Solution-adaptive finite element method in computational fracture mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1993-01-01
Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.
Adaptive finite element methods in electrochemistry.
Gavaghan, David J; Gillow, Kathryn; Süli, Endre
2006-12-05
In this article, we review some of our previous work that considers the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the edge effect. Our approach to overcoming this problem has involved the derivation of an a posteriori bound on the error in the numerical approximation for the current that can be used to drive an adaptive mesh-generation algorithm, allowing calculation of the quantity of interest (the current) to within a prescribed tolerance. We illustrate the generic applicability of the approach by considering a broad range of steady-state applications of the technique.
Parallel, adaptive finite element methods for conservation laws
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Devine, Karen D.; Flaherty, Joseph E.
1994-01-01
We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.
Adaptive Finite Element Methods for Continuum Damage Modeling
NASA Technical Reports Server (NTRS)
Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.
1995-01-01
The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.
Adaptive finite element methods for two-dimensional problems in computational fracture mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1994-01-01
Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.
Multi-level adaptive finite element methods. 1: Variation problems
NASA Technical Reports Server (NTRS)
Brandt, A.
1979-01-01
A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.
A Mass Conservation Algorithm for Adaptive Unrefinement Meshes Used by Finite Element Methods
2012-01-01
dimensional mesh generation. In: Proc. 4th ACM-SIAM Symp. on Disc. Algorithms. (1993) 83–92 [9] Weatherill, N., Hassan, O., Marcum, D., Marchant, M.: Grid ...Conference on Computational Science, ICCS 2012 A Mass Conservation Algorithm For Adaptive Unrefinement Meshes Used By Finite Element Methods Hung V. Nguyen...velocity fields, and chemical distribution, as well as conserve mass, especially for water quality applications. Solution accuracy depends highly on mesh
Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods
NASA Astrophysics Data System (ADS)
Bause, M.; Knabner, P.
2004-06-01
We present adaptive mixed hybrid finite element discretizations of the Richards equation, a nonlinear parabolic partial differential equation modeling the flow of water into a variably saturated porous medium. The approach simultaneously constructs approximations of the flux and the pressure head in Raviart-Thomas spaces. The resulting nonlinear systems of equations are solved by a Newton method. For the linear problems of the Newton iteration a multigrid algorithm is used. We consider two different kinds of error indicators for space adaptive grid refinement: superconvergence and residual based indicators. They can be calculated easily by means of the available finite element approximations. This seems attractive for computations since no additional (sub-)problems have to be solved. Computational experiments conducted for realistic water table recharge problems illustrate the effectiveness and robustness of the approach.
An h-adaptive finite element method for turbulent heat transfer
Carriington, David B
2009-01-01
A two-equation turbulence closure model (k-{omega}) using an h-adaptive grid technique and finite element method (FEM) has been developed to simulate low Mach flow and heat transfer. These flows are applicable to many flows in engineering and environmental sciences. Of particular interest in the engineering modeling areas are: combustion, solidification, and heat exchanger design. Flows for indoor air quality modeling and atmospheric pollution transport are typical types of environmental flows modeled with this method. The numerical method is based on a hybrid finite element model using an equal-order projection process. The model includes thermal and species transport, localized mesh refinement (h-adaptive) and Petrov-Galerkin weighting for the stabilizing the advection. This work develops the continuum model of a two-equation turbulence closure method. The fractional step solution method is stated along with the h-adaptive grid method (Carrington and Pepper, 2002). Solutions are presented for 2d flow over a backward-facing step.
1983-03-01
AN ANALYSIS OF A FINITE ELEMENT METHOD FOR CONVECTION- DIFFUSION PROBLEMS PART II: A POSTERIORI ERROR ESTIMATES AND ADAPTIVITY by W. G. Szymczak Y 6a...PERIOD COVERED AN ANALYSIS OF A FINITE ELEMENT METHOD FOR final life of the contract CONVECTION- DIFFUSION PROBLEM S. Part II: A POSTERIORI ERROR ...Element Method for Convection- Diffusion Problems. Part II: A Posteriori Error Estimates and Adaptivity W. G. Szvmczak and I. Babu~ka# Laboratory for
Higher-order adaptive finite-element methods for Kohn–Sham density functional theory
Motamarri, P.; Nowak, M.R.; Leiter, K.; Knap, J.; Gavini, V.
2013-11-15
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688
Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
NASA Astrophysics Data System (ADS)
Motamarri, P.; Nowak, M. R.; Leiter, K.; Knap, J.; Gavini, V.
2013-11-01
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss-Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100-200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn-Sham DFT problem. Our studies suggest that staggering computational savings-of the order of 1000-fold-relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn-Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using
NASA Astrophysics Data System (ADS)
Danaila, Ionut; Moglan, Raluca; Hecht, Frédéric; Le Masson, Stéphane
2014-10-01
We present a new numerical system using finite elements with mesh adaptivity for the simulation of solid-liquid phase change systems. In the liquid phase, the natural convection flow is simulated by solving the incompressible Navier-Stokes equations with Boussinesq approximation. A variable viscosity model allows the velocity to progressively vanish in the solid phase, through an intermediate mushy region. The phase change is modeled by introducing an implicit enthalpy source term in the heat equation. The final system of equations describing the liquid-solid system by a single domain approach is solved using a Newton iterative algorithm. The space discretization is based on a P2-P1 Taylor-Hood finite elements and mesh adaptivity by metric control is used to accurately track the solid-liquid interface or the density inversion interface for water flows. The numerical method is validated against classical benchmarks that progressively add strong non-linearities in the system of equations: natural convection of air, natural convection of water, melting of a phase-change material and water freezing. Very good agreement with experimental data is obtained for each test case, proving the capability of the method to deal with both melting and solidification problems with convection. The presented numerical method is easy to implement using FreeFem++ software using a syntax close to the mathematical formulation.
Adaptive Finite Element Method for Solving the Exact Kohn-Sham Equation of Density Functional Theory
Bylaska, Eric J.; Holst, Michael; Weare, John H.
2009-04-14
Results of the application of an adaptive finite element (FE) based solution using the FETK library of M. Holst to Density Functional Theory (DFT) approximation to the electronic structure of atoms and molecules are reported. The severe problem associated with the rapid variation of the electronic wave functions in the near singular regions of the atomic centers is treated by implementing completely unstructured simplex meshes that resolve these features around atomic nuclei. This concentrates the computational work in the regions in which the shortest length scales are necessary and provides for low resolution in regions for which there is no electron density. The accuracy of the solutions significantly improved when adaptive mesh refinement was applied, and it was found that the essential difficulties of the Kohn-Sham eigenvalues equation were the result of the singular behavior of the atomic potentials. Even though the matrix representations of the discrete Hamiltonian operator in the adaptive finite element basis are always sparse with a linear complexity in the number of discretization points, the overall memory and computational requirements for the solver implemented were found to be quite high. The number of mesh vertices per atom as a function of the atomic number Z and the required accuracy e (in atomic units) was esitmated to be v (e;Z) = 122:37 * Z2:2346 /1:1173 , and the number of floating point operations per minimization step for a system of NA atoms was found to be 0(N3A*v(e,Z0) (e.g. Z=26, e=0.0015 au, and NA=100, the memory requirement and computational cost would be ~0.2 terabytes and ~25 petaflops). It was found that the high cost of the method could be reduced somewhat by using a geometric based refinement strategy to fix the error near the singularities.
FEMHD: An adaptive finite element method for MHD and edge modelling
Strauss, H.R.
1995-07-01
This paper describes the code FEMHD, an adaptive finite element MHD code, which is applied in a number of different manners to model MHD behavior and edge plasma phenomena on a diverted tokamak. The code uses an unstructured triangular mesh in 2D and wedge shaped mesh elements in 3D. The code has been adapted to look at neutral and charged particle dynamics in the plasma scrape off region, and into a full MHD-particle code.
Lee, W H; Kim, T-S; Cho, M H; Ahn, Y B; Lee, S Y
2006-12-07
In studying bioelectromagnetic problems, finite element analysis (FEA) offers several advantages over conventional methods such as the boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropic conductivity. For FEA, mesh generation is the first critical requirement and there exist many different approaches. However, conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes (cMeshes), resulting in numerous nodes and elements in modelling the conducting domain, and thereby increasing computational load and demand. In this work, we present efficient content-adaptive mesh generation schemes for complex biological volumes of MR images. The presented methodology is fully automatic and generates FE meshes that are adaptive to the geometrical contents of MR images, allowing optimal representation of conducting domain for FEA. We have also evaluated the effect of cMeshes on FEA in three dimensions by comparing the forward solutions from various cMesh head models to the solutions from the reference FE head model in which fine and equidistant FEs constitute the model. The results show that there is a significant gain in computation time with minor loss in numerical accuracy. We believe that cMeshes should be useful in the FEA of bioelectromagnetic problems.
NASA Astrophysics Data System (ADS)
Lee, W. H.; Kim, T.-S.; Cho, M. H.; Ahn, Y. B.; Lee, S. Y.
2006-12-01
In studying bioelectromagnetic problems, finite element analysis (FEA) offers several advantages over conventional methods such as the boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropic conductivity. For FEA, mesh generation is the first critical requirement and there exist many different approaches. However, conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes (cMeshes), resulting in numerous nodes and elements in modelling the conducting domain, and thereby increasing computational load and demand. In this work, we present efficient content-adaptive mesh generation schemes for complex biological volumes of MR images. The presented methodology is fully automatic and generates FE meshes that are adaptive to the geometrical contents of MR images, allowing optimal representation of conducting domain for FEA. We have also evaluated the effect of cMeshes on FEA in three dimensions by comparing the forward solutions from various cMesh head models to the solutions from the reference FE head model in which fine and equidistant FEs constitute the model. The results show that there is a significant gain in computation time with minor loss in numerical accuracy. We believe that cMeshes should be useful in the FEA of bioelectromagnetic problems.
NASA Astrophysics Data System (ADS)
Ma, Xibo; Tian, Jie; Zhang, Bo; Zhang, Xing; Xue, Zhenwen; Dong, Di; Han, Dong
2011-03-01
Among many optical molecular imaging modalities, bioluminescence imaging (BLI) has more and more wide application in tumor detection and evaluation of pharmacodynamics, toxicity, pharmacokinetics because of its noninvasive molecular and cellular level detection ability, high sensitivity and low cost in comparison with other imaging technologies. However, BLI can not present the accurate location and intensity of the inner bioluminescence sources such as in the bone, liver or lung etc. Bioluminescent tomography (BLT) shows its advantage in determining the bioluminescence source distribution inside a small animal or phantom. Considering the deficiency of two-dimensional imaging modality, we developed three-dimensional tomography to reconstruct the information of the bioluminescence source distribution in transgenic mOC-Luc mice bone with the boundary measured data. In this paper, to study the osteocalcin (OC) accumulation in transgenic mOC-Luc mice bone, a BLT reconstruction method based on multilevel adaptive finite element (FEM) algorithm was used for localizing and quantifying multi bioluminescence sources. Optical and anatomical information of the tissues are incorporated as a priori knowledge in this method, which can reduce the ill-posedness of BLT. The data was acquired by the dual modality BLT and Micro CT prototype system that was developed by us. Through temperature control and absolute intensity calibration, a relative accurate intensity can be calculated. The location of the OC accumulation was reconstructed, which was coherent with the principle of bone differentiation. This result also was testified by ex vivo experiment in the black 96-plate well using the BLI system and the chemiluminescence apparatus.
Development of an adaptive hp-version finite element method for computational optimal control
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Warner, Michael S.
1994-01-01
In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications.
NASA Technical Reports Server (NTRS)
Demkowicz, L.; Oden, J. T.; Rachowicz, W.
1990-01-01
A new finite element method solving compressible Navier-Stokes equations is proposed. The method is based on a version of Strang's operator splitting and an h-p adaptive finite element approximation in space. This paper contains the formulation of the method with a detailed discussion of boundary conditions, a sample adaptive strategy and numerical examples involving compressible viscous flow over a flat plate with Reynolds number Re = 1000 and Re = 10,000.
Peridynamic Multiscale Finite Element Methods
Costa, Timothy; Bond, Stephen D.; Littlewood, David John; Moore, Stan Gerald
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
Adaptive finite element methods for the solution of inverse problems in optical tomography
NASA Astrophysics Data System (ADS)
Bangerth, Wolfgang; Joshi, Amit
2008-06-01
Optical tomography attempts to determine a spatially variable coefficient in the interior of a body from measurements of light fluxes at the boundary. Like in many other applications in biomedical imaging, computing solutions in optical tomography is complicated by the fact that one wants to identify an unknown number of relatively small irregularities in this coefficient at unknown locations, for example corresponding to the presence of tumors. To recover them at the resolution needed in clinical practice, one has to use meshes that, if uniformly fine, would lead to intractably large problems with hundreds of millions of unknowns. Adaptive meshes are therefore an indispensable tool. In this paper, we will describe a framework for the adaptive finite element solution of optical tomography problems. It takes into account all steps starting from the formulation of the problem including constraints on the coefficient, outer Newton-type nonlinear and inner linear iterations, regularization, and in particular the interplay of these algorithms with discretizing the problem on a sequence of adaptively refined meshes. We will demonstrate the efficiency and accuracy of these algorithms on a set of numerical examples of clinical relevance related to locating lymph nodes in tumor diagnosis.
Finite Element Methods: Principles for Their Selection.
1983-02-01
the finite element methods. 39 Various statements in the literature that certain mixed methods work well inspite of the fact that the LBB (BB...method, displacement and mixed methods , various adaptive approaches, etc. The examples discussed in Sections 2 and 3 show that the same computational...performance and their relation to mixed methods , SIAM J. Num. Anal., to appear. 5. F. Brezzi, On the existence uniqueness and approximation of saddle-point
Adaptive Finite-Element Computation In Fracture Mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1995-01-01
Report discusses recent progress in use of solution-adaptive finite-element computational methods to solve two-dimensional problems in linear elastic fracture mechanics. Method also shown extensible to three-dimensional problems.
H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows
NASA Technical Reports Server (NTRS)
Chang, H. J.; Bass, J. M.; Tworzydlo, W.; Oden, J. T.
1993-01-01
The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).
Domain decomposition methods for mortar finite elements
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
Improved finite-element methods for rotorcraft structures
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1991-01-01
An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.
NASA Astrophysics Data System (ADS)
Mostaghimi, P.; Percival, J. R.; Pavlidis, D.; Gorman, G.; Jackson, M.; Neethling, S.; Pain, C. C.
2013-12-01
Numerical simulation of multiphase flow in porous media is of importance in a wide range of applications in science and engineering. We present a novel control volume finite element method (CVFEM) to solve for multi-scale flow in heterogeneous geological formations. It employs a node centred control volume approach to discretize the saturation equation, while a control volume finite element method is applied for the pressure equation. We embed the discrete continuity equation into the pressure equation and assure that the continuity is exactly enforced. Anisotropic mesh adaptivity is used to accurately model the fine grained features of multiphase flow. The adaptive algorithm uses a metric tensor field based on solution error estimates to locally control the size and shape of elements in the metric. Moreover, it uses metric advection between adaptive meshes in order to predict the future required density of mesh thereby reducing numerical dispersion at the saturation front. The scheme is capable of capturing multi-scale heterogeneity such as those in fractured porous media through the use of several constraints on the element size in different regions of porous media. We show the application of our method for simulation of flow in some challenging benchmark problems. For flow in fractured reservoirs, the scheme adapts the mesh as the flow penetrates through the fracture and the matrix. The constraints for the element size within the fracture are smaller by several orders of magnitude than the generated mesh within the matrix. We show that the scheme captures the key multi-scale features of flow while preserving the geometry. We demonstrate that mesh adaptation can be used to accurately simulate flow in heterogeneous porous media at low computational cost.
Gauge finite element method for incompressible flows
NASA Astrophysics Data System (ADS)
E, Weinan; Liu, Jian-Guo
2000-12-01
A finite element method for computing viscous incompressible flows based on the gauge formulation introduced in [Weinan E, Liu J-G. Gauge method for viscous incompressible flows. Journal of Computational Physics (submitted)] is presented. This formulation replaces the pressure by a gauge variable. This new gauge variable is a numerical tool and differs from the standard gauge variable that arises from decomposing a compressible velocity field. It has the advantage that an additional boundary condition can be assigned to the gauge variable, thus eliminating the issue of a pressure boundary condition associated with the original primitive variable formulation. The computational task is then reduced to solving standard heat and Poisson equations, which are approximated by straightforward, piecewise linear (or higher-order) finite elements. This method can achieve high-order accuracy at a cost comparable with that of solving standard heat and Poisson equations. It is naturally adapted to complex geometry and it is much simpler than traditional finite element methods for incompressible flows. Several numerical examples on both structured and unstructured grids are presented. Copyright
Adaptive finite element strategies for shell structures
NASA Technical Reports Server (NTRS)
Stanley, G.; Levit, I.; Stehlin, B.; Hurlbut, B.
1992-01-01
The present paper extends existing finite element adaptive refinement (AR) techniques to shell structures, which have heretofore been neglected in the AR literature. Specific challenges in applying AR to shell structures include: (1) physical discontinuities (e.g., stiffener intersections); (2) boundary layers; (3) sensitivity to geometric imperfections; (4) the sensitivity of most shell elements to mesh distortion, constraint definition and/or thinness; and (5) intrinsic geometric nonlinearity. All of these challenges but (5) are addressed here.
A survey of mixed finite element methods
NASA Technical Reports Server (NTRS)
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Choi, Young Joon; Jorshari, Razzi Movassaghi; Djilali, Ned
2015-03-10
Direct numerical simulations of the flow-nanoparticle interaction in a colloidal suspension are presented using an extended finite element method (XFEM) in which the dynamics of the nanoparticles is solved in a fully-coupled manner with the flow. The method is capable of accurately describing solid-fluid interfaces without the need of boundary-fitted meshes to investigate the dynamics of particles in complex flows. In order to accurately compute the high interparticle shear stresses and pressures while minimizing computing costs, an adaptive meshing technique is incorporated with the fluid-structure interaction algorithm. The particle-particle interaction at the microscopic level is modeled using the Lennard-Jones (LJ) potential and the corresponding potential parameters are determined by a scaling procedure. The study is relevant to the preparation of inks used in the fabrication of catalyst layers for fuel cells. In this paper, we are particularly interested in investigating agglomeration of the nanoparticles under external shear flow in a sliding bi-periodic Lees-Edwards frame. The results indicate that the external shear has a crucial impact on the structure formation of colloidal particles in a suspension.
NASA Astrophysics Data System (ADS)
Noel, Jean
The feasibility of a two dimensional computation code for electric arc plasma is addressed. The nonstationary physics of a plasma arc can intervene at high gradients on all the variables, a high convection, as well as the considerable pressure variations (in space and time). Here the spatial finesse needed for the treatment of high gradient zones, is obtained by the use of a finite element method, improved by a mesh auto-adaptivity. The chosen time integration method is of the Runge-Kutta type with time step adjustment. This is presented, with the numerical methodology principles (multimesh, regularization, time step control). Results obtained in the study of classical partial differential equation systems, simplified versions of the Navier-Stokes equations (Burger equation, Dwyer-Sanders flame model), are presented. The numerical treatment of a confined arc plasma required the preliminary definition of a representative system of equations. This system is presented, with the thermal and dynamic modelings carried out. Different aspects of the models introduced are illustrated, and results obtained for an unstationary one dimensional arc plasma in industrial conditions are presented. Comparisons between these results and available experimental data are encouraging, but suggest that a better dynamic modeling is indispensable.
An adaptive streamline diffusion finite element method for hyperbolic systems in gas dynamics
NASA Astrophysics Data System (ADS)
Zhou, Guohui
1992-09-01
The paintwise error analysis of the streamline diffusion method for two dimensional stationary problem with constant coefficients is extended to the time dependent problem. The purpose of the study is to justify a local mesh refinement strategy. The one dimensional Euler equations coming from the shock tube and Riemann's problem in gas dynamics are used. The gas is assumed to be at rest on both sides of the membrane, with pressure and density different on each side. The case where the problem is scalar and linear is discussed. Linear systems of hyperbolic type in one space variable and nonlinear scalar problems are studied.
NASA Astrophysics Data System (ADS)
Grayver, Alexander V.
2015-07-01
This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated
A multidimensional finite element method for CFD
NASA Technical Reports Server (NTRS)
Pepper, Darrell W.; Humphrey, Joseph W.
1991-01-01
A finite element method is used to solve the equations of motion for 2- and 3-D fluid flow. The time-dependent equations are solved explicitly using quadrilateral (2-D) and hexahedral (3-D) elements, mass lumping, and reduced integration. A Petrov-Galerkin technique is applied to the advection terms. The method requires a minimum of computational storage, executes quickly, and is scalable for execution on computer systems ranging from PCs to supercomputers.
Lazarov, R; Pasciak, J; Jones, J
2002-02-01
Construction, analysis and numerical testing of efficient solution techniques for solving elliptic PDEs that allow for parallel implementation have been the focus of the research. A number of discretization and solution methods for solving second order elliptic problems that include mortar and penalty approximations and domain decomposition methods for finite elements and finite volumes have been investigated and analyzed. Techniques for parallel domain decomposition algorithms in the framework of PETC and HYPRE have been studied and tested. Hierarchical parallel grid refinement and adaptive solution methods have been implemented and tested on various model problems. A parallel code implementing the mortar method with algebraically constructed multiplier spaces was developed.
On Hybrid and mixed finite element methods
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1981-01-01
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Mixed Finite Element Method for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.; Hesse, M. A.; Arbogast, T.
2012-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium. Therefore, a numerical method must also carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. The finite element framework provides support for additional analysis of error and convergence. Moreover, both mesh refinement and anisotropy are naturally incorporated into finite elements. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. Mixed methods also produce discretely conservative fluxes that are required for the transport problem to remains stable without violating conservation of mass. Based preliminary investigations in 1D and derived energy estimates, we present a mixed formulation for the Darcy-Stokes system. Next, using novel elements of lowest order and
Adaptive Mesh Refinement Algorithms for Parallel Unstructured Finite Element Codes
Parsons, I D; Solberg, J M
2006-02-03
This project produced algorithms for and software implementations of adaptive mesh refinement (AMR) methods for solving practical solid and thermal mechanics problems on multiprocessor parallel computers using unstructured finite element meshes. The overall goal is to provide computational solutions that are accurate to some prescribed tolerance, and adaptivity is the correct path toward this goal. These new tools will enable analysts to conduct more reliable simulations at reduced cost, both in terms of analyst and computer time. Previous academic research in the field of adaptive mesh refinement has produced a voluminous literature focused on error estimators and demonstration problems; relatively little progress has been made on producing efficient implementations suitable for large-scale problem solving on state-of-the-art computer systems. Research issues that were considered include: effective error estimators for nonlinear structural mechanics; local meshing at irregular geometric boundaries; and constructing efficient software for parallel computing environments.
Mixed Finite Element Methods for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.
2013-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium so must carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. We present a mixed formulation for the Darcy-Stokes system. Next, we present novel elements of lowest order and compatible with both Darcy and Stokes flow Finally, we present our 2D mixed FEM code result for solving Stokes and Darcy flow as well as the coupled Darcy-Stokes system the mid-ocean ridge or corner flow problem.
A multigrid solution method for mixed hybrid finite elements
Schmid, W.
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Leapfrog/Finite Element Method for Fractional Diffusion Equation
Zhao, Zhengang; Zheng, Yunying
2014-01-01
We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an L 2-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis. PMID:24955431
The Relation of Finite Element and Finite Difference Methods
NASA Technical Reports Server (NTRS)
Vinokur, M.
1976-01-01
Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
Adaptive grid finite element model of the tokamak scrapeoff layer
Kuprat, A.P.; Glasser, A.H.
1995-07-01
The authors discuss unstructured grids for application to transport in the tokamak edge SOL. They have developed a new metric with which to judge element elongation and resolution requirements. Using this method, the authors apply a standard moving finite element technique to advance the SOL equations while inserting/deleting dynamically nodes that violate an elongation criterion. In a tokamak plasma, this method achieves a more uniform accuracy, and results in highly stretched triangular finite elements, except near separatrix X-point where transport is more isotropic.
NASA Astrophysics Data System (ADS)
Salinas, Pablo; Pavlidis, Dimitrios; Percival, James; Adam, Alexander; Xie, Zhihua; Pain, Christopher; Jackson, Matthew
2015-11-01
We present a new, high-order, control-volume-finite-element (CVFE) method with discontinuous representation for pressure and velocity to simulate multiphase flow in heterogeneous porous media. Time is discretized using an adaptive, fully implicit method. Heterogeneous geologic features are represented as volumes bounded by surfaces. Our approach conserves mass and does not require the use of CVs that span domain boundaries. Computational efficiency is increased by use of dynamic mesh optimization. We demonstrate that the approach, amongst other features, accurately preserves sharp saturation changes associated with high aspect ratio geologic domains, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at lower cost than an equivalent fine, fixed mesh and conventional CVFE methods. The use of implicit time integration allows the method to efficiently converge using highly anisotropic meshes without having to reduce the time-step. The work is significant for two key reasons. First, it resolves a long-standing problem associated with the use of classical CVFE methods. Second, it reduces computational cost/increases solution accuracy through the use of dynamic mesh optimization and time-stepping with large Courant number. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged.
Ablative Thermal Response Analysis Using the Finite Element Method
NASA Technical Reports Server (NTRS)
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
Optimal least-squares finite element method for elliptic problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Povinelli, Louis A.
1991-01-01
An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.
Application of the Finite Element Method to Rotary Wing Aeroelasticity
NASA Technical Reports Server (NTRS)
Straub, F. K.; Friedmann, P. P.
1982-01-01
A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.
A finite element conjugate gradient FFT method for scattering
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
Least-squares finite element methods for quantum chromodynamics
Ketelsen, Christian; Brannick, J; Manteuffel, T; Mccormick, S
2008-01-01
A significant amount of the computational time in large Monte Carlo simulations of lattice quantum chromodynamics (QCD) is spent inverting the discrete Dirac operator. Unfortunately, traditional covariant finite difference discretizations of the Dirac operator present serious challenges for standard iterative methods. For interesting physical parameters, the discretized operator is large and ill-conditioned, and has random coefficients. More recently, adaptive algebraic multigrid (AMG) methods have been shown to be effective preconditioners for Wilson's discretization of the Dirac equation. This paper presents an alternate discretization of the Dirac operator based on least-squares finite elements. The discretization is systematically developed and physical properties of the resulting matrix system are discussed. Finally, numerical experiments are presented that demonstrate the effectiveness of adaptive smoothed aggregation ({alpha}SA ) multigrid as a preconditioner for the discrete field equations resulting from applying the proposed least-squares FE formulation to a simplified test problem, the 2d Schwinger model of quantum electrodynamics.
NASA Technical Reports Server (NTRS)
Aberson, J. A.; Anderson, J. M.
1973-01-01
The recent introduction of special crack-tip singularity elements, usually referred to as cracked elements, has brought the power and flexibility of the finite-element method to bear much more effectively on fracture mechanics problems. This paper recalls the development of two cracked elements and presents the results of some applications proving their accuracy and economy. Judging from the available literature on numerical methods in fracture mechanics, it seems clear that the elements described have been used more extensively than any others in practical fracture mechanics applications.
A Finite Element Method for Simulation of Compressible Cavitating Flows
NASA Astrophysics Data System (ADS)
Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad
2016-11-01
This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.
NASA Astrophysics Data System (ADS)
Sarkis, C.; Silva, L.; Gandin, Ch-A.; Plapp, M.
2016-03-01
Dendritic growth is computed with automatic adaptation of an anisotropic and unstructured finite element mesh. The energy conservation equation is formulated for solid and liquid phases considering an interface balance that includes the Gibbs-Thomson effect. An equation for a diffuse interface is also developed by considering a phase field function with constant negative value in the liquid and constant positive value in the solid. Unknowns are the phase field function and a dimensionless temperature, as proposed by [1]. Linear finite element interpolation is used for both variables, and discretization stabilization techniques ensure convergence towards a correct non-oscillating solution. In order to perform quantitative computations of dendritic growth on a large domain, two additional numerical ingredients are necessary: automatic anisotropic unstructured adaptive meshing [2,[3] and parallel implementations [4], both made available with the numerical platform used (CimLib) based on C++ developments. Mesh adaptation is found to greatly reduce the number of degrees of freedom. Results of phase field simulations for dendritic solidification of a pure material in two and three dimensions are shown and compared with reference work [1]. Discussion on algorithm details and the CPU time will be outlined.
NASA Technical Reports Server (NTRS)
Chung, T. J. (Editor); Karr, Gerald R. (Editor)
1989-01-01
Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.
POD-Galerkin reduced-order modeling with adaptive finite element snapshots
NASA Astrophysics Data System (ADS)
Ullmann, Sebastian; Rotkvic, Marko; Lang, Jens
2016-11-01
We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical issues arising from the fact that the snapshots are members of different finite element spaces. We propose a method to create a POD-Galerkin model without interpolating the snapshots onto their common finite element mesh. The error of the reduced-order solution is not necessarily Galerkin orthogonal to the reduced space created from space-adapted snapshot. We analyze how this influences the error assessment for POD-Galerkin models of linear elliptic boundary value problems. As a numerical example we consider a two-dimensional convection-diffusion equation with a parametrized convective direction. To illustrate the applicability of our techniques to non-linear time-dependent problems, we present a test case of a two-dimensional viscous Burgers equation with parametrized initial data.
Methods and framework for visualizing higher-order finite elements.
Schroeder, William J; Bertel, François; Malaterre, Mathieu; Thompson, David; Pébay, Philippe P; O'Bara, Robert; Tendulkar, Saurabh
2006-01-01
The finite element method is an important, widely used numerical technique for solving partial differential equations. This technique utilizes basis functions for approximating the geometry and the variation of the solution field over finite regions, or elements, of the domain. These basis functions are generally formed by combinations of polynomials. In the past, the polynomial order of the basis has been low-typically of linear and quadratic order. However, in recent years so-called p and hp methods have been developed, which may elevate the order of the basis to arbitrary levels with the aim of accelerating the convergence of the numerical solution. The increasing complexity of numerical basis functions poses a significant challenge to visualization systems. In the past, such systems have been loosely coupled to simulation packages, exchanging data via file transfer, and internally reimplementing the basis functions in order to perform interpolation and implement visualization algorithms. However, as the basis functions become more complex and, in some cases, proprietary in nature, it becomes increasingly difficult if not impossible to reimplement them within the visualization system. Further, most visualization systems typically process linear primitives, in part to take advantage of graphics hardware and, in part, due to the inherent simplicity of the resulting algorithms. Thus, visualization of higher-order finite elements requires tessellating the basis to produce data compatible with existing visualization systems. In this paper, we describe adaptive methods that automatically tessellate complex finite element basis functions using a flexible and extensible software framework. These methods employ a recursive, edge-based subdivision algorithm driven by a set of error metrics including geometric error, solution error, and error in image space. Further, we describe advanced pretessellation techniques that guarantees capture of the critical points of the
Analysis of the Performance of Mixed Finite Element Methods.
1986-10-01
October 1986 SUMMARY The initial goal of this project is to analyze various mixed methods based on the p- and h-p versions of the finite element methods...The convergence of mixed methods depends on two factors: (1) Approximability of polynomial spaces used (2) Stability. In the past year, the question...significant portion of the research is geared towards the investigation of mixed methods based on the ’p’ and ’h-p’ versions of the finite element method
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.
Finite element method for eigenvalue problems in electromagnetics
NASA Technical Reports Server (NTRS)
Reddy, C. J.; Deshpande, Manohar D.; Cockrell, C. R.; Beck, Fred B.
1994-01-01
Finite element method (FEM) has been a very powerful tool to solve many complex problems in electromagnetics. The goal of the current research at the Langley Research Center is to develop a combined FEM/method of moments approach to three-dimensional scattering/radiation problem for objects with arbitrary shape and filled with complex materials. As a first step toward that goal, an exercise is taken to establish the power of FEM, through closed boundary problems. This paper demonstrates the developed of FEM tools for two- and three-dimensional eigenvalue problems in electromagnetics. In section 2, both the scalar and vector finite elements have been used for various waveguide problems to demonstrate the flexibility of FEM. In section 3, vector finite element method has been extended to three-dimensional eigenvalue problems.
Finite element simulation of adaptive aerospace structures with SMA actuators
NASA Astrophysics Data System (ADS)
Frautschi, Jason; Seelecke, Stefan
2003-07-01
The particular demands of aerospace engineering have spawned many of the developments in the field of adaptive structures. Shape memory alloys are particularly attractive as actuators in these types of structures due to their large strains, high specific work output and potential for structural integration. However, the requisite extensive physical testing has slowed development of potential applications and highlighted the need for a simulation tool for feasibility studies. In this paper we present an implementation of an extended version of the M'ller-Achenbach SMA model into a commercial finite element code suitable for such studies. Interaction between the SMA model and the solution algorithm for the global FE equations is thoroughly investigated with respect to the effect of tolerances and time step size on convergence, computational cost and accuracy. Finally, a simulation of a SMA-actuated flexible trailing edge of an aircraft wing modeled with beam elements is presented.
A weak Galerkin generalized multiscale finite element method
Mu, Lin; Wang, Junping; Ye, Xiu
2016-03-31
In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.
Finite element methods on supercomputers - The scatter-problem
NASA Technical Reports Server (NTRS)
Loehner, R.; Morgan, K.
1985-01-01
Certain problems arise in connection with the use of supercomputers for the implementation of finite-element methods. These problems are related to the desirability of utilizing the power of the supercomputer as fully as possible for the rapid execution of the required computations, taking into account the gain in speed possible with the aid of pipelining operations. For the finite-element method, the time-consuming operations may be divided into three categories. The first two present no problems, while the third type of operation can be a reason for the inefficient performance of finite-element programs. Two possibilities for overcoming certain difficulties are proposed, giving attention to a scatter-process.
Radiosity algorithms using higher order finite element methods
Troutman, R.; Max, N.
1993-08-01
Many of the current radiosity algorithms create a piecewise constant approximation to the actual radiosity. Through interpolation and extrapolation, a continuous solution is obtained. An accurate solution is found by increasing the number of patches which describe the scene. This has the effect of increasing the computation time as well as the memory requirements. By using techniques found in the finite element method, we can incorporate an interpolation function directly into our form factor computation. We can then use less elements to achieve a more accurate solution. Two algorithms, derived from the finite element method, are described and analyzed.
Robust Hybrid Finite Element Methods for Antennas and Microwave Circuits
NASA Technical Reports Server (NTRS)
Gong, J.; Volakis, John L.
1996-01-01
One of the primary goals in this dissertation is concerned with the development of robust hybrid finite element-boundary integral (FE-BI) techniques for modeling and design of conformal antennas of arbitrary shape. Both the finite element and integral equation methods will be first overviewed in this chapter with an emphasis on recently developed hybrid FE-BI methodologies for antennas, microwave and millimeter wave applications. The structure of the dissertation is then outlined. We conclude the chapter with discussions of certain fundamental concepts and methods in electromagnetics, which are important to this study.
Superconvergence in the Generalized Finite Element Method
2005-01-01
Galerkin method for elliptic equations based on tensor products of piecewise polynomials. RAIRO Anal. Numer., 8:61– 66, 1974. [19] M. Kř́ıžek...London, 1986. [22] P. Lesaint and M. Zlámal. Superconvergence of the gradient of finite ele- ment solutions. RAIRO Anal. Numer., 13:139–166, 1979. [23] Q
Discontinuous Galerkin finite element methods for gradient plasticity.
Garikipati, Krishna.; Ostien, Jakob T.
2010-10-01
In this report we apply discontinuous Galerkin finite element methods to the equations of an incompatibility based formulation of gradient plasticity. The presentation is motivated with a brief overview of the description of dislocations within a crystal lattice. A tensor representing a measure of the incompatibility with the lattice is used in the formulation of a gradient plasticity model. This model is cast in a variational formulation, and discontinuous Galerkin machinery is employed to implement the formulation into a finite element code. Finally numerical examples of the model are shown.
Engineering and Design: Geotechnical Analysis by the Finite Element Method
2007-11-02
used it to determine stresses and movements in embank- ments, and Reyes and Deer described its application to analysis of underground openings in rock...36 Hughes, T. J. R. (1987). The Finite Element Reyes , S. F., and Deene, D. K. (1966). “Elastic Method, Linear Static and Dynamic Finite Element...SM4), 1,435-1,457. Fernando Dams During the Earthquakes of February Davis, E. H., and Poulos, H. G. (1972). “Rate of Report EERC-73-2, Berkeley, CA
Coupling finite element and spectral methods: First results
NASA Technical Reports Server (NTRS)
Bernardi, Christine; Debit, Naima; Maday, Yvon
1987-01-01
A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.
Implicit extrapolation methods for multilevel finite element computations
Jung, M.; Ruede, U.
1994-12-31
The finite element package FEMGP has been developed to solve elliptic and parabolic problems arising in the computation of magnetic and thermomechanical fields. FEMGP implements various methods for the construction of hierarchical finite element meshes, a variety of efficient multilevel solvers, including multigrid and preconditioned conjugate gradient iterations, as well as pre- and post-processing software. Within FEMGP, multigrid {tau}-extrapolation can be employed to improve the finite element solution iteratively to higher order. This algorithm is based on an implicit extrapolation, so that the algorithm differs from a regular multigrid algorithm only by a slightly modified computation of the residuals on the finest mesh. Another advantage of this technique is, that in contrast to explicit extrapolation methods, it does not rely on the existence of global error expansions, and therefore neither requires uniform meshes nor global regularity assumptions. In the paper the authors will analyse the {tau}-extrapolation algorithm and present experimental results in the context of the FEMGP package. Furthermore, the {tau}-extrapolation results will be compared to higher order finite element solutions.
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.
Lee, Won Hee; Kim, Tae-Seong
2012-01-01
This study proposes an advanced finite element (FE) head modeling technique through which high-resolution FE meshes adaptive to the degree of tissue anisotropy can be generated. Our adaptive meshing scheme (called wMesh) uses MRI structural information and fractional anisotropy maps derived from diffusion tensors in the FE mesh generation process, optimally reflecting electrical properties of the human brain. We examined the characteristics of the wMeshes through various qualitative and quantitative comparisons to the conventional FE regular-sized meshes that are non-adaptive to the degree of white matter anisotropy. We investigated numerical differences in the FE forward solutions that include the electrical potential and current density generated by current sources in the brain. The quantitative difference was calculated by two statistical measures of relative difference measure (RDM) and magnification factor (MAG). The results show that the wMeshes are adaptive to the anisotropic density of the WM anisotropy, and they better reflect the density and directionality of tissue conductivity anisotropy. Our comparison results between various anisotropic regular mesh and wMesh models show that there are substantial differences in the EEG forward solutions in the brain (up to RDM=0.48 and MAG=0.63 in the electrical potential, and RDM=0.65 and MAG=0.52 in the current density). Our analysis results indicate that the wMeshes produce different forward solutions that are different from the conventional regular meshes. We present some results that the wMesh head modeling approach enhances the sensitivity and accuracy of the FE solutions at the interfaces or in the regions where the anisotropic conductivities change sharply or their directional changes are complex. The fully automatic wMesh generation technique should be useful for modeling an individual-specific and high-resolution anisotropic FE head model incorporating realistic anisotropic conductivity distributions
Least-squares finite element methods for compressible Euler equations
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Carey, G. F.
1990-01-01
A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.
Finite Element Analysis of Adaptive-Stiffening and Shape-Control SMA Hybrid Composites
NASA Technical Reports Server (NTRS)
Gao, Xiujie; Burton, Deborah; Turner, Travis L.; Brinson, Catherine
2005-01-01
Shape memory alloy hybrid composites with adaptive-stiffening or morphing functions are simulated using finite element analysis. The composite structure is a laminated fiber-polymer composite beam with embedded SMA ribbons at various positions with respect to the neutral axis of the beam. Adaptive stiffening or morphing is activated via selective resistance heating of the SMA ribbons or uniform thermal loads on the beam. The thermomechanical behavior of these composites was simulated in ABAQUS using user-defined SMA elements. The examples demonstrate the usefulness of the methods for the design and simulation of SMA hybrid composites. Keywords: shape memory alloys, Nitinol, ABAQUS, finite element analysis, post-buckling control, shape control, deflection control, adaptive stiffening, morphing, constitutive modeling, user element
Transient finite element method using edge elements for moving conductor
Tani, Koji; Nishio, Takayuki; Yamada, Takashi ); Kawase, Yoshihiro . Dept. of Information Science)
1999-05-01
For the next generation of high speed railway systems and automobiles new braking systems are currently under development. These braking systems take into account the eddy currents, which are produced by the movement of the conductor in the magnetic field. For their optimum design, it is necessary to know the distribution of eddy currents in the moving conductor. The finite element method (FEM) is often used to simulate them. Here, transient finite element method using edge elements for moving conductor is presented. Here the magnetic vector potential is interpolated at the upwind position and the time derivative term is discretized by the backward difference method. As a result, the system matrix becomes symmetric and the ICCG method is applicable to solve the matrix. This method is used to solve an eddy current rail brake system. The results demonstrate that this approach is suitable to solve transient problems involving movement.
Finite Element Method for Capturing Ultra-relativistic Shocks
NASA Technical Reports Server (NTRS)
Richardson, G. A.; Chung, T. J.
2003-01-01
While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.
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.
Discontinuous Galerkin Finite Element Method for Parabolic Problems
NASA Technical Reports Server (NTRS)
Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.
2004-01-01
In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.
