properties of a medium from a non-linear interaction are include generating, by first and second acoustic sources disposed on a surface of the medium on a first line, first and second acoustic waves. The first and second acoustic sources are controllable such that trajectories of the first and second acoustic waves intersect in a mixing zone within the medium. The method further includes receiving, by a receiver positioned in a plane containing the first and second acoustic sources, a third acoustic wave generated by a non-linear mixing process from the first and second acoustic waves in the mixing zone; and creating a first two-dimensional image of non-linear properties or a first ratio of compressional velocity and shear velocity, or both, of the medium in a first plane generally perpendicular to the surface and containing the first line, based on the received third acoustic wave.
NASA Technical Reports Server (NTRS)
Eichler, D.
1985-01-01
The nonlinear theory of shock acceleration developed in earlier papers, which treated the waves as being completely frozen into the fluid, is generalized to include wave dynamics. In the limit where damping keeps the wave amplitude small, it is found that a finite phase velocity (V sub ph) of the scattering waves through the background fluid, tempers the acceleration generated by high Mach number shocks. Asymptotic spectra proportional to 1/E sq are possible only when the ratio of wave velocity to shock velocity is less than 0.13. For a given asymptotic spectrum, the efficiency of relativistic particle production is found to be practically independent of the value of V sub ph, so that earlier results concerning its value remain valid for finite V sub ph. In the limit where there is no wave damping, it is shown that for modest Alfven Mach numbers, approximately greater than 4 and less than 6, the magnetic field is amplified by the energetic particles to the point of being in rough equipartition with them, as models of synchrotron emission frequently take the field to be. In this case, the disordering and amplification of field energy may play a major role in the shock transition.
Weakly nonlinear Rayleigh-Taylor instability of a finite-thickness fluid layer
Wang, L. F. Ye, W. H. Liu, Jie; He, X. T.; Guo, H. Y.; Wu, J. F. Zhang, W. Y.
2014-12-15
A weakly nonlinear (WN) model has been developed for the Rayleigh-Taylor instability of a finite-thickness incompressible fluid layer (slab). We derive the coupling evolution equations for perturbations on the (upper) “linearly stable” and (lower) “linearly unstable” interfaces of the slab. Expressions of temporal evolutions of the amplitudes of the perturbation first three harmonics on the upper and lower interfaces are obtained. The classical feedthrough (interface coupling) solution obtained by Taylor [Proc. R. Soc. London A 201, 192 (1950)] is readily recovered by the first-order results. Our third-order model can depict the WN perturbation growth and the saturation of linear (exponential) growth of the perturbation fundamental mode on both interfaces. The dependence of the WN perturbation growth and the slab distortion on the normalized layer thickness (kd) is analytically investigated via the third-order solutions. Comparison is made with Jacobs-Catton's formula [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988)] of the position of the “linearly unstable” interface. Using a reduced formula, the saturation amplitude of linear growth of the perturbation fundamental mode is studied. It is found that the finite-thickness effects play a dominant role in the WN evolution of the slab, especially when kd < 1. Thus, it should be included in applications where the interface coupling effects are important, such as inertial confinement fusion implosions and supernova explosions.
Weakly nonlinear Rayleigh-Taylor instability of a finite-thickness fluid layer
NASA Astrophysics Data System (ADS)
Wang, L. F.; Guo, H. Y.; Wu, J. F.; Ye, W. H.; Liu, Jie; Zhang, W. Y.; He, X. T.
2014-12-01
A weakly nonlinear (WN) model has been developed for the Rayleigh-Taylor instability of a finite-thickness incompressible fluid layer (slab). We derive the coupling evolution equations for perturbations on the (upper) "linearly stable" and (lower) "linearly unstable" interfaces of the slab. Expressions of temporal evolutions of the amplitudes of the perturbation first three harmonics on the upper and lower interfaces are obtained. The classical feedthrough (interface coupling) solution obtained by Taylor [Proc. R. Soc. London A 201, 192 (1950)] is readily recovered by the first-order results. Our third-order model can depict the WN perturbation growth and the saturation of linear (exponential) growth of the perturbation fundamental mode on both interfaces. The dependence of the WN perturbation growth and the slab distortion on the normalized layer thickness (kd) is analytically investigated via the third-order solutions. Comparison is made with Jacobs-Catton's formula [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988)] of the position of the "linearly unstable" interface. Using a reduced formula, the saturation amplitude of linear growth of the perturbation fundamental mode is studied. It is found that the finite-thickness effects play a dominant role in the WN evolution of the slab, especially when kd < 1. Thus, it should be included in applications where the interface coupling effects are important, such as inertial confinement fusion implosions and supernova explosions.
