Adaptive Finite Element Methods in Geodynamics
NASA Astrophysics Data System (ADS)
Davies, R.; Davies, H.; Hassan, O.; Morgan, K.; Nithiarasu, P.
2006-12-01
Adaptive finite element methods are presented for improving the quality of solutions to two-dimensional (2D) and three-dimensional (3D) convection dominated problems in geodynamics. The methods demonstrate the application of existing technology in the engineering community to problems within the `solid' Earth sciences. Two-Dimensional `Adaptive Remeshing': The `remeshing' strategy introduced in 2D adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code `ConMan'. An unstructured quadrilateral mesh generator is utilised, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermo-chemical problems with known benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy whilst increasing computational efficiency. For thermo-chemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies. Three-Dimensional Adaptive Multigrid: We extend the ideas from our 2D work into the 3D realm in the context of a pre-existing 3D-spherical mantle dynamics code, `TERRA'. In its original format, `TERRA' is computationally highly efficient since it employs a multigrid solver that depends upon a grid utilizing a clever
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 method for diffraction gratings
NASA Astrophysics Data System (ADS)
Bao, Gang; Chen, Zhiming; Wu, Haijun
2005-06-01
A second-order finite-element adaptive strategy with error control for one-dimensional grating problems is developed. The unbounded computational domain is truncated to a bounded one by a perfectly-matched-layer (PML) technique. The PML parameters, such as the thickness of the layer and the medium properties, are determined through sharp a posteriori error estimates. The adaptive finite-element method is expected to increase significantly the accuracy and efficiency of the discretization as well as reduce the computation cost. Numerical experiments are included to illustrate the competitiveness of the proposed adaptive method.
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
NASA Astrophysics Data System (ADS)
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.
2016-09-01
In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.
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.
An adaptive finite element method for convective heat transfer with variable fluid properties
NASA Astrophysics Data System (ADS)
Pelletier, Dominique; Ilinca, Florin; Hetu, Jean-Francois
1993-07-01
This paper presents an adaptive finite element method based on remeshing to solve incompressible viscous flow problems for which fluid properties present a strong temperature dependence. Solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids. Two general purpose error estimators, that take into account fluid properties variations, are presented. The methodology is applied to a problem of practical interest: the thermal convection of corn syrup in an enclosure with localized heating. Predictions are in good agreement with experimental measurements. The method leads to improved accuracy and reliability of finite element predictions.
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 massively parallel adaptive finite element method with dynamic load balancing
Devine, K.D.; Flaherty, J.E.; Wheat, S.R.; Maccabe, A.B.
1993-05-01
We construct massively parallel, adaptive 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. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We demonstrate parallel efficiency through computations on a 1024-processor nCUBE/2 hypercube. We also present results using adaptive p-refinement to reduce the computational cost of the method. We describe tiling, a dynamic, element-based data migration system. Tiling dynamically maintains global load balance in the adaptive method by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. We demonstrate the effectiveness of the dynamic load balancing with adaptive p-refinement examples.
A massively parallel adaptive finite element method with dynamic load balancing
Devine, K.D.; Flaherty, J.E.; Wheat, S.R.; Maccabe, A.B.
1993-12-31
The authors construct massively parallel adaptive finite element methods for the solution of hyperbolic conservation laws. 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. The resulting method is of high order and may be parallelized efficiently on MIMD computers. They demonstrate parallel efficiency through computations on a 1024-processor nCUBE/2 hypercube. They present results using adaptive p-refinement to reduce the computational cost of the method, and tiling, a dynamic, element-based data migration system that maintains global load balance of the adaptive method by overlapping neighborhoods of processors that each perform local balancing.