PWSCC Assessment by Using Extended Finite Element Method
NASA Astrophysics Data System (ADS)
Lee, Sung-Jun; Lee, Sang-Hwan; Chang, Yoon-Suk
2015-12-01
The head penetration nozzle of control rod driving mechanism (CRDM) is known to be susceptible to primary water stress corrosion cracking (PWSCC) due to the welding-induced residual stress. Especially, the J-groove dissimilar metal weld regions have received many attentions in the previous studies. However, even though several advanced techniques such as weight function and finite element alternating methods have been introduced to predict the occurrence of PWSCC, there are still difficulties in respect of applicability and efficiency. In this study, the extended finite element method (XFEM), which allows convenient crack element modeling by enriching degree of freedom (DOF) with special displacement function, was employed to evaluate structural integrity of the CRDM head penetration nozzle. The resulting stress intensity factors of surface cracks were verified for the reliability of proposed method through the comparison with those suggested in the American Society of Mechanical Engineering (ASME) code. The detailed results from the FE analyses are fully discussed in the manuscript.
Adaptive meshing technique applied to an orthopaedic finite element contact problem.
Roarty, Colleen M; Grosland, Nicole M
2004-01-01
Finite element methods have been applied extensively and with much success in the analysis of orthopaedic implants. Recently a growing interest has developed, in the orthopaedic biomechanics community, in how numerical models can be constructed for the optimal solution of problems in contact mechanics. New developments in this area are of paramount importance in the design of improved implants for orthopaedic surgery. Finite element and other computational techniques are widely applied in the analysis and design of hip and knee implants, with additional joints (ankle, shoulder, wrist) attracting increased attention. The objective of this investigation was to develop a simplified adaptive meshing scheme to facilitate the finite element analysis of a dual-curvature total wrist implant. Using currently available software, the analyst has great flexibility in mesh generation, but must prescribe element sizes and refinement schemes throughout the domain of interest. Unfortunately, it is often difficult to predict in advance a mesh spacing that will give acceptable results. Adaptive finite-element mesh capabilities operate to continuously refine the mesh to improve accuracy where it is required, with minimal intervention by the analyst. Such mesh adaptation generally means that in certain areas of the analysis domain, the size of the elements is decreased (or increased) and/or the order of the elements may be increased (or decreased). In concept, mesh adaptation is very appealing. Although there have been several previous applications of adaptive meshing for in-house FE codes, we have coupled an adaptive mesh formulation with the pre-existing commercial programs PATRAN (MacNeal-Schwendler Corp., USA) and ABAQUS (Hibbit Karlson and Sorensen, Pawtucket, RI). In doing so, we have retained several attributes of the commercial software, which are very attractive for orthopaedic implant applications.
Finite element methods for integrated aerodynamic heating analysis
NASA Technical Reports Server (NTRS)
Peraire, J.
1990-01-01
Over the past few years finite element based procedures for the solution of high speed viscous compressible flows were developed. The objective of this research is to build upon the finite element concepts which have already been demonstrated and to develop these ideas to produce a method which is applicable to the solution of large scale practical problems. The problems of interest range from three dimensional full vehicle Euler simulations to local analysis of three-dimensional viscous laminar flow. Transient Euler flow simulations involving moving bodies are also to be included. An important feature of the research is to be the coupling of the flow solution methods with thermal/structural modeling techniques to provide an integrated fluid/thermal/structural modeling capability. The progress made towards achieving these goals during the first twelve month period of the research is presented.
Application of Finite Element Method to Analyze Inflatable Waveguide Structures
NASA Technical Reports Server (NTRS)
Deshpande, M. D.
1998-01-01
A Finite Element Method (FEM) is presented to determine propagation characteristics of deformed inflatable rectangular waveguide. Various deformations that might be present in an inflatable waveguide are analyzed using the FEM. The FEM procedure and the code developed here are so general that they can be used for any other deformations that are not considered in this report. The code is validated by applying the present code to rectangular waveguide without any deformations and comparing the numerical results with earlier published results.
Least-squares finite element method for fluid dynamics
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Povinelli, Louis A.
1989-01-01
An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.
Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F
2010-07-01
Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1989-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
A class of hybrid finite element methods for electromagnetics: A review
NASA Technical Reports Server (NTRS)
Volakis, J. L.; Chatterjee, A.; Gong, J.
1993-01-01
Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.
Crystal level simulations using Eulerian finite element methods
Becker, R; Barton, N R; Benson, D J
2004-02-06
Over the last several years, significant progress has been made in the use of crystal level material models in simulations of forming operations. However, in Lagrangian finite element approaches simulation capabilities are limited in many cases by mesh distortion associated with deformation heterogeneity. Contexts in which such large distortions arise include: bulk deformation to strains approaching or exceeding unity, especially in highly anisotropic or multiphase materials; shear band formation and intersection of shear bands; and indentation with sharp indenters. Investigators have in the past used Eulerian finite element methods with material response determined from crystal aggregates to study steady state forming processes. However, Eulerian and Arbitrary Lagrangian-Eulerian (ALE) finite element methods have not been widely utilized for simulation of transient deformation processes at the crystal level. The advection schemes used in Eulerian and ALE codes control mesh distortion and allow for simulation of much larger total deformations. We will discuss material state representation issues related to advection and will present results from ALE simulations.
Experience with automatic, dynamic load balancing and adaptive finite element computation
Wheat, S.R.; Devine, K.D.; Maccabe, A.B.
1993-10-01
Distributed memory, Massively Parallel (MP), MIMD technology has enabled the development of applications requiring computational resources previously unobtainable. Structural mechanics and fluid dynamics applications, for example, are often solved by finite element methods (FEMs) requiring, millions of degrees of freedom to accurately simulate physical phenomenon. Adaptive methods, which automatically refine or coarsen meshes and vary the order of accuracy of the numerical solution, offer greater robustness and computational efficiency than traditional FEMs by reducing the amount of computation required away from physical structures such as shock waves and boundary layers. On MP computers, FEMs frequently result in distributed processor load imbalances. To overcome load imbalance, many MP FEMs use static load balancing as a preprocessor to the finite element calculation. Adaptive methods complicate the load imbalance problem since the work per element is not uniform across the solution domain and changes as the computation proceeds. Therefore, dynamic load balancing is required to maintain global load balance. We describe a dynamic, fine-grained, element-based data migration system that maintains global load balance and is effective in the presence of changing work loads. Global load balance is achieved by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. The method utilizes an automatic element management system library to which a programmer integrates the application`s computational description. The library`s flexibility supports a large class of finite element and finite difference based applications.
Dual Methods for Optimizing Finite Element Flexural Systems.
1981-02-01
ADAIO2. T.7 LIEGE UNIV -(BEL-GIUM) LABORATOIRE DE TECHNIQUES AERON--ETC F/B 13/13 DUAL METHODS FOR OPTIMIZING FINITE ELEMENT FLEXURAL SYSTEMS. (U...FEB 81 C FLEURY. G SANDER AFOSR-80-0060 UNLSSIFIED LTASSA-87 AFOSR-TR-8 -0601 NL *soonmmnmi GRANT AFOSR - 80 - 000 REPORT SA-87 DUAL METHODS FOR...block number) Modern numerical methods for the optimization of large discretized systems are now well developed and highly efficient in the case of
Efficient finite element method for grating profile reconstruction
NASA Astrophysics Data System (ADS)
Zhang, Ruming; Sun, Jiguang
2015-12-01
This paper concerns the reconstruction of grating profiles from scattering data. The inverse problem is formulated as an optimization problem with a regularization term. We devise an efficient finite element method (FEM) and employ a quasi-Newton method to solve it. For the direct problems, the FEM stiff and mass matrices are assembled once at the beginning of the numerical procedure. Then only minor changes are made to the mass matrix at each iteration, which significantly saves the computation cost. Numerical examples show that the method is effective and robust.
Analysis of Waveguide Junction Discontinuities Using Finite Element Method
NASA Technical Reports Server (NTRS)
Deshpande, Manohar D.
1997-01-01
A Finite Element Method (FEM) is presented to determine reflection and transmission coefficients of rectangular waveguide junction discontinuities. An H-plane discontinuity, an E-plane ridge discontinuity, and a step discontinuity in a concentric rectangular waveguide junction are analyzed using the FEM procedure. Also, reflection and transmission coefficients due to presence of a gap between two sections of a rectangular waveguide are determined using the FEM. The numerical results obtained by the present method are in excellent agreement with the earlier published results. The numerical results obtained by the FEM are compared with the numerical results obtained using the Mode Matching Method (MMM) and also with the measured data.
Generalization of mixed multiscale finite element methods with applications
Lee, C S
2016-08-01
Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii
Modeling of coal stockpiles using a finite elements method
Ozdeniz, A.H.; Sensogut, C.
2008-07-01
In the case of coal stockpiles finding suitable environmental conditions, spontaneous combustion phenomenon will be unavoidable. In this study, an industrial-sized stockpile having a shape of triangle prism was constituted in a coal stockyard of Western Lignite Corporation (WLC), Turkey. The parameters of time, humidity and temperature of air, atmospheric pressure, velocity and direction of wind values that are effective on coal stockpile were measured in a continuous manner. These experimental works were transferred into a computer media in order to obtain similar outcomes by carrying out 2-dimensional analysis of the stockpile with Finite Elements Method (FEM). The performed experimental studies and obtained results were then compared.
The sensitivity method in finite element model updating: A tutorial
NASA Astrophysics Data System (ADS)
Mottershead, John E.; Link, Michael; Friswell, Michael I.
2011-10-01
The sensitivity method is probably the most successful of the many approaches to the problem of updating finite element models of engineering structures based on vibration test data. It has been applied successfully to large-scale industrial problems and proprietary codes are available based on the techniques explained in simple terms in this article. A basic introduction to the most important procedures of computational model updating is provided, including tutorial examples to reinforce the reader's understanding and a large scale model updating example of a helicopter airframe.
Accurate optical CD profiler based on specialized finite element method
NASA Astrophysics Data System (ADS)
Carrero, Jesus; Perçin, Gökhan
2012-03-01
As the semiconductor industry is moving to very low-k1 patterning solutions, the metrology problems facing process engineers are becoming much more complex. Choosing the right optical critical dimension (OCD) metrology technique is essential for bridging the metrology gap and achieving the required manufacturing volume throughput. The critical dimension scanning electron microscope (CD-SEM) measurement is usually distorted by the high aspect ratio of the photoresist and hard mask layers. CD-SEM measurements cease to correlate with complex three-dimensional profiles, such as the cases for double patterning and FinFETs, thus necessitating sophisticated, accurate and fast computational methods to bridge the gap. In this work, a suite of computational methods that complement advanced OCD equipment, and enabling them to operate at higher accuracies, are developed. In this article, a novel method for accurately modeling OCD profiles is presented. A finite element formulation in primal form is used to discretize the equations. The implementation uses specialized finite element spaces to solve Maxwell equations in two dimensions.
Finite element methods for integrated aerodynamic heating analysis
NASA Technical Reports Server (NTRS)
Morgan, K.; Peraire, J.
1991-01-01
This report gives a description of the work which has been undertaken during the second year of a three year research program. The objectives of the program are to produce finite element based procedures for the solution of the large scale practical problems which are of interest to the Aerothermal Loads Branch (ALB) at NASA Langley Research Establishment. The problems of interest range from Euler simulations of full three dimensional vehicle configurations to local analyses of three dimensional viscous laminar flow. Adaptive meshes produced for both steady state and transient problems are to be considered. An important feature of the work is the provision of specialized techniques which can be used at ALB for the development of an integrated fluid/thermal/structural modeling capability.
A finite element conjugate gradient FFT method for scattering
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Zapp, John; Hsa, Chang-Yu; Volakis, John L.
1990-01-01
An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.
Simulating Space Capsule Water Landing with Explicit Finite Element Method
NASA Technical Reports Server (NTRS)
Wang, John T.; Lyle, Karen H.
2007-01-01
A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.
Numerical Analysis of a Finite Element/Volume Penalty Method
NASA Astrophysics Data System (ADS)
Maury, Bertrand
The penalty method makes it possible to incorporate a large class of constraints in general purpose Finite Element solvers like freeFEM++. We present here some contributions to the numerical analysis of this method. We propose an abstract framework for this approach, together with some general error estimates based on the discretization parameter ɛ and the space discretization parameter h. As this work is motivated by the possibility to handle constraints like rigid motion for fluid-particle flows, we shall pay a special attention to a model problem of this kind, where the constraint is prescribed over a subdomain. We show how the abstract estimate can be applied to this situation, in the case where a non-body-fitted mesh is used. In addition, we describe how this method provides an approximation of the Lagrange multiplier associated to the constraint.
HIFU Induced Heating Modelling by Using the Finite Element Method
NASA Astrophysics Data System (ADS)
Martínez, R.; Vera, A.; Leija, L.
High intensity focused ultrasound is a thermal therapy method used to treat malignant tumors and other medical conditions. Focused ultrasound concentrates acoustic energy at a focal zone. There, temperature rises rapidly over 56 °C to provoke tissue necrosis. Device performance depends on its fabrication placing computational modeling as a powerful tool to anticipate experimentation results. Finite element method allows modeling of multiphysics systems. Therefore, induced heating was modeled considering the acoustic field produced by a concave radiator excited with electric potentials from 5 V to 20 V. Nonlinear propagation was neglected and a linear response between the acoustic fields and pressure distribution was obtained. Finally, the results showed that acoustic propagation and heating models should be improved and validated with experimental measurements.
Multiscale finite-element method for linear elastic geomechanics
NASA Astrophysics Data System (ADS)
Castelletto, Nicola; Hajibeygi, Hadi; Tchelepi, Hamdi A.
2017-02-01
The demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community. High resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions. Such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies. We propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite-element method. After imposing a coarse-scale grid on the given fine-scale problem, the coarse-scale basis functions are obtained by solving local equilibrium problems within coarse elements. These basis functions form the restriction and prolongation operators used to obtain the coarse-scale system for the displacement-vector. Then, a two-stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine-scale linear system. Various numerical experiments are presented to demonstrate accuracy and robustness of the method.
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.
A responsive finite element method to aid interactive geometric modeling.
Umetani, N; Takayama, K; Mitani, J; Igarashi, T
2011-01-01
Current computer-aided engineering systems use numerical-simulation methods mainly as offline verification tools to reject designs that don't satisfy the required constraints, rather than as tools to guide users toward better designs. However, integrating real-time finite element method (FEM) into interactive geometric modeling can provide user guidance. During interactive editing, real-time feedback from numerical simulation guides users toward an improved design without tedious trial-and-error iterations. Careful reuse of previous computation results, such as meshes and matrices, on the basis of speed and accuracy trade-offs, have helped produce fast FEM analysis during interactive editing. Several 2D example applications and informal user studies show this approach's effectiveness. Such tools could help nonexpert users design objects that satisfy physical constraints and help those users understand the underlying physical properties.
Flow Applications of the Least Squares Finite Element Method
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
Large-eddy simulation using the finite element method
McCallen, R.C.; Gresho, P.M.; Leone, J.M. Jr.; Kollmann, W.
1993-10-01
In a large-eddy simulation (LES) of turbulent flows, the large-scale motion is calculated explicitly (i.e., approximated with semi-empirical relations). Typically, finite difference or spectral numerical schemes are used to generate an LES; the use of finite element methods (FEM) has been far less prominent. In this study, we demonstrate that FEM in combination with LES provides a viable tool for the study of turbulent, separating channel flows, specifically the flow over a two-dimensional backward-facing step. The combination of these methodologies brings together the advantages of each: LES provides a high degree of accuracy with a minimum of empiricism for turbulence modeling and FEM provides a robust way to simulate flow in very complex domains of practical interest. Such a combination should prove very valuable to the engineering community.
Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis
2005-12-01
This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.
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
NASA Technical Reports Server (NTRS)
Cook, C. H.
1977-01-01
The results of a comprehensive numerical investigation of the basic capabilities of the finite element method (FEM) for numerical solution of compressible flow problems governed by the two-dimensional and axis-symmetric Navier-Stokes equations in primitive variables are presented. The strong and weak points of the method as a tool for computational fluid dynamics are considered. The relation of the linear element finite element method to finite difference methods (FDM) is explored. The calculation of free shear layer and separated flows over aircraft boattail afterbodies with plume simulators indicate the strongest assets of the method are its capabilities for reliable and accurate calculation employing variable grids which readily approximate complex geometry and capably adapt to the presence of diverse regions of large solution gradients without the necessity of domain transformation.
NASA Astrophysics Data System (ADS)
Conley, Rebecca; Delaney, Tristan J.; Jiao, Xiangmin
2016-11-01
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the Adaptive Extended Stencil Finite Element Method (AES-FEM) as a means for overcoming this dependence on element shape quality. Our method replaces the traditional basis functions with a set of generalized Lagrange polynomial (GLP) basis functions, which we construct using local weighted least-squares approximations. The method preserves the theoretical framework of FEM, and allows imposing essential boundary conditions and integrating the stiffness matrix in the same way as the classical FEM. In addition, AES-FEM can use higher-degree polynomial basis functions than the classical FEM, while virtually preserving the sparsity pattern of the stiffness matrix. We describe the formulation and implementation of AES-FEM, and analyze its consistency and stability. We present numerical experiments in both 2D and 3D for the Poison equation and a time-independent convection-diffusion equation. The numerical results demonstrate that AES-FEM is more accurate than linear FEM, is also more efficient than linear FEM in terms of error versus runtime, and enables much better stability and faster convergence of iterative solvers than linear FEM over poor-quality meshes
The mixed finite element multigrid method for stokes equations.
Muzhinji, K; Shateyi, S; Motsa, S S
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results.
Architecting the Finite Element Method Pipeline for the GPU
Fu, Zhisong; Lewis, T. James; Kirby, Robert M.
2014-01-01
The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers. PMID:25202164
Architecting the Finite Element Method Pipeline for the GPU.
Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T
2014-02-01
The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.
The Mixed Finite Element Multigrid Method for Stokes Equations
Muzhinji, K.; Shateyi, S.; Motsa, S. S.
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361
MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements
NASA Technical Reports Server (NTRS)
Mitchell, William F.
1993-01-01
MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.
Nitsche Extended Finite Element Methods for Earthquake Simulation
NASA Astrophysics Data System (ADS)
Coon, Ethan T.
Modeling earthquakes and geologically short-time-scale events on fault networks is a difficult problem with important implications for human safety and design. These problems demonstrate a. rich physical behavior, in which distributed loading localizes both spatially and temporally into earthquakes on fault systems. This localization is governed by two aspects: friction and fault geometry. Computationally, these problems provide a stern challenge for modelers --- static and dynamic equations must be solved on domains with discontinuities on complex fault systems, and frictional boundary conditions must be applied on these discontinuities. The most difficult aspect of modeling physics on complicated domains is the mesh. Most numerical methods involve meshing the geometry; nodes are placed on the discontinuities, and edges are chosen to coincide with faults. The resulting mesh is highly unstructured, making the derivation of finite difference discretizations difficult. Therefore, most models use the finite element method. Standard finite element methods place requirements on the mesh for the sake of stability, accuracy, and efficiency. The formation of a mesh which both conforms to fault geometry and satisfies these requirements is an open problem, especially for three dimensional, physically realistic fault. geometries. In addition, if the fault system evolves over the course of a dynamic simulation (i.e. in the case of growing cracks or breaking new faults), the geometry must he re-meshed at each time step. This can be expensive computationally. The fault-conforming approach is undesirable when complicated meshes are required, and impossible to implement when the geometry is evolving. Therefore, meshless and hybrid finite element methods that handle discontinuities without placing them on element boundaries are a desirable and natural way to discretize these problems. Several such methods are being actively developed for use in engineering mechanics involving crack
High-order finite element methods for cardiac monodomain simulations
Vincent, Kevin P.; Gonzales, Matthew J.; Gillette, Andrew K.; Villongco, Christopher T.; Pezzuto, Simone; Omens, Jeffrey H.; Holst, Michael J.; McCulloch, Andrew D.
2015-01-01
Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783
High-order finite element methods for cardiac monodomain simulations.
Vincent, Kevin P; Gonzales, Matthew J; Gillette, Andrew K; Villongco, Christopher T; Pezzuto, Simone; Omens, Jeffrey H; Holst, Michael J; McCulloch, Andrew D
2015-01-01
Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.
A Successive Selection Method for finite element model updating
NASA Astrophysics Data System (ADS)
Gou, Baiyong; Zhang, Weijie; Lu, Qiuhai; Wang, Bo
2016-03-01
Finite Element (FE) model can be updated effectively and efficiently by using the Response Surface Method (RSM). However, it often involves performance trade-offs such as high computational cost for better accuracy or loss of efficiency for lots of design parameter updates. This paper proposes a Successive Selection Method (SSM), which is based on the linear Response Surface (RS) function and orthogonal design. SSM rewrites the linear RS function into a number of linear equations to adjust the Design of Experiment (DOE) after every FE calculation. SSM aims to interpret the implicit information provided by the FE analysis, to locate the Design of Experiment (DOE) points more quickly and accurately, and thereby to alleviate the computational burden. This paper introduces the SSM and its application, describes the solution steps of point selection for DOE in detail, and analyzes SSM's high efficiency and accuracy in the FE model updating. A numerical example of a simply supported beam and a practical example of a vehicle brake disc show that the SSM can provide higher speed and precision in FE model updating for engineering problems than traditional RSM.
Hierarchical flux-based thermal-structural finite element analysis method
NASA Technical Reports Server (NTRS)
Polesky, Sandra P.
1992-01-01
A hierarchical flux-based finite element method is developed for both a one and two dimensional thermal structural analyses. Derivation of the finite element equations is presented. The resulting finite element matrices associated with the flux based formulation are evaluated in a closed form. The hierarchical finite elements include additional degrees of freedom in the approximation of the element variable distributions by the use of nodeless variables. The nodeless variables offer increased solution accuracy without the need for defining actual nodes and rediscretizing the finite element model. Thermal and structural responses are obtained from a conventional linear finite element method and exact solutions. Results show that the hierarchical flux-based method can provide improved thermal and structural solution accuracy with fewer elements when compared to results for the conventional linear element method.
Optimization design of thumbspica splint using finite element method.
Huang, Tz-How; Feng, Chi-Kung; Gung, Yih-Wen; Tsai, Mei-Wun; Chen, Chen-Sheng; Liu, Chien-Lin
2006-12-01
De Quervain's tenosynovitis is often observed on repetitive flexion of the thumb. In the clinical setting, the conservative treatment is usually an applied thumbspica splint to immobilize the thumb. However, the traditional thumbspica splint is bulky and heavy. Thus, this study used the finite element (FE) method to remove redundant material in order to reduce the splint's weight and increase ventilation. An FE model of a thumbspica splint was constructed using ANSYS9.0 software. A maximum lateral thumb pinch force of 98 N was used as the input loading condition for the FE model. This study implemented topology optimization and design optimization to seek the optimal thickness and shape of the splint. This new design was manufactured and compared with the traditional thumbspica splint. Ten thumbspica splints were tested in a materials testing system, and statistically analyzed using an independent t test. The optimal thickness of the thumbspica splint was 3.2 mm. The new design is not significantly different from the traditional splint in the immobilization effect. However, the volume of this new design has been reduced by about 35%. This study produced a new thumbspica splint shape with less volume, but had a similar immobilization effect compared to the traditional shape. In a clinical setting, this result can be used by the occupational therapist as a reference for manufacturing lighter thumbspica splints for patients with de Quervain's tenosynovitis.
Scripted Finite Element Methods Applied to Global Geomagnetic Induction
NASA Astrophysics Data System (ADS)
Ribaudo, J.; Constable, C.
2007-12-01
Magnetic field observations from CHAMP, Ø rsted and SAC-C and improved techniques for comprehensive geomagnetic field modeling have generated renewed interest in using satellite and observatory data to study global scale electromagnetic induction in Earth's crust and mantle. The primary external source field derives from variations in the magnetospheric ring current, and recent studies show that over-simplified assumptions about its spatial structure lead to biased estimates of the frequency-dependent electromagnetic response functions generally used in inversions for mantle conductivity. The bias takes the form of local time dependence in the C- response estimates and highlights the need for flexible forward modeling tools for the global induction problem to accommodate 3D time-varying structure in both primary and induced fields. We are developing such tools using FlexPDE, a commercially available script-based finite element method (FEM) package for partial differential equations. Our strategy is to model the vector potential \\mathbf{A}, where \\mathbf{B} = \
Discontinuous finite element method for vector radiative transfer
NASA Astrophysics Data System (ADS)
Wang, Cun-Hai; Yi, Hong-Liang; Tan, He-Ping
2017-03-01
The discontinuous finite element method (DFEM) is applied to solve the vector radiative transfer in participating media. The derivation in a discrete form of the vector radiation governing equations is presented, in which the angular space is discretized by the discrete-ordinates approach with a local refined modification, and the spatial domain is discretized into finite non-overlapped discontinuous elements. The elements in the whole solution domain are connected by modelling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving radiative transfer equations. Several various problems of vector radiative transfer are tested to verify the performance of the developed DFEM, including vector radiative transfer in a one-dimensional parallel slab containing a Mie/Rayleigh/strong forward scattering medium and a two-dimensional square medium. The fact that DFEM results agree very well with the benchmark solutions in published references shows that the developed DFEM in this paper is accurate and effective for solving vector radiative transfer problems.
Structural optimization of thin shells using finite element method
NASA Technical Reports Server (NTRS)
Gotsis, Pascal K.
1992-01-01
The objective of the present work was the structural optimization of thin shell structures that are subjected to stress and displacement constraints. In order to accomplish this, the structural optimization computer program DESAP1 was modified and improved. In the static analysis part of the DESAP1 computer program the torsional spring elements, which are used to analyze thin, shallow shell structures, were eliminated by modifying the membrane stiffness matrix of the triangular elements in the local coordinate system and adding a fictitious rotational stiffness matrix. This simplified the DESAP1 program input, improved the accuracy of the analysis, and saved computation time. In the optimization part of the DESAP1 program the stress ratio formula, which redesigns the thickness of each finite element of the structure, was solved by an analytical method. This scheme replaced the iterative solution that was previously used in the DESAP1 program, thus increasing the accuracy and speed of the design. The modified program was used to design a thin, cylindrical shell structure with optimum weight, and the results are reported in this paper.
NASA Astrophysics Data System (ADS)
Astionenko, I. O.; Litvinenko, O. I.; Osipova, N. V.; Tuluchenko, G. Ya.; Khomchenko, A. N.
2016-10-01
Recently the interpolation bases of the hierarchical type have been used for the problem solving of the approximation of multiple arguments functions (such as in the finite-element method). In this work the cognitive graphical method of constructing of the hierarchical form bases on the serendipity finite elements is suggested, which allowed to get the alternative bases on a biquadratic finite element from the serendipity family without internal knots' inclusion. The cognitive-graphic method allowed to improve the known interpolation procedure of Taylor and to get the modified elements with irregular arrangement of knots. The proposed procedures are universal and are spread in the area of finite-elements.
Finite element methods of studying mechanical factors in blood flow.
Davids, N
1981-01-01
This paper reviews some biomechanical analyses of blood flow in large arteries based on a general computer modeling using the finite element method. We study the following question: What is the role played by the interrelated factors of mechanical stress, flow irregularities, and diffusion through the endothelium on the etiology of atherosclerosis or the aggravation of vascular injury. It presents the computational features of the method and stresses the physiological significance of the results, such as the effect of geometric complexities, material nonlinearities, and non-Newtonian rheology of the blood. The specific mechanical and fluid dynamic factors analyzed are wall shear stress, flow profiles, and pressure variations. After simulating tubes of circular cross section, we apply the analysis to a number of physiological situations of significance, including blood flow in the entrance region, at bifurcations, in the annular region between an inserted catheter of varying diameter and the vessel. A model study of pulsatile flow in a 60 degree bifurcated channel of velocity profiles provided corroborative measurements of these processes with special emphasis on reversed or distributed flow conditions. The corresponding analysis was extended to the situation in which flow separates and reverses in the neighborhood of stagnation points. This required developing the nonlinear expression for the convective velocity change in the medium. A computer algorithm was developed to handle simultaneous effects of pressure and viscous forces on velocity change across the element and applied to the canine prebranch arterial segment. For mean physiological flow conditions, low shear stresses (0-10 dynes/cm2) are predicted near the wall in the diverging plane, higher values (50 dynes/cm2) along the converging sides of the wall. Backflow is predicted along the outer wall, pressure recovery prior to and into the branches, and a peak shear at the divider lip.
High-order finite element methods for seismic wave propagation
NASA Astrophysics Data System (ADS)
de Basabe Delgado, Jonas De Dios
Purely numerical methods based on the Finite Element Method (FEM) are becoming increasingly popular in seismic modeling for the propagation of acoustic and elastic waves in geophysical models. These methods offer a better control on the accuracy and more geometrical flexibility than the Finite Difference methods that have been traditionally used for the generation of synthetic seismograms. However, the success of these methods has outpaced their analytic validation. The accuracy of the FEMs used for seismic wave propagation is unknown in most cases and therefore the simulation parameters in numerical experiments are determined by empirical rules. I focus on two methods that are particularly suited for seismic modeling: the Spectral Element Method (SEM) and the Interior-Penalty Discontinuous Galerkin Method (IP-DGM). The goals of this research are to investigate the grid dispersion and stability of SEM and IP-DGM, to implement these methods and to apply them to subsurface models to obtain synthetic seismograms. In order to analyze the grid dispersion and stability, I use the von Neumann method (plane wave analysis) to obtain a generalized eigenvalue problem. I show that the eigenvalues are related to the grid dispersion and that, with certain assumptions, the size of the eigenvalue problem can be reduced from the total number of degrees of freedom to one proportional to the number of degrees of freedom inside one element. The grid dispersion results indicate that SEM of degree greater than 4 is isotropic and has a very low dispersion. Similar dispersion properties are observed for the symmetric formulation of IP-DGM of degree greater than 4 using nodal basis functions. The low dispersion of these methods allows for a sampling ratio of 4 nodes per wavelength to be used. On the other hand, the stability analysis shows that, in the elastic case, the size of the time step required in IP-DGM is approximately 6 times smaller than that of SEM. The results from the analysis
Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.
2012-09-20
The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered
Relation between finite element methods and nodal methods in transport theory
Walters, W.F.
1985-01-01
This paper examines the relationship between nodal methods and finite-element methods for solving the discrete-ordinates form of the transport equation in x-y geometry. Specifically, we will examine the relation of three finite-element schemes to the linear-linear (LL) and linear-nodal (LN) nodal schemes. The three finite-element schemes are the linear-continuous-diamond-difference (DD) scheme, the linear-discontinuous (LD) scheme, and the quadratic-discontinuous (QD) scheme. A brief derivation of the (LL) and (LN) nodal schemes is given in the third section of this paper. The approximations that cause the LL scheme to reduce to the DD, LD, and QD schemes are then indicated. An extremely simple method of deriving the finite-element schemes is then introduced.
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.
ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION.
Holst, Michael; McCammon, James Andrew; Yu, Zeyun; Zhou, Youngcheng; Zhu, Yunrong
2012-01-01
We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L(∞) estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme
ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION
HOLST, MICHAEL; MCCAMMON, JAMES ANDREW; YU, ZEYUN; ZHOU, YOUNGCHENG; ZHU, YUNRONG
2011-01-01
We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L∞ estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme
An implementation analysis of the linear discontinuous finite element method
Becker, T. L.
2013-07-01
This paper provides an implementation analysis of the linear discontinuous finite element method (LD-FEM) that spans the space of (l, x, y, z). A practical implementation of LD includes 1) selecting a computationally efficient algorithm to solve the 4 x 4 matrix system Ax = b that describes the angular flux in a mesh element, and 2) choosing how to store the data used to construct the matrix A and the vector b to either reduce memory consumption or increase computational speed. To analyze the first of these, three algorithms were selected to solve the 4 x 4 matrix equation: Cramer's rule, a streamlined implementation of Gaussian elimination, and LAPACK's Gaussian elimination subroutine dgesv. The results indicate that Cramer's rule and the streamlined Gaussian elimination algorithm perform nearly equivalently and outperform LAPACK's implementation of Gaussian elimination by a factor of 2. To analyze the second implementation detail, three formulations of the discretized LD-FEM equations were provided for implementation in a transport solver: 1) a low-memory formulation, which relies heavily on 'on-the-fly' calculations and less on the storage of pre-computed data, 2) a high-memory formulation, which pre-computes much of the data used to construct A and b, and 3) a reduced-memory formulation, which lies between the low - and high-memory formulations. These three formulations were assessed in the Jaguar transport solver based on relative memory footprint and computational speed for increasing mesh size and quadrature order. The results indicated that the memory savings of the low-memory formulation were not sufficient to warrant its implementation. The high-memory formulation resulted in a significant speed advantage over the reduced-memory option (10-50%), but also resulted in a proportional increase in memory consumption (5-45%) for increasing quadrature order and mesh count; therefore, the practitioner should weigh the system memory constraints against any
Stress Recovery Based h-Adaptive Finite Element Simulation of Sheet Forming Operations
NASA Astrophysics Data System (ADS)
Ahmed, Mohd.; Singh, Devinder
2016-07-01
In the present work, stress recovery techniques based adaptive finite element analysis of sheet forming operations is presented. An adaptive two dimensional finite element computer code allows the analysis of sheet forming operations and results in distribution of adaptively refined mesh, effective strain, and punch load, stress and strain rate tensor in the domain that has been developed. The recovery scheme for determining more accurate stress field is based on the least squares fitting of the computed stresses in an element patch surrounding and including a particular node. The solution error is estimated on the basis of an energy norm. It is shown with the help of an illustrative example of axi-symmetric stretching of a metal blank by a hemispherical punch that the adaptive analysis may be usefully employed to predict accurately deformation process, the seats of large deformations and locations of possible instability.
Adaptive implicit-explicit finite element algorithms for fluid mechanics problems
NASA Technical Reports Server (NTRS)
Tezduyar, T. E.; Liou, J.
1988-01-01
The adaptive implicit-explicit (AIE) approach is presented for the finite-element solution of various problems in computational fluid mechanics. In the AIE approach, the elements are dynamically (adaptively) arranged into differently treated groups. The differences in treatment could be based on considerations such as the cost efficiency, the type of spatial or temporal discretization employed, the choice of field equations, etc. Several numerical tests are performed to demonstrate that this approach can achieve substantial savings in CPU time and memory.
Finite Element Method for Thermal Analysis. [with computer program
NASA Technical Reports Server (NTRS)
Heuser, J.
1973-01-01
A two- and three-dimensional, finite-element thermal-analysis program which handles conduction with internal heat generation, convection, radiation, specified flux, and specified temperature boundary conditions is presented. Elements used in the program are the triangle and tetrahedron for two- and three-dimensional analysis, respectively. The theory used in the program is developed, and several sample problems demonstrating the capability and reliability of the program are presented. A guide to using the program, description of the input cards, and program listing are included.
Edge-based finite element method for shallow water equations
NASA Astrophysics Data System (ADS)
Ribeiro, F. L. B.; Galeão, A. C.; Landau, L.
2001-07-01
This paper describes an edge-based implementation of the generalized residual minimum (GMRES) solver for the fully coupled solution of non-linear systems arising from finite element discretization of shallow water equations (SWEs). The gain in terms of memory, floating point operations and indirect addressing is quantified for semi-discrete and space-time analyses. Stabilized formulations, including Petrov-Galerkin models and discontinuity-capturing operators, are also discussed for both types of discretization. Results illustrating the quality of the stabilized solutions and the advantages of using the edge-based approach are presented at the end of the paper. Copyright
NASA Technical Reports Server (NTRS)
Tsai, C.; Szabo, B. A.
1973-01-01
An approch to the finite element method which utilizes families of conforming finite elements based on complete polynomials is presented. Finite element approximations based on this method converge with respect to progressively reduced element sizes as well as with respect to progressively increasing orders of approximation. Numerical results of static and dynamic applications of plates are presented to demonstrate the efficiency of the method. Comparisons are made with plate elements in NASTRAN and the high-precision plate element developed by Cowper and his co-workers. Some considerations are given to implementation of the constraint method into general purpose computer programs such as NASTRAN.
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
Integrated force method versus displacement method for finite element analysis
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Berke, Laszlo; Gallagher, Richard H.
1990-01-01
A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EE's) are integrated with the global compatibility conditions (CC's) to form the governing set of equations. In IFM the CC's are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.
Development and Application of the p-version of the Finite Element Method.
1985-11-21
this property hierarchic families of finite elements. The h-version of the finite element method has been the subject of inten- sive study since the...early 1950’s and perhaps even earlier. Study of the p-version of the finite element method, on the other hand, began at Washington University in St...Louis in the early 1970’s and led to a more recent study of * .the h-p version. Research in the p-version (formerly called The Constraint Method) has
An Error Analysis for the Finite Element Method Applied to Convection Diffusion Problems.
1981-03-01
D TFhG-]NOLOGY k 4b 00 \\" ) ’b Technical Note BN-962 AN ERROR ANALYSIS FOR THE FINITE ELEMENT METHOD APPLIED TO CONVECTION DIFFUSION PROBLEM by I...Babu~ka and W. G. Szym’czak March 1981 V.. UNVI I Of- ’i -S AN ERROR ANALYSIS FOR THE FINITE ELEMENT METHOD P. - 0 w APPLIED TO CONVECTION DIFFUSION ...AOAO98 895 MARYLAND UNIVYCOLLEGE PARK INST FOR PHYSICAL SCIENCE--ETC F/G 12/I AN ERROR ANALYIS FOR THE FINITE ELEMENT METHOD APPLIED TO CONV..ETC (U
Feng, Xiaobing
1996-12-31
A non-overlapping domain decomposition iterative method is proposed and analyzed for mixed finite element methods for a sequence of noncoercive elliptic systems with radiation boundary conditions. These differential systems describe the motion of a nearly elastic solid in the frequency domain. The convergence of the iterative procedure is demonstrated and the rate of convergence is derived for the case when the domain is decomposed into subdomains in which each subdomain consists of an individual element associated with the mixed finite elements. The hybridization of mixed finite element methods plays a important role in the construction of the discrete procedure.
NASA Astrophysics Data System (ADS)
Chen, Jiefu; Zeng, Shubin; Dong, Qiuzhao; Huang, Yueqin
2017-02-01
An axisymmetric semianalytical finite element method is proposed and employed for rapid simulations of electromagnetic telemetry in layered underground formation. In this method, the layered media is decomposed into several subdomains and the interfaces between subdomains are discretized by conventional finite elements. Then a Riccati equation based high precision integration scheme is applied to exploit the homogeneity along the vertical direction in each layer. This semianalytical finite element scheme is very efficient in modeling electromagnetic telemetry in layered formation. Numerical examples as well as a field case with water based mud as drilling fluid are given to demonstrate the validity and effectiveness of this method.
Error Estimation and h-Adaptivity for Optimal Finite Element Analysis
NASA Technical Reports Server (NTRS)
Cwik, Tom; Lou, John
1997-01-01
The objective of adaptive meshing and automatic error control in finite element analysis is to eliminate the need for the application engineer from re-meshing and re-running design simulations to verify numerical accuracy. The user should only need to enter the component geometry and a coarse finite element mesh. The software will then autonomously and adaptively refine this mesh where needed, reducing the error in the fields to a user prescribed value. The ideal end result of the simulation is a measurable quantity (e.g. scattered field, input impedance), calculated to a prescribed error, in less time and less machine memory than if the user applied typical uniform mesh refinement by hand. It would also allow for the simulation of larger objects since an optimal mesh is created.
A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations
NASA Technical Reports Server (NTRS)
Hu, Changqing; Shu, Chi-Wang
1998-01-01
In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.
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.
A finite element method for analysis of vibration induced by maglev trains
NASA Astrophysics Data System (ADS)
Ju, S. H.; Ho, Y. S.; Leong, C. C.
2012-07-01
This paper developed a finite element method to perform the maglev train-bridge-soil interaction analysis with rail irregularities. An efficient proportional integral (PI) scheme with only a simple equation is used to control the force of the maglev wheel, which is modeled as a contact node moving along a number of target nodes. The moving maglev vehicles are modeled as a combination of spring-damper elements, lumped mass and rigid links. The Newmark method with the Newton-Raphson method is then used to solve the nonlinear dynamic equation. The major advantage is that all the proposed procedures are standard in the finite element method. The analytic solution of maglev vehicles passing a Timoshenko beam was used to validate the current finite element method with good agreements. Moreover, a very large-scale finite element analysis using the proposed scheme was also tested in this paper.
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 Technical Reports Server (NTRS)
Wilt, T. E.
1995-01-01
The Generalized Method of Cells (GMC), a micromechanics based constitutive model, is implemented into the finite element code MARC using the user subroutine HYPELA. Comparisons in terms of transverse deformation response, micro stress and strain distributions, and required CPU time are presented for GMC and finite element models of fiber/matrix unit cell. GMC is shown to provide comparable predictions of the composite behavior and requires significantly less CPU time as compared to a finite element analysis of the unit cell. Details as to the organization of the HYPELA code are provided with the actual HYPELA code included in the appendix.
Kim, S.
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
NASA Technical Reports Server (NTRS)
Fix, G. J.; Rose, M. E.
1983-01-01
A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.
The simulation of Lamb waves in a cracked plate using the scaled boundary finite element method.
Gravenkamp, Hauke; Prager, Jens; Saputra, Albert A; Song, Chongmin
2012-09-01
The scaled boundary finite element method is applied to the simulation of Lamb waves for ultrasonic testing applications. With this method, the general elastodynamic problem is solved, while only the boundary of the domain under consideration has to be discretized. The reflection of the fundamental Lamb wave modes from cracks of different geometry in a steel plate is modeled. A test problem is compared with commercial finite element software, showing the efficiency and convergence of the scaled boundary finite element method. A special formulation of this method is utilized to calculate dispersion relations for plate structures. For the discretization of the boundary, higher-order elements are employed to improve the efficiency of the simulations. The simplicity of mesh generation of a cracked plate for a scaled boundary finite element analysis is illustrated.