NASA Astrophysics Data System (ADS)
Griebel, Matt; Buleri, Christine; Baylor, Andrew; Gunnels, Steve; Hull, Charlie; Palunas, Povilas; Phillips, Mark
2016-07-01
The Magellan Telescopes are a set of twin 6.5 meter ground based optical/near-IR telescopes operated by the Carnegie Institution for Science at the Las Campanas Observatory (LCO) in Chile. The primary mirrors are f/1.25 paraboloids made of borosilicate glass and a honeycomb structure. The secondary mirror provides both f/11 and f/5 focal lengths with two Nasmyth, three auxiliary, and a Cassegrain port on the optical support structure (OSS). The telescopes have been in operation since 2000 and have experienced several small earthquakes with no damage. Measurement of in situ response of the telescopes to seismic events showed significant dynamic amplification, however, the response of the telescopes to a survival level earthquake, including component level forces, displacements, accelerations, and stresses were unknown. The telescopes are supported with hydrostatic bearings that can lift up under high seismic loading, thus causing a nonlinear response. For this reason, the typical response spectrum analysis performed to analyze a survival level seismic earthquake is not sufficient in determining the true response of the structure. Therefore, a nonlinear transient finite element analysis (FEA) of the telescope structure was performed to assess high risk areas and develop acceleration responses for future instrument design. Several configurations were considered combining different installed components and altitude pointing directions. A description of the models, methodology, and results are presented.
Potential of minicomputer/array-processor system for nonlinear finite-element analysis
NASA Technical Reports Server (NTRS)
Strohkorb, G. A.; Noor, A. K.
1983-01-01
The potential of using a minicomputer/array-processor system for the efficient solution of large-scale, nonlinear, finite-element problems is studied. A Prime 750 is used as the host computer, and a software simulator residing on the Prime is employed to assess the performance of the Floating Point Systems AP-120B array processor. Major hardware characteristics of the system such as virtual memory and parallel and pipeline processing are reviewed, and the interplay between various hardware components is examined. Effective use of the minicomputer/array-processor system for nonlinear analysis requires the following: (1) proper selection of the computational procedure and the capability to vectorize the numerical algorithms; (2) reduction of input-output operations; and (3) overlapping host and array-processor operations. A detailed discussion is given of techniques to accomplish each of these tasks. Two benchmark problems with 1715 and 3230 degrees of freedom, respectively, are selected to measure the anticipated gain in speed obtained by using the proposed algorithms on the array processor.
Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem
NASA Astrophysics Data System (ADS)
Terekhov, Kirill M.; Mallison, Bradley T.; Tchelepi, Hamdi A.
2017-02-01
We present two new cell-centered nonlinear finite-volume methods for the heterogeneous, anisotropic diffusion problem. The schemes split the interfacial flux into harmonic and transversal components. Specifically, linear combinations of the transversal vector and the co-normal are used that lead to significant improvements in terms of the mesh-locking effects. The harmonic component of the flux is represented using a conventional monotone two-point flux approximation; the component along the parameterized direction is treated nonlinearly to satisfy either positivity of the solution as in [29], or the discrete maximum principle as in [9]. In order to make the method purely cell-centered, we derive a homogenization function that allows for seamless interpolation in the presence of heterogeneity following a strategy similar to [46]. The performance of the new schemes is compared with existing multi-point flux approximation methods [3,5]. The robustness of the scheme with respect to the mesh-locking problem is demonstrated using several challenging test cases.
Stability of orbits in nonlinear mechanics for finite but very long times
Warnock, R.L.; Ruth, R.D.
1990-07-01
In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, {Psi}), such that action J is nearly constant while the angle {Psi} advances almost linearly with the time. By examining the change in J during a time T{sub 0} from many initial conditions in the open domain {Omega} of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain {Omega}{sub 0} {contained in} {Omega}. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10{sup 8} turns). 10 refs., 6 figs., 1 tab.