Large-eddy simulation in complex domains using the finite element method
McCallen, R.C.; Kornblum, B.T.; Kollman, W.
1996-11-12
Finite element methods (FEM) are demonstrated in combination with large-eddy simulations (LES) as a valuable tool for the study of turbulent, separating channel flows, specifically the flow over a backward facing step.
NASA Technical Reports Server (NTRS)
Achar, N. S.; Gaonkar, G. H.
1993-01-01
Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.
Wang, Wansheng; Chen, Long; Zhou, Jie
2016-05-01
A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures.
The h-p Version of the Finite Element Method with Quasiuniform Meshes.
1986-05-01
Noetic Technologies, St. Louis).1 The theoretical aspects have been studied only recently. The first theoretical paper appeared in 1981 (see [6...Research Reports :~ :~THE h-p VERSION OF THE FINITE ELEMENT METHOD WITH QUASIUNIFORM MESHES I. Babuska Institute for Physical Science and Technology...p VERSION OF THE FINITE ELEMENT METHOD > ’ WITH QUASIUNIFORM MESHES t. Ba bus aka1 Institute for Physical Science and Technology University of
Large-scale All-electron Density Functional Theory Calculations using Enriched Finite Element Method
NASA Astrophysics Data System (ADS)
Kanungo, Bikash; Gavini, Vikram
We present a computationally efficient method to perform large-scale all-electron density functional theory calculations by enriching the Lagrange polynomial basis in classical finite element (FE) discretization with atom-centered numerical basis functions, which are obtained from the solutions of the Kohn-Sham (KS) problem for single atoms. We term these atom-centered numerical basis functions as enrichment functions. The integrals involved in the construction of the discrete KS Hamiltonian and overlap matrix are computed using an adaptive quadrature grid based on gradients in the enrichment functions. Further, we propose an efficient scheme to invert the overlap matrix by exploiting its LDL factorization and employing spectral finite elements along with Gauss-Lobatto quadrature rules. Finally, we use a Chebyshev polynomial based acceleration technique to compute the occupied eigenspace in each self-consistent iteration. We demonstrate the accuracy, efficiency and scalability of the proposed method on various metallic and insulating benchmark systems, with systems ranging in the order of 10,000 electrons. We observe a 50-100 fold reduction in the overall computational time when compared to classical FE calculations while being commensurate with the desired chemical accuracy. We acknowledge the support of NSF (Grant No. 1053145) and ARO (Grant No. W911NF-15-1-0158) in conducting this work.
Using Multi-threading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes
NASA Technical Reports Server (NTRS)
Heber, Gerd; Biswas, Rupak; Thulasiraman, Parimala; Gao, Guang R.; Saini, Subhash (Technical Monitor)
1998-01-01
In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the adaption phase of FE applications oil triangular meshes and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments oil EARTH-SP2, on implementation of EARTH on the IBM SP2 with different load balancing strategies that are built into the runtime system.
A new approach in cascade flow analysis using the finite element method
NASA Technical Reports Server (NTRS)
Baskharone, E.; Hamed, A.
1980-01-01
A new approach in analyzing the potential flow past cascades and single airfoils using the finite element method is developed. In this analysis the circulation around the airfoil is not externally imposed but is directly computed in the numerical solution. Different finite element discretization patterns, orders of piecewise approximation, and grid sizes are used in the solution. The results obtained are compared with existing experimental measurements and exact solutions in cascades and single airfoils.
NASA Astrophysics Data System (ADS)
Hintermüller, M.; Hinze, M.; Kahle, C.
2013-02-01
An adaptive a posteriori error estimator based finite element method for the numerical solution of a coupled Cahn-Hilliard/Navier-Stokes system with a double-obstacle homogenous free (interfacial) energy density is proposed. A semi-implicit Euler scheme for the time-integration is applied which results in a system coupling a quasi-Stokes or Oseen-type problem for the fluid flow to a variational inequality for the concentration and the chemical potential according to the Cahn-Hilliard model [16]. A Moreau-Yosida regularization is employed which relaxes the constraints contained in the variational inequality and, thus, enables semi-smooth Newton solvers with locally superlinear convergence in function space. Moreover, upon discretization this yields a mesh independent method for a fixed relaxation parameter. For the finite dimensional approximation of the concentration and the chemical potential piecewise linear and globally continuous finite elements are used, and for the numerical approximation of the fluid velocity Taylor-Hood finite elements are employed. The paper ends by a report on numerical examples showing the efficiency of the new method.
A parallel implementation of an EBE solver for the finite element method
Silva, R.P.; Las Casas, E.B.; Carvalho, M.L.B.
1994-12-31
A parallel implementation using PVM on a cluster of workstations of an Element By Element (EBE) solver using the Preconditioned Conjugate Gradient (PCG) method is described, along with an application in the solution of the linear systems generated from finite element analysis of a problem in three dimensional linear elasticity. The PVM (Parallel Virtual Machine) system, developed at the Oak Ridge Laboratory, allows the construction of a parallel MIMD machine by connecting heterogeneous computers linked through a network. In this implementation, version 3.1 of PVM is used, and 11 SLC Sun workstations and a Sun SPARC-2 model are connected through Ethernet. The finite element program is based on SDP, System for Finite Element Based Software Development, developed at the Brazilian National Laboratory for Scientific Computation (LNCC). SDP provides the basic routines for a finite element application program, as well as a standard for programming and documentation, intended to allow exchanges between research groups in different centers.
Solving the ECG forward problem by means of a meshless finite element method.
Li, Z S; Zhu, S A; He, Bin
2007-07-07
The conventional numerical computational techniques such as the finite element method (FEM) and the boundary element method (BEM) require laborious and time-consuming model meshing. The new meshless FEM only uses the boundary description and the node distribution and no meshing of the model is required. This paper presents the fundamentals and implementation of meshless FEM and the meshless FEM method is adapted to solve the electrocardiography (ECG) forward problem. The method is evaluated on a single-layer torso model, in which the analytical solution exists, and tested in a realistic geometry homogeneous torso model, with satisfactory results being obtained. The present results suggest that the meshless FEM may provide an alternative for ECG forward solutions.
An iterative finite-element collocation method for parabolic problems using domain decomposition
Curran, M.C.
1992-01-01
Advection-dominated flows occur widely in the transport of groundwater contaminants, the movements of fluids in enhanced oil recovery projects, and many other contexts. In numerical models of such flows, adaptive local grid refinement is a conceptually attractive approach for resolving the sharp fronts or layers that tend to characterize the solutions. However, this approach can be difficult to implement in practice. A domain decomposition method developed by Bramble, Ewing, Pasciak, and Schatz, known as the BEPS method, overcomes many of the difficulties. We demonstrate the applicability of the iterative BEPS ideas to finite-element collocation on trial spaces of piecewise Hermite bicubics. The resulting scheme allows one to refine selected parts of a spatial grid without destroying algebraic efficiencies associated with the original coarse grid. We apply the method to two dimensional time-dependent advection-diffusion problems.
An iterative finite-element collocation method for parabolic problems using domain decomposition
Curran, M.C.
1992-11-01
Advection-dominated flows occur widely in the transport of groundwater contaminants, the movements of fluids in enhanced oil recovery projects, and many other contexts. In numerical models of such flows, adaptive local grid refinement is a conceptually attractive approach for resolving the sharp fronts or layers that tend to characterize the solutions. However, this approach can be difficult to implement in practice. A domain decomposition method developed by Bramble, Ewing, Pasciak, and Schatz, known as the BEPS method, overcomes many of the difficulties. We demonstrate the applicability of the iterative BEPS ideas to finite-element collocation on trial spaces of piecewise Hermite bicubics. The resulting scheme allows one to refine selected parts of a spatial grid without destroying algebraic efficiencies associated with the original coarse grid. We apply the method to two dimensional time-dependent advection-diffusion problems.
Enrichment of the finite element method with reproducing kernel particle method
Chen, Y.; Liu, W.K.; Uras, R.A.
1995-07-01
Based on the reproducing kernel particle method on enrichment procedure is introduced to enhance the effectiveness of the finite element method. The basic concepts for the reproducing kernel particle method are briefly reviewed. By adopting the well-known completeness requirements, a generalized form of the reproducing kernel particle method is developed. Through a combination of these two methods their unique advantages can be utilized. An alternative approach, the multiple field method is also introduced.
Adaptive finite element simulation of flow and transport applications on parallel computers
NASA Astrophysics Data System (ADS)
Kirk, Benjamin Shelton
The subject of this work is the adaptive finite element simulation of problems arising in flow and transport applications on parallel computers. Of particular interest are new contributions to adaptive mesh refinement (AMR) in this parallel high-performance context, including novel work on data structures, treatment of constraints in a parallel setting, generality and extensibility via object-oriented programming, and the design/implementation of a flexible software framework. This technology and software capability then enables more robust, reliable treatment of multiscale--multiphysics problems and specific studies of fine scale interaction such as those in biological chemotaxis (Chapter 4) and high-speed shock physics for compressible flows (Chapter 5). The work begins by presenting an overview of key concepts and data structures employed in AMR simulations. Of particular interest is how these concepts are applied in the physics-independent software framework which is developed here and is the basis for all the numerical simulations performed in this work. This open-source software framework has been adopted by a number of researchers in the U.S. and abroad for use in a wide range of applications. The dynamic nature of adaptive simulations pose particular issues for efficient implementation on distributed-memory parallel architectures. Communication cost, computational load balance, and memory requirements must all be considered when developing adaptive software for this class of machines. Specific extensions to the adaptive data structures to enable implementation on parallel computers is therefore considered in detail. The libMesh framework for performing adaptive finite element simulations on parallel computers is developed to provide a concrete implementation of the above ideas. This physics-independent framework is applied to two distinct flow and transport applications classes in the subsequent application studies to illustrate the flexibility of the
NASA Astrophysics Data System (ADS)
Parkinson, S. D.; Hill, J.; Piggott, M. D.; Allison, P. A.
2014-09-01
High-resolution direct numerical simulations (DNSs) are an important tool for the detailed analysis of turbidity current dynamics. Models that resolve the vertical structure and turbulence of the flow are typically based upon the Navier-Stokes equations. Two-dimensional simulations are known to produce unrealistic cohesive vortices that are not representative of the real three-dimensional physics. The effect of this phenomena is particularly apparent in the later stages of flow propagation. The ideal solution to this problem is to run the simulation in three dimensions but this is computationally expensive. This paper presents a novel finite-element (FE) DNS turbidity current model that has been built within Fluidity, an open source, general purpose, computational fluid dynamics code. The model is validated through re-creation of a lock release density current at a Grashof number of 5 × 106 in two and three dimensions. Validation of the model considers the flow energy budget, sedimentation rate, head speed, wall normal velocity profiles and the final deposit. Conservation of energy in particular is found to be a good metric for measuring model performance in capturing the range of dynamics on a range of meshes. FE models scale well over many thousands of processors and do not impose restrictions on domain shape, but they are computationally expensive. The use of adaptive mesh optimisation is shown to reduce the required element count by approximately two orders of magnitude in comparison with fixed, uniform mesh simulations. This leads to a substantial reduction in computational cost. The computational savings and flexibility afforded by adaptivity along with the flexibility of FE methods make this model well suited to simulating turbidity currents in complex domains.
Application of the Finite-Element Z-Matrix Method to e-H2 Collisions
NASA Technical Reports Server (NTRS)
Huo, Winifred M.; Brown, David; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
The present study adapts the Z-matrix formulation using a mixed basis of finite elements and Gaussians. This is a energy-independent basis which allows flexible boundary conditions and is amenable to efficient algorithms for evaluating the necessary matrix elements with molecular targets.
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.
An enriched finite element method to fractional advection-diffusion equation
NASA Astrophysics Data System (ADS)
Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam
2017-03-01
In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.
Immersed smoothed finite element method for fluid-structure interaction simulation of aortic valves
NASA Astrophysics Data System (ADS)
Yao, Jianyao; Liu, G. R.; Narmoneva, Daria A.; Hinton, Robert B.; Zhang, Zhi-Qian
2012-12-01
This paper presents a novel numerical method for simulating the fluid-structure interaction (FSI) problems when blood flows over aortic valves. The method uses the immersed boundary/element method and the smoothed finite element method and hence it is termed as IS-FEM. The IS-FEM is a partitioned approach and does not need a body-fitted mesh for FSI simulations. It consists of three main modules: the fluid solver, the solid solver and the FSI force solver. In this work, the blood is modeled as incompressible viscous flow and solved using the characteristic-based-split scheme with FEM for spacial discretization. The leaflets of the aortic valve are modeled as Mooney-Rivlin hyperelastic materials and solved using smoothed finite element method (or S-FEM). The FSI force is calculated on the Lagrangian fictitious fluid mesh that is identical to the moving solid mesh. The octree search and neighbor-to-neighbor schemes are used to detect efficiently the FSI pairs of fluid and solid cells. As an example, a 3D idealized model of aortic valve is modeled, and the opening process of the valve is simulated using the proposed IS-FEM. Numerical results indicate that the IS-FEM can serve as an efficient tool in the study of aortic valve dynamics to reveal the details of stresses in the aortic valves, the flow velocities in the blood, and the shear forces on the interfaces. This tool can also be applied to animal models studying disease processes and may ultimately translate to a new adaptive methods working with magnetic resonance images, leading to improvements on diagnostic and prognostic paradigms, as well as surgical planning, in the care of patients.
Two-scale extended finite element method for studying crack propagation of porous bioceramic
NASA Astrophysics Data System (ADS)
Chen, Jinlong; Wang, Mingguo; Zhan, Nan; Ji, Xinhua
2008-11-01
Extended finite element method (X-FEM) is a new method to solve the discontinuous problems, the basic theory of XFEM is presented in this paper, then the X-FEM is used to simulate the crack growth process of the hydroxyapatite material by three points bending test, and its deformation and stress field distribution is analyzed. The numerical results show the effectiveness of the method, the mesh in extended finite element method is independent of the internal geometry and physical interfaces, such that the trouble of high density meshing and re-meshing in the discontinuous field can be avoided. This greatly simplifies the analysis of the crack propagation process, showing the unique advantages of the extended finite element method in fracture expansion analysis of bioceramic. We also propose a two-scale strategy for crack propagation which enables one to use a refined mesh only in the crack's vicinity where it is required.
A Floating Node Method for the Modelling of Discontinuities Within a Finite Element
NASA Technical Reports Server (NTRS)
Pinho, Silvestre T.; Chen, B. Y.; DeCarvalho, Nelson V.; Baiz, P. M.; Tay, T. E.
2013-01-01
This paper focuses on the accurate numerical representation of complex networks of evolving discontinuities in solids, with particular emphasis on cracks. The limitation of the standard finite element method (FEM) in approximating discontinuous solutions has motivated the development of re-meshing, smeared crack models, the eXtended Finite Element Method (XFEM) and the Phantom Node Method (PNM). We propose a new method which has some similarities to the PNM, but crucially: (i) does not introduce an error on the crack geometry when mapping to natural coordinates; (ii) does not require numerical integration over only part of a domain; (iii) can incorporate weak discontinuities and cohesive cracks more readily; (iv) is ideally suited for the representation of multiple and complex networks of (weak, strong and cohesive) discontinuities; (v) leads to the same solution as a finite element mesh where the discontinuity is represented explicitly; and (vi) is conceptually simpler than the PNM.
Domain decomposition methods for nonconforming finite element spaces of Lagrange-type
NASA Technical Reports Server (NTRS)
Cowsar, Lawrence C.
1993-01-01
In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.
A simple finite element method for non-divergence form elliptic equation
Mu, Lin; Ye, Xiu
2017-03-01
Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.
Efficient Finite Element Methods for Transient Analysis of Shells.
1985-04-01
classified as (1) implicit projection methods, such as reduced integration, and (2) explicit projection methods, such as -’. mixed methods and mode...PROJECTION METHODS In this Section a simple form of the element stiffness matrix for mixed methods will be developed and then compared to the explicit...decomposition V.’... projection methods and mixed methods appears straightforward, establishing the exact equivalence is not possible in some elements
The use of Galerkin finite-element methods to solve mass-transport equations
Grove, David B.
1977-01-01
The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)
Application of the control volume mixed finite element method to a triangular discretization
Naff, R.L.
2012-01-01
A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.
A Method for Connecting Dissimilar Finite Element Meshes in Three Dimensions
Dohrmann, C.R.; Heinstein, M.W.; Key, S.W.
1998-11-12
A method is presented for connecting dissimilar finite element meshes in three dimensions. The method combines the concept of master and slave surfaces with the uniform strain approach for surface, corrections finite elements- By modifyhg the are made to element formulations boundaries of elements on the slave such that first-order patch tests are passed. The method can be used to connect meshes which use different element types. In addition, master and slave surfaces can be designated independently of relative mesh resolutions. Example problems in three-dimensional linear elasticity are presented.
Locally Conservative, Stabilized Finite Element Methods for Variably Saturated Flow
2007-11-06
mixed methods for Richards’ equation. The effectiveness of the multiscale stabilization strategy varied somewhat. For a steady-state, variably...Arbogast, Z. Chen, On the implementation of mixed methods as non- conforming methods for second order elliptic problems, Mathematics of Computation 64...211) (1995) 943–972. [53] Z. Chen, Equivalence between and multigrid algorithms for nonconform- ing and mixed methods for second order elliptic
Reliability of elasto-plastic structure using finite element method
NASA Astrophysics Data System (ADS)
Ning, Liu; Wilson H, Tang; Jiashou, Zhuo
2002-02-01
A solution of probabilistic FEM for elastic-plastic materials is presented based on the incremental theory of plasticity and a modified initial stress method. The formulations are deduced through a direct differentiation scheme. Partial differentiation of displacement, stress and the performance function can be iteratively performed with the computation of the mean values of displacement and stress. The presented method enjoys the efficiency of both the perturbation method and the finite difference method, but avoids the approximation during the partial differentiation calculation. In order to improve the efficiency, the adjoint vector method is introduced to calculate the differentiation of stress and displacement with respect to random variables. In addition, a time-saving computational method for reliability index of elastic-plastic materials is suggested based upon the advanced First Order Second Moment (FOSM) and by the usage of Taylor expansion for displacement. The suggested method is also applicable to 3-D cases.
A variational method for finite element stress recovery and error estimation
NASA Technical Reports Server (NTRS)
Tessler, A.; Riggs, H. R.; Macy, S. C.
1993-01-01
A variational method for obtaining smoothed stresses from a finite element derived nonsmooth stress field is presented. The method is based on minimizing a functional involving discrete least-squares error plus a penalty constraint that ensures smoothness of the stress field. An equivalent accuracy criterion is developed for the smoothing analysis which results in a C sup 1-continuous smoothed stress field possessing the same order of accuracy as that found at the superconvergent optimal stress points of the original finite element analysis. Application of the smoothing analysis to residual error estimation is also demonstrated.
P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems
NASA Technical Reports Server (NTRS)
Kang, Kab S.
2002-01-01
The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning
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.
Compressible seal flow analysis using the finite element method with Galerkin solution technique
NASA Technical Reports Server (NTRS)
Zuk, J.
1974-01-01
High pressure gas sealing involves not only balancing the viscous force with the pressure gradient force but also accounting for fluid inertia--especially for choked flow. The conventional finite element method which uses a Rayleigh-Ritz solution technique is not convenient for nonlinear problems. For these problems, a finite element method with a Galerkin solution technique (FEMGST) was formulated. One example, a three-dimensional axisymmetric flow formulation has nonlinearities due to compressibility, area expansion, and convective inertia. Solutions agree with classical results in the limiting cases. The development of the choked flow velocity profile is shown.
Finite Element Analysis of Adaptive-Stiffening and Shape-Control SMA Hybrid Composites
NASA Technical Reports Server (NTRS)
Gao, Xiu-Jie; Turner, Travis L.; Burton, Deborah; Brinson, L. Catherine
2005-01-01
The usage of shape memory materials has extended rapidly to many fields, including medical devices, actuators, composites, structures and MEMS devices. For these various applications, shape memory alloys (SMAs) are available in various forms: bulk, wire, ribbon, thin film, and porous. In this work, the focus is on SMA hybrid composites with adaptive-stiffening or morphing functions. These composites are created by using SMA ribbons or wires embedded in a polymeric based composite panel/beam. Adaptive stiffening or morphing is activated via selective resistance heating or uniform thermal loads. To simulate the thermomechanical behavior of these composites, a SMA model was implemented using ABAQUS user element interface and finite element simulations of the systems were studied. Several examples are presented which show that the implemented model can be a very useful design and simulation tool for SMA hybrid composites.
2006-02-01
International Journal of Computational Methods for...Fluids, in review. "* V. Prabhakar and J. N. Reddy, "Orthogonality of Modal Bases," International Journal of Computational Methods for Fluids...Least-Squares Finite Element Model for Incompressible Navier-Stokes Equations," International Journal of Computational Methods for Fluids, in review.
Cyclic-stress analysis of notches for supersonic transport conditions. [using finite element method
NASA Technical Reports Server (NTRS)
1974-01-01
The feasibility of using the finite element method to account for the effects of cyclic load and temperature on local stresses and strains at a notch was demonstrated. The behavior of a notched titanium panel was studied under variable loads and temperatures representative of flight conditions for the lower wing surface of a Supersonic Transport (SST). The analysis was performed with the use of the BOPACE finite-element computer program which provides capability to determine high temperature and large viscoplastic effects caused by cyclic thermal and mechanical loads. The analysis involves the development of the finite-element model as well as determination of the structural behavior of the notched panel. Results are presented for twelve SST flights comprised of five different load-temperature cycles. The results show the approach is feasible, but material response to cyclic loads, temperatures, and hold times requires improved understanding to allow proper modeling of the material.
A finite element-boundary integral method for cavities in a circular cylinder
NASA Technical Reports Server (NTRS)
Kempel, Leo C.; Volakis, John L.
1992-01-01
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. However, due to a lack of rigorous mathematical models for conformal antenna arrays, antenna designers resort to measurement and planar antenna concepts for designing non-planar conformal antennas. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We extend this formulation to conformal arrays on large metallic cylinders. In this report, we develop the mathematical formulation. In particular, we discuss the shape functions, the resulting finite elements and the boundary integral equations, and the solution of the conformal finite element-boundary integral system. Some validation results are presented and we further show how this formulation can be applied with minimal computational and memory resources.
NASA Astrophysics Data System (ADS)
Ribaudo, J. T.; Constable, C.; Parker, R. L.
2009-12-01
Scripted finite element methods allow flexible investigations of the influence of asymmetric external source fields and 3-dimensional (3D) internal electrical conductivity structure in the problem of global geomagnetic depth sounding. Our forward modeling is performed in the time and frequency domains via FlexPDE, a commercial finite element modeling package, and the technique has been validated against known solutions to 3D steady state and time-dependent problems. The induction problem is formulated in terms of the magnetic vector potential and electric scalar potential, and mesh density is managed both explicitly and through adaptive mesh refinement. We investigate the effects of 3D Earth conductivity on both satellite and ground-based magnetic field observations in the form of a geographically varying conductance map of the crust and oceans overlying a radially symmetric core and mantle. This map is used in conjunction with a novel boundary condition based on Ampere's Law to model variable near-surface induction without the computational expense of a 3D crust/ocean mesh and is valid for magnetic signals in the frequency range of interest for satellite induction studies. The simulated external magnetic field is aligned with Earth's magnetic pole, rather than its rotational pole, and increases in magnitude along the Earth/Sun axis. Earth rotates through this field with a period of 24 hours. Electromagnetic c-responses estimated from satellite data under the assumption that the primary and induced fields are dipolar in structure are known to be biased with respect to local time. We investigate the influence of Earth's rotation through the non-uniform external field on these c-responses, to determine whether this can explain the observed local time bias.
Phased Array Antenna Analysis Using Hybrid Finite Element Methods
1993-06-01
Waveguide ; (b) Geometry Model for Method of Moments ........................ 4 2. Printed Dipole Radiator: (a) Actual Geometry with Microstrip Balun and...Finite Elem ents . ............................................. 19 11. Equivalence Model for Waveguide /Cavity Problem: (a) Original Problem; (b... Waveguide Array Active Reflection Coefficient - Comparison of Results Uscig Cavity Array (CAVIARR) and General Array (PARANA) Models . 76 45. Rectangular
Bramble, J.H.; King, J.T.
1994-07-01
In this paper the authors consider a simple finite element method on an approximately polygonal domain using linear elements. The Dirichlet data are transferred in a natural way and the resulting linear system can be solved using multigrid techniques. Their analysis takes into account the change in domain and data transfer, and optimal-error estimates are obtained that are robust in the regularity of the boundary data provided they are at least square integrable. It is proved that the natural extension of this finite element approximation to the original domain is optimal-order accurate.
Error analysis of finite element method for Poisson–Nernst–Planck equations
Sun, Yuzhou; Sun, Pengtao; Zheng, Bin; Lin, Guang
2016-08-01
A priori error estimates of finite element method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.
Visualization of High-Order Finite Element Methods
2013-03-27
Peters , Valerio Pascucci, Robert M. Kirby and Claudio T. Silva, "Topology Verification for Isosurface Extraction", IEEE Transactions on Visualization...Visualization of High-Order Methods Professor Robert M. Kirby , Mr. Robert Haimes University of Utah Office of Sponsored Programs University of Utah Salt Lake...ORGANIZATION REPORT NUMBER 19a. NAME OF RESPONSIBLE PERSON 19b. TELEPHONE NUMBER Robert Kirby 801-585-3421 3. DATES COVERED (From - To) 26-Sep-2008
Unconstrained paving and plastering method for generating finite element meshes
Staten, Matthew L.; Owen, Steven J.; Blacker, Teddy D.; Kerr, Robert
2010-03-02
Computer software for and a method of generating a conformal all quadrilateral or hexahedral mesh comprising selecting an object with unmeshed boundaries and performing the following while unmeshed voids are larger than twice a desired element size and unrecognizable as either a midpoint subdividable or pave-and-sweepable polyhedra: selecting a front to advance; based on sizes of fronts and angles with adjacent fronts, determining which adjacent fronts should be advanced with the selected front; advancing the fronts; detecting proximities with other nearby fronts; resolving any found proximities; forming quadrilaterals or unconstrained columns of hexahedra where two layers cross; and establishing hexahedral elements where three layers cross.
Carpenter, D.C.
1998-01-01
This bibliography provides a list of references on finite element and related methods analysis in reactor physics computations. These references have been published in scientific journals, conference proceedings, technical reports, thesis/dissertations and as chapters in reference books from 1971 to the present. Both English and non-English references are included. All references contained in the bibliography are sorted alphabetically by the first author`s name and a subsort by date of publication. The majority of the references relate to reactor physics analysis using the finite element method. Related topics include the boundary element method, the boundary integral method, and the global element method. All aspects of reactor physics computations relating to these methods are included: diffusion theory, deterministic radiation and neutron transport theory, kinetics, fusion research, particle tracking in finite element grids, and applications. For user convenience, many of the listed references have been categorized. The list of references is not all inclusive. In general, nodal methods were purposely excluded, although a few references do demonstrate characteristics of finite element methodology using nodal methods (usually as a non-conforming element basis). This area could be expanded. The author is aware of several other references (conferences, thesis/dissertations, etc.) that were not able to be independently tracked using available resources and thus were not included in this listing.
Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows
NASA Technical Reports Server (NTRS)
Kim, Sang-Wook
1988-01-01
Velocity-pressure integrated and consistent penalty finite element computations of high Reynolds number, laminar flows are presented. In both of the methods, the pressure has been interpolated using linear shape functions for a triangular element. The triangular element is contained inside the bi-quadratic isoparametric element. It has been reported previously that the pressure interpolation method, when used in the velocity-pressure integrated method, yielded accurate computational results for high Reynolds number flows. It is shown that use of the same pressure interpolation method in the consistent penalty finite element method yielded accurate velocity and pressure fields which were comparable to those obtained using the velocity-pressure integrated method. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine-grid finite difference computational results. Advantages and disadvantages of the two methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow for Reynolds number of 10,000, a laminar backward-facing step flow, a laminar flow through a nest of cylinders, and a channel flow with an internal blockage. A finite element computer program (NSFLOW/P) for the 2-D, incompressible Navier-Stokes equations is also presented.
A finite element method for the computation of transonic flow past airfoils
NASA Technical Reports Server (NTRS)
Eberle, A.
1980-01-01
A finite element method for the computation of the transonic flow with shocks past airfoils is presented using the artificial viscosity concept for the local supersonic regime. Generally, the classic element types do not meet the accuracy requirements of advanced numerical aerodynamics requiring special attention to the choice of an appropriate element. A series of computed pressure distributions exhibits the usefulness of the method.
A variational method for finite element stress recovery: Applications in one-dimension
NASA Technical Reports Server (NTRS)
Riggs, H. Ronald
1992-01-01
It is well-known that stresses (and strains) calculated by a displacement-based finite element analysis are generally not as accurate as the displacements. In addition, the calculated stress field is typically discontinuous at element interfaces. Because the stresses are typically of more interest than the displacements, several procedures have been proposed to obtain a smooth stress field, given the finite element stresses, and to improve the accuracy. Hinton and Irons introduced global least squares smoothing of discrete data defined on a plane using a finite element formulation. Tessler and co-workers recently developed a conceptually similar formulation for smoothing of two-dimensional data based on a discrete least square approximation with a penalty constraint. The penalty constraint results in a stress field which is C(exp 1)-continuous, a result not previously obtained. The approach requires additional, 'smoothing' finite element analysis and for their two-dimensional application, they used a conforming C(exp 0)-continuous triangular finite element based on a conforming plate element. This paper presents the results of a detailed investigation into the application of Tessler's smoothing procedure to the smoothing of finite element stresses from one-dimensional problems. Although the one-dimensional formulation has some practical applicability, such as in truss, beam, axisymmetric mechanics, and one-dimensional heat conduction, the primary motivation for developing the one-dimensional smoothing case is to explore the characteristics of the general smoothing strategy. In particular, it is used to describe the behavior of the method and to explore the suitability of criteria proposed for the smoothing analysis. Prior to presenting numerical results, the variational formulation of the smoothing strategy is presented and a criterion for the smoothing analysis is described.
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.
System and Method for Finite Element Simulation of Helicopter Turbulence
NASA Technical Reports Server (NTRS)
McFarland, R. E. (Inventor); Dulsenberg, Ken (Inventor)
1999-01-01
The present invention provides a turbulence model that has been developed for blade-element helicopter simulation. This model uses an innovative temporal and geometrical distribution algorithm that preserves the statistical characteristics of the turbulence spectra over the rotor disc, while providing velocity components in real time to each of five blade-element stations along each of four blades. for a total of twenty blade-element stations. The simulator system includes a software implementation of flight dynamics that adheres to the guidelines for turbulence set forth in military specifications. One of the features of the present simulator system is that it applies simulated turbulence to the rotor blades of the helicopter, rather than to its center of gravity. The simulator system accurately models the rotor penetration into a gust field. It includes time correlation between the front and rear of the main rotor, as well as between the side forces felt at the center of gravity and at the tail rotor. It also includes features for added realism, such as patchy turbulence and vertical gusts in to which the rotor disc penetrates. These features are realized by a unique real time implementation of the turbulence filters. The new simulator system uses two arrays one on either side of the main rotor to record the turbulence field and to produce time-correlation from the front to the rear of the rotor disc. The use of Gaussian Interpolation between the two arrays maintains the statistical properties of the turbulence across the rotor disc. The present simulator system and method may be used in future and existing real-time helicopter simulations with minimal increase in computational workload.
NASA Astrophysics Data System (ADS)
Bazhenov, V. A.; Sakharov, A. S.; Maksimyuk, Yu. V.; Shkryl', A. A.
2016-03-01
Numerical experiments are performed to analyze the invariance and reliability of the results of evaluation of the J-integral by the modified method of reactions in problems of mixed fracture. Bodies with cracks undergoing elastoplastic deformation under static loading are considered. To demonstrate the universality of the method to finite-element schemes, prismatic bodies are considered. This allows using not only conventional finite-element schemes, but also the semi-analytical finite-element method
An extended finite element method for dislocations in arbitrary three-dimensional entities
NASA Astrophysics Data System (ADS)
Oswald, Jay
A finite element method is developed for dislocations in arbitrary, three-dimensional bodies, including micro-/nano-devices, and layered materials, such as thin films. The method is also compatible with anisotropic materials, and can readily be applied to non-linear media. In this method, dislocation are modeled by adding discontinuities to extend the conventional finite element basis. Two approaches for adding discontinuities to the conventional finite element basis are proposed. In the first, a simple discontinuous enrichment imposes a constant jump in displacement across dislocation glide planes. In the second approach, the enrichments more accurately approximate the dislocations by capture the singular asymptotic behavior near the dislocation core. A basis of singular enrichments are formed from the analytical solutions to straight dislocation lines, but are applicable for more general, curved dislocation configurations. Methods for computing the configurational forces on dislocation lines within the XFEM framework have also been developed. For jump enrichments, an approach based on an energy release rate or J-integral is proposed. When singular enrichments are available, it is shown that the Peach-Koehler equation can be used to compute forces directly. This new approach differs from many existing methods for studying dislocations because it does not rely on superposition of solutions derived analytically or through Green's functions. This extended finite element approach is suitable to study dislocations in micro- and nano-devices, and in specific material micro-structures, where complicated boundaries and material interfaces are pervasive.
A new strategy for stress analysis using the finite element method
NASA Technical Reports Server (NTRS)
Kamat, M. P.; Vandenbrink, D.
1983-01-01
In the paper the authors examine the effectiveness of the Powell-Toint strategy for evaluating the Hessian of the potential energy surface of a finite element model that can be used for linear stress analysis and transient response predictions of structures. Cases for which the Powell-Toint strategy may be cost-effective with the conventional method of stress analysis are identified.
A new weak Galerkin finite element method for elliptic interface problems
NASA Astrophysics Data System (ADS)
Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan
2016-11-01
A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. Extensive numerical experiments have been conducted to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.
A new weak Galerkin finite element method for elliptic interface problems
Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan
2016-08-26
We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments in order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.
An Introduction of Finite Element Method in the Engineering Teaching at the University of Camaguey.
ERIC Educational Resources Information Center
Napoles, Elsa; Blanco, Ramon; Jimenez, Rafael; Mc.Pherson, Yoanka
This paper illuminates experiences related to introducing finite element methods (FEM) in mechanical and civil engineering courses at the University of Camaguey in Cuba and provides discussion on using FEM in postgraduate courses for industry engineers. Background information on the introduction of FEM in engineering teaching is focused on…
A Stimulating Approach To Teaching, Learning and Assessing Finite Element Methods: A Case Study.
ERIC Educational Resources Information Center
Karadelis, J. N.
1998-01-01
Examines the benefits of introducing finite element methods into the curriculum of undergraduate courses. Analyzes the structure of the computer-assisted-design module and the extent to which it fulfills its main objectives. Discusses the efficiency of modern teaching and learning techniques used to develop skills for solving engineering problems;…
Highly Accurate Beam Torsion Solutions Using the p-Version Finite Element Method
NASA Technical Reports Server (NTRS)
Smith, James P.
1996-01-01
A new treatment of the classical beam torsion boundary value problem is applied. Using the p-version finite element method with shape functions based on Legendre polynomials, torsion solutions for generic cross-sections comprised of isotropic materials are developed. Element shape functions for quadrilateral and triangular elements are discussed, and numerical examples are provided.
SQA of finite element method (FEM) codes used for analyses of pit storage/transport packages
Russel, E.
1997-11-01
This report contains viewgraphs on the software quality assurance of finite element method codes used for analyses of pit storage and transport projects. This methodology utilizes the ISO 9000-3: Guideline for application of 9001 to the development, supply, and maintenance of software, for establishing well-defined software engineering processes to consistently maintain high quality management approaches.
Advanced finite-element methods for design and analysis of nanooptical structures: applications
NASA Astrophysics Data System (ADS)
Burger, Sven; Zschiedrich, Lin; Pomplun, Jan; Blome, Mark; Schmidt, Frank
2013-03-01
An overview on recent applications of the finite-element method Maxwell-solver JCMsuite to simulation tasks in nanooptics is given. Numerical achievements in the fields of optical metamaterials, plasmonics, photonic crystal fibers, light emitting devices, solar cells, optical lithography, optical metrology, integrated optics, and photonic crystals are summarized.
Optimizing the seamless tube extrusion process using the finite element method
NASA Astrophysics Data System (ADS)
Li, Feng; Li, Li; Wang, Xiang; Ma, Xu Liang
2010-03-01
In order to reveal the mechanism of extrusion forming for large-scale aluminum alloy seamless pipe, in this research the rigid-viscous plastic finite element method was used to analyze the effect of the technological parameters of the aluminum alloy pipe extrusion process, consistent with the use requirements.
Error analysis of mixed finite element methods for wave propagation in double negative metamaterials
NASA Astrophysics Data System (ADS)
Li, Jichun
2007-12-01
In this paper, we develop both semi-discrete and fully discrete mixed finite element methods for modeling wave propagation in three-dimensional double negative metamaterials. Optimal error estimates are proved for Nedelec spaces under the assumption of smooth solutions. To our best knowledge, this is the first error analysis obtained for Maxwell's equations when metamaterials are involved.
Applications of Taylor-Galerkin finite element method to compressible internal flow problems
NASA Technical Reports Server (NTRS)
Sohn, Jeong L.; Kim, Yongmo; Chung, T. J.
1989-01-01
A two-step Taylor-Galerkin finite element method with Lapidus' artificial viscosity scheme is applied to several test cases for internal compressible inviscid flow problems. Investigations for the effect of supersonic/subsonic inlet and outlet boundary conditions on computational results are particularly emphasized.
Simulation of wind effects on tall structures by finite element method
NASA Astrophysics Data System (ADS)
Ebrahimi, Masood
2016-06-01
In the present study finite element method is used to predict the wind forces on a tall structure. The governing equations of mass and momentum with boundary conditions are solved. The κ- ɛ turbulence model is utilized to calculate the turbulence viscosity. The results are independent from the generated mesh. The numerical results are validated with American Society of Civil Engineering standards.
A new weak Galerkin finite element method for elliptic interface problems
Mu, Lin; Wang, Junping; Ye, Xiu; ...
2016-08-26
We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less
NASA Astrophysics Data System (ADS)
Xie, Zhihua; Pavlidis, Dimitrios; Percival, James; Gomes, Jefferson; Pain, Christopher; Matar, Omar
2013-11-01
Interfacial flows with surface tension are often found in industrial and practical engineering applications, including bubbles, droplets, liquid film and jets. Accurate modelling of such flows is challenging due to their highly complex dynamics, which often involve changes of interfacial topology. We present a balanced-force finite-element method with adaptive unstructured meshes for interfacial flows. The method uses a mixed control-volume and finite element formulation, which ensures the surface tension forces, and the resulting pressure gradients, are exactly balanced, minimising the spurious velocities often found in numerical simulations of such flows. A volume-of-fluid-type method is employed for interface capturing based on a compressive control-volume advection method, and second-order finite element methods. A distance function is reconstructed from the volume fraction on the unstructured meshes, which provides accurate estimation of the curvature. Numerical examples of an equilibrium drop and dynamics of bubbles (droplets) are presented to demonstrate the capability of this method.
NASA Astrophysics Data System (ADS)
Salamon, Joe
In this dissertation, I will discuss and explore the various theoretical pillars re- quired to investigate the world of discretized gauge theories in a purely classical setting, with the long-term aim of achieving a fully-fledged discretization of General Relativity (GR). I will start with a brief review of differential forms, then present some results on the geometric framework of finite element exterior calculus (FEEC); in particular, I will elaborate on integrating metric structures within the framework and categorize the dual spaces of the various spaces of polynomial differential forms P rLambdak(R n). After a brief pedagogical detour on Noether's two theorems, I will apply all of the above into discretizations of electromagnetism and linearized GR. I will conclude with an excursion into the geodesic finite element method (GFEM) as a way to generalize some of the above notions to curved manifolds.
Body-oriented coordinates applied to the finite-element method
Cook, W.A.
1986-10-01
The objective of this research is to increase the accuracy of the finite-element method using coordinates intrinsic to the shape of the body being analyzed. We refer to these coordinates as body coordinates. Existing finite elements use Cartesian coordinates and are more accurate for solving rectangular-shaped problems than for solving nonrectangular-shaped problems. To check the feasibility of this research, we developed finite-element codes that used both cylindrical and Cartesian coordinates to solve problems in which the bodies were cylindrical-shaped. We obtained the most accurate solutions using the code that used cylindrical coordinates. Body coordinates become Cartesian coordinates for rectangular-shaped bodies and cylindrical coordinates for circular-shaped bodies. The body coordinate's finite-element formulation uses coordinate transformations from the body to the Cartesian coordinates. These transformations are developed using blending functions and boundary functions. Gradients of the Cartesian coordinates, with respect to body coordinates, are needed for stiffness calculations. Thus, the criterion for the blending function derivation is ''the nearest boundaries dominate,'' both for coordinate transformations and for gradient of coordinate transformations. For our studies, we developed two codes, one that uses body coordinates and one that uses Cartesian coordinates. These codes have been used to solve six example problems. 7 refs., 14 figs.
NASA Astrophysics Data System (ADS)
Matveev, A. D.
2016-11-01
To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.
The least-squares finite element method for low-mach-number compressible viscous flows
NASA Technical Reports Server (NTRS)
Yu, Sheng-Tao
1994-01-01
The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.
A finite-element alternating method for two-dimensional Mode-1 crack configurations
NASA Technical Reports Server (NTRS)
Raju, I. S.; Fichter, W. B.
1988-01-01
A finite-element alternating method is presented for 2-D Mode-1 crack problems. An analytical solution for an arbitrary polynomial normal pressure distribution applied to the crack faces is obtained and used as the basic solution in the method. The method is applied to several crack problems to study its efficiency and the results are compared to accurate stress-intensity factor solutions in the literature. The method gave reasonably accurate stress-intensity factors and crack opening displacements with minimal computing effort. Because the method must model only the uncracked body, finite-element models with many degrees of freedom are not warranted and therefore, the method has been implemented on personal computers.
An implicit control-volume finite element method for well-reservoir modelling
NASA Astrophysics Data System (ADS)
Pavlidis, Dimitrios; Salinas, Pablo; Xie, Zhihua; Pain, Christopher; Matar, Omar
2016-11-01
Here a novel implicit approach (embodied within the IC-Ferst) is presented for modelling wells with potentially a large number of laterals within reservoirs. IC-Ferst is a conservative and consistent, control-volume finite element method (CV-FEM) model and fully unstructured/geology conforming meshes with anisotropic mesh adaptivity. As far as the wells are concerned, a multi-phase/multi-well approach, where well systems are represented as phases, is taken here. Phase volume fraction conservation equations are solved for in both the reservoir and the wells, in addition, the field within wells is also solved for. A second novel aspect of the work is the combination of modelling and resolving of the motherbore and laterals. In this case wells do not have to be explicitly discretised in space. This combination proves to be accurate (in many situations) as well as computationally efficient. The method is applied to a number of multi-phase reservoir problems in order to gain an insight into the effectiveness, in terms of production rate, of perforated laterals. Model results are compared with semi-analytical solutions for simple cases and industry-standard codes for more complicated cases. EPSRC UK Programme Grant MEMPHIS (EP/K003976/1).
Recent Progress in the p and h-p Version of the Finite Element Method.
1987-07-01
THE p AND h-p VERSION OF THE FINITE ELDIEr METHOD I. Babu~ka Institute tor Physical Science and Technology University of Maryland, College Park, MD...85-K-0169 9. PERFORMING ORGANIZATION NAME ANO ADDRESS 1* -PROGRAM ELEMENT. PROJECT . T ASK AREA & WORK UNIT NUMBE RS University of Maryland Institute ...METHOD by I. Babu~ka Institute for Physical Science and Technology University of Maryland, College Park, MD 20742 1. INTRODUCTION finite element method
NASA Technical Reports Server (NTRS)
Mei, Chuh; Pates, Carl S., III
1994-01-01
A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.
A finite element method for shear stresses calculation in composite blade models
NASA Astrophysics Data System (ADS)
Paluch, B.
1991-09-01
A finite-element method is developed for accurately calculating shear stresses in helicopter blade models, induced by torsion and shearing forces. The method can also be used to compute the equivalent torsional stiffness of the section, their transverse shear coefficient, and the position of their center of torsion. A grid generator method which is a part of the calculation program is also described and used to discretize the sections quickly and to condition the grid data reliably. The finite-element method was validated on a few sections composed of isotropic materials and was then applied to a blade model sections made of composite materials. Good agreement was obtained between the calculated and experimental data.
Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing
NASA Technical Reports Server (NTRS)
Gerstl, S. A. W.; Zardecki, A.
1985-01-01
The principal features of the discrete-ordinates finite-element method are reviewed, and the applicability of general-purpose discrete-ordinates codes to atmospheric radiative transfer and remote sensing problems is demonstrated. In particular, numerical results for typical problems arising in meteorology, climatology, and remote sensing are shown to be in good agreement with results from other methods and measurements. A sample two-dimensional calculation demonstrates that specific capabilities available in the discrete-ordinates code TWOTRAN can produce new results that are valuable in the characterization of atmospheric effects on remote sensing (e.g., the adjacency effect). The intrinsic limitations of the method are also considered, and it is concluded that the strengths of the discrete-ordinates finite-element method outweigh its weaknesses.
NASA Astrophysics Data System (ADS)
Torres, D. A. F.; Mendonça, P. T. R.
2010-03-01
This paper presents a procedure to numerically analyze the coupled electro-structural response of laminated plates with orthotropic fiber reinforced layers and piezoelectric layers using the generalized finite element method (GFEM). The mechanical unknowns, the displacements, are modeled by a higher order shear deformation theory (HSDT) of the third order, involving seven generalized displacement functions. The electrical unknowns, the potentials, are modeled by a layerwise theory, utilizing piecewise linear functions along the thickness of the piezoelectric layers. All fields are enriched in the in-plane domain of the laminate, according to the GFEM, utilizing polynomial enrichment functions, defined in global coordinates, applied on a bilinear partition of unities defined on each element. The formulation is developed from an extended principle of Hamilton and results in a standard discrete algebraic linear motion equation. Numerical results are obtained for some static cases and are compared with several numerical and experimental results published in the literature. These comparisons show consistent and reliable responses from the formulation. In addition, the results show that GFEM meshes require the least number of elements and nodes possible for the distribution of piezoelectric patches and the enrichment provides more flexibility to reproduce the deformed shapes of adaptive laminated plates.
Numerical quadrature and operator splitting in finite element methods for cardiac electrophysiology.
Krishnamoorthi, Shankarjee; Sarkar, Mainak; Klug, William S
2013-11-01
We study the numerical accuracy and computational efficiency of alternative formulations of the finite element solution procedure for the monodomain equations of cardiac electrophysiology, focusing on the interaction of spatial quadrature implementations with operator splitting and examining both nodal and Gauss quadrature methods and implementations that mix nodal storage of state variables with Gauss quadrature. We evaluate the performance of all possible combinations of 'lumped' approximations of consistent capacitance and mass matrices. Most generally, we find that quadrature schemes and lumped approximations that produce decoupled nodal ionic equations allow for the greatest computational efficiency, this being afforded through the use of asynchronous adaptive time-stepping of the ionic state variable ODEs. We identify two lumped approximation schemes that exhibit superior accuracy, rivaling that of the most expensive variationally consistent implementations. Finally, we illustrate some of the physiological consequences of discretization error in electrophysiological simulation relevant to cardiac arrhythmia and fibrillation. These results suggest caution with the use of semi-automated free-form tetrahedral and hexahedral meshing algorithms available in most commercially available meshing software, which produce nonuniform meshes having a large distribution of element sizes.
Finite Element Analysis of Folded Airbag in Frontal Impact of Adapted Vehicles for Disabled Drivers
NASA Astrophysics Data System (ADS)
Masiá, J.; Eixerés, B.; Dols, J. F.; Esquerdo, T. V.
2009-11-01
The car control adaptations are used in vehicles in order to facilitate the driving to persons with physical handicaps. This does not have to suppose a decrease of the passive safety that is required to the vehicles. In order to analyze this relation there will be characterized the different control adaptations that are in use together with the different devices of passive safety that can be mounted in the vehicles in diverse cases of impact in order to generate models of simulation. The methodology used to generate this simulation consists of the first phase in which there develops the three-dimensional model of the driving place. For it, there has been used a commercial software of three-dimensional design. Once realized this one divides, the model is imported to the finite elements software in which meshing is generated. Finally, dynamic simulation software is used to assign the most important characteristics like material properties, contact interfaces, gas expansion models, airbag fold types, etc.
A p-version finite element method for steady incompressible fluid flow and convective heat transfer
NASA Technical Reports Server (NTRS)
Winterscheidt, Daniel L.
1993-01-01
A new p-version finite element formulation for steady, incompressible fluid flow and convective heat transfer problems is presented. The steady-state residual equations are obtained by considering a limiting case of the least-squares formulation for the transient problem. The method circumvents the Babuska-Brezzi condition, permitting the use of equal-order interpolation for velocity and pressure, without requiring the use of arbitrary parameters. Numerical results are presented to demonstrate the accuracy and generality of the method.
A stable cutting method for finite elements based virtual surgery simulation.
Jerábková, Lenka; Jerábek, Jakub; Chudoba, Rostislav; Kuhlen, Torsten
2007-01-01
In this paper we present a novel approach for stable interactive cutting of deformable objects in virtual environments. Our method is based on the extended finite elements method, allowing for a modeling of discontinuities without remeshing. As no new elements are created, the impact on simulation performance is minimized. We also propose an appropriate mass lumping technique to guarantee for the stability of the simulation regardless of the position of the cut.
RCS Predictions From a Method of Moments and a Finite-Element Code for Several Targets
2010-07-01
01803 14. ABSTRACT This report presents results of radar cross section (RCS) calculations for several interesting targets using a method-of-moments...TERMS radar cross section, method of moments, finite element, modeling 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18... radar cross section (RCS) simulation that require an exact code for solution. In this report, we compare RCS calculations with two very different
Discontinuous Galerkin finite element method applied to the 1-D spherical neutron transport equation
Machorro, Eric . E-mail: machorro@amath.washington.edu
2007-04-10
Discontinuous Galerkin finite element methods are used to estimate solutions to the non-scattering 1-D spherical neutron transport equation. Various trial and test spaces are compared in the context of a few sample problems whose exact solution is known. Certain trial spaces avoid unphysical behaviors that seem to plague other methods. Comparisons with diamond differencing and simple corner-balancing are presented to highlight these improvements.
On Computing the Pressure by the p Version of the Finite Element Method for Stokes Problem
1990-02-15
approximation of saddlepoint prob- lems arising from Lagrangian multipliers. RAIRO , 8:129-151, 1974. [9] M. Dauge. Stationary Stokes and Navier-Stokes systems...Jensen and M. Vogelius. Divergence stability in connection with the p version of the finite element method. RAIRO , Modelisation Math. Anal. Numer., 1990...element method for elliptic problems of order 2 1. RAIRO , Modelisation Math. Anal. Numer., 24:107-146, 1990. 1261 M. Suri. On the stability and convergence
A finite element method for the thermochemical decomposition of polymeric materials. I - Theory
NASA Technical Reports Server (NTRS)
Sullivan, R. M.; Salamon, N. J.
1992-01-01
The governing differential equations are developed to model the thermomechanical behavior of chemically decomposing, polymeric materials. These equations account for thermal and gaseous diffusion through a poroelastic, transversely isotropic solid. The Bubnov-Galerkin finite element method is applied to the governing equations to cast the coupled set into a single matrix equation. A method for solving these equations simultaneously at each time step is discussed.
The L sub 1 finite element method for pure convection problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1991-01-01
The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.
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.
Finite element evaluation of three methods of stable fixation of condyle base fractures.
de Jesus, G P; Vaz, L G; Gabrielli, M F R; Passeri, L A; V Oliveira, T; Noritomi, P Y; Jürgens, P
2014-10-01
The surgical treatment of mandibular condyle fractures currently offers several possibilities for stable internal fixation. In this study, a finite element model evaluation was performed of three different methods for osteosynthesis of low subcondylar fractures: (1) two four-hole straight plates, (2) one seven-hole lambda plate, and (3) one four-hole trapezoidal plate. The finite element model evaluation considered a load applied to the first molar on the contralateral side to the fracture. Results showed that, although the three methods are capable of withstanding functional loading, the lambda plate displayed a more homogeneous stress distribution for both osteosynthesis material and bone and may be a better method when single-plate fixation is the option.
NASA Technical Reports Server (NTRS)
Jara-Almonte, J.; Mitchell, L. D.
1988-01-01
The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.
Finite elements: Theory and application
NASA Technical Reports Server (NTRS)
Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)
1988-01-01
Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.
Coupling equivalent plate and finite element formulations in multiple-method structural analyses
NASA Technical Reports Server (NTRS)
Giles, Gary L.; Norwood, Keith
1994-01-01
A coupled multiple-method analysis procedure for use late in conceptual design or early in preliminary design of aircraft structures is described. Using this method, aircraft wing structures are represented with equivalent plate models, and structural details such as engine/pylon structure, landing gear, or a 'stick' model of a fuselage are represented with beam finite element models. These two analysis methods are implemented in an integrated multiple-method formulation that involves the assembly and solution of a combined set of linear equations. The corresponding solution vector contains coefficients of the polynomials that describe the deflection of the wing and also the components of translations and rotations at the joints of the beam members. Two alternative approaches for coupling the methods are investigated; one using transition finite elements and the other using Lagrange multipliers. The coupled formulation is applied to the static analysis and vibration analysis of a conceptual design model of a fighter aircraft. The results from the coupled method are compared with corresponding results from an analysis in which the entire model is composed of finite elements.
Valentín, A; Humphrey, J D; Holzapfel, G A
2013-08-01
We implemented a constrained mixture model of arterial growth and remodeling in a nonlinear finite element framework to facilitate numerical analyses of diverse cases of arterial adaptation and maladaptation, including disease progression, resulting in complex evolving geometries and compositions. This model enables hypothesis testing by predicting consequences of postulated characteristics of cell and matrix turnover, including evolving quantities and orientations of fibrillar constituents and nonhomogenous degradation of elastin or loss of smooth muscle function. The nonlinear finite element formulation is general within the context of arterial mechanics, but we restricted our present numerical verification to cylindrical geometries to allow comparisons with prior results for two special cases: uniform transmural changes in mass and differential growth and remodeling within a two-layered cylindrical model of the human aorta. The present finite element model recovers the results of these simplified semi-inverse analyses with good agreement.
Valentín, A.; Humphrey, J. D.; Holzapfel, G. A.
2013-01-01
We implemented a constrained mixture model of arterial growth and remodeling (G&R) in a nonlinear finite element framework to facilitate numerical analyses of diverse cases of arterial adaptation and maladaptation, including disease progression, resulting in complex evolving geometries and compositions. This model enables hypothesis testing by predicting consequences of postulated characteristics of cell and matrix turnover, including evolving quantities and orientations of fibrillar constituents and non-homogenous degradation of elastin or loss of smooth muscle function. The non-linear finite element formulation is general within the context of arterial mechanics, but we restricted our present numerical verification to cylindrical geometries to allow comparisons to prior results for two special cases: uniform transmural changes in mass and differential G&R within a two-layered cylindrical model of the human aorta. The present finite element model recovers the results of these simplified semi-inverse analyses with good agreement. PMID:23713058
Finite-Element Methods for Real-Time Simulation of Surgery
NASA Technical Reports Server (NTRS)
Basdogan, Cagatay
2003-01-01
Two finite-element methods have been developed for mathematical modeling of the time-dependent behaviors of deformable objects and, more specifically, the mechanical responses of soft tissues and organs in contact with surgical tools. These methods may afford the computational efficiency needed to satisfy the requirement to obtain computational results in real time for simulating surgical procedures as described in Simulation System for Training in Laparoscopic Surgery (NPO-21192) on page 31 in this issue of NASA Tech Briefs. Simulation of the behavior of soft tissue in real time is a challenging problem because of the complexity of soft-tissue mechanics. The responses of soft tissues are characterized by nonlinearities and by spatial inhomogeneities and rate and time dependences of material properties. Finite-element methods seem promising for integrating these characteristics of tissues into computational models of organs, but they demand much central-processing-unit (CPU) time and memory, and the demand increases with the number of nodes and degrees of freedom in a given finite-element model. Hence, as finite-element models become more realistic, it becomes more difficult to compute solutions in real time. In both of the present methods, one uses approximate mathematical models trading some accuracy for computational efficiency and thereby increasing the feasibility of attaining real-time up36 NASA Tech Briefs, October 2003 date rates. The first of these methods is based on modal analysis. In this method, one reduces the number of differential equations by selecting only the most significant vibration modes of an object (typically, a suitable number of the lowest-frequency modes) for computing deformations of the object in response to applied forces.
NASA Technical Reports Server (NTRS)
Vazquez, Sixto L.; Tessler, Alexander; Quach, Cuong C.; Cooper, Eric G.; Parks, Jeffrey; Spangler, Jan L.
2005-01-01
In an effort to mitigate accidents due to system and component failure, NASA s Aviation Safety has partnered with industry, academia, and other governmental organizations to develop real-time, on-board monitoring capabilities and system performance models for early detection of airframe structure degradation. NASA Langley is investigating a structural health monitoring capability that uses a distributed fiber optic strain system and an inverse finite element method for measuring and modeling structural deformations. This report describes the constituent systems that enable this structural monitoring function and discusses results from laboratory tests using the fiber strain sensor system and the inverse finite element method to demonstrate structural deformation estimation on an instrumented test article
Structural Anomaly Detection Using Fiber Optic Sensors and Inverse Finite Element Method
NASA Technical Reports Server (NTRS)
Quach, Cuong C.; Vazquez, Sixto L.; Tessler, Alex; Moore, Jason P.; Cooper, Eric G.; Spangler, Jan. L.
2005-01-01
NASA Langley Research Center is investigating a variety of techniques for mitigating aircraft accidents due to structural component failure. One technique under consideration combines distributed fiber optic strain sensing with an inverse finite element method for detecting and characterizing structural anomalies anomalies that may provide early indication of airframe structure degradation. The technique identifies structural anomalies that result in observable changes in localized strain but do not impact the overall surface shape. Surface shape information is provided by an Inverse Finite Element Method that computes full-field displacements and internal loads using strain data from in-situ fiberoptic sensors. This paper describes a prototype of such a system and reports results from a series of laboratory tests conducted on a test coupon subjected to increasing levels of damage.
Tissue Modeling and Analyzing with Finite Element Method: A Review for Cranium Brain Imaging
Yue, Xianfang; Wang, Li; Wang, Ruonan
2013-01-01
For the structure mechanics of human body, it is almost impossible to conduct mechanical experiments. Then the finite element model to simulate mechanical experiments has become an effective tool. By introducing several common methods for constructing a 3D model of cranial cavity, this paper carries out systematically the research on the influence law of cranial cavity deformation. By introducing the new concepts and theory to develop the 3D cranial cavity model with the finite-element method, the cranial cavity deformation process with the changing ICP can be made the proper description and reasonable explanation. It can provide reference for getting cranium biomechanical model quickly and efficiently and lay the foundation for further biomechanical experiments and clinical applications. PMID:23476630
NASA Astrophysics Data System (ADS)
Sarakorn, Weerachai
2017-04-01
In this research, the finite element (FE) method incorporating quadrilateral elements for solving 2-D MT modeling was presented. The finite element software was developed, employing a paving algorithm to generate the unstructured quadrilateral mesh. The accuracy, efficiency, reliability, and flexibility of our FE forward modeling are presented, compared and discussed. The numerical results indicate that our FE codes using an unstructured quadrilateral mesh provide good accuracy when the local mesh refinement is applied around sites and in the area of interest, with superior results when compared to other FE methods. The reliability of the developed codes was also confirmed when comparing both analytical solutions and COMMEMI2D model. Furthermore, our developed FE codes incorporating an unstructured quadrilateral mesh showed useful and powerful features such as handling irregular and complex subregions and providing local refinement of the mesh for a 2-D domain as closely as unstructured triangular mesh but it requires less number of elements in a mesh.
Three dimensional finite element methods: Their role in the design of DC accelerator systems
NASA Astrophysics Data System (ADS)
Podaru, Nicolae C.; Gottdang, A.; Mous, D. J. W.
2013-04-01
High Voltage Engineering has designed, built and tested a 2 MV dual irradiation system that will be applied for radiation damage studies and ion beam material modification. The system consists of two independent accelerators which support simultaneous proton and electron irradiation (energy range 100 keV - 2 MeV) of target sizes of up to 300 × 300 mm2. Three dimensional finite element methods were used in the design of various parts of the system. The electrostatic solver was used to quantify essential parameters of the solid-state power supply generating the DC high voltage. The magnetostatic solver and ray tracing were used to optimize the electron/ion beam transport. Close agreement between design and measurements of the accelerator characteristics as well as beam performance indicate the usefulness of three dimensional finite element methods during accelerator system design.
Modified Immersed Finite Element Method For Fully-Coupled Fluid-Structure Interations
Wang, Xingshi; Zhang, Lucy T.
2013-01-01
In this paper, we develop a “modified” immersed finite element method (mIFEM), a non-boundary-fitted numerical technique, to study fluid-structure interactions. Using this method, we can more precisely capture the solid dynamics by solving the solid governing equation instead of imposing it based on the fluid velocity field as in the original immersed finite element (IFEM). Using the IFEM may lead to severe solid mesh distortion because the solid deformation is been over-estimated, especially for high Reynolds number flows. In the mIFEM, the solid dynamics is solved using appropriate boundary conditions generated from the surrounding fluid, therefore produces more accurate and realistic coupled solutions. We show several 2-D and 3-D testing cases where the mIFEM has a noticeable advantage in handling complicated fluid-structure interactions when the solid behavior dominates the fluid flow. PMID:24223445
NASA Technical Reports Server (NTRS)
Leser, William P.; Yuan, Fuh-Gwo; Leser, William P.
2013-01-01
A method of numerically estimating dynamic Green's functions using the finite element method is proposed. These Green's functions are accurate in a limited frequency range dependent on the mesh size used to generate them. This range can often match or exceed the frequency sensitivity of the traditional acoustic emission sensors. An algorithm is also developed to characterize an acoustic emission source by obtaining information about its strength and temporal dependence. This information can then be used to reproduce the source in a finite element model for further analysis. Numerical examples are presented that demonstrate the ability of the band-limited Green's functions approach to determine the moment tensor coefficients of several reference signals to within seven percent, as well as accurately reproduce the source-time function.
A hybridized formulation for the weak Galerkin mixed finite element method
Mu, Lin; Wang, Junping; Ye, Xiu
2016-01-14
This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising from the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.
A hybridized formulation for the weak Galerkin mixed finite element method
Mu, Lin; Wang, Junping; Ye, Xiu
2016-01-14
This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less
Hybrid finite element-finite difference method for thermal analysis of blood vessels.
Blanchard, C H; Gutierrez, G; White, J A; Roemer, R B
2000-01-01
A hybrid finite-difference/finite-element technique for the thermal analysis of blood vessels embedded in perfused tissue has been developed and evaluated. This method provides efficient and accurate solutions to the conjugated heat transfer problem of convection by blood coupled to conduction in the tissue. The technique uses a previously developed 3D automatic meshing method for creating a finite element mesh in the tissue surrounding the vessels, coupled iteratively with a 1-D marching finite difference method for the interior of the vessels. This hybrid technique retains the flexibility and ease of automated finite-element meshing techniques for modelling the complex geometry of blood vessels and irregularly shaped tissues, and speeds the solution time by using a simple finite-difference method to calculate the bulk mean temperatures within all blood vessels. The use of the 1D finite-difference technique in the blood vessels also eliminates the large computer memory requirements needed to accurately solve large vessel network problems when fine FE meshes are used in the interior of vessels. The accuracy of the hybrid technique has been verified against previously verified numerical solutions. In summary, the hybrid technique combines the accuracy and flexibility found in automated finite-element techniques, with the speed and reduction of computational memory requirements associated with the 1D finite-difference technique, something which has not been done before. This method, thus, has the potential to provide accurate, flexible and relatively fast solutions for the thermal analysis of coupled perfusion/blood vessel problems, and large vessel network problems.
XFEM: Exploratory Research into the Extended Finite-Element Method, FY02 LDRD Final Report
MISH, K
2003-02-26
This report is one of two components, the first an overview document outlining the goals and results of the XFEM LDRD project, and the other (titled ''Structured Extended Finite Element Methods of Solids defined by Implicit Surfaces'') detailing the scientific advances developed under FY01/FY02 LDRD funding. The XFEM (Extended Finite-Element Method) Engineering LDRD/ER Project was motivated by three research and development goals: (1) the extensions of standard finite-element technology into important new research venues of interest to the Engineering Directorate, (2) the automation of much of the engineering analysis workflow, so as to improve the productivity of mesh-generation and problem setup processes, and (3) the development of scalable software tools to facilitate innovation in XFEM analysis and methods development. The driving principle behind this LDRD project was to demonstrate the computational technology required to perform mechanical analysis of complex solids, with minimal extra effort required on the part of mechanical analysts. This need arises both from the growing workload of LLNL analysts in problem setup and mesh generation, and from the requirement that actual as-built mechanical configurations be analyzed. Many of the most important programmatic drivers for mechanical analysis require that the actual (e.g., deformed, aged, damaged) geometric configuration of the solid be deduced and then accurately modeled: for this programmatic need, XFEM provides one of the only accurate methods available that can provide high-fidelity results.
The finite element method for micro-scale modeling of ultrasound propagation in cancellous bone.
Vafaeian, B; El-Rich, M; El-Bialy, T; Adeeb, S
2014-08-01
Quantitative ultrasound for bone assessment is based on the correlations between ultrasonic parameters and the properties (mechanical and physical) of cancellous bone. To elucidate the correlations, understanding the physics of ultrasound in cancellous bone is demanded. Micro-scale modeling of ultrasound propagation in cancellous bone using the finite-difference time-domain (FDTD) method has been so far utilized as one of the approaches in this regard. However, the FDTD method accompanies two disadvantages: staircase sampling of cancellous bone by finite difference grids leads to generation of wave artifacts at the solid-fluid interface inside the bone; additionally, this method cannot explicitly satisfy the needed perfect-slip conditions at the interface. To overcome these disadvantages, the finite element method (FEM) is proposed in this study. Three-dimensional finite element models of six water-saturated cancellous bone samples with different bone volume were created. The values of speed of sound (SOS) and broadband ultrasound attenuation (BUA) were calculated through the finite element simulations of ultrasound propagation in each sample. Comparing the results with other experimental and simulation studies demonstrated the capabilities of the FEM for micro-scale modeling of ultrasound in water-saturated cancellous bone.
The Optimal Convergence Rate of the p-Version of the Finite Element Method.
1985-10-01
pSFOBSOLETE. THE OPTIMAL CONVERGENCE RATE OF THE p-VERSION OF THE FINITE ELEMENT METHOD I. Babu’ka 1 Institute for Physical Science and Technology...commercial and research codes. The p-version and h-p versions are new developments. There is only one commercial code, the system PROBE ( Noetic Tech, St...Louis). The theoretical aspects have been studied only recently. The first theoretical paper appeared in 1981 (see [7)). See also [1), [7], [81, [9
1988-09-01
Institute for Physical Science and Teennology rUniversity of Maryland o College Park, MD 20742 B. Gix) Engineering Mechanics Research Corporation Troy...OF THE FINITE ELEMENT METHOD by Ivo Babuska Institute for Physical Science and Technology University of Maryland College Park, MD 20742 B. Guo 2...2Research partially supported by the National Science Foundation under Grant DMS-85-16191 during the stay at the Institute for Physical Science and
Viscoplastic and Creep Crack Growth Analysis by the Finite Element Method.
1981-07-01
Strain Matrix and Its Application for the Solution of Elastic- Plastic Problems by the Finite Element Method," Int’l Journ. of Mechani- cal Sciences, Vol...constant. Therefore only one solution is required to obtain displacements for the elastic structure. However, for elastic- plastic problems the...form as dP= ;I.3 deP~i dEYi.. (A-28) 4. ELASTIC-PLASTIC SOLUTION TECHNIQUES The procedures used to solve small displacement elastic- plastic problems incrementally
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.
Balima, O.; Favennec, Y.; Rousse, D.
2013-10-15
Highlights: •New strategies to improve the accuracy of the reconstruction through mesh and finite element parameterization. •Use of gradient filtering through an alternative inner product within the adjoint method. •An integral form of the cost function is used to make the reconstruction compatible with all finite element formulations, continuous and discontinuous. •Gradient-based algorithm with the adjoint method is used for the reconstruction. -- Abstract: Optical tomography is mathematically treated as a non-linear inverse problem where the optical properties of the probed medium are recovered through the minimization of the errors between the experimental measurements and their predictions with a numerical model at the locations of the detectors. According to the ill-posed behavior of the inverse problem, some regularization tools must be performed and the Tikhonov penalization type is the most commonly used in optical tomography applications. This paper introduces an optimized approach for optical tomography reconstruction with the finite element method. An integral form of the cost function is used to take into account the surfaces of the detectors and make the reconstruction compatible with all finite element formulations, continuous and discontinuous. Through a gradient-based algorithm where the adjoint method is used to compute the gradient of the cost function, an alternative inner product is employed for preconditioning the reconstruction algorithm. Moreover, appropriate re-parameterization of the optical properties is performed. These regularization strategies are compared with the classical Tikhonov penalization one. It is shown that both the re-parameterization and the use of the Sobolev cost function gradient are efficient for solving such an ill-posed inverse problem.
A Stochastic Mixed Finite Element Heterogeneous Multiscale Method for Flow in Porous Media
2010-08-01
quickly. However, for reservoir simulation the most crucial factor is the transport prop- erties of a velocity field. That is, a large local error in the...streamline methods for reservoir simulation of large geomodels, Advances in Water Resources 28 (2005) 257 – 271. [11] P. Jenny, S. H. Lee, H. A. Tchelepi... Reservoir Simulation , 2003, pp. 23–27. [53] R. Ghanem, P. D. Spanos, Stochastic Finite Elements: A Spectral Approach, Springer - Verlag, New York
A strongly conservative finite element method for the coupling of Stokes and Darcy flow
NASA Astrophysics Data System (ADS)
Kanschat, G.; Rivière, B.
2010-08-01
We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in Hdiv( Ω) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders.
An approach to parameter estimation for breast tumor by finite element method
NASA Astrophysics Data System (ADS)
Xu, A.-qing; Yang, Hong-qin; Ye, Zhen; Su, Yi-ming; Xie, Shu-sen
2009-02-01
The temperature of human body on the surface of the skin depends on the metabolic activity, the blood flow, and the temperature of the surroundings. Any abnormality in the tissue, such as the presence of a tumor, alters the normal temperature on the skin surface due to increased metabolic activity of the tumor. Therefore, abnormal skin temperature profiles are an indication of diseases such as tumor or cancer. This study is to present an approach to detect the female breast tumor and its related parameter estimations by combination the finite element method with infrared thermography for the surface temperature profile. A 2D simplified breast embedded a tumor model based on the female breast anatomical structure and physiological characteristics was first established, and then finite element method was used to analyze the heat diffuse equation for the surface temperature profiles of the breast. The genetic optimization algorithm was used to estimate the tumor parameters such as depth, size and blood perfusion by minimizing a fitness function involving the temperature profiles simulated data by finite element method to the experimental data obtained by infrared thermography. This preliminary study shows it is possible to determine the depth and the heat generation rate of the breast tumor by using infrared thermography and the optimization analysis, which may play an important role in the female breast healthcare and diseases evaluation or early detection. In order to develop the proposed methodology to be used in clinical, more accurate anatomy 3D breast geometry should be considered in further investigations.
Chakrabarty, Siddhartha P; Hanson, Floyd B
2009-06-01
In this paper, we present a distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method. The dynamic model comprises system of three coupled reaction-diffusion models, involving the tumor cells, the normal tissues and the drug concentration. An optimal control problem is formulated with the goal of minimizing the tumor cell density and reducing the side effects of the drug. A distributed parameters method based on the application of variational calculus is used on an integral-Hamiltonian, which is then used to obtain an optimal coupled system of forward state equations and backward co-state equations. The Galerkin finite element method is used to realistically represent the brain structure as well as to facilitate computation. Finally a three-dimensional test case is considered and partitioned into a set of spherical finite elements, using tri-linear basis functions, except for the elements affected by singularities of polar and azimuthal angles, as well as the origin.
Sensitivity analysis based preform die shape design using the finite element method
NASA Astrophysics Data System (ADS)
Zhao, G. Q.; Hufi, R.; Hutter, A.; Grandhi, R. V.
1997-06-01
This paper uses a finite element-based sensitivity analysis method to design the preform die shape for metal forming processes. The sensitivity analysis was developed using the rigid visco-plastic finite element method. The preform die shapes are represented by cubic B-spline curves. The control points or coefficients of the B-spline are used as the design variables. The optimization problem is to minimize the difference between the realized and the desired final forging shapes. The sensitivity analysis includes the sensitivities of the objective function, nodal coordinates, and nodal velocities with respect to the design variables. The remeshing procedure and the interpolation/transfer of the history/dependent parameters are considered. An adjustment of the volume loss resulting from the finite element analysis is used to make the workpiece volume consistent in each optimization iteration and improve the optimization convergence. In addition, a technique for dealing with fold-over defects during the forming simulation is employed in order to continue the optimization procedures of the preform die shape design. The method developed in this paper is used to design the preform die shape for both plane strain and axisymmetric deformations with shaped cavities. The analysis shows that satisfactory final forging shapes are obtained using the optimized preform die shapes.
Application of Finite Element Method to the structure design of the Space Solar Telescope
NASA Astrophysics Data System (ADS)
Zhang, Rui; Chen, Zhi-Yuan; Chen, Zhi-Ping; Yang, Shi-Mo
2005-12-01
Finite Element Method (FEM), the primary numerical means to process structure analysis in the modern engineering field, is adopted widely in the design of astronomical instruments at present. It can help designers to find out various characteristics of the object, to discover the weakness in stiffness and strength, and to improve and optimize the design as well. It is also used widely in many processes during the designing of the Space Solar Telescope (SST), such as in the main truss and the primary cell. From the beginning of the geometry modeling and the finite element creating, many aspects such as linear static, modal analysis, transient response and thermal analysis are demonstrated in SST. The error existing in the FEM, why it exists, and how to reduce it are discussed. Finally, the development trend of FEM in the astronomical instruments especially the space astronomical instruments is presented.
A finite element-boundary integral method for conformal antenna arrays on a circular cylinder
NASA Technical Reports Server (NTRS)
Kempel, Leo C.; Volakis, John L.; Woo, Alex C.; Yu, C. Long
1992-01-01
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This is due to the lack of rigorous mathematical models for conformal antenna arrays, and as a result the design of conformal arrays is primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. Herewith we shall extend this formulation for conformal arrays on large metallic cylinders. In this we develop the mathematical formulation. In particular we discuss the finite element equations, the shape elements, and the boundary integral evaluation, and it is shown how this formulation can be applied with minimal computation and memory requirements. The implementation shall be discussed in a later report.
Method for patient-specific finite element modeling and simulation of deep brain stimulation.
Aström, Mattias; Zrinzo, Ludvic U; Tisch, Stephen; Tripoliti, Elina; Hariz, Marwan I; Wårdell, Karin
2009-01-01
Deep brain stimulation (DBS) is an established treatment for Parkinson's disease. Success of DBS is highly dependent on electrode location and electrical parameter settings. The aim of this study was to develop a general method for setting up patient-specific 3D computer models of DBS, based on magnetic resonance images, and to demonstrate the use of such models for assessing the position of the electrode contacts and the distribution of the electric field in relation to individual patient anatomy. A software tool was developed for creating finite element DBS-models. The electric field generated by DBS was simulated in one patient and the result was visualized with isolevels and glyphs. The result was evaluated and it corresponded well with reported effects and side effects of stimulation. It was demonstrated that patient-specific finite element models and simulations of DBS can be useful for increasing the understanding of the clinical outcome of DBS.
Solution of the neutronics code dynamic benchmark by finite element method
NASA Astrophysics Data System (ADS)
Avvakumov, A. V.; Vabishchevich, P. N.; Vasilev, A. O.; Strizhov, V. F.
2016-10-01
The objective is to analyze the dynamic benchmark developed by Atomic Energy Research for the verification of best-estimate neutronics codes. The benchmark scenario includes asymmetrical ejection of a control rod in a water-type hexagonal reactor at hot zero power. A simple Doppler feedback mechanism assuming adiabatic fuel temperature heating is proposed. The finite element method on triangular calculation grids is used to solve the three-dimensional neutron kinetics problem. The software has been developed using the engineering and scientific calculation library FEniCS. The matrix spectral problem is solved using the scalable and flexible toolkit SLEPc. The solution accuracy of the dynamic benchmark is analyzed by condensing calculation grid and varying degree of finite elements.
Study of matrix crack-tilted fiber bundle interaction using caustics and finite element method.
Hao, Wenfeng; Zhu, Jianguo; Zhu, Qi; Yuan, Yanan
2016-02-01
In this work, the interaction between the matrix crack and a tilted fiber bundle was investigated via caustics and the finite element method (FEM). First, the caustic patterns at the crack tip with different distances from the tilted fiber were obtained and the stress intensity factors were extracted from the geometry of the caustic patterns. Subsequently, the shielding effect of the fiber bundle in front of the crack tip was analyzed. Furthermore, the interaction between the matrix crack and the broken fiber bundle was discussed. Finally, a finite element simulation was carried out using ABAQUS to verify the experimental results. The results demonstrate that the stress intensity factors extracted from caustic experiments are in excellent agreement with the data calculated by FEM.
Gradient plasticity crack tip characterization by means of the extended finite element method
NASA Astrophysics Data System (ADS)
Martínez-Pañeda, E.; Natarajan, S.; Bordas, S.
2017-01-01
Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary dislocations. Characterizing the behavior at the small scales involved in crack tip deformation requires, however, the use of a very refined mesh within microns to the crack. In this work a novel and efficient gradient-enhanced numerical framework is developed by means of the extended finite element method (X-FEM). A mechanism-based gradient plasticity model is employed and the approximation of the displacement field is enriched with the stress singularity of the gradient-dominated solution. Results reveal that the proposed numerical methodology largely outperforms the standard finite element approach. The present work could have important implications on the use of microstructurally-motivated models in large scale applications. The non-linear X-FEM code developed in MATLAB can be downloaded from http://www.empaneda.com/codes.
NASA Astrophysics Data System (ADS)
Tang, Weiqin; Li, Dayong; Zhang, Shaorui; Peng, Yinghong
2013-12-01
As a light-weight structural material, magnesium alloys show good potential in improving the fuel efficiency of vehicles and reducing CO2 emissions. However, it is well known that polycrystalline Mg alloys develop pronounced crystallographic texture and plastic anisotropy during rolling, which leads to earing phenomenon during deep drawing of the rolled sheets. It is vital to predict this phenomenon accurately for application of magnesium sheet metals. In the present study, a crystal plasticity model for AZ31 magnesium alloy that incorporates both slip and twinning is established. Then the crystal plasticity model is implemented in the commercial finite element software ABAQUS/Explicit through secondary development interface (VUMAT). Finally, the stamping process of a cylindrical cup is simulated using the developed crystal plasticity finite element model, and the predicting method is verified by comparing with experimental results from both earing profile and deformation texture.
NASA Astrophysics Data System (ADS)
Geddes, Earl Russell
The details of the low frequency sound field for a rectangular room can be studied by the use of an established analytic technique--separation of variables. The solution is straightforward and the results are well-known. A non -rectangular room has boundary conditions which are not separable and therefore other solution techniques must be used. This study shows that the finite element method can be adapted for use in the study of sound fields in arbitrary shaped enclosures. The finite element acoustics problem is formulated and the modification of a standard program, which is necessary for solving acoustic field problems, is examined. The solution of the semi-non-rectangular room problem (one where the floor and ceiling remain parallel) is carried out by a combined finite element/separation of variables approach. The solution results are used to construct the Green's function for the low frequency sound field in five rooms (or data cases): (1) a rectangular (Louden) room; (2) The smallest wall of the Louden room canted 20 degrees from normal; (3) The largest wall of the Louden room canted 20 degrees from normal; (4) both the largest and the smallest walls are canted 20 degrees; and (5) a five-sided room variation of Case 4. Case 1, the rectangular room was calculated using both the finite element method and the separation of variables technique. The results for the two methods are compared in order to access the accuracy of the finite element method models. The modal damping coefficient are calculated and the results examined. The statistics of the source and receiver average normalized RMS P('2) responses in the 80 Hz, 100 Hz, and 125 Hz one-third octave bands are developed. The receiver averaged pressure response is developed to determine the effect of the source locations on the response. Twelve source locations are examined and the results tabulated for comparison. The effect of a finite sized source is looked at briefly. Finally, the standard deviation of the
Finite element analysis of low-cost membrane deformable mirrors for high-order adaptive optics
NASA Astrophysics Data System (ADS)
Winsor, Robert S.; Sivaramakrishnan, Anand; Makidon, Russell B.
1999-10-01
We demonstrate the feasibility of glass membrane deformable mirror (DM) support structures intended for very high order low-stroke adaptive optics systems. We investigated commercially available piezoelectric ceramics. Piezoelectric tubes were determined to offer the largest amount of stroke for a given amount of space on the mirror surface that each actuator controls. We estimated the minimum spacing and the maximum expected stroke of such actuators. We developed a quantitative understanding of the response of a membrane mirror surface by performing a Finite Element Analysis (FEA) study. The results of the FEA analysis were used to develop a design and fabrication process for membrane deformable mirrors of 200 - 500 micron thicknesses. Several different values for glass thickness and actuator spacing were analyzed to determine the best combination of actuator stoke and surface deformation quality. We considered two deformable mirror configurations. The first configuration uses a vacuum membrane attachment system where the actuator tubes' central holes connect to an evacuated plenum, and atmospheric pressure holds the membrane against the actuators. This configuration allows the membrane to be removed from the actuators, facilitating easy replacement of the glass. The other configuration uses precision bearing balls epoxied to the ends of the actuator tubes, with the glass membrane epoxied to the ends of the ball bearings. While this kind of DM is not serviceable, it allows actuator spacings of 4 mm, in addition to large stroke. Fabrication of a prototype of the latter kind of DM was started.
NASA Technical Reports Server (NTRS)
Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander
2011-01-01
A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.
Failure analysis of laminated composites by using iterative three-dimensional finite element method
NASA Astrophysics Data System (ADS)
Hwang, W. C.; Sun, C. T.
1989-05-01
A failure analysis of laminated composites is accomplished by using an iterative three-dimensional finite element method. Based on Tsai-Wu failure theory, three different modes of failure are proposed: fiber breakage, matrix cracking, and delamination. The first ply failure load is then evaluated. As the applied load exceeds the first ply failure load, localized structural failure occurs and the global structural stiffness should change. The global stiffness matrix is modified by taking nonlinearity due to partial failures within a laminate into consideration. The first ply failure load is analyzed by using a iterative mixed field method in solving the linear part of the finite element equations. The progressive failure problem is solved numerically by using Newton-Raphson iterative schemes for the solution of nonlinear finite element equations. Numerical examples include angle-ply symmetric Thornel 300 graphite/934 resin epoxy laminates under uniaxial tension. First ply failure loads as well as the final failure loads are evaluated. Good correlation between analytical results and experimental data are observed. Numerical results also include the investigation of composite specimens with a centered hole, under uniaxial tension. Excellent correlation with the experimental data is observed.