Finite Larmor radius effects in the nonlinear dynamics of collisionless magnetic reconnection
NASA Astrophysics Data System (ADS)
Del Sarto, D.; Marchetto, C.; Pegoraro, F.; Califano, F.
2011-03-01
We provide numerical evidence of the role of finite Larmor radius effects in the nonlinear dynamics of magnetic field line reconnection in high-temperature, strong guide field plasmas in a slab configuration, in the large Δ' regime. Both ion and electron temperature effects introduce internal energy variations related to mechanical compression terms in the energy balance, thus contributing to regularize the gradients of the ion density with respect to the cold regimes. For values of the Larmor radii that are not asymptotically small, the two temperature effects are no longer interchangeable, in contrast to what is expected from linear theory, and the differences are measurable in the numerical growth rates and in the nonlinear evolution of the density layers. We interpret such differences in terms of the change, due to ion temperature effects, of the Lagrangian advection of the 'plasma invariants' that are encountered in the cold-ion, warm-electron regime. The different roles of the ion and ion-sound Larmor radii in the reconnection dynamics near the X- and O-points are evidenced by means of a local quadratic expansion of the fields.
Huang, Chun-Yuh; Stankiewicz, Anna; Ateshian, Gerard A; Mow, Van C
2005-04-01
The tensile and compressive properties of human glenohumeral cartilage were determined by testing 120 rectangular strips in uniaxial tension and 70 cylindrical plugs in confined compression, obtained from five human glenohumeral joints. Specimens were harvested from five regions across the articular surface of the humeral head and two regions on the glenoid. Tensile strips were obtained along two orientations, parallel and perpendicular to the split-line directions. Two serial slices through the thickness, corresponding to the superficial and middle zones of the cartilage layers, were prepared from each tensile strip and each compressive plug. The equilibrium tensile modulus and compressive aggregate modulus of cartilage were determined from the uniaxial tensile and confined compression tests, respectively. Significant differences in the tensile moduli were found with depth and orientation relative to the local split-line direction. Articular cartilage of the humeral head was significantly stiffer in tension than that of the glenoid. There were significant differences in the aggregate compressive moduli of articular cartilage between superficial and middle zones in the humeral head. Furthermore, tensile and compressive stress-strain responses exhibited nonlinearity under finite strain, while the tensile modulus differed by up to two orders of magnitude from the compressive aggregate modulus at 0% strain, demonstrating a high degree of tension-compression nonlinearity. The complexity of the mechanical properties of human glenohumeral cartilage was exposed in this study, showing anisotropy, inhomogeneity, and tension-compression nonlinearity within the same joint. The observed differences in the tensile properties of human glenohumeral cartilage suggest that the glenoid may be more susceptible to cartilage degeneration than the humeral head.
NASA Astrophysics Data System (ADS)
Jabari, Elahe; Tong, Steven; Azhari, Amir; Toyserkani, Ehsan
2014-03-01
Non-planar (3D) interconnects have an important role in the electronic packaging industry these days. These unconventional interconnects allow manufacturers to save materials and space while connecting circuit components on flexible and non-planar substrates. Among a variety of flexible boards, double-sided flexible substrates have attracted the electronic industry to effectively and compactly develop miniaturized flexible devices such as sensors-on-chips. This study reports our developmental procedure for the creation of non-planar silver interconnects on the edge of double-sided copper substrates separated by a layer of polyethylene terephthalate (PET) using laser-assisted maskless microdeposition (LAMM). The article consists of the characterization of the LAMM process to effectively deposit Ag nanoparticles for production of conductive interconnects. Several parameters, including the deposition and laser processing parameters, are optimized to achieve interconnects free of pores, cracks and delamination. For investigating the topography and microstructure of interconnects, various analytical tools, such as SEM, XRD, Profilometery, and EDS were used. Furthermore, a 3D finite element numerical model was developed to predict the laser processing of silver nanoparticles on the substrate. The model includes a coupled thermal and structural governing physics to derive the temperature history throughout the simulation as well as strain/displacement within the substrate, which is identified the major source of cark formation in Ag tracks. The SEM micrographs of the laser processed nanoparticles suggest that a minimum of 1.24 W laser power was needed for an effective nanoparticles sintering to obtain conductive 3D interconnects with minimum amount of cracks whereas a 1.7 W laser power caused PET to decompose.