The p-version of the finite element method in incremental elasto-plastic analysis
NASA Technical Reports Server (NTRS)
Holzer, Stefan M.; Yosibash, Zohar
1993-01-01
Whereas the higher-order versions of the finite elements method (the p- and hp-version) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. Aspects of incremental elasto-plastic finite element analysis which are particularly amenable to improvements by the p-version is discussed. These theoretical considerations are supported by several numerical experiments. First, an example for which an analytical solution is available is studied. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared to the traditional h-version but also in respect to the exact solution. Finally, an example of considerable practical importance - the analysis of a cold-worked lug - is presented which demonstrates how the modeling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.
Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods
NASA Astrophysics Data System (ADS)
Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco
2015-04-01
The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface
Simulation and evaluation of tablet-coating burst based on finite element method.
Yang, Yan; Li, Juan; Miao, Kong-Song; Shan, Wei-Guang; Tang, Lan; Yu, Hai-Ning
2016-09-01
The objective of this study was to simulate and evaluate the burst behavior of coated tablets. Three-dimensional finite element models of tablet-coating were established using software ANSYS. Swelling pressure of cores was measured by a self-made device and applied at the internal surface of the models. Mechanical properties of the polymer film were determined using a texture analyzer and applied as material properties of the models. The resulted finite element models were validated by experimental data. The validated models were used to assess the factors those influenced burst behavior and predict the coating burst behavior. The simulation results of coating burst and failure location were strongly matched with the experimental data. It was found that internal swelling pressure, inside corner radius and corner thickness were three main factors controlling the stress distribution and burst behavior. Based on the linear relationship between the internal pressure and the maximum principle stress on coating, burst pressure of coatings was calculated and used to predict the burst behavior. This study demonstrated that burst behavior of coated tablets could be simulated and evaluated by finite element method.
NASA Technical Reports Server (NTRS)
Cerracchio, Priscilla; Gherlone, Marco; Di Sciuva, Marco; Tessler, Alexander
2013-01-01
The marked increase in the use of composite and sandwich material systems in aerospace, civil, and marine structures leads to the need for integrated Structural Health Management systems. A key capability to enable such systems is the real-time reconstruction of structural deformations, stresses, and failure criteria that are inferred from in-situ, discrete-location strain measurements. This technology is commonly referred to as shape- and stress-sensing. Presented herein is a computationally efficient shape- and stress-sensing methodology that is ideally suited for applications to laminated composite and sandwich structures. The new approach employs the inverse Finite Element Method (iFEM) as a general framework and the Refined Zigzag Theory (RZT) as the underlying plate theory. A three-node inverse plate finite element is formulated. The element formulation enables robust and efficient modeling of plate structures instrumented with strain sensors that have arbitrary positions. The methodology leads to a set of linear algebraic equations that are solved efficiently for the unknown nodal displacements. These displacements are then used at the finite element level to compute full-field strains, stresses, and failure criteria that are in turn used to assess structural integrity. Numerical results for multilayered, highly heterogeneous laminates demonstrate the unique capability of this new formulation for shape- and stress-sensing.
Garvie, Marcus R; Burkardt, John; Morgan, Jeff
2015-03-01
We describe simple finite element schemes for approximating spatially extended predator-prey dynamics with the Holling type II functional response and logistic growth of the prey. The finite element schemes generalize 'Scheme 1' in the paper by Garvie (Bull Math Biol 69(3):931-956, 2007). We present user-friendly, open-source MATLAB code for implementing the finite element methods on arbitrary-shaped two-dimensional domains with Dirichlet, Neumann, Robin, mixed Robin-Neumann, mixed Dirichlet-Neumann, and Periodic boundary conditions. Users can download, edit, and run the codes from http://www.uoguelph.ca/~mgarvie/ . In addition to discussing the well posedness of the model equations, the results of numerical experiments are presented and demonstrate the crucial role that habitat shape, initial data, and the boundary conditions play in determining the spatiotemporal dynamics of predator-prey interactions. As most previous works on this problem have focussed on square domains with standard boundary conditions, our paper makes a significant contribution to the area.
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.
A least-squares finite element method for incompressible Navier-Stokes problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1989-01-01
A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method, and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.
A method for determining spiral-bevel gear tooth geometry for finite element analysis
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.; Litvin, Faydor L.
1991-01-01
An analytical method was developed to determine gear tooth surface coordinates of face-milled spiral bevel gears. The method uses the basic gear design parameters in conjunction with the kinematical aspects of spiral bevel gear manufacturing machinery. A computer program, SURFACE, was developed. The computer program calculates the surface coordinates and outputs 3-D model data that can be used for finite element analysis. Development of the modeling method and an example case are presented. This analysis method could also find application for gear inspection and near-net-shape gear forging die design.
A least-squares finite element method for incompressible Navier-Stokes problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1992-01-01
A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.
Numerical computation of transonic flows by finite-element and finite-difference methods
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.
1978-01-01
Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.
NASA Technical Reports Server (NTRS)
Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.
1996-01-01
The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.
Neuert, Mark A C; Dunning, Cynthia E
2013-09-01
Strain energy-based adaptive material models are used to predict bone resorption resulting from stress shielding induced by prosthetic joint implants. Generally, such models are governed by two key parameters: a homeostatic strain-energy state (K) and a threshold deviation from this state required to initiate bone reformation (s). A refinement procedure has been performed to estimate these parameters in the femur and glenoid; this study investigates the specific influences of these parameters on resulting density distributions in the distal ulna. A finite element model of a human ulna was created using micro-computed tomography (µCT) data, initialized to a homogeneous density distribution, and subjected to approximate in vivo loading. Values for K and s were tested, and the resulting steady-state density distribution compared with values derived from µCT images. The sensitivity of these parameters to initial conditions was examined by altering the initial homogeneous density value. The refined model parameters selected were then applied to six additional human ulnae to determine their performance across individuals. Model accuracy using the refined parameters was found to be comparable with that found in previous studies of the glenoid and femur, and gross bone structures, such as the cortical shell and medullary canal, were reproduced. The model was found to be insensitive to initial conditions; however, a fair degree of variation was observed between the six specimens. This work represents an important contribution to the study of changes in load transfer in the distal ulna following the implementation of commercial orthopedic implants.
NASA Astrophysics Data System (ADS)
Parkinson, S. D.; Hill, J.; Piggott, M. D.; Allison, P. A.
2014-05-01
High resolution direct numerical simulations (DNS) are an important tool for the detailed analysis of turbidity current dynamics. Models that resolve the vertical structure and turbulence of the flow are typically based upon the Navier-Stokes equations. Two-dimensional simulations are known to produce unrealistic cohesive vortices that are not representative of the real three-dimensional physics. The effect of this phenomena is particularly apparent in the later stages of flow propagation. The ideal solution to this problem is to run the simulation in three dimensions but this is computationally expensive. This paper presents a novel finite-element (FE) DNS turbidity current model that has been built within Fluidity, an open source, general purpose, computational fluid dynamics code. The model is validated through re-creation of a lock release density current at a Grashof number of 5 × 106 in two, and three-dimensions. Validation of the model considers the flow energy budget, sedimentation rate, head speed, wall normal velocity profiles and the final deposit. Conservation of energy in particular is found to be a good metric for measuring mesh performance in capturing the range of dynamics. FE models scale well over many thousands of processors and do not impose restrictions on domain shape, but they are computationally expensive. Use of discontinuous discretisations and adaptive unstructured meshing technologies, which reduce the required element count by approximately two orders of magnitude, results in high resolution DNS models of turbidity currents at a fraction of the cost of traditional FE models. The benefits of this technique will enable simulation of turbidity currents in complex and large domains where DNS modelling was previously unachievable.
Finite element analysis of resistivity measurement with van der Pauw method in a diamond anvil cell
NASA Astrophysics Data System (ADS)
Huang, Xiaowei; Gao, Chunxiao; Han, Yonghao; Li, Ming; He, Chunyuan; Hao, Aimin; Zhang, Dongmei; Yu, Cuiling; Zou, Guangtian; Ma, Yanzhang
2007-06-01
Using finite element analysis, the authors studied the steady current field distribution under the configuration of van der Pauw method [L. J. van der Pauw, Philips Tech. Rev. 20, 220 (1958)] for resistivity measurement in a diamond anvil cell. Based on the theoretical analysis, the authors obtained the theoretical accuracy curve of the van der Pauw method. This method provides accurate determination of sample resistivity when the ratio of sample thickness to its diameter is less than 0.45. They found that the contact area between electrode and sample is a key factor in the resistivity measurement accuracy and its size is dependent on the sample diameter for a given measurement accuracy.
A Kernel-Free Particle-Finite Element Method for Hypervelocity Impact Simulation. Chapter 4
NASA Technical Reports Server (NTRS)
Park, Young-Keun; Fahrenthold, Eric P.
2004-01-01
An improved hybrid particle-finite element method has been developed for the simulation of hypervelocity impact problems. Unlike alternative methods, the revised formulation computes the density without reference to any kernel or interpolation functions, for either the density or the rate of dilatation. This simplifies the state space model and leads to a significant reduction in computational cost. The improved method introduces internal energy variables as generalized coordinates in a new formulation of the thermomechanical Lagrange equations. Example problems show good agreement with exact solutions in one dimension and good agreement with experimental data in a three dimensional simulation.
An hybrid finite volume finite element method for variable density incompressible flows
NASA Astrophysics Data System (ADS)
Calgaro, Caterina; Creusé, Emmanuel; Goudon, Thierry
2008-04-01
This paper is devoted to the numerical simulation of variable density incompressible flows, modeled by the Navier-Stokes system. We introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint. The breakthrough relies on the definition of a suitable footbridge between the two methods, through the design of compatibility condition. In turn, the method is very flexible and allows to deal with unstructured meshes. Several numerical tests are performed to show the scheme capabilities. In particular, the viscous Rayleigh-Taylor instability evolution is carefully investigated.
Parallel implementation of the finite element method using compressed data structures
NASA Astrophysics Data System (ADS)
Ribeiro, F. L. B.; Ferreira, I. A.
2007-12-01
This paper presents a parallel implementation of the finite element method designed for coarse-grain distributed memory architectures. The MPI standard is used for message passing and tests are run on a PC cluster and on an SGI Altix 350. Compressed data structures are employed to store the coefficient matrix and obtain iterative solutions, based on Krylov methods, in a subdomain-by-subdomain approach. Two mesh partitioning schemes are compared: non-overlapping and overlapping. The pros and cons of these partitioning methods are discussed. Numerical examples of symmetric and non-symmetric problems in two and three dimensions are presented.
Permeability computation on a REV with an immersed finite element method
Laure, P.; Puaux, G.; Silva, L.; Vincent, M.
2011-05-04
An efficient method to compute permeability of fibrous media is presented. An immersed domain approach is used to represent the porous material at its microscopic scale and the flow motion is computed with a stabilized mixed finite element method. Therefore the Stokes equation is solved on the whole domain (including solid part) using a penalty method. The accuracy is controlled by refining the mesh around the solid-fluid interface defined by a level set function. Using homogenisation techniques, the permeability of a representative elementary volume (REV) is computed. The computed permeabilities of regular fibre packings are compared to classical analytical relations found in the bibliography.
Vibration band gaps for elastic metamaterial rods using wave finite element method
NASA Astrophysics Data System (ADS)
Nobrega, E. D.; Gautier, F.; Pelat, A.; Dos Santos, J. M. C.
2016-10-01
Band gaps in elastic metamaterial rods with spatial periodic distribution and periodically attached local resonators are investigated. New techniques to analyze metamaterial systems are using a combination of analytical or numerical method with wave propagation. One of them, called here wave spectral element method (WSEM), consists of combining the spectral element method (SEM) with Floquet-Bloch's theorem. A modern methodology called wave finite element method (WFEM), developed to calculate dynamic behavior in periodic acoustic and structural systems, utilizes a similar approach where SEM is substituted by the conventional finite element method (FEM). In this paper, it is proposed to use WFEM to calculate band gaps in elastic metamaterial rods with spatial periodic distribution and periodically attached local resonators of multi-degree-of-freedom (M-DOF). Simulated examples with band gaps generated by Bragg scattering and local resonators are calculated by WFEM and verified with WSEM, which is used as a reference method. Results are presented in the form of attenuation constant, vibration transmittance and frequency response function (FRF). For all cases, WFEM and WSEM results are in agreement, provided that the number of elements used in WFEM is sufficient to convergence. An experimental test was conducted with a real elastic metamaterial rod, manufactured with plastic in a 3D printer, without local resonance-type effect. The experimental results for the metamaterial rod with band gaps generated by Bragg scattering are compared with the simulated ones. Both numerical methods (WSEM and WFEM) can localize the band gap position and width very close to the experimental results. A hybrid approach combining WFEM with the commercial finite element software ANSYS is proposed to model complex metamaterial systems. Two examples illustrating its efficiency and accuracy to model an elastic metamaterial rod unit-cell using 1D simple rod element and 3D solid element are
Finite element method formulation in polar coordinates for transient heat conduction problems
NASA Astrophysics Data System (ADS)
Duda, Piotr
2016-04-01
The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method (FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.
Improved accuracy for finite element structural analysis via a new integrated force method
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Hopkins, Dale A.; Aiello, Robert A.; Berke, Laszlo
1992-01-01
A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.
Improved accuracy for finite element structural analysis via an integrated force method
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Hopkins, D. A.; Aiello, R. A.; Berke, L.
1992-01-01
A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.
A general algorithm using finite element method for aerodynamic configurations at low speeds
NASA Technical Reports Server (NTRS)
Balasubramanian, R.
1975-01-01
A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.
An Embedded Statistical Method for Coupling Molecular Dynamics and Finite Element Analyses
NASA Technical Reports Server (NTRS)
Saether, E.; Glaessgen, E.H.; Yamakov, V.
2008-01-01
The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.
Development and Application of the p-Version of the Finite Element Method.
1987-12-30
element method has been the subject of intensive study since the early 1950’s and perhaps even earlier. Study of the p-version of the finite element...method, on the other hand, began at *Washington University in St. Louis in the early 1970’s and led to a more recent study of the h-p version. Research...infinite strip to a bounded domain. 3.3 A Numerical Argument Principle In order to assure that all roots have indeed been obtained, we have studied the
A finite element beam propagation method for simulation of liquid crystal devices.
Vanbrabant, Pieter J M; Beeckman, Jeroen; Neyts, Kristiaan; James, Richard; Fernandez, F Anibal
2009-06-22
An efficient full-vectorial finite element beam propagation method is presented that uses higher order vector elements to calculate the wide angle propagation of an optical field through inhomogeneous, anisotropic optical materials such as liquid crystals. The full dielectric permittivity tensor is considered in solving Maxwell's equations. The wide applicability of the method is illustrated with different examples: the propagation of a laser beam in a uniaxial medium, the tunability of a directional coupler based on liquid crystals and the near-field diffraction of a plane wave in a structure containing micrometer scale variations in the transverse refractive index, similar to the pixels of a spatial light modulator.
A locking-free immersed finite element method for planar elasticity interface problems
NASA Astrophysics Data System (ADS)
Lin, Tao; Sheen, Dongwoo; Zhang, Xu
2013-08-01
This article proposes a nonconforming immersed finite element (IFE) method for solving planar elasticity interface problems with structured (or Cartesian) meshes even if the material interface has a nontrivial geometry. IFE functions developed in this article are applicable to arbitrary configurations of elasticity materials and interface locations. Optimal approximation capability is observed for this new IFE space. The displacement Galerkin method based on this IFE space is robust (locking-free). Numerical experiments are presented to demonstrate that the IFE solution converges optimally for both compressible and nearly incompressible materials.
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.
Application of the Finite Element Method in Atomic and Molecular Physics
NASA Technical Reports Server (NTRS)
Shertzer, Janine
2007-01-01
The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.
NASA Astrophysics Data System (ADS)
Chen, Jiefu
2015-03-01
A discontinuous Galerkin finite element method is employed to study the responses of microresistivity imaging tools used in the oil and gas exploration industry. The multiscale structure of an imaging problem is decomposed into several nested subdomains based on its geometric characteristics. Each subdomain is discretized independently, and numerical flux is used to couple all subdomains together. The nested domain decomposition scheme will lead to a block tridiagonal linear system, and the block Thomas algorithm is utilized here to eliminate the subdomain based iteration in the step of solving the linear system. Numerical results demonstrate the validity and efficiency of this method.
Finite-size scaling for quantum criticality using the finite-element method.
Antillon, Edwin; Wehefritz-Kaufmann, Birgit; Kais, Sabre
2012-03-01
Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite-element method was shown to be a powerful numerical method for ab initio electronic-structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite-element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, local density approximation, and an "exact" formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.
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.
NASA Astrophysics Data System (ADS)
Pieczynska-Kozlowska, Joanna
2014-05-01
One of a geotechnical problem in the area of Wroclaw is an anthropogenic embankment layer delaying to the depth of 4-5m, arising as a result of historical incidents. In such a case an assumption of bearing capacity of strip footing might be difficult. The standard solution is to use a deep foundation or foundation soil replacement. However both methods generate significant costs. In the present paper the authors focused their attention on the influence of anthropogenic embankment variability on bearing capacity. Soil parameters were defined on the basis of CPT test and modeled as 2D anisotropic random fields and the assumption of bearing capacity were made according deterministic finite element methods. Many repeated of the different realizations of random fields lead to stable expected value of bearing capacity. The algorithm used to estimate the bearing capacity of strip footing was the random finite element method (e.g. [1]). In traditional approach of bearing capacity the formula proposed by [2] is taken into account. qf = c'Nc + qNq + 0.5γBN- γ (1) where: qf is the ultimate bearing stress, cis the cohesion, qis the overburden load due to foundation embedment, γ is the soil unit weight, Bis the footing width, and Nc, Nq and Nγ are the bearing capacity factors. The method of evaluation the bearing capacity of strip footing based on finite element method incorporate five parameters: Young's modulus (E), Poisson's ratio (ν), dilation angle (ψ), cohesion (c), and friction angle (φ). In the present study E, ν and ψ are held constant while c and φ are randomized. Although the Young's modulus does not affect the bearing capacity it governs the initial elastic response of the soil. Plastic stress redistribution is accomplished using a viscoplastic algorithm merge with an elastic perfectly plastic (Mohr - Coulomb) failure criterion. In this paper a typical finite element mesh was assumed with 8-node elements consist in 50 columns and 20 rows. Footings width B
Simulation of nanoparticle transport in airways using Petrov-Galerkin finite element methods.
Rajaraman, Prathish; Heys, Jeffrey J
2014-01-01
The transport and deposition properties of nanoparticles with a range of aerodynamic diameters ( 1 nm ≤ d ≤ 150 nm) were studied for the human airways. A finite element code was developed that solved both the Navier-Stokes and advection-diffusion equations monolithically. When modeling nanoparticle transport in the airways, the finite element method becomes unstable, and, in order resolve this issue, various stabilization methods were considered in terms of accuracy and computational cost. The stabilization methods considered here include the streamline upwind, streamline upwind Petrov-Galerkin, and Galerkin least squares approaches. In order to compare the various stabilization approaches, the approximate solution from each stabilization approach was compared to the analytical Graetz solution, which is a model for monodispersed, dilute particle transport in a straight cylinder. The optimal stabilization method, especially with regard to accuracy, was found to be the Galerkin least squares approach for the Graetz problem when the Péclet number was larger than 10(4). In the human airways geometry, the Galerkin least squares stabilization approach once more provided the most accurate approximate solution for particles with an aerodynamic diameter of 10 nm or larger, but mesh size had a much greater effect on accuracy than the choice of stabilization method. The choice of stabilization method had a greater impact than mesh size for particles with an aerodynamic diameter 10 nm or smaller, but the most accurate stabilization method was streamline upwind Petrov-Galerkin in these cases.
On the accuracy of creep-damage predictions in thinwalled structures using the finite element method
NASA Astrophysics Data System (ADS)
Altenbach, H.; Kolarow, G.; Morachkovsky, O. K.; Naumenko, K.
The constitutive model with a single damage parameter describing creep-damage behaviour of metals with respect to the different sensitivity of the damage process due to tension and compression is incorporated into the ANSYS finite element code by modifying the user defined creep material subroutine. The procedure is verified by comparison with solutions for beams and rectangular plates in bending based on the Ritz method. Various numerical tests show the sensitivity of long-term predictions to the mesh sizes and element types available for the creep analysis of thinwalled structures.
The p and h-p Versions of the Finite Element Method; State of the Art.
1986-09-01
INSTITUTE FOp [m]Yci C Z... S’- -_ AND TECH-INOLOGY (11111:1;) ,. Technical Note BN-1156 (0 I . % I. ,,8’ .- *.° . ’ .4’ .- o%_ THE p AND h-p VERSIONS...OF THE FINITE ELEMENT METHOD. THE STATE OF THE ART -.. ; U.S.A. %%.Z - 4’ ° DTIC .21 R U-noW _STkl;,.CT.2,1986 I. Babu~ka €’ ",’- Institute ror... Institute for Physical Science and Technology AREAS WOrK UNT NUMBERS University of Maryland College Park, MD 20742 ii. CONTROLLING OFFICE NAME AND
Computational Aspects of the h, p and h-p Versions of the Finite Element Method.
1987-03-01
and T. Scapolla BN-1 061 March 1987 %" iqAppr,- - " . ..utr""o":" S Appr..: ’ ...... tor pilbhc j0 ,oe "IDI .. ,%~~~~1 %-... z u n Unliz~ited INSTITUTE ...PROGRAM ELEMENT. PROJECT. TASK AREA & WORK UNIT NUMIERS Institute for Physical Science and Technology University of Maryland College Park, MD 20742 it...the h, p and h-p versions of the finite element method Ivo Babulka 1" Institute for Physical Science and Technology University of Maryland, College
The Theory and Practice of the h-p Version of Finite Element Method.
1987-04-01
85-K-0169 I. Babuska and B. Guo NSF DMS-85-16191 9. PERFORMING ORGANIZATION NAME AND ADDRES 10. PROGRAM ELEMENT. PROJECT. TASK Institute for Physical...uitered) THE THEORY AND PRACTICE O THE h-p vERSION OF FINITE ElEMENT METHOD Ben Qi Guo* Ivo Babuska** Institute of Physical Science & Technology and...1Wr-194 ’The problem with none-hmogeneous Dirichlet problem is to find the finite element solution u. £ data was studied by Babuika, Guo.im- 4401 The h
Numerical simulation and design of a fluxset sensor by finite element method
Preis, K.; Bardi, I.; Biro, O.; Richter, K.R.; Pavo, J.; Gasparics, A.; Ticar, I.
1998-09-01
A 3D model of a fluxset sensor serving to measure magnetic fields arising in Eddy Current Nondestructive Testing applications is analyzed by the finite element method. The voltage induced in the pick-up coil is obtained by computing the flux of the core of the sensor for several values of the exciting current at various external fields. It is shown that the time shift of the ensuing voltage impulse depends linearly on the external field in a wide range. The behavior of the sensor is furthermore simulated in a real nondestructive testing arrangement consisting of an exciting coil located above a conducting plate with a crack.
Survey of the status of finite element methods for partial differential equations
NASA Technical Reports Server (NTRS)
Temam, Roger
1986-01-01
The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.
Domain decomposition for a mixed finite element method in three dimensions
Cai, Z.; Parashkevov, R.R.; Russell, T.F.; Wilson, J.D.; Ye, X.
2003-01-01
We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the reduction relies on a local basis, presented here, for the divergence-free subspace of the velocity space. We consider additive and multiplicative domain decomposition methods for solving the reduced elliptic problem, and their uniform convergence is established.
Electron-H2 Collisions Studied Using the Finite Element Z-Matrix Method
NASA Technical Reports Server (NTRS)
Huo, Winifred M.; Brown, David; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
We have applied the Z-matrix method, using a mixed basis of finite elements and Gaussians, to study e-H2 elastic and inelastic collisions. Special attention is paid to the quality of the basis set and the treatment of electron correlation. The calculated cross sections are invariant, to machine accuracy, with respect to the choice of parameters a, b, d, e as long as they satisfy Equation (3). However, the log derivative approach, i.e., the choice a = -e = 1, b = d = 0 appears to converge slightly faster than other choices. The cross sections agree well with previous theoretical results. Comparison will be made with available experimental data.
Study on interaction between induced and natural fractures by extended finite element method
NASA Astrophysics Data System (ADS)
Xu, DanDan; Liu, ZhanLi; Zhuang, Zhuo; Zeng, QingLei; Wang, Tao
2017-02-01
Fracking is one of the kernel technologies in the remarkable shale gas revolution. The extended finite element method is used in this paper to numerically investigate the interaction between hydraulic and natural fractures, which is an important issue of the enigmatic fracture network formation in fracking. The criteria which control the opening of natural fracture and crossing of hydraulic fracture are tentatively presented. Influence factors on the interaction process are systematically analyzed, which include the approach angle, anisotropy of in-situ stress and fluid pressure profile.
Ahmed, B.; Ahmad, J.; Guy, G.
1994-09-01
A finite elements method coupled with the Preisach model of hysteresis is used to compute-the ferrite losses in medium power transformers (10--60 kVA) working at relatively high frequencies (20--60 kHz) and with an excitation level of about 0.3 Tesla. The dynamic evolution of the permeability is taken into account. The simple and doubly cubic spline functions are used to account for temperature effects respectively on electric and on magnetic parameters of the ferrite cores. The results are compared with test data obtained with 3C8 and B50 ferrites at different frequencies.
Solving the Fokker-Planck equation with the finite-element method
Galán, Roberto F.; Ermentrout, G. Bard; Urban, Nathaniel N.
2008-01-01
We apply an efficient approach from computational engineering, the finite-element method, to numerically solve the Fokker-Planck equation in two dimensions. This approach permits us to find the solution to stochastic problems that cannot be solved analytically. We illustrate our strategy with an example from neuroscience that recently has attracted considerable attention - synchronization of neural oscillators. In particular, we show that resonators (type II neural oscillators) respond and synchronize more reliably when provided correlated stochastic inputs than do integrators (type I neural oscillators). This result is consistent with recent experimental and computational work. We briefly discuss its relevance for neuroscience. PMID:18233721
NASA Astrophysics Data System (ADS)
Felice, Maria V.; Velichko, Alexander; Wilcox, Paul D.; Barden, Tim J.; Dunhill, Tony K.
2014-02-01
A hybrid model to simulate the ultrasonic array response from stress corrosion cracks is presented. These cracks are branched and difficult to detect so the model is required to enable optimization of an array design. An efficient frequency-domain finite element method is described and selected to simulate the ultrasonic scattering. Experimental validation results are presented, followed by an example of the simulated ultrasonic array response from a real stress corrosion crack whose geometry is obtained from an X-ray Computed Tomography image. A simulation-assisted array design methodology, which includes the model and use of real crack geometries, is proposed.
Kozień, Marek S; Lorkowski, Jacek; Szczurek, Sławomir; Hładki, Waldemar; Trybus, Marek
2008-01-01
The aim of this study was to construct a computed simulation of an isolated lesion of tibiofibular syndesmosis on typical clinical range of value. The analysis was made using the method of finite elements with a simplified plain model of a bone and assuming material of bone and ankle joint as isotropic and homogeneous. The distraction processes were modelled by external generalized forces. The computed programme ANSYS was used. For evaluation obtained was the computed image of changes of anatomy in relation to forces.
Finite element method calculations of ZnO nanowires for nanogenerators
NASA Astrophysics Data System (ADS)
Schubert, M. A.; Senz, S.; Alexe, M.; Hesse, D.; Gösele, U.
2008-03-01
The bending of a nonconducting piezoelectric ZnO nanowire is simulated by finite element method calculations. The top part is bent by a lateral force, which could be applied by an atomic force microscope tip. The generated electrical potential is ±0.3V. This relatively high signal is, however, difficult to measure due to the low capacitance of the ZnO nanowire (˜4×10-5pF) as compared to the capacitance of most preamplifiers (˜5pF). A further problem arises from the semiconducting properties of experimentally fabricated ZnO nanowires which causes the disappearance of the voltage signal within picoseconds.
Finite elements and the method of conjugate gradients on a concurrent processor
NASA Technical Reports Server (NTRS)
Lyzenga, G. A.; Raefsky, A.; Hager, B. H.
1984-01-01
An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90% for sufficiently large problems.
Effects of welding technology on welding stress based on the finite element method
NASA Astrophysics Data System (ADS)
Fu, Jianke; Jin, Jun
2017-01-01
Finite element method is used to simulate the welding process under four different conditions of welding flat butt joints. Welding seams are simulated with birth and death elements. The size and distribution of welding residual stress is obtained in the four kinds of welding conditions by Q345 manganese steel plate butt joint of the work piece. The results shown that when using two-layers welding,the longitudinal and transverse residual stress were reduced;When welding from Middle to both sides,the residual stress distribution will change,and the residual stress in the middle of the work piece was reduced.
Simulation of viscous flows using a multigrid-control volume finite element method
Hookey, N.A.
1994-12-31
This paper discusses a multigrid control volume finite element method (MG CVFEM) for the simulation of viscous fluid flows. The CVFEM is an equal-order primitive variables formulation that avoids spurious solution fields by incorporating an appropriate pressure gradient in the velocity interpolation functions. The resulting set of discretized equations is solved using a coupled equation line solver (CELS) that solves the discretized momentum and continuity equations simultaneously along lines in the calculation domain. The CVFEM has been implemented in the context of both FMV- and V-cycle multigrid algorithms, and preliminary results indicate a five to ten fold reduction in execution times.
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.
Felice, Maria V.; Velichko, Alexander; Wilcox, Paul D.; Barden, Tim J.; Dunhill, Tony K.
2014-02-18
A hybrid model to simulate the ultrasonic array response from stress corrosion cracks is presented. These cracks are branched and difficult to detect so the model is required to enable optimization of an array design. An efficient frequency-domain finite element method is described and selected to simulate the ultrasonic scattering. Experimental validation results are presented, followed by an example of the simulated ultrasonic array response from a real stress corrosion crack whose geometry is obtained from an X-ray Computed Tomography image. A simulation-assisted array design methodology, which includes the model and use of real crack geometries, is proposed.
Method and apparatus for connecting finite element meshes and performing simulations therewith
Dohrmann, Clark R.; Key, Samuel W.; Heinstein, Martin W.
2003-05-06
The present invention provides a method of connecting dissimilar finite element meshes. A first mesh, designated the master mesh, and a second mesh, designated the slave mesh, each have interface surfaces proximal the other. Each interface surface has a corresponding interface mesh comprising a plurality of interface nodes. Each slave interface node is assigned new coordinates locating the interface node on the interface surface of the master mesh. The slave interface surface is further redefined to be the projection of the slave interface mesh onto the master interface surface.
Numerical study of human vocal folds vibration using Immersed Finite Element Method
NASA Astrophysics Data System (ADS)
Wang, Xingshi; Zhang, Lucy; Krane, Michael
2011-11-01
The voice production procedure is a self-oscillating, fluid-structure interaction problem. In this study, the vocal folds vibration during phonation will be simulated by self-oscillated layered-structure vocal folds model, using Immersed Finite Element Method. With the numerical results, we will find out the vocal folds vibration pattern, and also show how the lung pressure, stiffness and geometry of vocal folds will affect the vocal folds vibration. With further analysis, we shall get better understanding of the dynamics of voice production. National Institute on Deafness and Other Communication Disorders.
A blended continuous-discontinuous finite element method for solving the multi-fluid plasma model
NASA Astrophysics Data System (ADS)
Sousa, E. M.; Shumlak, U.
2016-12-01
The multi-fluid plasma model represents electrons, multiple ion species, and multiple neutral species as separate fluids that interact through short-range collisions and long-range electromagnetic fields. The model spans a large range of temporal and spatial scales, which renders the model stiff and presents numerical challenges. To address the large range of timescales, a blended continuous and discontinuous Galerkin method is proposed, where the massive ion and neutral species are modeled using an explicit discontinuous Galerkin method while the electrons and electromagnetic fields are modeled using an implicit continuous Galerkin method. This approach is able to capture large-gradient ion and neutral physics like shock formation, while resolving high-frequency electron dynamics in a computationally efficient manner. The details of the Blended Finite Element Method (BFEM) are presented. The numerical method is benchmarked for accuracy and tested using two-fluid one-dimensional soliton problem and electromagnetic shock problem. The results are compared to conventional finite volume and finite element methods, and demonstrate that the BFEM is particularly effective in resolving physics in stiff problems involving realistic physical parameters, including realistic electron mass and speed of light. The benefit is illustrated by computing a three-fluid plasma application that demonstrates species separation in multi-component plasmas.
Finite Element Method (FEM), Mechanobiology and Biomimetic Scaffolds in Bone Tissue Engineering
Boccaccio, A.; Ballini, A.; Pappalettere, C.; Tullo, D.; Cantore, S.; Desiate, A.
2011-01-01
Techniques of bone reconstructive surgery are largely based on conventional, non-cell-based therapies that rely on the use of durable materials from outside the patient's body. In contrast to conventional materials, bone tissue engineering is an interdisciplinary field that applies the principles of engineering and life sciences towards the development of biological substitutes that restore, maintain, or improve bone tissue function. Bone tissue engineering has led to great expectations for clinical surgery or various diseases that cannot be solved with traditional devices. For example, critical-sized defects in bone, whether induced by primary tumor resection, trauma, or selective surgery have in many cases presented insurmountable challenges to the current gold standard treatment for bone repair. The primary purpose of bone tissue engineering is to apply engineering principles to incite and promote the natural healing process of bone which does not occur in critical-sized defects. The total market for bone tissue regeneration and repair was valued at $1.1 billion in 2007 and is projected to increase to nearly $1.6 billion by 2014. Usually, temporary biomimetic scaffolds are utilized for accommodating cell growth and bone tissue genesis. The scaffold has to promote biological processes such as the production of extra-cellular matrix and vascularisation, furthermore the scaffold has to withstand the mechanical loads acting on it and to transfer them to the natural tissues located in the vicinity. The design of a scaffold for the guided regeneration of a bony tissue requires a multidisciplinary approach. Finite element method and mechanobiology can be used in an integrated approach to find the optimal parameters governing bone scaffold performance. In this paper, a review of the studies that through a combined use of finite element method and mechano-regulation algorithms described the possible patterns of tissue differentiation in biomimetic scaffolds for bone
Kılıç, Emre Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
NASA Technical Reports Server (NTRS)
Chen, T.; Raju, I. S.
2002-01-01
A coupled finite element (FE) method and meshless local Petrov-Galerkin (MLPG) method for analyzing two-dimensional potential problems is presented in this paper. The analysis domain is subdivided into two regions, a finite element (FE) region and a meshless (MM) region. A single weighted residual form is written for the entire domain. Independent trial and test functions are assumed in the FE and MM regions. A transition region is created between the two regions. The transition region blends the trial and test functions of the FE and MM regions. The trial function blending is achieved using a technique similar to the 'Coons patch' method that is widely used in computer-aided geometric design. The test function blending is achieved by using either FE or MM test functions on the nodes in the transition element. The technique was evaluated by applying the coupled method to two potential problems governed by the Poisson equation. The coupled method passed all the patch test problems and gave accurate solutions for the problems studied.
Rajaraman, Prathish K; Manteuffel, T A; Belohlavek, M; Heys, Jeffrey J
2017-01-01
A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier-Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier-Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation. Copyright © 2016 John Wiley & Sons, Ltd.
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.
Thermoelastic analysis of multiple defects with the extended finite element method
NASA Astrophysics Data System (ADS)
Jia, Honggang; Nie, Yufeng
2016-12-01
In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or microscopic defects under thermal/mechanical load. The effects of different shapes of multiple inclusions on the material thermomechanical response are investigated, and the level set method is coupled with XFEM to analyze the interaction of multiple defects. Further, the discretized extended finite element approximations in relation to thermoelastic problems of multiple defects under displacement or temperature field are given. Also, the interfaces of cracks or materials are represented by level set functions, which allow the mesh assignment not to conform to crack or material interfaces. Moreover, stress intensity factors of cracks are obtained by the interaction integral method or the M-integral method, and the stress/strain/stiffness fields are simulated in the case of multiple cracks or multiple inclusions. Finally, some numerical examples are provided to demonstrate the accuracy of our proposed method.
Fracture Capabilities in Grizzly with the extended Finite Element Method (X-FEM)
Dolbow, John; Zhang, Ziyu; Spencer, Benjamin; Jiang, Wen
2015-09-01
Efforts are underway to develop fracture mechanics capabilities in the Grizzly code to enable it to be used to perform deterministic fracture assessments of degraded reactor pressure vessels (RPVs). A capability was previously developed to calculate three-dimensional interaction- integrals to extract mixed-mode stress-intensity factors. This capability requires the use of a finite element mesh that conforms to the crack geometry. The eXtended Finite Element Method (X-FEM) provides a means to represent a crack geometry without explicitly fitting the finite element mesh to it. This is effected by enhancing the element kinematics to represent jump discontinuities at arbitrary locations inside of the element, as well as the incorporation of asymptotic near-tip fields to better capture crack singularities. In this work, use of only the discontinuous enrichment functions was examined to see how accurate stress intensity factors could still be calculated. This report documents the following work to enhance Grizzly’s engineering fracture capabilities by introducing arbitrary jump discontinuities for prescribed crack geometries; X-FEM Mesh Cutting in 3D: to enhance the kinematics of elements that are intersected by arbitrary crack geometries, a mesh cutting algorithm was implemented in Grizzly. The algorithm introduces new virtual nodes and creates partial elements, and then creates a new mesh connectivity; Interaction Integral Modifications: the existing code for evaluating the interaction integral in Grizzly was based on the assumption of a mesh that was fitted to the crack geometry. Modifications were made to allow for the possibility of a crack front that passes arbitrarily through the mesh; and Benchmarking for 3D Fracture: the new capabilities were benchmarked against mixed-mode three-dimensional fracture problems with known analytical solutions.
NASA Astrophysics Data System (ADS)
Kim, D.-J.; Duarte, C. A.; Proenca, S. P.
2012-11-01
The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J 2 plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.
Miller, K; Horton, A; Joldes, G R; Wittek, A
2012-10-11
To be useful in clinical (surgical) simulations, a method must use fully nonlinear (both geometric and material) formulations to deal with large (finite) deformations of tissues. The method must produce meaningful results in a short time on consumer hardware and not require significant manual work while discretizing the problem domain. In this paper, we showcase the Meshless Total Lagrangian Explicit Dynamics Method (MTLED) which meets these requirements, and use it for computing brain deformations during surgery. The problem geometry is based on patient-specific MRI data and includes the parenchyma, tumor, ventricles and skull. Nodes are distributed automatically through the domain rendering the normally difficult problem of creating a patient-specific computational grid a trivial exercise. Integration is performed over a simple, regular background grid which does not need to conform to the geometry boundaries. Appropriate nonlinear material formulation is used. Loading is performed by displacing the parenchyma surface nodes near the craniotomy and a finite frictionless sliding contact is enforced between the skull (rigid) and parenchyma. The meshless simulation results are compared to both intraoperative MRIs and Finite Element Analysis results for multiple 2D sections. We also calculate Hausdorff distances between the computed deformed surfaces of the ventricles and those observed intraoperatively. The difference between previously validated Finite Element results and the meshless results presented here is less than 0.2mm. The results are within the limits of neurosurgical and imaging equipment accuracy (~1 mm) and demonstrate the method's ability to fulfill all of the important requirements for surgical simulation.
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.
NASA Astrophysics Data System (ADS)
Kingan, Michael J.; Yang, Yi; Mace, Brian R.
2016-09-01
This paper concerns the prediction of sound transmission through a cylindrical structure. The problem considered is that of sound generated by a line source located exterior to a two-dimensional circular cylinder which produces sound waves which transmit through the cylinder to an internal medium. An analytical solution is presented for the case of sound transmission through a thin cylindrical shell, by modelling the shell response using the Flugge- Byrne-Lur'ye equations. This solution is then compared to calculations where the response of the cylinder is calculated using the Wave and Finite Element (WFE) method. The WFE method involves modelling a small segment of a structure using traditional finite element (FE) methods. The mass and stiffness matrices of the segment are then used to calculate the response of the structure to excitation by an acoustic field. The WFE approach for calculating sound transmission is validated by comparison with the analytic solution. Formulating analytic solutions for more complicated structures can be cumbersome whereas using a numerical technique, such as the WFE method, is relatively straightforward.
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.
Use of the finite-element method for a dielectric-constant gas-thermometry experiment
NASA Astrophysics Data System (ADS)
Zandt, T.; Gaiser, C.; Fellmuth, B.; Haft, N.; Thiele-Krivoi, B.; Kuhn, A.
2013-09-01
The finite-element method is a well-established computational methodology for the numerical treatment of partial differential equations. It is primarily used for solving problems in applied engineering and science. In previous publications, we have shown that the method is suitable to solve problems in temperature metrology, for instance to predict temperature profiles and thermal equilibration processes in complex measurement setups. In this paper, the method is used for a primary thermometry experiment, namely dielectric-constant gas thermometry. Within the framework of an international project directed to the new definition of the base unit kelvin, measurements were performed at the triple point of water in order to determine the Boltzmann constant k. The finite-element method was used for the data evaluation in different ways: calculation of the effective compressibility of the measuring capacitor by describing the deformation of its electrodes under the influence of the pressure of the gas, the dielectric constant of which has to be determined; calculation of resonance frequencies for the determination of the elastic constants of the electrode material by resonant ultrasound spectroscopy; electrostatic simulations for calculating capacitance values; estimation of uncertainty components, which allowed to draw conclusions concerning the future reduction of uncertainty components.
Modelling of tunnelling processes and rock cutting tool wear with the particle finite element method
NASA Astrophysics Data System (ADS)
Carbonell, Josep Maria; Oñate, Eugenio; Suárez, Benjamín
2013-09-01
Underground construction involves all sort of challenges in analysis, design, project and execution phases. The dimension of tunnels and their structural requirements are growing, and so safety and security demands do. New engineering tools are needed to perform a safer planning and design. This work presents the advances in the particle finite element method (PFEM) for the modelling and the analysis of tunneling processes including the wear of the cutting tools. The PFEM has its foundation on the Lagrangian description of the motion of a continuum built from a set of particles with known physical properties. The method uses a remeshing process combined with the alpha-shape technique to detect the contacting surfaces and a finite element method for the mechanical computations. A contact procedure has been developed for the PFEM which is combined with a constitutive model for predicting the excavation front and the wear of cutting tools. The material parameters govern the coupling of frictional contact and wear between the interacting domains at the excavation front. The PFEM allows predicting several parameters which are relevant for estimating the performance of a tunnelling boring machine such as wear in the cutting tools, the pressure distribution on the face of the boring machine and the vibrations produced in the machinery and the adjacent soil/rock. The final aim is to help in the design of the excavating tools and in the planning of the tunnelling operations. The applications presented show that the PFEM is a promising technique for the analysis of tunnelling problems.
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.
NASA Astrophysics Data System (ADS)
Blanloeuil, P.; Meziane, A.
2015-10-01
The non-collinear mixing technique is applied for detection and characterization of closed cracks. The method is based on the nonlinear interaction of two shear waves generated with an oblique incidence. This interaction leads to the scattering of a longitudinal wave. A Finite Element model is used to demonstrate its application to a closed crack. Contact acoustic nonlinearity is the nonlinear effect considered here and is modeled using unilateral contact law with Coulomb's friction. Directivity patterns are computed using a two-step procedure. The Finite Element (FE) model provides the near-field solution on a circular boundary surrounding the closed crack. The solution in the far-field is then determined assuming that the material has a linear behavior. Directivity patterns will be used to analyze the direction of propagation of longitudinal wave(s) scattered from the closed crack. Numerical results show that the method is effective and promising when applied to a closed crack. Scattering of the longitudinal wave also enables us to image the crack, giving position and size indications. Finally, the method offers the possibility to distinguish classical nonlinearity from contact acoustic nonlinearity.
Crack modeling of rotating blades with cracked hexahedral finite element method
NASA Astrophysics Data System (ADS)
Liu, Chao; Jiang, Dongxiang
2014-06-01
Dynamic analysis is the basis in investigating vibration features of cracked blades, where the features can be applied to monitor health state of blades, detect cracks in an early stage and prevent failures. This work presents a cracked hexahedral finite element method for dynamic analysis of cracked blades, with the purpose of addressing the contradiction between accuracy and efficiency in crack modeling of blades in rotor system. The cracked hexahedral element is first derived with strain energy release rate method, where correction of stress intensity factors of crack front and formulation of load distribution of crack surface are carried out to improve the modeling accuracy. To consider nonlinear characteristics of time-varying opening and closure effects caused by alternating loads, breathing function is proposed for the cracked hexahedral element. Second, finite element method with contact element is analyzed and used for comparison. Finally, validation of the cracked hexahedral element is carried out in terms of breathing effects of cracked blades and natural frequency in different crack depths. Good consistency is acquired between the results with developed cracked hexahedral element and contact element, while the computation time is significantly reduced in the previous one. Therefore, the developed cracked hexahedral element achieves good accuracy and high efficiency in crack modeling of rotating blades.
Description of plastic anisotropy in AA6063-T6 using the crystal plasticity finite element method
NASA Astrophysics Data System (ADS)
Dumoulin, S.; Engler, O.; Hopperstad, O. S.; Lademo, O. G.
2012-07-01
The crystal plasticity finite element method has been used in combination with crystallographic texture data to predict the plastic anisotropy of the extruded aluminium alloy AA6063 in temper T6. The results are compared with experimental data from tensile tests at different angles between the tensile and extrusion directions. Inverse modelling based on the tensile test in a reference direction is used to identify the parameters of the work-hardening model at slip system level. To investigate the influence of grain interactions, various discretizations of the grains are applied in the representative volume element modelled with finite elements. In addition, alternative homogenization schemes, such as the full-constraint Taylor and viscoplastic self-consistent methods, are used to model the behaviour of the polycrystal. It is found that the grain discretization and the homogenization scheme have only minor influence on the predicted plastic anisotropy. While the crystal plasticity-based methods all give reasonable predictions of the directional variations of flow stresses and plastic strain ratios measured experimentally, there are still significant deviations, indicating there are other sources to the plastic anisotropy than crystallographic texture.
Modeling the mechanics of axonal fiber tracts using the embedded finite element method.
Garimella, Harsha T; Kraft, Reuben H
2016-08-08
A subject-specific human head finite element model with embedded axonal fiber tractography obtained from diffusion tensor imaging was developed. The axonal fiber tractography finite element model was coupled with the volumetric elements in the head model using the embedded element method. This technique enables the calculation of axonal strains and real-time tracking of the mechanical response of the axonal fiber tracts. The coupled model was then verified using pressure and relative displacement-based (between skull and brain) experimental studies and was employed to analyze a head impact, demonstrating the applicability of this method in studying axonal injury. Following this, a comparison study of different injury criteria was performed. This model was used to determine the influence of impact direction on the extent of the axonal injury. The results suggested that the lateral impact loading is more dangerous compared to loading in the sagittal plane, a finding in agreement with previous studies. Through this analysis, we demonstrated the viability of the embedded element method as an alternative numerical approach for studying axonal injury in patient-specific human head models.
Wave motion analysis in arch structures via wavelet finite element method
NASA Astrophysics Data System (ADS)
Yang, Zhibo; Chen, Xuefeng; Li, Xiang; Jiang, Yongying; Miao, Huihui; He, Zhengjia
2014-01-01
The application of B-spline wavelet on interval (BSWI) finite element method for wave motion analysis in arch structures is presented in this paper. Instead of traditional polynomial interpolation, scaling functions at certain scales have been adopted to form the shape functions and construct wavelet-based elements. Different from other wavelet numerical methods adding wavelets directly, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix. The energy functional of the arch is obtained by the generalized shell theory, and the finite element model for wave motion analysis is constructed according to Hamilton's principle and the central difference method in time domain. Taking the practical application into account, damaged arch waveguides are also investigated. Proper analysis of the responses from structure damages allows one to indicate the location very precisely. This paper mainly focuses on the crack in structures. Based on Castigliano's theorem and the Pairs equation, the local flexibility of crack is formulated for BSWI element. Numerical experiments are performed to study the effect of wave propagations in arch waveguides, that is, frequency dispersion and mode spilt in the arch. The responses of the arch with cracks are simulated under the broad-band, narrow-band and chirp excitations. In order to estimate the spatial, time and frequency concentrations of responses, the reciprocal length, time-frequency transform and correlation coefficient are introduced in this investigation.
Taylor, G.; Dong, C.; Sun, S.
2010-03-18
A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods, i.e. mixed finite element (MFE) and the finite volume methods. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocities field for both the fractures and matrix which are crucial to the convection part of the transport equation. The finite volume method and the standard MFE method are used to approximate the convection and dispersion terms respectively. The model is used to investigate the interaction of adsorption with transport and to extract information on effective adsorption distribution coefficients. Numerical examples in different fractured media illustrate the robustness and efficiency of the proposed numerical model.
2013-01-01
Background The resistance of the bone against damage by repairing itself and adapting to environmental conditions is its most important property. These adaptive changes are regulated by physiological process commonly called the bone remodeling. Better understanding this process requires that we apply the theory of elastic-damage under the hypothesis of small displacements to a bone structure and see its mechanical behavior. Results The purpose of the present study is to simulate a two dimensional model of a proximal femur by taking into consideration elastic-damage and mechanical stimulus. Here, we present a mathematical model based on a system of nonlinear ordinary differential equations and we develop the variational formulation for the mechanical problem. Then, we implement our mathematical model into the finite element method algorithm to investigate the effect of the damage. Conclusion The results are consistent with the existing literature which shows that the bone stiffness drops in damaged bone structure under mechanical loading. PMID:23663260
NASA Technical Reports Server (NTRS)
Nakazawa, Shohei
1989-01-01
The internal structure is discussed of the MHOST finite element program designed for 3-D inelastic analysis of gas turbine hot section components. The computer code is the first implementation of the mixed iterative solution strategy for improved efficiency and accuracy over the conventional finite element method. The control structure of the program is covered along with the data storage scheme and the memory allocation procedure and the file handling facilities including the read and/or write sequences.
NASA Technical Reports Server (NTRS)
Gong, Jian; Volakis, John L.; Nurnberger, Michael W.
1995-01-01
This semi-annual report describes progress up to mid-January 1995. The report contains five sections all dealing with the modeling of spiral and patch antennas recessed in metallic platforms. Of significance is the development of decomposition schemes which separate the different regions of the antenna volume. Substantial effort was devoted to improving the feed model in the context of the finite element method (FEM). Finally, an innovative scheme for truncating finite element meshes is presented.
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
Stability analysis of flexible wind turbine blades using finite element method
NASA Technical Reports Server (NTRS)
Kamoulakos, A.
1982-01-01
Static vibration and flutter analysis of a straight elastic axis blade was performed based on a finite element method solution. The total potential energy functional was formulated according to linear beam theory. The inertia and aerodynamic loads were formulated according to the blade absolute acceleration and absolute velocity vectors. In vibration analysis, the direction of motion of the blade during the first out-of-lane and first in-plane modes was examined; numerical results involve NASA/DOE Mod-0, McCauley propeller, north wind turbine and flat plate behavior. In flutter analysis, comparison cases were examined involving several references. Vibration analysis of a nonstraight elastic axis blade based on a finite element method solution was performed in a similar manner with the straight elastic axis blade, since it was recognized that a curved blade can be approximated by an assembly of a sufficient number of straight blade elements at different inclinations with respect to common system of axes. Numerical results involve comparison between the behavior of a straight and a curved cantilever beam during the lowest two in-plane and out-of-plane modes.
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Berke, Laszlo; Gallagher, Richard H.
1991-01-01
The equilibrium equations and the compatibility conditions are fundamental to the analyses of structures. However, anyone who undertakes even a cursory generic study of the compatibility conditions can discover, with little effort, that historically this facet of structural mechanics had not been adequately researched by the profession. Now the compatibility conditions (CC's) have been researched and are understood to a great extent. For finite element discretizations, the CC's are banded and can be divided into three distinct categories: (1) the interface CC's, (2) the cluster or field CC's, and (3) the external CC's. The generation of CC's requires the separating of a local region, then writing the deformation displacement relation (ddr) for the region, and finally, the eliminating of the displacements from the ddr. The procedure to generate all three types of CC's is presented and illustrated through examples of finite element models. The uniqueness of the CC's thus generated is shown. The utilization of CC's has resulted in the novel integrated force method (IFM). The solution that is obtained by the IFM converges with a significantly fewer number of elements, compared to the stiffness and the hybrid methods.
Kilinç, Yeliz; Erkmen, Erkan; Kurt, Ahmet
2016-01-01
The aim of the current study was to comparatively evaluate the mechanical behavior of 3 different fixation methods following various amounts of superior repositioning of mandibular anterior segment. In this study, 3 different rigid fixation configurations comprising double right L, double left L, or double I miniplates with monocortical screws were compared under vertical, horizontal, and oblique load conditions by means of finite element analysis. A three-dimensional finite element model of a fully dentate mandible was generated. A 3 and 5 mm superior repositioning of mandibular anterior segmental osteotomy were simulated. Three different finite element models corresponding to different fixation configurations were created for each superior repositioning. The von Mises stress values on fixation appliances and principal maximum stresses (Pmax) on bony structures were predicted by finite element analysis. The results have demonstrated that double right L configuration provides better stability with less stress fields in comparison with other fixation configurations used in this study.
NASA Astrophysics Data System (ADS)
Resapu, Rajeswara Reddy
The most common approaches to determining mechanical material properties of materials are tension and compression tests. However, tension and compression testing cannot be implemented under certain loading conditions (immovable object, not enough space to hold object for testing, etc). Similarly, tensile and compression testing cannot be performed on certain types of materials (delicate, bulk, non-machinable, those that cannot be separated from a larger structure, etc). For such cases, other material testing methods need to be implemented. Indentation testing is one such method; this approach is often non-destructive and can be used to characterize regions that are not compatible with other testing methods. However, indentation testing typically leads to force-displacement data as opposed to the direct stress-strain data normally used for the mechanical characterization of materials; this data needs to be analyzed using a suitable approach to determine the associated material properties. As such, methods to establish material properties from force-displacement indentation data need to be identified. In this work, a finite element approach using parameter optimization is developed to determine the mechanical properties from the experimental indentation data. Polymers and tissues tend to have time-dependent mechanical behavior; this means that their mechanical response under load changes with time. This dissertation seeks to characterize the properties of these materials using indentation testing under the assumption that they are linear viscoelastic. An example of a material of interest is the polymer poly vinyl chloride (PVC) that is used as the insulation of some aircraft wiring. Changes in the mechanical properties of this material over years of service can indicate degradation and a potential hazard to continued use. To investigate the validity of using indentation testing to monitor polymer insulation degradation, PVC film and PVC-insulated aircraft wiring are
Ernest Valeo, Jay R. Johnson, Eun-Hwa and Cynthia Phillips
2012-03-13
A wide variety of plasma waves play an important role in the energization and loss of particles in the inner magnetosphere. Our ability to understand and model wave-particle interactions in this region requires improved knowledge of the spatial distribution and properties of these waves as well as improved understanding of how the waves depend on changes in solar wind forcing and/or geomagnetic activity. To this end, we have developed a two-dimensional, finite element code that solves the full wave equations in global magnetospheric geometry. The code describes three-dimensional wave structure including mode conversion when ULF, EMIC, and whistler waves are launched in a two-dimensional axisymmetric background plasma with general magnetic field topology. We illustrate the capabilities of the code by examining the role of plasmaspheric plumes on magnetosonic wave propagation; mode conversion at the ion-ion and Alfven resonances resulting from external, solar wind compressions; and wave structure and mode conversion of electromagnetic ion cyclotron waves launched in the equatorial magnetosphere, which propagate along the magnetic field lines toward the ionosphere. We also discuss advantages of the finite element method for resolving resonant structures, and how the model may be adapted to include nonlocal kinetic effects.
Numerical simulation of a flow-like landslide using the particle finite element method
NASA Astrophysics Data System (ADS)
Zhang, Xue; Krabbenhoft, Kristian; Sheng, Daichao; Li, Weichao
2015-01-01
In this paper, an actual landslide process that occurred in Southern China is simulated by a continuum approach, the particle finite element method (PFEM). The PFEM attempts to solve the boundary-value problems in the framework of solid mechanics, satisfying the governing equations including momentum conservation, displacement-strain relation, constitutive relation as well as the frictional contact between the sliding mass and the slip surface. To warrant the convergence behaviour of solutions, the problem is formulated as a mathematical programming problem, while the particle finite element procedure is employed to tackle the issues of mesh distortion and free-surface evolution. The whole procedure of the landslide, from initiation, sliding to deposition, is successfully reproduced by the continuum approach. It is shown that the density of the mass has little influence on the sliding process in the current landslide, whereas both the geometry and the roughness of the slip surface play important roles. Comparative studies are also conducted where a satisfactory agreement is obtained.
Bochev, Pavel Blagoveston
2011-06-01
We develop a new formulation of the Control Volume Finite Element Method (CVFEM) with a multidimensional Scharfetter-Gummel (SG) upwinding for the drift-diffusion equations. The formulation uses standard nodal elements for the concentrations and expands the flux in terms of the lowest-order Nedelec H(curl; {Omega})-compatible finite element basis. The SG formula is applied to the edges of the elements to express the Nedelec element degree of freedom on this edge in terms of the nodal degrees of freedom associated with the endpoints of the edge. The resulting upwind flux incorporates the upwind effects from all edges and is defined at the interior of the element. This allows for accurate evaluation of integrals on the boundaries of the control volumes for arbitrary quadrilateral elements. The new formulation admits efficient implementation through a standard loop over the elements in the mesh followed by loops over the element nodes (associated with control volume fractions in the element) and element edges (associated with flux degrees of freedom). The quantities required for the SG formula can be precomputed and stored for each edge in the mesh for additional efficiency gains. For clarity the details are presented for two-dimensional quadrilateral grids. Extension to other element shapes and three dimensions is straightforward.
Siauve, N; Nicolas, L; Vollaire, C; Marchal, C
2004-12-01
This article describes an optimization process specially designed for local and regional hyperthermia in order to achieve the desired specific absorption rate in the patient. It is based on a genetic algorithm coupled to a finite element formulation. The optimization method is applied to real human organs meshes assembled from computerized tomography scans. A 3D finite element formulation is used to calculate the electromagnetic field in the patient, achieved by radiofrequency or microwave sources. Space discretization is performed using incomplete first order edge elements. The sparse complex symmetric matrix equation is solved using a conjugate gradient solver with potential projection pre-conditionning. The formulation is validated by comparison of calculated specific absorption rate distributions in a phantom to temperature measurements. A genetic algorithm is used to optimize the specific absorption rate distribution to predict the phases and amplitudes of the sources leading to the best focalization. The objective function is defined as the specific absorption rate ratio in the tumour and healthy tissues. Several constraints, regarding the specific absorption rate in tumour and the total power in the patient, may be prescribed. Results obtained with two types of applicators (waveguides and annular phased array) are presented and show the faculties of the developed optimization process.
An inverse finite element method for determining the anisotropic properties of the cornea.
Nguyen, T D; Boyce, B L
2011-06-01
An inverse finite element method was developed to determine the anisotropic properties of bovine cornea from an in vitro inflation experiment. The experiment used digital image correlation (DIC) to measure the three-dimensional surface geometry and displacement field of the cornea at multiple pressures. A finite element model of a bovine cornea was developed using the DIC measured surface geometry of the undeformed specimen. The model was applied to determine five parameters of an anisotropic hyperelastic model that minimized the error between the measured and computed surface displacement field and to investigate the sensitivity of the measured bovine inflation response to variations in the anisotropic properties of the cornea. The results of the parameter optimization revealed that the collagen structure of bovine cornea exhibited a high degree of anisotropy in the limbus region, which agreed with recent histological findings, and a transversely isotropic central region. The parameter study showed that the bovine corneal response to the inflation experiment was sensitive to the shear modulus of the matrix at pressures below the intraocular pressure, the properties of the collagen lamella at higher pressures, and the degree of anisotropy in the limbus region. It was not sensitive to a weak collagen anisotropy in the central region.
Numerical simulation of pressure therapy glove by using Finite Element Method.
Yu, Annie; Yick, Kit Lun; Ng, Sun Pui; Yip, Joanne; Chan, Ying Fan
2016-02-01
Pressure therapy garments apply pressure to suppress the growth and flatten hypertrophic scars caused by serious burns. The amount of pressure given by the pressure garments is critical to the treatment adherence and outcomes. In the present study, a biomechanical model for simulating the pressure magnitudes and distribution over hand dorsum given by a pressure glove was developed by using finite element method. In this model, the shape geometry of the hand, the mechanical properties of the glove and human body tissues were incorporated in the numerical stress analyses. The geometry of the hand was obtained by a 3D laser scanner. The material properties of two warp knitted fabrics were considered in the glove fabric model that developed from the glove production pattern with 10% size reduction in circumferential dimensions. The glove was regarded an isotropic elastic shell and the hand was assumed to be a homogeneous, isotropic and linearly elastic body. A glove wearing process was carried in the finite element analysis and the surface-to-surface contact pressure between hand and glove fabric was hence obtained. Through validation, the simulated contact pressure showed a good agreement with the experimental interface pressure measurement. The simulation model can be used to predict and visualise the pressure distribution exerted by a pressure therapy glove onto hand dorsum. It can provide information for optimising the material mechanical properties in pressure garment design and development, give a clue to understand the mechanisms of pressure action on hypertrophic scars and ultimately improve the medical functions of pressure garment.
Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation
Chen, Zhangxin; Cockburn, Bernardo; Jerome, Joseph W.; ...
1995-01-01
In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions. The method combines a standard mixed finite element method, used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing the performance of the new method are displayed, and the results compared with those obtained by using Essentially Nonoscillatory (ENO) finite difference schemes. Frommore » the perspective of device modeling, these methods are robust, since they are capable of encompassing broad parameter ranges, including those for which shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but we have tested them much more generally with considerable success.« less
Mohammadi, Hadi; Bahramian, Fereshteh; Wan, Wankei
2009-11-01
Modeling soft tissue using the finite element method is one of the most challenging areas in the field of biomechanical engineering. To date, many models have been developed to describe heart valve leaflet tissue mechanics, which are accurate to some extent. Nevertheless, there is no comprehensive method to modeling soft tissue mechanics, This is because (1) the degree of anisotropy in the heart valve leaflet changes layer by layer due to a variety of collagen fiber densities and orientations that cannot be taken into account in the model and also (2) a constitutive material model fully describing the mechanical properties of the leaflet structure is not available in the literature. In this framework, we develop a new high-order element using p-type finite element formulation to create anisotropic material properties similar to those of the heart valve leaflet tissue in only one single element. This element also takes the nonlinearity of the leaflet tissue into consideration using a bilinear material model. This new element is composed a two-dimensional finite element in the principal directions of leaflet tissue and a p-type finite element in the direction of thickness. The proposed element is easy to implement, much more efficient than standard elements available in commercial finite element packages. This study is one step towards the modeling of soft tissue mechanics using a meshless finite element approach to be applied in real-time haptic feedback of soft-tissue models in virtual reality simulation.
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.
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
Static Aeroelastic Analysis of Transonic Wind Tunnel Models Using Finite Element Methods
NASA Technical Reports Server (NTRS)
Hooker, John R.; Burner, Alpheus W.; Valla, Robert
1997-01-01
A computational method for accurately predicting the static aeroelastic deformations of typical transonic transport wind tunnel models is described. The method utilizes a finite element method (FEM) for predicting the deformations. Extensive calibration/validation of this method was carried out using a novel wind-off wind tunnel model static loading experiment and wind-on optical wing twist measurements obtained during a recent wind tunnel test in the National Transonic Facility (NTF) at NASA LaRC. Further validations were carried out using a Navier-Stokes computational fluid dynamics (CFD) flow solver to calculate wing pressure distributions about several aeroelastically deformed wings and comparing these predictions with NTF experimental data. Results from this aeroelastic deformation method are in good overall agreement with experimentally measured values. Including the predicted deformations significantly improves the correlation between CFD predicted and experimentally measured wing & pressures.
Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity
Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu
2014-11-01
This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure. The new methods are quite different than many existing numerical methods in that they are locally conservative by design, the resulting discrete linear systems are symmetric and positive-definite, and there is no need for tuning problem-dependent penalty factors. We test the WGFEMs on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in Darcy flow.
One-dimensional finite-elements method for the analysis of whispering gallery microresonators.
Bagheri-Korani, Ebrahim; Mohammad-Taheri, Mahmoud; Shahabadi, Mahmoud
2014-07-01
By taking advantage of axial symmetry of the planar whispering gallery microresonators, the three-dimensional (3D) problem of the resonator is reduced to a two-dimensional (2D) one; thus, only the cross section of the resonator needs to be analyzed. Then, the proposed formulation, which works based on a combination of the finite-elements method (FEM) and Fourier expansion of the fields, can be applied to the 2D problem. First, the axial field variation is expressed in terms of a Fourier series. Then, a FEM method is applied to the radial field variation. This formulation yields an eigenvalue problem with sparse matrices and can be solved using a well-known numerical technique. This method takes into account both the radiation loss and the dielectric loss; hence, it works efficiently either for high number or low number modes. Efficiency of the method was investigated by comparison of the results with those of commercial software.
A Finite Element Method for Computation of Structural Intensity by the Normal Mode Approach
NASA Astrophysics Data System (ADS)
Gavrić, L.; Pavić, G.
1993-06-01
A method for numerical computation of structural intensity in thin-walled structures is presented. The method is based on structural finite elements (beam, plate and shell type) enabling computation of real eigenvalues and eigenvectors of the undamped structure which then serve in evaluation of complex response. The distributed structural damping is taken into account by using the modal damping concept, while any localized damping is treated as an external loading, determined by use of impedance matching conditions and eigenproperties of the structure. Emphasis is given to aspects of accuracy of the results and efficiency of the numerical procedures used. High requirements on accuracy of the structural response (displacements and stresses) needed in intensity applications are satisfied by employing the "swept static solution", which effectively takes into account the influence of higher modes otherwise inaccessible to numerical computation. A comparison is made between the results obtained by using analytical methods and the proposed numerical procedure to demonstrate the validity of the method presented.
NASA Astrophysics Data System (ADS)
Arbatani, Siamak; Callejo, Alfonso; Kövecses, József; Kalantari, Masoud; Marchand, Nick R.; Dargahi, Javad
2016-06-01
Directional drilling is a popular technique for oil well drilling. Accurate prediction of the directional performance is critical in order to achieve the desired well profile. Simplified geometry methods are, to date, the industry standard for predicting directional performance. A comprehensive, high-fidelity method for the simulation of directional drilling is presented here. It consists of a detailed discretization of the actual geometry and a rigorous application of two modeling techniques: the finite element and the finite segment methods. By doing so, the dynamic problem is addressed from two different yet complementary perspectives: structural mechanics and rigid-body motion. Collision detection and contact dynamics algorithms are also presented. Results show that both methods agree in terms of the dynamic response, and that the build rate estimations are consistent with available experimental data. Owing to the framework efficiency and physics-based nature, the presented tools are very well-suited for design engineering and real-time simulation.
NASA Astrophysics Data System (ADS)
Haddouche, Issam; Cherbi, Lynda
2017-01-01
In this paper, we investigate Surface Plasmon Polaritons (SPPs) in the visible regime at a metal/dielectric interface within two different waveguide structures, the first is a Photonic Crystal Fiber where the Full Vector Finite Element Method (FVFEM) is used and the second is a slab waveguide where the transfer matrix method (TMM) is used. Knowing the diversities between the two methods in terms of speed, simplicity, and scope of application, computation is implemented with respect to wavelength and metal layer thickness in order to analyze and compare the performances of the two methods. Simulation results show that the TMM can be a good approximation for the FVFEM and that SPPs behave more like modes propagating in a semi infinite metal/dielectric structure as metal thickness increases from about 150 nm.
A Runge-Kutta discontinuous finite element method for high speed flows
NASA Technical Reports Server (NTRS)
Bey, Kim S.; Oden, J. T.
1991-01-01
A Runge-Kutta discontinuous finite element method is developed for hyperbolic systems of conservation laws in two space variables. The discontinuous Galerkin spatial approximation to the conservation laws results in a system of ordinary differential equations which are marched in time using Runge-Kutta methods. Numerical results for the two-dimensional Burger's equation show that the method is (p+1)-order accurate in time and space, where p is the degree of the polynomial approximation of the solution within an element and is capable of capturing shocks over a single element without oscillations. Results for this problem also show that the accuracy of the solution in smooth regions is unaffected by the local projection and that the accuracy in smooth regions increases as p increases. Numerical results for the Euler equations show that the method captures shocks without oscillations and with higher resolution than a first-order scheme.
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.
Piras, P; Sansalone, G; Teresi, L; Kotsakis, T; Colangelo, P; Loy, A
2012-07-01
The shape and mechanical performance in Talpidae humeri were studied by means of Geometric Morphometrics and Finite Element Analysis, including both extinct and extant taxa. The aim of this study was to test whether the ability to dig, quantified by humerus mechanical performance, was characterized by convergent or parallel adaptations in different clades of complex tunnel digger within Talpidae, that is, Talpinae+Condylura (monophyletic) and some complex tunnel diggers not belonging to this clade. Our results suggest that the pattern underlying Talpidae humerus evolution is evolutionary parallelism. However, this insight changed to true convergence when we tested an alternative phylogeny based on molecular data, with Condylura moved to a more basal phylogenetic position. Shape and performance analyses, as well as specific comparative methods, provided strong evidence that the ability to dig complex tunnels reached a functional optimum in distantly related taxa. This was also confirmed by the lower phenotypic variance in complex tunnel digger taxa, compared to non-complex tunnel diggers. Evolutionary rates of phenotypic change showed a smooth deceleration in correspondence with the most recent common ancestor of the Talpinae+Condylura clade.
Cutting force predication based on integration of symmetric fuzzy number and finite element method.
Wang, Zhanli; Hu, Yanjuan; Wang, Yao; Dong, Chao; Pang, Zaixiang
2014-01-01
In the process of turning, pointing at the uncertain phenomenon of cutting which is caused by the disturbance of random factors, for determining the uncertain scope of cutting force, the integrated symmetric fuzzy number and the finite element method (FEM) are used in the prediction of cutting force. The method used symmetric fuzzy number to establish fuzzy function between cutting force and three factors and obtained the uncertain interval of cutting force by linear programming. At the same time, the change curve of cutting force with time was directly simulated by using thermal-mechanical coupling FEM; also the nonuniform stress field and temperature distribution of workpiece, tool, and chip under the action of thermal-mechanical coupling were simulated. The experimental result shows that the method is effective for the uncertain prediction of cutting force.
Cutting Force Predication Based on Integration of Symmetric Fuzzy Number and Finite Element Method
Wang, Zhanli; Hu, Yanjuan; Wang, Yao; Dong, Chao; Pang, Zaixiang
2014-01-01
In the process of turning, pointing at the uncertain phenomenon of cutting which is caused by the disturbance of random factors, for determining the uncertain scope of cutting force, the integrated symmetric fuzzy number and the finite element method (FEM) are used in the prediction of cutting force. The method used symmetric fuzzy number to establish fuzzy function between cutting force and three factors and obtained the uncertain interval of cutting force by linear programming. At the same time, the change curve of cutting force with time was directly simulated by using thermal-mechanical coupling FEM; also the nonuniform stress field and temperature distribution of workpiece, tool, and chip under the action of thermal-mechanical coupling were simulated. The experimental result shows that the method is effective for the uncertain prediction of cutting force. PMID:24790556
NASA Astrophysics Data System (ADS)
Bao, Weizhu; Jiang, Wei; Wang, Yan; Zhao, Quan
2017-02-01
We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the sharp-interface models belong to a new type of high-order (4th- or 6th-order) geometric evolution partial differential equations about open curve/surface interface tracking problems which include anisotropic surface diffusion flow and contact line migration. Compared to the traditional methods (e.g., marker-particle methods), the proposed PFEM not only has very good accuracy, but also poses very mild restrictions on the numerical stability, and thus it has significant advantages for solving this type of open curve evolution problems with applications in the simulation of solid-state dewetting. Extensive numerical results are reported to demonstrate the accuracy and high efficiency of the proposed PFEM.
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.
Divergence Stability in Connection with the P-Version of the Finite Element Method.
1987-11-01
RAIRO 8 (1974), pp. 129-151. [8] C. Canuto, Y. Maday and A. Quarteroni, Combined Finite Element and Spectral approximation of the Navier-Stokes...R. Verfuhrt, Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO , Numer. Anal., 18 (1984), pp. 175-182. (15] M
Spatial and angular finite element method for radiative transfer in participating media
NASA Astrophysics Data System (ADS)
Castro, Rafael O.; Trelles, Juan Pablo
2015-05-01
A computational approach for the modeling of multi-dimensional radiative transfer in participating media, including scattering, is presented. The approach is based on the sequential use of angular and spatial Finite Element Methods for the discretization of the Radiative Transfer Equation (RTE). The angular discretization is developed with an Angular Finite Element Method (AFEM) based on the Galerkin approach. The AFEM leads to a counterpart of the RTE consisting of a coupled set of transient-advective-reactive equations that are continuously dependent on space and time. The AFEM is ideally suited for so-called h- and/or p-refinement for the discretization of the angular domain: h-refinement is obtained by increasing the number of angular elements and p-refinement by increasing the order of the angular interpolating functions. The spatial discretization of the system of equations obtained after the angular discretization is based on a Variational Multi-Scale Finite Element Method (VMS-FEM) suitable for the solution of generic transport problems. The angularly and spatially discretized system is solved with a second-order accurate implicit predictor multi-corrector time stepper together with a globalized inexact Newton-Krylov nonlinear solver. The overall approach is designed and implemented to allow the seamless inclusion of other governing equations necessary to solve coupled fluid-radiative systems, such as those in combustion, high-temperature chemically reactive, and plasma flow models. The combined AFEM and VMS-FEM for the solution of the RTE is validated with two- and three-dimensional benchmark problems, each solved for 3 levels of angular partitioning (h-refinement) and for 2 orders of angular basis functions (p-refinement), i.e. piecewise constant (P0) and piecewise linear (P1) basis over spherical triangles. The overall approach is also applied to the simulation of radiative transfer in a parabolic concentrator with participating media, as encountered in
NASA Technical Reports Server (NTRS)
Abdul-Aziz, Ali; Baaklini, George Y.; Zagidulin, Dmitri; Rauser, Richard W.
2000-01-01
Capabilities and expertise related to the development of links between nondestructive evaluation (NDE) and finite element analysis (FEA) at Glenn Research Center (GRC) are demonstrated. Current tools to analyze data produced by computed tomography (CT) scans are exercised to help assess the damage state in high temperature structural composite materials. A utility translator was written to convert velocity (an image processing software) STL data file to a suitable CAD-FEA type file. Finite element analyses are carried out with MARC, a commercial nonlinear finite element code, and the analytical results are discussed. Modeling was established by building MSC/Patran (a pre and post processing finite element package) generated model and comparing it to a model generated by Velocity in conjunction with MSC/Patran Graphics. Modeling issues and results are discussed in this paper. The entire process that outlines the tie between the data extracted via NDE and the finite element modeling and analysis is fully described.
Evaluating the performance of the particle finite element method in parallel architectures
NASA Astrophysics Data System (ADS)
Gimenez, Juan M.; Nigro, Norberto M.; Idelsohn, Sergio R.
2014-05-01
This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative based formulation of the equations with a hybrid spatial discretization which uses an Eulerian mesh and Lagrangian particles. The main aim of PFEM-2 is to solve transport equations as fast as possible keeping some level of accuracy. The method was found to be competitive with classical Eulerian alternatives for these targets, even in their range of optimal application. To evaluate the goodness of the method with large simulations, it is imperative to use of parallel environments. Parallel strategies for Finite Element Method have been widely studied and many libraries can be used to solve Eulerian stages of PFEM-2. However, Lagrangian stages, such as streamline integration, must be developed considering the parallel strategy selected. The main drawback of PFEM-2 is the large amount of memory needed, which limits its application to large problems with only one computer. Therefore, a distributed-memory implementation is urgently needed. Unlike a shared-memory approach, using domain decomposition the memory is automatically isolated, thus avoiding race conditions; however new issues appear due to data distribution over the processes. Thus, a domain decomposition strategy for both particle and mesh is adopted, which minimizes the communication between processes. Finally, performance analysis running over multicore and multinode architectures are presented. The Courant-Friedrichs-Lewy number used influences the efficiency of the parallelization and, in some cases, a weighted partitioning can be used to improve the speed-up. However the total cputime for cases presented is lower than that obtained when using classical Eulerian strategies.
A 2D wavelet-based spectral finite element method for elastic wave propagation
NASA Astrophysics Data System (ADS)
Pahlavan, L.; Kassapoglou, C.; Suiker, A. S. J.; Gürdal, Z.
2012-10-01
A wavelet-based spectral finite element method (WSFEM) is presented that may be used for an accurate and efficient analysis of elastic wave propagation in two-dimensional (2D) structures. The approach is characterised by a temporal transformation of the governing equations to the wavelet domain using a wavelet-Galerkin approach, and subsequently performing the spatial discretisation in the wavelet domain with the finite element method (FEM). The final solution is obtained by transforming the nodal displacements computed in the wavelet domain back to the time domain. The method straightforwardly eliminates artificial temporal edge effects resulting from the discrete wavelet transform and allows for the modelling of structures with arbitrary geometries and boundary conditions. The accuracy and applicability of the method is demonstrated through (i) the analysis of a benchmark problem on axial and flexural waves (Lamb waves) propagating in an isotropic layer, and (ii) the study of a plate subjected to impact loading. The wave propagation response for the impact problem is compared to the result computed with standard FEM equipped with a direct time-integration scheme. The effect of anisotropy on the response is demonstrated by comparing the numerical result for an isotropic plate to that of an orthotropic plate, and to that of a plate made of two dissimilar materials, with and without a cut-out at one of the plate corners. The decoupling of the time-discretised equations in the wavelet domain makes the method inherently suitable for parallel computation, and thus an appealing candidate for efficiently studying high-frequency wave propagation in engineering structures with a large number of degrees of freedom.
Analysis of temperature rise for piezoelectric transformer using finite-element method.
Joo, Hyun-Woo; Lee, Chang-Hwan; Rho, Jong-Seok; Jung, Hyun-Kyo
2006-08-01
Analysis of heat problem and temperature field of a piezoelectric transformer, operated at steady-state conditions, is described. The resonance frequency of the transformer is calculated from impedance and electrical gain analysis using a finite-element method. Mechanical displacement and electric potential of the transformer at the calculated resonance frequency are used to calculate the loss distribution of the transformer. Temperature distribution using discretized heat transfer equation is calculated from the obtained losses of the transformer. Properties of the piezoelectric material, dependent on the temperature field, are measured to recalculate the losses, temperature distribution, and new resonance characteristics of the transformer. Iterative method is adopted to recalculate the losses and resonance frequency due to the changes of the material constants from temperature increase. Computed temperature distributions and new resonance characteristics of the transformer at steady-state temperature are verified by comparison with experimental results.
A Least-Squares Finite Element Method for Electromagnetic Scattering Problems
NASA Technical Reports Server (NTRS)
Wu, Jie; Jiang, Bo-nan
1996-01-01
The least-squares finite element method (LSFEM) is applied to electromagnetic scattering and radar cross section (RCS) calculations. In contrast to most existing numerical approaches, in which divergence-free constraints are omitted, the LSFF-M directly incorporates two divergence equations in the discretization process. The importance of including the divergence equations is demonstrated by showing that otherwise spurious solutions with large divergence occur near the scatterers. The LSFEM is based on unstructured grids and possesses full flexibility in handling complex geometry and local refinement Moreover, the LSFEM does not require any special handling, such as upwinding, staggered grids, artificial dissipation, flux-differencing, etc. Implicit time discretization is used and the scheme is unconditionally stable. By using a matrix-free iterative method, the computational cost and memory requirement for the present scheme is competitive with other approaches. The accuracy of the LSFEM is verified by several benchmark test problems.
NASA Technical Reports Server (NTRS)
Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.
2004-01-01
A recent paper is generalized to a case where the spatial region is taken in R(sup 3). The region is assumed to be a thin body, such as a panel on the wing or fuselage of an aerospace vehicle. The traditional h- as well as hp-finite element methods are applied to the surface defined in the x - y variables, while, through the thickness, the technique of the p-element is employed. Time and spatial discretization scheme based upon an assumption of certain weak singularity of double vertical line u(sub t) double vertical line 2, is used to derive an optimal a priori error estimate for the current method.
NASA Astrophysics Data System (ADS)
Craggs, A.
1989-08-01
When making an acoustic finite element model of a duct system, the resulting matrices can be very large due to the length of ductwork, the complex changes in geometry and the numerous junctions, and a full model may require several thousand nodes. In this paper two techniques are given for reducing the size of the matrices; the transfer matrix method and the condensed stiffness matrix approach—both of which lead to equations expressed in terms of the input and output nodes only. The methods are demonstrated with examples on a straight section of duct and a branched duct network. The substantial reductions in computer memory shown imply that duct acoustic problems can be studied using a desktop work station.
Analysis of Residual Stress for Narrow Gap Welding Using Finite Element Method
NASA Astrophysics Data System (ADS)
Lee, Choon Yeol; Hwang, Jae Keun; Bae, Joon Woo
Reactor coolant loop (RCL) pipes circulating the heat generated in a nuclear power plant consist of so large diameter pipes that the installation of these pipes is one of the major construction processes. Conventionally, a shield metal arc welding (SMAW) process has been mainly used in RCL piping installations, which sometimes caused severe deformations, dislocation of main equipments and various other complications due to excessive heat input in welding processes. Hence, automation of the work of welding is required and narrow-gap welding (NGW) process is being reviewed for new nuclear power plants as an alternative method of welding. In this study, transient heat transfer and thermo-elastic-plastic analyses have been performed for the residual stress distribution on the narrow gap weldment of RCL by finite element method under various conditions including surface heat flux and temperature dependent thermo-physical properties.
NASA Astrophysics Data System (ADS)
Kamiński, M.; Szafran, J.
2015-05-01
The main purpose of this work is to verify the influence of the weighting procedure in the Least Squares Method on the probabilistic moments resulting from the stability analysis of steel skeletal structures. We discuss this issue also in the context of the geometrical nonlinearity appearing in the Stochastic Finite Element Method equations for the stability analysis and preservation of the Gaussian probability density function employed to model the Young modulus of a structural steel in this problem. The weighting procedure itself (with both triangular and Dirac-type) shows rather marginal influence on all probabilistic coefficients under consideration. This hybrid stochastic computational technique consisting of the FEM and computer algebra systems (ROBOT and MAPLE packages) may be used for analogous nonlinear analyses in structural reliability assessment.