Parr, W C H; Chamoli, U; Jones, A; Walsh, W R; Wroe, S
2013-01-04
Most modelling of whole bones does not incorporate trabecular geometry and treats bone as a solid non-porous structure. Some studies have modelled trabecular networks in isolation. One study has modelled the performance of whole human bones incorporating trabeculae, although this required considerable computer resources and purpose-written code. The difference between mechanical behaviour in models that incorporate trabecular geometry and non-porous models has not been explored. The ability to easily model trabecular networks may shed light on the mechanical consequences of bone loss in osteoporosis and remodelling after implant insertion. Here we present a Finite Element Analysis (FEA) of a human ankle bone that includes trabecular network geometry. We compare results from this model with results from non-porous models and introduce protocols achievable on desktop computers using widely available softwares. Our findings show that models including trabecular geometry are considerably stiffer than non-porous whole bone models wherein the non-cortical component has the same mass as the trabecular network, suggesting inclusion of trabecular geometry is desirable. We further present new methods for the construction and analysis of 3D models permitting: (1) construction of multi-property, non-porous models wherein cortical layer thickness can be manipulated; (2) maintenance of the same triangle network for the outer cortical bone surface in both 3D reconstruction and non-porous models allowing exact replication of load and restraint cases; and (3) creation of an internal landmark point grid allowing direct comparison between 3D FE Models (FEMs).
NASA Astrophysics Data System (ADS)
Hammerand, Daniel C.
Over the past several decades, the use of composite materials has grown considerably. Typically, fiber-reinforced polymer-matrix composites are modeled as being linear elastic. However, it is well-known that polymers are viscoelastic in nature. Furthermore, the analysis of complex structures requires a numerical approach such as the finite element method. In the present work, a triangular flat shell element for linear elastic composites is extended to model linear viscoelastic composites. Although polymers are usually modeled as being incompressible, here they are modeled as compressible. Furthermore, the macroscopic constitutive properties for fiber-reinforced composites are assumed to be known and are not determined using the matrix and fiber properties along with the fiber volume fraction. Hygrothermo-rheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Both the temperature and moisture are taken to be prescribed. Hence, the heat energy generated by the viscoelastic deformations is not considered. When the deformations and rotations are small under an applied load history, the usual engineering stress and strain measures can be used and the time history of a viscoelastic deformation process is determined using the original geometry of the structure. If, however, sufficiently large loads are applied, the deflections and rotations will be large leading to changes in the structural stiffness characteristics and possibly the internal loads carried throughout the structure. Hence, in such a case, nonlinear effects must be taken into account and the appropriate stress and strain measures must be used. Although a geometrically-nonlinear finite element code could always be used to compute geometrically-linear deformation processes, it is inefficient to use such a code for small deformations, due to
Technology Transfer Automated Retrieval System (TEKTRAN)
Axisymmetric finite element (FE) method was developed using a commercial computer program to simulate cone penetration process in layered granular soil. Soil was considered as a non-linear elastic plastic material which was modeled using variable elastic parameters of Young’s Modulus and Poisson’s r...
NASA Technical Reports Server (NTRS)
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
Digital holography and 3-D imaging.
Banerjee, Partha; Barbastathis, George; Kim, Myung; Kukhtarev, Nickolai
2011-03-01
This feature issue on Digital Holography and 3-D Imaging comprises 15 papers on digital holographic techniques and applications, computer-generated holography and encryption techniques, and 3-D display. It is hoped that future work in the area leads to innovative applications of digital holography and 3-D imaging to biology and sensing, and to the development of novel nonlinear dynamic digital holographic techniques.
Cai, Ya; Wang, Yan; Li, Yizhi; Wang, Xiaoshu; Xin, Xinquan; Liu, Caiming; Zheng, Hegen
2005-12-12
A new 3D polymeric inorganic cluster with Cu in mixed-valence states was synthesized by the solid-state reaction of (NH4)2WS4, S8, CuCl, and Et4NCl; S8 may be regarded as the oxidizing agent converting Cu(I) to Cu(II) and causing the polymerization of [WS4]2-. The third-order nonlinear optical (NLO) properties are determined, and the results show that the cluster exhibits both large NLO absorptive and strong refractive behaviors.