NASA Astrophysics Data System (ADS)
Jia, Zhiqiang; Zeng, Weidong; Xu, Jianwei; Zhou, Jianhua; Wang, Xiaoying
2015-04-01
In this work, a finite element method (FEM) model for predicting dynamic globularization of Ti-17 titanium alloy is established. For obtaining the microstructure evolution during dynamic globularization under varying processing parameters, isothermal hot compression tests and quantitative metallographic analysis were conducted on Ti-17 titanium alloy with initial lamellar microstructure. The prediction model, which quantitatively described the non-linear relationship between the dynamic globularization fraction and the deformation strain, temperature, and strain rate, was developed on the basis of the Avrami equation. Then the developed model was incorporated into DEFORM software as a user subroutine. Finally, the large-sized step-shaped workpiece was isothermally forged and corresponding FEM simulation was conducted to verify the reliability and accuracy of the integrated FEM model. The reasonable coincidence of the predicted results with experimental ones indicated that the established FEM model provides an easy and a practical method to predict dynamic globularization for Ti-17 titanium alloy with complex shape.
Optimal design of switched reluctance motor using two-dimensional finite element method
NASA Astrophysics Data System (ADS)
Kim, Youn-Hyun; Choi, Jae-Hak; Jung, Sung-In; Chun, Yon-Do; Kim, Sol; Lee, Ju; Chu, Min-Sik; Hong, Kyung-Jin; Choi, Dong-Hoon
2002-05-01
Switched reluctance motor (SRM) has some advantages such as low cost, high torque density, etc., but SRM has essentially high torque ripple due to its salient structure. To apply SRM to the industrial field, we have to minimize torque ripple, which is the weak point of SRM. This article introduces optimal design process of SRM using a numerical method such as two-dimensional (2D) finite element method. The electrical and geometrical design parameters have been adopted as 2D design variables. From this work, we can obtain the optimal design, which minimizes the torque ripple. We also can obtain the optimal design, which maximizes the average torque. Finally, this article presents performance comparison of two optimal designs, the minimized torque ripple, and the maximized average torque.
NASA Astrophysics Data System (ADS)
Bour, M.; Toumanari, A.; Khatib, D.
2007-04-01
This paper presents the application of the Finite Element Method FEM to the resolution of system Helmholtz coupled equations that has been obtained in the coaxial waveguides containing magnetic anisotropic materials with loss. This application is based on variational method which necessitates the construction of functional stationary written in the form of integral equation and dependent on the electromagnetic fields. After being minimized, this functional leads to algebraic equation system to which we can apply many numerical resolution algorithms. The electromagnetic study of the waveguide led us to a system of Helmholtz coupled equations which is difficult to be solved analytically. Our software code allows us to determine the electromagnetic field distribution in all points of the coaxial waveguide. The result has been validated when the coaxial waveguide was entirely loaded with air. This software has later been applied when the waveguide was partially filled with a magnetic anisotropic material with loss (\\varepsilon_r, overline{overline{μ_r}}).
Zhang, Lucy T.
2015-01-01
This paper presents some biomedical applications that involve fluid-structure interactions which are simulated using the Immersed Finite Element Method (IFEM). Here, we first review the original and enhanced IFEM methods that are suitable to model incompressible or compressible fluid that can have densities that are significantly lower than the solid, such as air. Then, three biomedical applications are studied using the IFEM. Each of the applications may require a specific set of IFEM formulation for its respective numerical stability and accuracy due to the disparities between the fluid and the solid. We show that these biomedical applications require a fully-coupled and stable numerical technique in order to produce meaningful results. PMID:26855688
Forward Modeling of Electromagnetic Methods Using General Purpose Finite Element Software
NASA Astrophysics Data System (ADS)
Butler, S. L.
2015-12-01
Electromagnetic methods are widely used in mineral exploration and environmental applications and are increasingly being used in hydrocarbon exploration. Forward modeling of electromagnetic methods remains challenging and is mostly carried out using purpose-built research software. General purpose commercial modeling software has become increasingly flexible and powerful in recent years and is now capable of modeling field geophysical electromagnetic techniques. In this contribution, I will show examples of the use of commercial finite element modeling software Comsol Multiphysics for modeling frequency and time-domain electromagnetic techniques as well as for modeling the Very Low Frequency technique and magnetometric resistivity. Comparisons are made with analytical solutions, benchmark numerical solutions, analog experiments and field data. Although some calculations take too long to be practical as part of an inversion scheme, I suggest that modeling of this type will be useful for modeling novel techniques and for educational purposes.
Dynamic Analysis of Overhead Power Lines after Ice-Shedding Using Finite Element Method
NASA Astrophysics Data System (ADS)
Murín, Justín; Hrabovský, Juraj; Gogola, Roman; Janíček, František
2016-12-01
In this paper, the analysis of ice-shedding from ACSR conductors to its swing up height and vibration using Finite Element Method (FEM) is presented. For the numerical simulations the effective material properties of the ACSR conductor are calculated using the homogenisation method. Numerical analysis concerning vibration of one and triple-bundle conductors with icing for a whole range or on their certain parts are performed. The impact of ice-shedding to the mechanical tension in the conductors at the points of attachment is investigated and evaluated. Identification of the impact of ice-shedding from the ACSR conductors on its mechanical state may contribute to increasing the safety and quality of an electrical transmission system.
Fission-Fusion Adaptivity in Finite Elements for Nonlinear Dynamics of Shells
1988-11-30
where mesh refinement will prove useful. In fact, the deviation of a bilinear element from a smooth shell midsurface can be related to the angle between...comparisons with nonadaptive meshes. Conclusions and further discussions are given in Section 6. -5- 2. FINITE ELEMENT FORMULATION The shape of the midsurface ...8217 22 , and e3 is defined so that e, and e2 are tangent to the midsurface and rotate with the element; 2. for each node, a triad b i is defined so that
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.
An approximate waves-bordering algorithm for adaptive finite elements analysis
NASA Astrophysics Data System (ADS)
Morandi Cecchi, M.; Marcuzzi, F.
1999-09-01
In this paper an Approximate Waves-Bordering algorithm (AWB) is presented. It computes the finite elements linear system solution-update after a refinement/unrefinement step. This is done taking into consideration only the equations that correspond to the nodes whose solution is modified above a certain tolerance and it appears to be very efficient. The algorithm considers an increasing set of equations that updates recursively and stops when the norm of the residual has gone under a user-defined threshold.
NASA Astrophysics Data System (ADS)
Lakshminarayana, A.; Vijayakumar, R.; Krishnamohana Rao, G.
2016-09-01
The progressive failure analysis of symmetrically laminated composite plate [0°/+45°/-45°/90°]2s with circular or elliptical cutout under uniform uniaxial compression loading is carried out using finite element method. Hashin's failure criterion is used to predict the lamina failure. A parametric study has been carried out to study the effect of elliptical / circular cutout orientation, cutout size and plate thickness on the ultimate failure load of laminated composite plate under uni-axial compression loading. It is noticed that elliptical cutout orientation has influence on the strength of the notched composite plates. It is observed that the laminate size of the elliptical/circular cutout and plate thickness has substantial influence on the ultimate failure load of notched composite plates.
Implementation of Hybrid V-Cycle Multilevel Methods for Mixed Finite Element Systems with Penalty
NASA Technical Reports Server (NTRS)
Lai, Chen-Yao G.
1996-01-01
The goal of this paper is the implementation of hybrid V-cycle hierarchical multilevel methods for the indefinite discrete systems which arise when a mixed finite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system containing the small penalty parameter for the velocity unknown alone. We stabilize the hierarchical spatial decomposition approach proposed by Cai, Goldstein, and Pasciak for the reduced system. We demonstrate that the relative condition number of the preconditioner is bounded uniformly with respect to the penalty parameter, the number of levels and possible jumps of the coefficients as long as they occur only across the edges of the coarsest elements.
Generalized multiscale finite element method for non-Newtonian fluid flow in perforated domain
NASA Astrophysics Data System (ADS)
Chung, E. T.; Iliev, O.; Vasilyeva, M. V.
2016-10-01
In this work, we consider a non-Newtonian fluid flow in perforated domains. Fluid flow in perforated domains have a multiscale nature and solution techniques for such problems require high resolution. In particular, the discretization needs to honor the irregular boundaries of perforations. This gives rise to a fine-scale problems with many degrees of freedom which can be very expensive to solve. In this work, we develop a multiscale approach that attempt to solve such problems on a coarse grid by constructing multiscale basis functions. We follow Generalized Multiscale Finite Element Method (GMsFEM) [1, 2] and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems [3, 4]. We show that with a few basis functions in each coarse block, one can accurately approximate the solution, where each coarse block can contain many small inclusions.
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.
NASA Astrophysics Data System (ADS)
Bai, YanHong; Wu, YongKe; Xie, XiaoPing
2016-09-01
Superconvergence and a posteriori error estimators of recovery type are analyzed for the 4-node hybrid stress quadrilateral finite element method proposed by Pian and Sumihara (Int. J. Numer. Meth. Engrg., 1984, 20: 1685-1695) for linear elasticity problems. Uniform superconvergence of order $O(h^{1+\\min\\{\\alpha,1\\}})$ with respect to the Lam\\'{e} constant $\\lambda$ is established for both the recovered gradients of the displacement vector and the stress tensor under a mesh assumption, where $\\alpha>0$ is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. A posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.
Calculation of leaky Lamb waves with a semi-analytical finite element method.
Hayashi, Takahiro; Inoue, Daisuke
2014-08-01
A semi-analytical finite element method (SAFE) has been widely used for calculating dispersion curves and mode shapes of guided waves as well as transient waves in a bar like structures. Although guided wave inspection is often conducted for water-loaded plates and pipes, most of the SAFE techniques have not been extended to a plate with leaky media. This study describes leaky Lamb wave calculation with the SAFE. We formulated a new solution using a feature that a single Lamb wave mode generates a harmonic plane wave in leaky media. Dispersion curves obtained with the SAFE agreed well with the previous theoretical studies, which represents that the SAFE calculation was conducted with sufficient accuracy. Moreover, we discussed dispersion curves, attenuation curves, and displacement distributions for total transmission modes and leaky plate modes in a single side and both two side water-loaded plate.
Finite element method simulation of the molding process for thermal nano-imprint lithography.
Cho, Bumgoo; Kim, Kwangsik; Won, Taeyoung
2012-07-01
We made a numerical study on the deformation of a viscoelastic polymethyl methacrylene (PMMA) resist when a rigid SiO2 stamp with a rectangular line pattern is imprinted into the PMMA resist for thermal nano-imprint lithography (NIL). The stress distribution in the polymer resist during the molding process is calculated by a finite element method (FEM). Our simulation results reveal that the asymmetric von Mises stress is distributed over the polymer around the external line, which seems to be due to the squeezing flow under the flat space. The stress seems to be concentrated at the sidewall close to the centerline of the whole structure. Our simulation also reveals that a micro gap is formed between the replicated structure and the outer wall of the mold.
A Parallel Multigrid Method for the Finite Element Analysis of Mechanical Contact
Hales, J D; Parsons, I D
2002-03-21
A geometrical multigrid method for solving the linearized matrix equations arising from node-on-face three-dimensional finite element contact is described. The development of an efficient implementation of this combination that minimizes both the memory requirements and the computational cost requires careful construction and storage of the portion of the coarse mesh stiffness matrices that are associated with the contact stiffness on the fine mesh. The multigrid contact algorithm is parallelized in a manner suitable for distributed memory architectures: results are presented that demonstrates the scheme's scalability. The solution of a large contact problem derived from an analysis of the factory joints present in the Space Shuttle reusable solid rocket motor demonstrates the usefulness of the general approach.
NASA Astrophysics Data System (ADS)
Okawa, Shinpei; Hirasawa, Takeshi; Kushibiki, Toshihiro; Ishihara, Miya
2013-09-01
An image reconstruction algorithm for biomedical photoacoustic imaging is discussed. The algorithm solves the inverse problem of the photoacoustic phenomenon in biological media and images the distribution of large optical absorption coefficients, which can indicate diseased tissues such as cancers with angiogenesis and the tissues labeled by exogenous photon absorbers. The linearized forward problem, which relates the absorption coefficients to the detected photoacoustic signals, is formulated by using photon diffusion and photoacoustic wave equations. Both partial differential equations are solved by a finite element method. The inverse problem is solved by truncated singular value decomposition, which reduces the effects of the measurement noise and the errors between forward modeling and actual measurement systems. The spatial resolution and the robustness to various factors affecting the image reconstruction are evaluated by numerical experiments with 2D geometry.
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.
Alani, Amir M; Faramarzi, Asaad
2015-06-10
In this paper, a stochastic finite element method (SFEM) is employed to investigate the probability of failure of cementitious buried sewer pipes subjected to combined effect of corrosion and stresses. A non-linear time-dependant model is used to determine the extent of concrete corrosion. Using the SFEM, the effects of different random variables, including loads, pipe material, and corrosion on the remaining safe life of the cementitious sewer pipes are explored. A numerical example is presented to demonstrate the merit of the proposed SFEM in evaluating the effects of the contributing parameters upon the probability of failure of cementitious sewer pipes. The developed SFEM offers many advantages over traditional probabilistic techniques since it does not use any empirical equations in order to determine failure of pipes. The results of the SFEM can help the concerning industry (e.g., water companies) to better plan their resources by providing accurate prediction for the remaining safe life of cementitious sewer pipes.
Maini, Surita; Marwaha, Anupma
2013-09-01
In this article, new interstitial antenna operating at a frequency of 2.45 GHz for the treatment of hepatocellular carcinoma (HCC) using microwave ablation has been investigated. This antenna is basically an asymmetrical miniaturized choke dipole antenna with a pointed needle at the tip. A commercial finite element method (FEM) package, COMSOL Multiphysics 3.4a, has been used to simulate the performance of needle tip choke antenna. The performance of the antenna has been evaluated numerically, taking into account the specific absorption rate, antenna impedance matching and geometry of the obtained thermal lesion, and the temperature distribution plot obtained shows that maximum temperature was attained in this simulation. The antenna is also capable of creating a spherical-shaped ablation zone. The size and shape of the ablation zone can be slightly adjusted by adjusting the choke position in order to maintain spherical ablation zones.
NASA Astrophysics Data System (ADS)
Ali, Elaf Jaafar; Gao, David Yang
2016-10-01
The goal of this paper is to solve the post buckling phenomena of a large deformed elastic beam by a canonical dual mixed finite element method (CD-FEM). The total potential energy of this beam is a nonconvex functional which can be used to model both pre-and post-buckling problems. Different types of dual stress interpolations are used in order to verify the triality theory. Applications are illustrated with different boundary conditions and external loads by using semi-definite programming (SDP) algorithm. The results show that the global minimum of the total potential energy is stable buckled configuration, the local maximum solution leads to the unbuckled state, and both of these two solutions are numerically stable. While the local minimum is unstable buckled configuration and very sensitive to both stress interpolations and the external loads.
Maliassov, S.Y.
1996-12-31
An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.
Barkaoui, Abdelwahed; Tlili, Brahim; Vercher-Martínez, Ana; Hambli, Ridha
2016-10-01
Bone is a living material with a complex hierarchical structure which entails exceptional mechanical properties, including high fracture toughness, specific stiffness and strength. Bone tissue is essentially composed by two phases distributed in approximately 30-70%: an organic phase (mainly type I collagen and cells) and an inorganic phase (hydroxyapatite-HA-and water). The nanostructure of bone can be represented throughout three scale levels where different repetitive structural units or building blocks are found: at the first level, collagen molecules are arranged in a pentameric structure where mineral crystals grow in specific sites. This primary bone structure constitutes the mineralized collagen microfibril. A structural organization of inter-digitating microfibrils forms the mineralized collagen fibril which represents the second scale level. The third scale level corresponds to the mineralized collagen fibre which is composed by the binding of fibrils. The hierarchical nature of the bone tissue is largely responsible of their significant mechanical properties; consequently, this is a current outstanding research topic. Scarce works in literature correlates the elastic properties in the three scale levels at the bone nanoscale. The main goal of this work is to estimate the elastic properties of the bone tissue in a multiscale approach including a sensitivity analysis of the elastic behaviour at each length scale. This proposal is achieved by means of a novel hybrid multiscale modelling that involves neural network (NN) computations and finite elements method (FEM) analysis. The elastic properties are estimated using a neural network simulation that previously has been trained with the database results of the finite element models. In the results of this work, parametric analysis and averaged elastic constants for each length scale are provided. Likewise, the influence of the elastic constants of the tissue constituents is also depicted. Results highlight
Cochran, R.J.
1992-01-01
A study of the finite element method applied to two-dimensional incompressible fluid flow analysis with heat transfer is performed using a mixed Galerkin finite element method with the primitive variable form of the model equations. Four biquadratic, quadrilateral elements are compared in this study--the serendipity biquadratic element with bilinear continuous pressure interpolation (Q2(8)-Q1) and the Lagrangian biquadratic element with bilinear continuous pressure interpolation (Q2-Q1) of the Taylor-Hood form. A modified form of the Q2-Q1 element is also studied. The pressure interpolation is augmented by a discontinuous constant shape function for pressure (Q2-Q1+). The discontinuous pressure element formulation makes use of biquadratic shape functions and a discontinuous linear interpolation of the pressure (Q2-P1(3)). Laminar flow solutions, with heat transfer, are compared to analytical and computational benchmarks for flat channel, backward-facing step and buoyancy driven flow in a square cavity. It is shown that the discontinuous pressure elements provide superior solution characteristics over the continuous pressure elements. Highly accurate heat transfer solutions are obtained and the Q2-P1(3) element is chosen for extension to turbulent flow simulations. Turbulent flow solutions are presented for both low turbulence Reynolds number and high Reynolds number formulations of two-equation turbulence models. The following three forms of the length scale transport equation are studied; the turbulence energy dissipation rate ([var epsilon]), the turbulence frequency ([omega]) and the turbulence time scale (tau). It is shown that the low turbulence Reynolds number model consisting of the K - [tau] transport equations, coupled with the damping functions of Shih and Hsu, provides an optimal combination of numerical stability and solution accuracy for the flat channel flow.
A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids
Bungartz, H.J.
1996-12-31
In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.
Finite-element method for calculation of the effective permittivity of random inhomogeneous media
NASA Astrophysics Data System (ADS)
Myroshnychenko, Viktor; Brosseau, Christian
2005-01-01
The challenge of designing new solid-state materials from calculations performed with the help of computers applied to models of spatial randomness has attracted an increasing amount of interest in recent years. In particular, dispersions of particles in a host matrix are scientifically and technologically important for a variety of reasons. Herein, we report our development of an efficient computer code to calculate the effective (bulk) permittivity of two-phase disordered composite media consisting of hard circular disks made of a lossless dielectric (permittivity ɛ2 ) randomly placed in a plane made of a lossless homogeneous dielectric (permittivity ɛ1 ) at different surface fractions. Specifically, the method is based on (i) a finite-element description of composites in which both the host and the randomly distributed inclusions are isotropic phases, and (ii) an ordinary Monte Carlo sampling. Periodic boundary conditions are employed throughout the simulation and various numbers of disks have been considered in the calculations. From this systematic study, we show how the number of Monte Carlo steps needed to achieve equilibrated distributions of disks increases monotonically with the surface fraction. Furthermore, a detailed study is made of the dependence of the results on a minimum separation distance between disks. Numerical examples are presented to connect the macroscopic property such as the effective permittivity to microstructural characteristics such as the mean coordination number and radial distribution function. In addition, several approximate effective medium theories, exact bounds, exact results for two-dimensional regular arrays, and the exact dilute limit are used to test and validate the finite-element algorithm. Numerical results indicate that the fourth-order bounds provide an excellent estimate of the effective permittivity for a wide range of surface fractions, in accordance with the fact that the bounds become progressively narrower as
Stabilized finite element methods to simulate the conductances of ion channels
NASA Astrophysics Data System (ADS)
Tu, Bin; Xie, Yan; Zhang, Linbo; Lu, Benzhuo
2015-03-01
We have previously developed a finite element simulator, ichannel, to simulate ion transport through three-dimensional ion channel systems via solving the Poisson-Nernst-Planck equations (PNP) and Size-modified Poisson-Nernst-Planck equations (SMPNP), and succeeded in simulating some ion channel systems. However, the iterative solution between the coupled Poisson equation and the Nernst-Planck equations has difficulty converging for some large systems. One reason we found is that the NP equations are advection-dominated diffusion equations, which causes troubles in the usual FE solution. The stabilized schemes have been applied to compute fluids flow in various research fields. However, they have not been studied in the simulation of ion transport through three-dimensional models based on experimentally determined ion channel structures. In this paper, two stabilized techniques, the SUPG and the Pseudo Residual-Free Bubble function (PRFB) are introduced to enhance the numerical robustness and convergence performance of the finite element algorithm in ichannel. The conductances of the voltage dependent anion channel (VDAC) and the anthrax toxin protective antigen pore (PA) are simulated to validate the stabilization techniques. Those two stabilized schemes give reasonable results for the two proteins, with decent agreement with both experimental data and Brownian dynamics (BD) simulations. For a variety of numerical tests, it is found that the simulator effectively avoids previous numerical instability after introducing the stabilization methods. Comparison based on our test data set between the two stabilized schemes indicates both SUPG and PRFB have similar performance (the latter is slightly more accurate and stable), while SUPG is relatively more convenient to implement.
NASA Astrophysics Data System (ADS)
Gillet-Chaulet, F.; Gagliardini, O.; Nodet, M.; Ritz, C.; Durand, G.; Zwinger, T.; Seddik, H.; Greve, R.
2010-12-01
About a third of the current sea level rise is attributed to the release of Greenland and Antarctic ice, and their respective contribution is continuously increasing since the first diagnostic of the acceleration of their coastal outlet glaciers, a decade ago. Due to their related societal implications, good scenario of the ice sheets evolutions are needed to constrain the sea level rise forecast in the coming centuries. The quality of the model predictions depend primary on the good description of the physical processes involved and on a good initial state reproducing the main present observations (geometry, surface velocities and ideally the trend in elevation change). We model ice dynamics on the whole Greenland ice sheet using the full-Stokes finite element code Elmer. The finite element mesh is generated using the anisotropic mesh adaptation tool YAMS, and shows a high density around the major ice streams. For the initial state, we use an iterative procedure to compute the ice velocities, the temperature field, and the basal sliding coefficient field. The basal sliding coefficient is obtained with an inverse method by minimizing a cost function that measures the misfit between the present day surface velocities and the modelled surface velocities. We use two inverse methods for this: an inverse Robin problem recently proposed by Arthern and Gudmundsson (J. Glaciol. 2010), and a control method taking advantage of the fact that the Stokes equations are self adjoint in the particular case of a Newtonian rheology. From the initial states obtained by these two methods, we run transient simulations to evaluate the impact of the initial state of the Greenland ice sheet onto its related contribution to sea level rise for the next centuries.
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)
Jin, Jian-Ming; Volakis, John L.; Collins, Jeffery D.
1991-01-01
A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability.
NASA Technical Reports Server (NTRS)
Ko, William L.
1995-01-01
Thermal buckling characteristics of hypersonic aircraft sandwich panels of various aspect ratios were investigated. The panel is fastened at its four edges to the substructures under four different edge conditions and is subjected to uniform temperature loading. Minimum potential energy theory and finite element methods were used to calculate the panel buckling temperatures. The two methods gave fairly close buckling temperatures. However, the finite element method gave slightly lower buckling temperatures than those given by the minimum potential energy theory. The reasons for this slight discrepancy in eigensolutions are discussed in detail. In addition, the effect of eigenshifting on the eigenvalue convergence rate is discussed.
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.
Towards Realistic Global Geomagnetic Induction Modeling Using Scripted Finite Element Methods
NASA Astrophysics Data System (ADS)
Ribaudo, J. T.; Constable, C. G.
2008-12-01
We present recent progress in forward modeling the global induction problem with realistic external field structure, 3D Earth conductivity, and rotation. The modeling is performed in the time and frequency domains via a commercially-available, general-purpose, finite element modeling package called FlexPDE, and has been validated against known solutions to 3D steady state and time-dependent problems. The induction problem is formulated in terms of the magnetic vector potential and electric scalar potential, and mesh density is managed both explicitly and through adaptive mesh refinement. The modeling routine allows for arbitrary conductivity and external field structure. The strength of the external magnetic field generated by the magnetospheric ring current is known to vary as a function of local time, giving it an asymmetric spatial structure. Electromagnetic c-responses estimated from satellite data are known to be biased with respect to local time. We investigate the influence that Earth's rotation through the non-uniform external field should have on these c-responses.
NASA Astrophysics Data System (ADS)
Peeters, J.; Arroud, G.; Ribbens, B.; Dirckx, J. J. J.; Steenackers, G.
2015-12-01
In non-destructive evaluation the use of finite element models to evaluate structural behavior and experimental setup optimization can complement with the inspector's experience. A new adaptive response surface methodology, especially adapted for thermal problems, is used to update the experimental setup parameters in a finite element model to the state of the test sample measured by pulsed thermography. Poly Vinyl Chloride (PVC) test samples are used to examine the results for thermal insulator models. A comparison of the achieved results is made by changing the target values from experimental pulsed thermography data to a fixed validation model. Several optimizers are compared and discussed with the focus on speed and accuracy. A time efficiency increase of over 20 and an accuracy of over 99.5% are achieved by the choice of the correct parameter sets and optimizer. Proper parameter set selection criteria are defined and the influence of the choice of the optimization algorithm and parameter set on the accuracy and convergence time are investigated.
NASA Astrophysics Data System (ADS)
González-Estrada, Octavio A.; Natarajan, Sundararajan; Ródenas, Juan José; Nguyen-Xuan, Hung; Bordas, Stéphane P. A.
2013-07-01
An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a "smooth + singular" decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.
A Statistical Approach for the Concurrent Coupling of Molecular Dynamics and Finite Element Methods
NASA Technical Reports Server (NTRS)
Saether, E.; Yamakov, V.; Glaessgen, E.
2007-01-01
Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, increasing the size of the MD domain quickly presents intractable computational demands. A robust approach to surmount this computational limitation has been to unite continuum modeling procedures such as the finite element method (FEM) with MD analyses thereby reducing the region of atomic scale refinement. The challenging problem is to seamlessly connect the two inherently different simulation techniques at their interface. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the typical boundary value problem used to define a coupled domain. The method uses statistical averaging of the atomistic MD domain to provide displacement interface boundary conditions to the surrounding continuum FEM region, which, in return, generates interface reaction forces applied as piecewise constant traction boundary conditions to the MD domain. The two systems are computationally disconnected and communicate only through a continuous update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM) as opposed to a direct coupling method where interface atoms and FEM nodes are individually related. The methodology is inherently applicable to three-dimensional domains, avoids discretization of the continuum model down to atomic scales, and permits arbitrary temperatures to be applied.
Large-scale computation of incompressible viscous flow by least-squares finite element method
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Lin, T. L.; Povinelli, Louis A.
1993-01-01
The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of 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. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.
Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung
2015-02-01
Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons.
Fu, Y B; Chui, C K; Teo, C L
2013-04-01
Biological soft tissue is highly inhomogeneous with scattered stress-strain curves. Assuming that the instantaneous strain at a specific stress varies according to a normal distribution, a nondeterministic approach is proposed to model the scattered stress-strain relationship of the tissue samples under compression. Material parameters of the liver tissue modeled using Mooney-Rivlin hyperelastic constitutive equation were represented by a statistical function with normal distribution. Mean and standard deviation of the material parameters were determined using inverse finite element method and inverse mean-value first-order second-moment (IMVFOSM) method respectively. This method was verified using computer simulation based on direct Monte-Carlo (MC) method. The simulated cumulative distribution function (CDF) corresponded well with that of the experimental stress-strain data. The resultant nondeterministic material parameters were able to model the stress-strain curves from other separately conducted liver tissue compression tests. Stress-strain data from these new tests could be predicted using the nondeterministic material parameters.
Inversion of potential field data using the finite element method on parallel computers
NASA Astrophysics Data System (ADS)
Gross, L.; Altinay, C.; Shaw, S.
2015-11-01
In this paper we present a formulation of the joint inversion of potential field anomaly data as an optimization problem with partial differential equation (PDE) constraints. The problem is solved using the iterative Broyden-Fletcher-Goldfarb-Shanno (BFGS) method with the Hessian operator of the regularization and cross-gradient component of the cost function as preconditioner. We will show that each iterative step requires the solution of several PDEs namely for the potential fields, for the adjoint defects and for the application of the preconditioner. In extension to the traditional discrete formulation the BFGS method is applied to continuous descriptions of the unknown physical properties in combination with an appropriate integral form of the dot product. The PDEs can easily be solved using standard conforming finite element methods (FEMs) with potentially different resolutions. For two examples we demonstrate that the number of PDE solutions required to reach a given tolerance in the BFGS iteration is controlled by weighting regularization and cross-gradient but is independent of the resolution of PDE discretization and that as a consequence the method is weakly scalable with the number of cells on parallel computers. We also show a comparison with the UBC-GIF GRAV3D code.
Application of the wave finite element method to reinforced concrete structures with damage
NASA Astrophysics Data System (ADS)
El Masri, Evelyne; Ferguson, Neil; Waters, Timothy
2016-09-01
Vibration based methods are commonly deployed to detect structural damage using sensors placed remotely from potential damage sites. Whilst many such techniques are modal based there are advantages to adopting a wave approach, in which case it is essential to characterise wave propagation in the structure. The Wave Finite Element method (WFE) is an efficient approach to predicting the response of a composite waveguide using a conventional FE model of a just a short segment. The method has previously been applied to different structures such as laminated plates, thinwalled structures and fluid-filled pipes. In this paper, the WFE method is applied to a steel reinforced concrete beam. Dispersion curves and wave mode shapes are first presented from free wave solutions, and these are found to be insensitive to loss of thickness in a single reinforcing bar. A reinforced beam with localised damage is then considered by coupling an FE model of a short damaged segment into the WFE model of the undamaged beam. The fundamental bending, torsion and axial waves are unaffected by the damage but some higher order waves of the cross section are significantly reflected close to their cut-on frequencies. The potential of this approach for detecting corrosion and delamination in reinforced concrete beams will be investigated in future work.
Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry
NASA Astrophysics Data System (ADS)
Kitzmann, D.; Bolte, J.; Patzer, A. B. C.
2016-11-01
The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case owing to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause severe numerical problems for other radiative transfer solution methods.
Lyard, F.; Genco, M.L.
1994-10-01
A bidimensional, spectral in time, quasi-linearised hydrodynamic ocean tide model has been developed at the Institut de Mecanique de Grenoble. This model is derived from the classical shallow water equations by removing the velocity unknowns in the continuity equation, that leads to an elliptic, second-order differential equation where tide denivellation remains the only unknown quantity. The problem is solved in its variational formulation and the finite elements method is used to discretise the equations in the spatial domain with a Lagrange-P2 approximation. Bottom topography has to be known at the integration points of the elements. In the case of the large oceanic basins, a specific method, called the bathymetry optimisation method, is needed to correctly take into account the bottom topography inside the model. The accuracy of the model`s solutions is also strongly dependent on the quality of the open boundary conditions because of the elliptic characteristics of the problem. The optimisation method for open boundary conditions relies on the use of the in situ data available in the modelled domain. The aim of this paper is to present the basis of these optimisations of bathymetry and open boundary conditions. An illustration of the related improvements is presented on the North Atlantic Basin. 36 refs., 10 figs., 5 tabs.
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...
NASA Technical Reports Server (NTRS)
Seybert, A. F.; Wu, X. F.; Oswald, Fred B.
1992-01-01
Analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise radiated from the box. The FEM was used to predict the vibration, and the surface vibration was used as input to the BEM to predict the sound intensity and sound power. Vibration predicted by the FEM model was validated by experimental modal analysis. Noise predicted by the BEM was validated by sound intensity measurements. Three types of results are presented for the total radiated sound power: (1) sound power predicted by the BEM modeling using vibration data measured on the surface of the box; (2) sound power predicted by the FEM/BEM model; and (3) sound power measured by a sound intensity scan. The sound power predicted from the BEM model using measured vibration data yields an excellent prediction of radiated noise. The sound power predicted by the combined FEM/BEM model also gives a good prediction of radiated noise except for a shift of the natural frequencies that are due to limitations in the FEM model.
Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong
2014-01-01
We discuss and analyze an H(1)-Galerkin mixed finite element (H(1)-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H(1)-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H(1)-GMFE method. Based on the discussion on the theoretical error analysis in L(2)-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H(1)-norm. Moreover, we derive and analyze the stability of H(1)-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure.
An optimal local active noise control method based on stochastic finite element models
NASA Astrophysics Data System (ADS)
Airaksinen, T.; Toivanen, J.
2013-12-01
A new method is presented to obtain a local active noise control that is optimal in stochastic environment. The method uses numerical acoustical modeling that is performed in the frequency domain by using a sequence of finite element discretizations of the Helmholtz equation. The stochasticity of domain geometry and primary noise source is considered. Reference signals from an array of microphones are mapped to secondary loudspeakers, by an off-line optimized linear mapping. The frequency dependent linear mapping is optimized to minimize the expected value of error in a quiet zone, which is approximated by the numerical model and can be interpreted as a stochastic virtual microphone. A least squares formulation leads to a quadratic optimization problem. The presented active noise control method gives robust and efficient noise attenuation, which is demonstrated by a numerical study in a passenger car cabin. The numerical results demonstrate that a significant, stable local noise attenuation of 20-32 dB can be obtained at lower frequencies (<500 Hz) by two microphones, and 8-36 dB attenuation at frequencies up to 1000 Hz, when 8 microphones are used.
NASA Astrophysics Data System (ADS)
Vu, Thu Hang; Deeks, Andrew J.
2014-04-01
This paper introduces a new technique for solving concentrated load problems in the scaled boundary finite element method (FEM). By employing fundamental solutions for the displacements and the stresses, the solution is computed as summation of a fundamental solution part and a regular part. The singularity at the point of load application is modelled exactly by the fundamental solution, and only the regular part, which enforces the boundary conditions of the domain onto the fundamental solution, needs to be approximated in the solution space of the scaled boundary FEM. Examples are provided illustrating that the new approach is much simpler to implement and more accurate than the method currently used for solving concentrated load problems with the scaled boundary method. In each illustration, solution convergence is examined. The relative error is described in terms of the scalar energy norm of the stress field. Mesh refinement is performed using p-refinement with high order element based on the Lobatto shape functions. The proposed technique is described for two-dimensional problems in this paper, but extension to any linear problem, for which fundamental solutions exist, is straightforward.
A semi-discrete finite element method for a class of time-fractional diffusion equations.
Sun, HongGuang; Chen, Wen; Sze, K Y
2013-05-13
As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly used in the related mathematical descriptions. These models usually involve long-time-range computation, which is a critical obstacle for their application; improvement of computational efficiency is of great significance. In this paper, a semi-discrete method is presented for solving a class of time-fractional diffusion equations that overcome the critical long-time-range computation problem. In the procedure, the spatial domain is discretized by the finite element method, which reduces the fractional diffusion equations to approximate fractional relaxation equations. As analytical solutions exist for the latter equations, the burden arising from long-time-range computation can effectively be minimized. To illustrate its efficiency and simplicity, four examples are presented. In addition, the method is used to solve the time-fractional advection-diffusion equation characterizing the bromide transport process in a fractured granite aquifer. The prediction closely agrees with the experimental data, and the heavy-tail decay of the anomalous transport process is well represented.
Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong
2014-01-01
We discuss and analyze an H1-Galerkin mixed finite element (H1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H1-GMFE method. Based on the discussion on the theoretical error analysis in L2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H1-norm. Moreover, we derive and analyze the stability of H1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148
NASA Technical Reports Server (NTRS)
Panczak, Tim; Ring, Steve; Welch, Mark
1999-01-01
Thermal engineering has long been left out of the concurrent engineering environment dominated by CAD (computer aided design) and FEM (finite element method) software. Current tools attempt to force the thermal design process into an environment primarily created to support structural analysis, which results in inappropriate thermal models. As a result, many thermal engineers either build models "by hand" or use geometric user interfaces that are separate from and have little useful connection, if any, to CAD and FEM systems. This paper describes the development of a new thermal design environment called the Thermal Desktop. This system, while fully integrated into a neutral, low cost CAD system, and which utilizes both FEM and FD methods, does not compromise the needs of the thermal engineer. Rather, the features needed for concurrent thermal analysis are specifically addressed by combining traditional parametric surface based radiation and FD based conduction modeling with CAD and FEM methods. The use of flexible and familiar temperature solvers such as SINDA/FLUINT (Systems Improved Numerical Differencing Analyzer/Fluid Integrator) is retained.
Baradari, F.
1982-01-01
In this work the applicability of a ''Boundary Element method'' for the numerical solution of the Liouville and Helmholtz eigenvalue problem for different two dimensional geometries including a typical reactor configuration was investigated. The method is based on the discretization of the unknown along the boundary and Green's function representation of the governing equation. To compare the capability of this method with the finite element method, a finite element code which uses quadratic quadrilateral isoparametric elements was developed. A boundary element code was also written. These codes were used to determine the fundamental eigenvalue for several two dimensional geometries--square, ''L'' shaped, circular, and a quarter of a typical reactor core. The results of both codes were compared with each other and with analytical solutions where available. To optimize the computer time for the code based on the boundary element method, a powerful search technique called Fibonacci search was used to determine the fundamental eigenvalues. During the course of this study, it was found that eliminating the imaginary part of the fundamental solution of the Helmholtz equation produced an instability in the result. The results show that, due to the use of the iteration procedure in the boundary element method to evaluate the determinant of the deduced matrix, more computer time is required for the boundary element solution than the finite element solution. However, the results obtained on the basis of the boundary element technique are more accurate than those from the finite element method.
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
Elastoplastic dynamic analysis of strike-slip faults with bends using finite element method
NASA Astrophysics Data System (ADS)
Duan, B.; Day, S. M.
2006-12-01
Nonelastic off-fault response may play a role in rupture dynamics on geometrically complex faults, particularly in the vicinity of bends or other points of stress concentration. In this study, we have performed nonelastic dynamic analysis of strike-slip faults with bends by using a finite element method. The Coulomb yield criterion has been implemented in the code to model off-fault nonelastic response. We find that a smooth scheme (such as viscoplasticity) is required to regularize the numerical calculation of plastic yielding near a fault bend. The method is extensible to other material rheologies (e.g., damage mechanics models, tensile failure, etc), and amenable to parallel implementation. Compared with those from a calculation with elastic off-fault response, results from a calculation with nonelastic off-fault response show that (1) bends are locations of large plastic deformation; (2) stress near a bend is less heterogeneous; (3) less radiation is generated from a bend; (4) lower strong ground motion is produced.
NASA Astrophysics Data System (ADS)
Zukir, Muhammad; Srigutomo, Wahyu
2016-08-01
Magnetotelluric (MT) method is a passive geophysical exploration technique utilizing natural electromagnetic source to obtain variation of the electric field and magnetic field on the surface of the earth. The frequency range used in this modeling is 10-4 Hz to 102 Hz. The two-dimensional (2D) magnetotelluric modeling is aimed to determine the value of electromagnetic field in the earth, the apparent resistivity, and the impedance phase. The relation between the geometrical and physical parameters used are governed by the Maxwell's equations. These equations are used in the case of Transverse Electric polarization (TE) and Transverse Magnetic polarization (TM). To calculate the solutions of electric and magnetic fields in the entire domain, the modeling domain is discretized into smaller elements using the finite element method, whereas the assembled matrix of equation system is solved using the Biconjugate Gradient Stabilized (BiCGStab) technique combined with the Incomplete Lower - Upper (ILU) preconditioner. This scheme can minimize the iteration process (computational cost) and is more effective than the Biconjugate Gradient (BiCG) technique with LU preconditions and Conjugate Gradient Square (CGS).
Study on interaction between soil and anchor chain with finite element method
NASA Astrophysics Data System (ADS)
Li, Sa; Xu, Bao-zhao; Wu, Yun-zhou; Li, Zhong-gang
2016-12-01
With the development of offshore engineering, deeply embedded anchors are needed to be penetrated to appreciable depth and attached at the pad-eye. The interaction between anchor chain and soil is a very complex process and has not been thoroughly understood yet. In this paper, the finite element method (FEM) was used to study the interaction of soil-chain system. Results of the analysis show that when the attachment point is at a shallow depth, the load-development characteristics of the chain from FEM are in good agreement with that from the model tests and theoretical analysis. But with the depth increment, the results are different obviously in different methods. This phenomenon is resulted from a variety of reasons, and the plastic zone around the chain was studied to try finding the mechanism behind it. It could be seen that the plastic zone extended in different modes at different depths of attachment points. The interaction between the soil and anchor chain makes the load acting on the anchor decrease, but the soil disturbed surrounding the chain increases the anchor failure possibility. When the anchor bearing capacity is evaluated, these two factors should be considered properly at the same time.
Full wave simulation of lower hybrid waves in Maxwellian plasma based on the finite element method
Meneghini, O.; Shiraiwa, S.; Parker, R.
2009-09-15
A full wave simulation of the lower-hybrid (LH) wave based on the finite element method is presented. For the LH wave, the most important terms of the dielectric tensor are the cold plasma contribution and the electron Landau damping (ELD) term, which depends only on the component of the wave vector parallel to the background magnetic field. The nonlocal hot plasma ELD effect was expressed as a convolution integral along the magnetic field lines and the resultant integro-differential Helmholtz equation was solved iteratively. The LH wave propagation in a Maxwellian tokamak plasma based on the Alcator C experiment was simulated for electron temperatures in the range of 2.5-10 keV. Comparison with ray tracing simulations showed good agreement when the single pass damping is strong. The advantages of the new approach include a significant reduction of computational requirements compared to full wave spectral methods and seamless treatment of the core, the scrape off layer and the launcher regions.
A new cortical thickness mapping method with application to an in vivo finite element model.
Kim, Young Ho; Kim, Jong-Eun; Eberhardt, Alan W
2014-01-01
Finite element modelling of musculoskeletal systems, with geometrical structures constructed from computed tomography (CT) scans, is a useful and powerful tool for biomechanical studies. The use of CT scans from living human subjects, however, is still limited. Accurate reconstruction of thin cortical bone structures from CT scans of living human subjects is especially problematic, due to low CT resolution that results from mandatory low radiation doses and/or involuntary movements of the subject. In this study, a new method for mapping cortical thickness is described. Using the method, cortical thickness measurements of a coxal (pelvis) bone obtained from CT scans of a cadaver were mapped to the coxal geometry as obtained through CT scans of a live human subject, resulting in accurate cortical thickness while maintaining geometric fidelity of the live subject. The mapping procedure includes shape-preserving parameterisation, mesh movement and interpolation of thickness using a search algorithm. The methodology is applicable to modelling of other bones where accurate cortical thickness is needed and for which such data exist.
Numerical modeling of fiber specklegram sensors by using finite element method (FEM).
Arístizabal, V H; Vélez, F J; Rueda, E; Gómez, N D; Gómez, J A
2016-11-28
Although experimental advances in the implementation and characterization of fiber speckle sensor have been reported, a suitable model to interpret the speckle-pattern variation under perturbation is desirable but very challenging to be developed due to the various factors influencing the speckle pattern. In this work, a new methodology based on the finite element method (FEM) for modeling and optimizing fiber specklegram sensors (FSSs) is proposed. The numerical method allows computational visualization and quantification, in near field, of changes of a step multi-mode fiber (SMMF) specklegram, due to the application of a uniformly distributed force line (UDFL). In turn, the local modifications of the fiber speckle produce changes in the optical power captured by a step single-mode fiber (SSMF) located just at the output end of the SMMF, causing a filtering effect that explains the operation of the FSSs. For each external force, the stress distribution and the propagations modes supported by the SMMF are calculated numerically by means of FEM. Then, those modes are vectorially superposed to reconstruct each perturbed fiber specklegram. Finally, the performance of the sensing mechanism is evaluated for different radius of the filtering SSMF and force-gauges, what evidences design criteria for these kinds of measuring systems. Results are in agreement with those theoretical and experimental ones previously reported.
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
A Finite-Element Method Model of Soft Tissue Response to Impulsive Acoustic Radiation Force
Palmeri, Mark L.; Sharma, Amy C.; Bouchard, Richard R.; Nightingale, Roger W.; Nightingale, Kathryn R
2010-01-01
Several groups are studying acoustic radiation force and its ability to image the mechanical properties of tissue. Acoustic radiation force impulse (ARFI) imaging is one modality using standard diagnostic ultrasound scanners to generate localized, impulsive, acoustic radiation forces in tissue. The dynamic response of tissue is measured via conventional ultrasonic speckle-tracking methods and provides information about the mechanical properties of tissue. A finite-element method (FEM) model has been developed that simulates the dynamic response of tissues, with and without spherical inclusions, to an impulsive acoustic radiation force excitation from a linear array transducer. These FEM models were validated with calibrated phantoms. Shear wave speed, and therefore elasticity, dictates tissue relaxation following ARFI excitation, but Poisson’s ratio and density do not significantly alter tissue relaxation rates. Increased acoustic attenuation in tissue increases the relative amount of tissue displacement in the near field compared with the focal depth, but relaxation rates are not altered. Applications of this model include improving image quality, and distilling material and structural information from tissue’s dynamic response to ARFI excitation. Future work on these models includes incorporation of viscous material properties and modeling the ultrasonic tracking of displaced scatterers. PMID:16382621
Bifurcation analysis of brown tide by reaction-diffusion equation using finite element method
Kawahara, Mutsuto; Ding, Yan
1997-03-01
In this paper, we analyze the bifurcation of a biodynamics system in a two-dimensional domain by virtue of reaction-diffusion equations. The discretization method in space is the finite element method. The computational algorithm for an eigenspectrum is described in detail. On the basis of an analysis of eigenspectra according to Helmholtz`s equation, the discrete spectra in regards to the physical variables are numerically obtained in two-dimensional space. In order to investigate this mathematical model in regards to its practical use, we analyzed the stability of two cases, i.e., hydranth regeneration in the marine hydroid Tubularia and a brown tide in a harbor in Japan. By evaluating the stability according to the linearized stability definition, the critical parameters for outbreaks of brown tide can be theoretically determined. In addition, results for the linear combination of eigenspectrum coincide with the distribution of the observed brown tide. Its periodic characteristic was also verified. 10 refs., 8 figs., 5 tabs.
NASA Astrophysics Data System (ADS)
Hooper, Russell; Toose, Matthijs; Macosko, Christopher W.; Derby, Jeffrey J.
2001-12-01
A modified boundary element method (BEM) and the DEVSS-G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start-up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd-B differential model, are considered for the drop phase using both FEM and BEM and for both the drop and matrix phases using FEM. Where possible, results are compared with the linear deformation theory. Consistent predictions are obtained among the BEM, FEM, and linear theory for purely Newtonian systems and between FEM and linear theory for fully viscoelastic systems. FEM and BEM predictions for viscoelastic drops in a Newtonian matrix agree very well at short times but differ at longer times, with worst agreement occurring as critical flow strength is approached. This suggests that the dominant computational advantages held by the BEM over the FEM for this and similar problems may diminish or even disappear when the issue of accuracy is appropriately considered. Fully viscoelastic problems, which are only feasible using the FEM formulation, shed new insight on the role of viscoelasticity of the matrix fluid in drop deformation. Copyright
Saeedizadeh, N; Kermani, S; Rabbani, H
2011-07-01
In this study, a hp-version of Finite Element Method (FEM) was applied for forward modeling in image reconstruction of Electrical Impedance Tomography (EIT). The EIT forward solver is normally based on the conventional Finite Element Method (h-FEM). In h-FEM, the polynomial order (p) of the element shape functions is constant and the element size (h) is decreasing. To have an accurate simulation with the h-FEM, a mesh with large number of nodes and elements is usually needed. In order to overcome this problem, the high order finite element method (p-FEM) was proposed. In the p-version, the polynomial order is increasing and the mesh size is constant. Combining the advantages of two previously mentioned methods, the element size (h) was decreased and the polynomial order (p) was increased, simultaneously, which is called the hp-version of Finite Element Method (hp-FEM). The hp-FEM needs a smaller number of nodes and consequently, less computational time and less memory to achieve the same or even better accuracy than h-FEM. The SNR value is 42db for hp-FEM and is 9db for h-FEM. The numerical results are presented and verified that the performance of the hp-version is better than of the h-version in image reconstruction of EIT.
NASA Astrophysics Data System (ADS)
Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick; Ortensi, Javier; Baker, Benjamin; Laboure, Vincent; Wang, Congjian; DeHart, Mark; Martineau, Richard
2017-06-01
This work presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the SN transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form is based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. While NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in
A coupled/uncoupled deformation and fatigue damage algorithm utilizing the finite element method
NASA Technical Reports Server (NTRS)
Wilt, Thomas E.; Arnold, Steven M.
1994-01-01
A fatigue damage computational algorithm utilizing a multiaxial, isothermal, continuum based fatigue damage model for unidirectional metal matrix composites has been implemented into the commercial finite element code MARC using MARC user subroutines. Damage is introduced into the finite element solution through the concept of effective stress which fully couples the fatigue damage calculations with the finite element deformation solution. An axisymmetric stress analysis was performed on a circumferentially reinforced ring, wherein both the matrix cladding and the composite core were assumed to behave elastic-perfectly plastic. The composite core behavior was represented using Hill's anisotropic continuum based plasticity model, and similarly, the matrix cladding was represented by an isotropic plasticity model. Results are presented in the form of S-N curves and damage distribution plots.
Biomechanical Analysis of Hearing in Whales Using Nanoindentation and the Finite Element Method
NASA Astrophysics Data System (ADS)
Tubelli, Andrew A.; Zosuls, Aleks; Ketten, Darlene R.; Mountain, David C.
2011-11-01
The detailed biomechanics of hearing in baleen whales are almost entirely unknown. As a first step to predicting the audiogram for these species, a linear three-dimensional finite-element model of the minke whale (Balaenoptera acutorostrata) middle ear was developed. A reconstruction of the ear was made from CT scans and imported into a finite element solver. Young's modulus of the bone was estimated via nanoindentation. The middle-ear transfer function was estimated by applying a pressure to the glove finger (the thick, everted equivalent of the tympanic membrane) with velocity calculated at the stapes footplate. It was found that the most sensitive frequencies corresponded with vocalization frequencies. For all frequencies tested, the malleus-incus complex flexed about the anterior process of the malleus and the stapes rotated within the oval window. Results indictae that finite element modeling is a useful approach for studying the mechanics of hearing in species that are difficult to study in vivo.
Development of an hp-version finite element method for computational optimal control
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Warner, Michael S.
1993-01-01
The purpose of this research effort is to develop a means to use, and to ultimately implement, hp-version finite elements in the numerical solution of optimal control problems. The hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element.
NASA Astrophysics Data System (ADS)
Morales Rivera, A. M.; Albino, F.; Amelug, F.; Gregg, P. M.; Mothes, P. A.
2015-12-01
Tungurahua volcano has been intermittently erupting since 1999, with observed deformation between 2007-2011 using Interferometric Synthetic Aperture Radar (InSAR) from the ALOS satellite of the Japanese Aerospace Exploration Agency. Our recent analysis during that time period has provided insights into the characteristics of the subsurface, suggesting multiple connected magma chambers underneath the edifice with distinct temporal and spatial behaviors. However, the previous source models are too simplistic and fail to incorporate realistic physical properties and forces acting within the volcano that would generate the observed deformation. We use deformation data from InSAR and solve for the optimal deformation source parameters with Finite Element Methods (FEM) by incorporating into the models the material heterogeneities (e.g. temperature, density, elastic, viscoelastic), and stresses (e.g. background stresses, edifice loading, magma chamber overpressure) acting on the volcano. We attempt to integrate previous multidisciplinary volcanological studies with our results to constrain the subsurface characteristics and understand the volcanic processes generating the observed deformation.
NASA Astrophysics Data System (ADS)
Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander
2014-04-01
Shape sensing, i.e., reconstruction of the displacement field of a structure from surface-measured strains, has relevant implications for the monitoring, control and actuation of smart structures. The inverse finite element method (iFEM) is a shape-sensing methodology shown to be fast, accurate and robust. This paper aims to demonstrate that the recently presented iFEM for beam and frame structures is reliable when experimentally measured strains are used as input data. The theoretical framework of the methodology is first reviewed. Timoshenko beam theory is adopted, including stretching, bending, transverse shear and torsion deformation modes. The variational statement and its discretization with C0-continuous inverse elements are briefly recalled. The three-dimensional displacement field of the beam structure is reconstructed under the condition that least-squares compatibility is guaranteed between the measured strains and those interpolated within the inverse elements. The experimental setup is then described. A thin-walled cantilevered beam is subjected to different static and dynamic loads. Measured surface strains are used as input data for shape sensing at first with a single inverse element. For the same test cases, convergence is also investigated using an increasing number of inverse elements. The iFEM-recovered deflections and twist rotations are then compared with those measured experimentally. The accuracy, convergence and robustness of the iFEM with respect to unavoidable measurement errors, due to strain sensor locations, measurement systems and geometry imperfections, are demonstrated for both static and dynamic loadings.
Representation of bioelectric current sources using Whitney elements in the finite element method.
Tanzer, I Oğuz; Järvenpää, Seppo; Nenonen, Jukka; Somersalo, Erkki
2005-07-07
Bioelectric current sources of magneto- and electroencephalograms (MEG, EEG) are usually modelled with discrete delta-function type current dipoles, despite the fact that the currents in the brain are naturally continuous throughout the neuronal tissue. In this study, we represent bioelectric current sources in terms of Whitney-type elements in the finite element method (FEM) using a tetrahedral mesh. The aim is to study how well the Whitney elements can reproduce the potential and magnetic field patterns generated by a point current dipole in a homogeneous conducting sphere. The electric potential is solved for a unit sphere model with isotropic conductivity and magnetic fields are calculated for points located on a cap outside the sphere. The computed potential and magnetic field are compared with analytical solutions for a current dipole. Relative difference measures between the FEM and analytical solutions are less than 1%, suggesting that Whitney elements as bioelectric current sources are able to produce the same potential and magnetic field patterns as the point dipole sources.
Diarra, Harona; Mazel, Vincent; Busignies, Virginie; Tchoreloff, Pierre
2015-09-30
Finite elements method was used to study the influence of tablet thickness and punch curvature on the density distribution inside convex faced (CF) tablets. The modeling of the process was conducted on 2 pharmaceutical excipients (anhydrous calcium phosphate and microcrystalline cellulose) by using Drucker-Prager Cap model in Abaqus(®) software. The parameters of the model were obtained from experimental tests. Several punch shapes based on industrial standards were used. A flat-faced (FF) punch and 3 convex faced (CF) punches (8R11, 8R8 and 8R6) with a diameter of 8mm were chosen. Different tablet thicknesses were studied at a constant compression force. The simulation of the compaction of CF tablets with increasing thicknesses showed an important change on the density distribution inside the tablet. For smaller thicknesses, low density zones are located toward the center. The density is not uniform inside CF tablets and the center of the 2 faces appears with low density whereas the distribution inside FF tablets is almost independent of the tablet thickness. These results showed that FF and CF tablets, even obtained at the same compression force, do not have the same density at the center of the compact. As a consequence differences in tensile strength, as measured by diametral compression, are expected. This was confirmed by experimental tests.
Performance of mixed formulations for the particle finite element method in soil mechanics problems
NASA Astrophysics Data System (ADS)
Monforte, Lluís; Carbonell, Josep Maria; Arroyo, Marcos; Gens, Antonio
2016-11-01
This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the particle finite element method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well established in current geotechnical analyses (Darcy's law; Modified Cam Clay; Houlsby hyperelasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behaviour; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydromechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behaviour under undrained conditions. In order to use equal-order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.
Numerical solution of an elastic and viscoelastic gravitational models by the finite element method
NASA Astrophysics Data System (ADS)
Arjona Almodóvar, A.; Chacón Rebollo, T.; Gómez Marmol, M.
2014-12-01
Volcanic areas present a lower effective viscosity than usually in the Earth's crust. Both the elastic-gravitational and the viscoelastic-gravitational models allow the computation of gravity, deformation, and gravitational potential changes in order to investigate crustal deformations of Earth (see for instance Battaglia & Segall, 2004; Fernández et al. 1999, 2001; Rundle 1980 and 1983). These models can be represented by a coupled system of linear parabolic (for the elastic deformations), hyperbolic (for the viscoelastic deformations) and elliptic partial differential equations (for gravitational potential changes) (see for instance Arjona et al. 2008 and 2010). The existence and uniqueness of weak solutions for both the elastic-gravitational and viscoelastic-gravitational problem was demonstrated in Arjona et al. (2008 and 2014). The stabilization to solutions of the associated stationary system was proved in Arjona and Díaz (2007). Here we consider the internal source as response to the effect of a pressurized magma reservoir into a multilayered, elastic-gravitational and viscoelastic-gravitational earth model. We introduce the numerical analysis of a simplified steady elastic-gravitational model, solved by means of the finite element method. We also present some numerical tests in realistic situations that confirm the predictions of theoretical order of convergence. Finally, we describe the methodology for both the elastic-gravitational and the viscoelastic-gravitational models using 2D and 3D test examples performed with FreeFEM++.
Finite Element Method Based Modeling for Prediction of Cutting Forces in Micro-end Milling
NASA Astrophysics Data System (ADS)
Pratap, Tej; Patra, Karali
2017-02-01
Micro-end milling is one of the widely used processes for producing micro features/components in micro-fluidic systems, biomedical applications, aerospace applications, electronics and many more fields. However in these applications, the forces generated in the micro-end milling process can cause tool vibration, process instability and even cause tool breakage if not minimized. Therefore, an accurate prediction of cutting forces in micro-end milling is essential. In this work, a finite element method based model is developed using ABAQUS/Explicit 6.12 software for prediction of cutting forces in micro-end milling with due consideration of tool edge radius effect, thermo-mechanical properties and failure parameters of the workpiece material including friction behaviour at tool-chip interface. Experiments have been performed for manufacturing of microchannels on copper plate using 500 µm diameter tungsten carbide micro-end mill and cutting forces are acquired through a dynamometer. Predicted cutting forces in feed and cross feed directions are compared with experimental results and are found to be in good agreements. Results also show that FEM based simulations can be applied to analyze size effects of specific cutting forces in micro-end milling process.
NASA Astrophysics Data System (ADS)
Sirait, S. H.; Edison, R. E.; Baidillah, M. R.; Taruno, W. P.; Haryanto, F.
2016-08-01
The aim of this study is to simulate the potential distribution of 2D brain geometry based on two electrodes ECVT. ECVT (electrical capacitance tomography) is a tomography modality which produces dielectric distribution image of a subject from several capacitance electrodes measurements. This study begins by producing the geometry of 2D brain based on MRI image and then setting the boundary conditions on the boundaries of the geometry. The values of boundary conditions follow the potential values used in two electrodes brain ECVT, and for this reason the first boundary is set to 20 volt and 2.5 MHz signal and another boundary is set to ground. Poisson equation is implemented as the governing equation in the 2D brain geometry and finite element method is used to solve the equation. Simulated Hodgkin-Huxley action potential is applied as disturbance potential in the geometry. We divide this study into two which comprises simulation without disturbance potential and simulation with disturbance potential. From this study, each of time dependent potential distributions from non-disturbance and disturbance potential of the 2D brain geometry has been generated.
Analysis of the Dynamic Behavior of the Inner Hair Cell Stereocilia by the Finite Element Method
NASA Astrophysics Data System (ADS)
Matsui, Toshihiro; Nakajima, Chihiro; Yamamoto, Yuichi; Andoh, Masayoshi; Iida, Koji; Murakoshi, Michio; Kumano, Shun; Wada, Hiroshi
The motion of the inner hair cell (IHC) stereocilia, which results in tension in the tip links connected to mechanically gated ion channels, mediates the auditory transduction process. However, it is difficult to directly observe the motion of the stereocilia because of their minute dimensions and complex structure. In this study, to investigate such motion, a finite element method model of the tall, middle and short IHC stereocilia, including the tip and lateral links extending between the stereocilia, was constructed. By applying an analytically estimated fluid force caused by a stimulus of 60dB SPL at 500Hz to the model, the dynamic behavior of the stereocilia was analyzed. Numerical results showed that the stereocilia moved in phase and that the maximum tensions of 2.5fN and 2.1fN occurred in the tip link connecting the tall and middle stereocilia and in the tip link connecting the middle and short stereocilia, respectively. By contrast, under the condition in which the lateral links were removed, maximum tension in the former increased to 11.6fN, while that in the latter only increased to 2.3fN. It was therefore suggested that the lateral links protect the MET channels located at taller stereocilia against large stimuli and subject the channels located in the same IHC to forces of similar size.
Alani, Amir M.; Faramarzi, Asaad
2015-01-01
In this paper, a stochastic finite element method (SFEM) is employed to investigate the probability of failure of cementitious buried sewer pipes subjected to combined effect of corrosion and stresses. A non-linear time-dependant model is used to determine the extent of concrete corrosion. Using the SFEM, the effects of different random variables, including loads, pipe material, and corrosion on the remaining safe life of the cementitious sewer pipes are explored. A numerical example is presented to demonstrate the merit of the proposed SFEM in evaluating the effects of the contributing parameters upon the probability of failure of cementitious sewer pipes. The developed SFEM offers many advantages over traditional probabilistic techniques since it does not use any empirical equations in order to determine failure of pipes. The results of the SFEM can help the concerning industry (e.g., water companies) to better plan their resources by providing accurate prediction for the remaining safe life of cementitious sewer pipes. PMID:26068092
NASA Astrophysics Data System (ADS)
Yan Li, Sheng; Gang Xu, Bin; Ming Tao, Xiao
2010-05-01
Spun yarns are used worldwide for making a wide range of textiles and apparel. The spun yarn is formed by twisting an assembly of short fibers in order to obtain sufficient strength for the downstream processing. In spinning triangle, the fibers will be finally twisted into yarn. Thus the properties of yarn were greatly influenced by the shape and the fiber stress distribution of the spinning triangle. In this study, the theoretical issue of ring spinning triangle was examined by using the finite element method. In order to address more complicated condition of the spinning triangle, some important factors ignored previously, including the yarn spinning torque, the inclined spinning tension and fiber torsional strains, were considered. With the input of different spinning parameters, such as yarn count (yarn linear density), yarn twist, spinning tension and torque, some essential parameters of the spinning triangle, including the fiber tension distribution, fiber torsion distribution and the height of the spinning triangle, were numerically obtained and their quantitative relationships were discussed in detail.
Use of finite element analysis to optimize probe design for double sensor method-based thermometer.
Sim, Soo Young; Joo, Kwang Min; Park, Kwang Suk
2015-08-01
Body temperature is an essential vital sign for assessing physiological functions. The double sensor method-based thermometer is a promising technology that may be applicable to body temperature monitoring in daily life. It continuously estimates deep tissue temperature from the intact skin surface. Despite its considerable potential for monitoring body temperature, its key design features have not been investigated. In this study, we considered four design factors: the cover material, insulator material, insulator radius, and insulator height. We also evaluated their effects on the performance of the double sensor thermometer in terms of accuracy, initial waiting time, and the ability to track changes in body temperature. The probe material and size influenced the accuracy and initial waiting time. Finite element analysis revealed that four thermometers of different sizes composed of an aluminum cover and foam insulator provided high accuracy (<0.1°C) under various ambient temperatures and blood perfusion rates: R=20mm, H=5mm; R=15mm, H=10mm; R=20mm, H=10mm; and R=15mm, H=15mm. The initial waiting time was approximately 10min with almost the same traceability of temperature change. Our findings may provide thermometer manufacturers with new insights into probe design and help them fabricate thermometers optimized for specific applications.
Representation of bioelectric current sources using Whitney elements in the finite element method
NASA Astrophysics Data System (ADS)
Oguz Tanzer, I.; Järvenpää, Seppo; Nenonen, Jukka; Somersalo, Erkki
2005-07-01
Bioelectric current sources of magneto- and electroencephalograms (MEG, EEG) are usually modelled with discrete delta-function type current dipoles, despite the fact that the currents in the brain are naturally continuous throughout the neuronal tissue. In this study, we represent bioelectric current sources in terms of Whitney-type elements in the finite element method (FEM) using a tetrahedral mesh. The aim is to study how well the Whitney elements can reproduce the potential and magnetic field patterns generated by a point current dipole in a homogeneous conducting sphere. The electric potential is solved for a unit sphere model with isotropic conductivity and magnetic fields are calculated for points located on a cap outside the sphere. The computed potential and magnetic field are compared with analytical solutions for a current dipole. Relative difference measures between the FEM and analytical solutions are less than 1%, suggesting that Whitney elements as bioelectric current sources are able to produce the same potential and magnetic field patterns as the point dipole sources.
NASA Astrophysics Data System (ADS)
Günay, E.
2016-04-01
In this study, the modulus of elasticity and shear modulus values of single-walled carbon nanotubes SWCNTs were modelled by using both finite element method and the Matlab code. Initially, cylindrical armchair and zigzag single walled 3D space frames were demonstrated as carbon nanostructures. Thereafter, macro programs were written by the Matlab code producing the space truss for zigzag and armchair models. 3D space frames were introduced to the ANSYS software and then tension, compression and additionally torsion tests were performed on zigzag and armchair carbon nanotubes with BEAM4 element in obtaining the exact values of elastic and shear modulus values. In this study, two different boundary conditions were tested and especially used in torsion loading. The equivalent shear modulus data was found by averaging the corresponding values obtained from ten different nodal points on the nanotube path. Finally, in this study it was determined that the elastic constant values showed proportional changes by increasing the carbon nanotube diameters up to a certain level but beyond this level these values remained stable.
Nakamachi, Eiji; Yoshida, Takashi; Yamaguchi, Toshihiko; Morita, Yusuke; Kuramae, Hiroyuki; Morimoto, Hideo
2014-10-06
We developed two-scale FE analysis procedure based on the crystallographic homogenization method by considering the hierarchical structure of poly-crystal aluminium alloy metal. It can be characterized as the combination of two-scale structure, such as the microscopic polycrystal structure and the macroscopic elastic plastic continuum. Micro polycrystal structure can be modeled as a three dimensional representative volume element (RVE). RVE is featured as by 3×3×3 eight-nodes solid finite elements, which has 216 crystal orientations. This FE analysis code can predict the deformation, strain and stress evolutions in the wire drawing processes in the macro- scales, and further the crystal texture and hardening evolutions in the micro-scale. In this study, we analyzed the texture evolution in the wire drawing processes by our two-scale FE analysis code under conditions of various drawing angles of dice. We evaluates the texture evolution in the surface and center regions of the wire cross section, and to clarify the effects of processing conditions on the texture evolution.
Numerical analysis of tire/contact pressure using finite element method
NASA Astrophysics Data System (ADS)
Pranoto, Sarwo Edy; Hidayat, Royan; Tauviqirrahman, Mohammad; Bayuseno, Athanasius P.
2016-04-01
The interaction between the road surface and vehicle's tire may significantly determine the stability of a vehicle. We could study the tire contact-pressure to road surfaces through a numerical simulation in this present study. In particular, the main purpose of the study was to present an illustration of the effect of the varied loads to the tire, which would affect the contact pressure on the road surface sand stress distribution on the tire by employing a commercial ABAQUS software, based on the finite element method. To make the process of data analysis easier, the tire was assumed to be made from natural rubber which composition consisted of 2 layers of the inner tire and 1 layer of carcass. In pre-conditions, the tire was given air pressure as much as 17 psi, and loads as much as 2 KN, 6 KN, and 10 KN; then, the air pressure was increased to be 30 psi; consequently, the simulation results of stress distribution and deformation on each of loads condition would be acquired. The simulation results indicated that the loads carried by the tire on the vehicle were an important factor to determine the tire-stress profile.
A Study to Investigate the Sleeping Comfort of Mattress using Finite Element Method
NASA Astrophysics Data System (ADS)
Yoshida, Hiroaki; Kamijo, Masayoshi; Shimizu, Yoshio
Sleep is an essential physiological activity for human beings and many studies have so far investigated sleeping comfort of mattresses. The appropriate measurement of stress distribution within the human body would provide valuable information to us. For the appropriate measurement to estimate stress distribution within the human body, numerical analysis is considered one of the most desirable techniques, and Finite Element Method (FEM), which is widely accepted as a useful numerical technique, was utilized in this study. Since human body dimensions have individual differences, however, it is presumed that the way of the internal stress distribution also changes due to the differences and that the mattress preference varies among different body forms. Thus, we developed three human FEM models reproducing the body forms of three types of male subjects, and investigated the sleeping comfort of mattress based on the relationship between FEM analysis findings and sensory testing results. In comparison with the results of both FEM analysis and sensory testing in the neck region, we found, the sensory testing results corresponded to the FEM analysis findings, and it was possible to estimate subjects' preferences of mattress and comfort in the neck region using the FEM analysis. In this study, we believe, the FEM analysis managed to quantify the subjects' preferences for mattress and to prove itself that it is the valuable tools to examine the sleeping comfort of mattress.
Finite Element Method Based Modeling for Prediction of Cutting Forces in Micro-end Milling
NASA Astrophysics Data System (ADS)
Pratap, Tej; Patra, Karali
2016-04-01
Micro-end milling is one of the widely used processes for producing micro features/components in micro-fluidic systems, biomedical applications, aerospace applications, electronics and many more fields. However in these applications, the forces generated in the micro-end milling process can cause tool vibration, process instability and even cause tool breakage if not minimized. Therefore, an accurate prediction of cutting forces in micro-end milling is essential. In this work, a finite element method based model is developed using ABAQUS/Explicit 6.12 software for prediction of cutting forces in micro-end milling with due consideration of tool edge radius effect, thermo-mechanical properties and failure parameters of the workpiece material including friction behaviour at tool-chip interface. Experiments have been performed for manufacturing of microchannels on copper plate using 500 µm diameter tungsten carbide micro-end mill and cutting forces are acquired through a dynamometer. Predicted cutting forces in feed and cross feed directions are compared with experimental results and are found to be in good agreements. Results also show that FEM based simulations can be applied to analyze size effects of specific cutting forces in micro-end milling process.
Evaluation of Test Methods for Triaxially Braided Composites using a Meso-Scale Finite Element Model
Zhang, Chao
2015-10-01
The characterization of triaxially braided composite is complicate due to the nonuniformity of deformation within the unit cell as well as the possibility of the freeedge effect related to the large size of the unit cell. Extensive experimental investigation has been conducted to develop more accurate test approaches in characterizing the actual mechanical properties of the material we are studying. In this work, a meso-scale finite element model is utilized to simulate two complex specimens: notched tensile specimen and tube tensile specimen, which are designed to avoid the free-edge effect and free-edge effect induced premature edge damage. The full field strain data is predicted numerically and compared with experimental data obtained by Digit Image Correlation. The numerically predicted tensile strength values are compared with experimentally measured results. The discrepancy between numerically predicted and experimentally measured data, the capability of different test approaches are analyzed and discussed. The presented numerical model could serve as assistance to the evaluation of different test methods, and is especially useful in identifying potential local damage events.
Full wave simulation of waves in ECRIS plasmas based on the finite element method
Torrisi, G.; Mascali, D.; Neri, L.; Castro, G.; Patti, G.; Celona, L.; Gammino, S.; Ciavola, G.; Di Donato, L.; Sorbello, G.; Isernia, T.
2014-02-12
This paper describes the modeling and the full wave numerical simulation of electromagnetic waves propagation and absorption in an anisotropic magnetized plasma filling the resonant cavity of an electron cyclotron resonance ion source (ECRIS). The model assumes inhomogeneous, dispersive and tensorial constitutive relations. Maxwell's equations are solved by the finite element method (FEM), using the COMSOL Multiphysics{sup ®} suite. All the relevant details have been considered in the model, including the non uniform external magnetostatic field used for plasma confinement, the local electron density profile resulting in the full-3D non uniform magnetized plasma complex dielectric tensor. The more accurate plasma simulations clearly show the importance of cavity effect on wave propagation and the effects of a resonant surface. These studies are the pillars for an improved ECRIS plasma modeling, that is mandatory to optimize the ion source output (beam intensity distribution and charge state, especially). Any new project concerning the advanced ECRIS design will take benefit by an adequate modeling of self-consistent wave absorption simulations.
Anisotropic mode-dependent damage of cortical bone using the extended finite element method (XFEM).
Feerick, Emer M; Liu, Xiangyi Cheryl; McGarry, Patrick
2013-04-01
Anisotropic damage initiation criteria were developed for extended finite element method (XFEM) prediction of crack initiation and propagation in cortical bone. This anisotropic damage model was shown to accurately predict the dependence of crack propagation patterns and fracture toughness on mode mixity and on osteon orientations, as observed experimentally. Four initiation criteria were developed to define crack trajectories relative to osteon orientations and max principal stress for single and mixed mode fracture. Alternate failure strengths for tensile and compressive loading were defined to simulate the asymmetric failure of cortical bone. The dependence of cortical bone elasticity and failure properties on osteon orientation is analogous to the dependence of composite properties on fibre orientation. Hence, three of the criteria developed in the present study were based upon the Hashin damage criteria. The fourth criterion developed was defined in terms of the max principal stress. This criterion initiated off axis crack growth perpendicular to the direction of the max principal stress. The unique set of parameters calibrated accurately predicted; (i) the relationship between fracture energy and osteon alignment, (ii) the alternate crack patterns for both varying osteon orientations and loading angle. Application of the developed anisotropic damage models to cortical bone screw pullout highlights the potential application for orthopaedic device design evaluation.
NASA Astrophysics Data System (ADS)
Salazar, Fernando; San-Mauro, Javier; Celigueta, Miguel Ángel; Oñate, Eugenio
2016-06-01
Dam bottom outlets play a vital role in dam operation and safety, as they allow controlling the water surface elevation below the spillway level. For partial openings, water flows under the gate lip at high velocity and drags the air downstream of the gate, which may cause damages due to cavitation and vibration. The convenience of installing air vents in dam bottom outlets is well known by practitioners. The design of this element depends basically on the maximum air flow through the air vent, which in turn is a function of the specific geometry and the boundary conditions. The intrinsic features of this phenomenon makes it hard to analyse either on site or in full scaled experimental facilities. As a consequence, empirical formulas are frequently employed, which offer a conservative estimate of the maximum air flow. In this work, the particle finite element method was used to model the air-water interaction in Susqueda Dam bottom outlet, with different gate openings. Specific enhancements of the formulation were developed to consider air-water interaction. The results were analysed as compared to the conventional design criteria and to information gathered on site during the gate operation tests. This analysis suggests that numerical modelling with the PFEM can be helpful for the design of this kind of hydraulic works.
NASA Astrophysics Data System (ADS)
Senveli, Sukru U.; Tigli, Onur
2013-12-01
This paper introduces the use of finite element method analysis tools to investigate the use of a Rayleigh type surface acoustic wave (SAW) sensor to interrogate minute amounts of liquids trapped in microcavities placed on the delay line. Launched surface waves in the ST-X quartz substrate couple to the liquid and emit compressional waves. These waves form a resonant cavity condition and interfere with the surface waves in the substrate. Simulations show that the platform operates in a different mechanism than the conventional mass loading of SAW devices. Based on the proposed detection mechanism, it is able to distinguish between variations of 40% and 90% glycerin based on phase relations while using liquid volumes smaller than 10 pl. Results from shallow microcavities show high correlation with sound velocity parameter of the liquid whereas deeper microcavities display high sensitivities with respect to glycerin concentration. Simulated devices yield a maximum sensitivity of -0.77°/(% glycerin) for 16 μm wavelength operation with 8 μm deep, 24 μm wide, and 24 μm long microcavities.
NASA Astrophysics Data System (ADS)
Konar, G.; Chakraborty, N.; Das, J.
Hysteresis motors being capable of producing a steady torque at low speeds and providing good starting properties at loaded condition became popular among different fractional horse power electrical motors. High temperature superconducting materials being intrinsically hysteretic are suitable for this type of motor. In the present work, performance study of a 2-pole, 50 Hz HTS hysteresis motor with conventional stator and HTS rotor has been carried out numerically using finite element method. The simulation results confirm the ability of the segmented HTS rotor with glued circular sectors to trap the magnetic field as high as possible compared to the ferromagnetic rotor. Also the magnetization loops in the HTS hysteresis motor are obtained and the corresponding torque and AC losses are calculated. The motor torque thus obtained is linearly proportional to the current which is the common feature of any hysteresis motor. Calculations of torques, current densities etc are done using MATLAB program developed in-house and validated using COMSOL Multiphysics software. The simulation result shows reasonable agreement with the published results.
NASA Technical Reports Server (NTRS)
Ransom, Jonathan B.
2002-01-01
A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.
NASA Astrophysics Data System (ADS)
Villanueva Perez, Carlos Hernan
Computational design optimization provides designers with automated techniques to develop novel and non-intuitive optimal designs. Topology optimization is a design optimization technique that allows for the evolution of a broad variety of geometries in the optimization process. Traditional density-based topology optimization methods often lack a sufficient resolution of the geometry and physical response, which prevents direct use of the optimized design in manufacturing and the accurate modeling of the physical response of boundary conditions. The goal of this thesis is to introduce a unified topology optimization framework that uses the Level Set Method (LSM) to describe the design geometry and the eXtended Finite Element Method (XFEM) to solve the governing equations and measure the performance of the design. The methodology is presented as an alternative to density-based optimization approaches, and is able to accommodate a broad range of engineering design problems. The framework presents state-of-the-art methods for immersed boundary techniques to stabilize the systems of equations and enforce the boundary conditions, and is studied with applications in 2D and 3D linear elastic structures, incompressible flow, and energy and species transport problems to test the robustness and the characteristics of the method. A comparison of the framework against density-based topology optimization approaches is studied with regards to convergence, performance, and the capability to manufacture the designs. Furthermore, the ability to control the shape of the design to operate within manufacturing constraints is developed and studied. The analysis capability of the framework is validated quantitatively through comparison against previous benchmark studies, and qualitatively through its application to topology optimization problems. The design optimization problems converge to intuitive designs and resembled well the results from previous 2D or density-based studies.
NASA Technical Reports Server (NTRS)
Frank, Andreas O.; Twombly, I. Alexander; Barth, Timothy J.; Smith, Jeffrey D.; Dalton, Bonnie P. (Technical Monitor)
2001-01-01
We have applied the linear elastic finite element method to compute haptic force feedback and domain deformations of soft tissue models for use in virtual reality simulators. Our results show that, for virtual object models of high-resolution 3D data (>10,000 nodes), haptic real time computations (>500 Hz) are not currently possible using traditional methods. Current research efforts are focused in the following areas: 1) efficient implementation of fully adaptive multi-resolution methods and 2) multi-resolution methods with specialized basis functions to capture the singularity at the haptic interface (point loading). To achieve real time computations, we propose parallel processing of a Jacobi preconditioned conjugate gradient method applied to a reduced system of equations resulting from surface domain decomposition. This can effectively be achieved using reconfigurable computing systems such as field programmable gate arrays (FPGA), thereby providing a flexible solution that allows for new FPGA implementations as improved algorithms become available. The resulting soft tissue simulation system would meet NASA Virtual Glovebox requirements and, at the same time, provide a generalized simulation engine for any immersive environment application, such as biomedical/surgical procedures or interactive scientific applications.
Analysis of the Abfraction Lesions Formation Mechanism by the Finite Element Method
Jakupovic, Selma; Cerjakovic, Edin; Topcic, Alan; Ajanovic, Muhamed; Prcic, Alma Konjhodzic-; Vukovic, Amra
2014-01-01
Introduction: An abfraction lesion is a type of a non-carious cervical lesion (NCCL) that represents a sharp defect on the cervical part of tooth, caused by occlusal biomechanical forces. The largest prevalence of the NCCL is found on the mandibular first premolar. The goal of the study is, by means of a numerical method – the finite element method (FEM), in an appropriate computer program, conduct a stress analysis of the mandibular premolar under various static loads, with a special reference to the biomechanics of cervical tooth region. Material and methods: A three-dimensional model of the mandibular premolar is gained from a µCT x-ray image. By using the FEM, straining of the enamel, dentin, peridontal ligament and alveolar bone under axial and paraxial forces of 200 [N] is analyzed. The following software were used in the analysis: CT images processing–CTAn program and FEM analysis–AnsysWorkbench 14.0. Results: According to results obtained through the FEM method, the calculated stress is higher with eccentric forces within all tested tooth tissue. The occlusal load leads to a significant stress in the cervical tooth area, especially in the sub-superficial layer of the enamel (over 50 MPa). The measured stress in the peridontal ligament is approximately three times higher under paraxial load with regard to the axial load, while stress calculated in the alveolar bone under paraxial load is almost ten times higher with regard to the axial load. The highest stress values were calculated in the cervical part of the alveoli, where bone resorption is most commonly seen. Conclusion: Action of occlusal forces, especially paraxial ones, leads to significant stress in the cervical part of tooth. The stress values in the cervical sub-superficial enamel layer are almost 5 times higher in relation to the superficial enamel, which additionally confirms complexity of biomechanical processes in the creation of abfraction lesions. PMID:25395725
NASA Technical Reports Server (NTRS)
Seybert, A. F.; Wu, T. W.; Wu, X. F.
1994-01-01
This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis; noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: sound power predicted by the BEM model using vibration data measured on the surface of the box; sound power predicted by the FEM/BEM model; and sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. The predicted vibration and radiated noise were then validated through experimentation.
Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients
Kalchev, D
2012-04-02
This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-{rho}AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the
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 progress report on estuary modeling by the finite-element method
Gray, William G.
1978-01-01
Various schemes are investigated for finite-element modeling of two-dimensional surface-water flows. The first schemes investigated combine finite-element spatial discretization with split-step time stepping schemes that have been found useful in finite-difference computations. Because of the large number of numerical integrations performed in space and the large sparse matrices solved, these finite-element schemes were found to be economically uncompetitive with finite-difference schemes. A very promising leapfrog scheme is proposed which, when combined with a novel very fast spatial integration procedure, eliminates the need to solve any matrices at all. Additional problems attacked included proper propagation of waves and proper specification of the normal flow-boundary condition. This report indicates work in progress and does not come to a definitive conclusion as to the best approach for finite-element modeling of surface-water problems. The results presented represent findings obtained between September 1973 and July 1976. (Woodard-USGS)
Overall design of actively controlled smart structures by the finite element method
NASA Astrophysics Data System (ADS)
Gabbert, Ulrich; Koeppe, Heinz; Seeger, Falko
2001-08-01
The design process of engineering smart structures requires a virtual overall model, which includes the main functional parts such as the passive structure, the actuators and sensors as well as the control algorithm. The objective of the paper is to pre-sent such a design concept for vibration suppression of thin-walled shell structures controlled by piezoelectric wafers and fi-bers. This concept is based on a recently developed finite element package for the simulation of multi-physics problems. At first a rough design of actuator and sensor distributions is estimated which is based on the controllability and observabilty indices. Then the Matlab/Simulink software tool is used for controller design. From the finite element model all required data and information are transferred to Matlab/Simulink via a data exchange interface. After having designed the controller the result in form of the controller matrices or as C-codes can be transferred back into the finite element simulation package. Within the finite element code the controlled structural behavior can be studied under different disturbances. The structural design can be improved in an iterative way, e.g. by changing the actuator and sensor positions based on a sensitivity analy-sis. As an example an actively controlled smart plate structure is designed and tested to demonstrate the proposed procedure.