3d-3d correspondence revisited
Chung, Hee -Joong; Dimofte, Tudor; Gukov, Sergei; ...
2016-04-21
In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N = 2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. As a result, we also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.
Assessment of the non-linear behaviour of plastic ankle foot orthoses by the finite element method.
Syngellakis, S; Arnold, M A; Rassoulian, H
2000-01-01
The stiffness characteristics of plastic ankle foot orthoses (AFOs) are studied through finite element modelling and stress analysis. Particular attention is given to the modelling and prediction of non-linear AFO behaviour, which has been frequently observed in previous experimental studies but not fully addressed analytically. Both large deformation effects and material non-linearity are included in the formulation and their individual influence on results assessed. The finite element program is subsequently applied to the simulation of a series of tests designed to investigate the relation between AFO trimline location and stiffness for moderate and large rotations. Through careful consideration and identification of key modelling parameters, the developed finite element solution proves to be a reliable and effective alternative means of assessing variations of a typical plastic AFO design so that particular patient requirements could be met, in the long term.
NASA Astrophysics Data System (ADS)
Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.
2012-11-01
Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff-Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress-strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)
Kardaś, Tomasz M; Nejbauer, Michał; Wnuk, Paweł; Resan, Bojan; Radzewicz, Czesław; Wasylczyk, Piotr
2017-02-22
Although new optical materials continue to open up access to more and more wavelength bands where femtosecond laser pulses can be generated, light frequency conversion techniques are still indispensable in filling the gaps on the ultrafast spectral scale. With high repetition rate, low pulse energy laser sources (oscillators) tight focusing is necessary for a robust wave mixing and the efficiency of broadband nonlinear conversion is limited by diffraction as well as spatial and temporal walk-off. Here we demonstrate a miniature third harmonic generator (tripler) with conversion efficiency exceeding 30%, producing 246 fs UV pulses via cascaded second order processes within a single laser beam focus. Designing this highly efficient and ultra compact frequency converter was made possible by full 3-dimentional modelling of propagation of tightly focused, broadband light fields in nonlinear and birefringent media.
Kardaś, Tomasz M.; Nejbauer, Michał; Wnuk, Paweł; Resan, Bojan; Radzewicz, Czesław; Wasylczyk, Piotr
2017-01-01
Although new optical materials continue to open up access to more and more wavelength bands where femtosecond laser pulses can be generated, light frequency conversion techniques are still indispensable in filling the gaps on the ultrafast spectral scale. With high repetition rate, low pulse energy laser sources (oscillators) tight focusing is necessary for a robust wave mixing and the efficiency of broadband nonlinear conversion is limited by diffraction as well as spatial and temporal walk-off. Here we demonstrate a miniature third harmonic generator (tripler) with conversion efficiency exceeding 30%, producing 246 fs UV pulses via cascaded second order processes within a single laser beam focus. Designing this highly efficient and ultra compact frequency converter was made possible by full 3-dimentional modelling of propagation of tightly focused, broadband light fields in nonlinear and birefringent media. PMID:28225007
NASA Astrophysics Data System (ADS)
Kardaś, Tomasz M.; Nejbauer, Michał; Wnuk, Paweł; Resan, Bojan; Radzewicz, Czesław; Wasylczyk, Piotr
2017-02-01
Although new optical materials continue to open up access to more and more wavelength bands where femtosecond laser pulses can be generated, light frequency conversion techniques are still indispensable in filling the gaps on the ultrafast spectral scale. With high repetition rate, low pulse energy laser sources (oscillators) tight focusing is necessary for a robust wave mixing and the efficiency of broadband nonlinear conversion is limited by diffraction as well as spatial and temporal walk-off. Here we demonstrate a miniature third harmonic generator (tripler) with conversion efficiency exceeding 30%, producing 246 fs UV pulses via cascaded second order processes within a single laser beam focus. Designing this highly efficient and ultra compact frequency converter was made possible by ful