Multiscale Simulation of Microcrack Based on a New Adaptive Finite Element Method
NASA Astrophysics Data System (ADS)
Xu, Yun; Chen, Jun; Chen, Dong Quan; Sun, Jin Shan
In this paper, a new adaptive finite element (FE) framework based on the variational multiscale method is proposed and applied to simulate the dynamic behaviors of metal under loadings. First, the extended bridging scale method is used to couple molecular dynamics and FE. Then, macro damages evolvements of those micro defects are simulated by the adaptive FE method. Some auxiliary strategies, such as the conservative mesh remapping, failure mechanism and mesh splitting technique are also included in the adaptive FE computation. Efficiency of our method is validated by numerical experiments.
A Lagrangian-Eulerian finite element method with adaptive gridding for advection-dispersion problems
Ijiri, Y.; Karasaki, K.
1994-02-01
In the present paper, a Lagrangian-Eulerian finite element method with adaptive gridding for solving advection-dispersion equations is described. The code creates new grid points in the vicinity of sharp fronts at every time step in order to reduce numerical dispersion. The code yields quite accurate solutions for a wide range of mesh Peclet numbers and for mesh Courant numbers well in excess of 1.
Directionally adaptive finite element method for multidimensional Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Tan, Zhiqiang; Varghese, Philip L.
1993-01-01
A directionally adaptive finite element method for multidimensional compressible flows is presented. Quadrilateral and hexahedral elements are used because they have several advantages over triangular and tetrahedral elements. Unlike traditional methods that use quadrilateral/hexahedral elements, our method allows an element to be divided in each of the three directions in 3D and two directions in 2D. Some restrictions on mesh structure are found to be necessary, especially in 3D. The refining and coarsening procedures, and the treatment of constraints are given. A new implementation of upwind schemes in the constrained finite element system is presented. Some example problems, including a Mach 10 shock interaction with the walls of a 2D channel, a 2D viscous compression corner flow, and inviscid and viscous 3D flows in square channels, are also shown.
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.
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 meshless local maximum-entropy finite element method for convection-diffusion problems
NASA Astrophysics Data System (ADS)
Wu, C. T.; Young, D. L.; Hong, H. K.
2014-01-01
In this paper, a meshless local maximum-entropy finite element method (LME-FEM) is proposed to solve 1D Poisson equation and steady state convection-diffusion problems at various Peclet numbers in both 1D and 2D. By using local maximum-entropy (LME) approximation scheme to construct the element shape functions in the formulation of finite element method (FEM), additional nodes can be introduced within element without any mesh refinement to increase the accuracy of numerical approximation of unknown function, which procedure is similar to conventional p-refinement but without increasing the element connectivity to avoid the high conditioning matrix. The resulted LME-FEM preserves several significant characteristics of conventional FEM such as Kronecker-delta property on element vertices, partition of unity of shape function and exact reproduction of constant and linear functions. Furthermore, according to the essential properties of LME approximation scheme, nodes can be introduced in an arbitrary way and the continuity of the shape function along element edge is kept at the same time. No transition element is needed to connect elements of different orders. The property of arbitrary local refinement makes LME-FEM be a numerical method that can adaptively solve the numerical solutions of various problems where troublesome local mesh refinement is in general necessary to obtain reasonable solutions. Several numerical examples with dramatically varying solutions are presented to test the capability of the current method. The numerical results show that LME-FEM can obtain much better and stable solutions than conventional FEM with linear element.
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.
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.
Adaptive explicit and implicit finite element methods for transient thermal analysis
NASA Technical Reports Server (NTRS)
Probert, E. J.; Hassan, O.; Morgan, K.; Peraire, J.
1992-01-01
The application of adaptive finite element methods to the solution of transient heat conduction problems in two dimensions is investigated. The computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid, using an error estimation procedure coupled to an automatic triangular mesh generator. Two alternative solution procedures are considered. In the first procedure, the solution is advanced by explicit timestepping, with domain decomposition being used to improve the computational efficiency of the method. In the second procedure, an algorithm for constructing continuous lines which pass only once through each node of the mesh is employed. The lines are used as the basis of a fully implicit method, in which the equation system is solved by line relaxation using a block tridiagonal equation solver. The numerical performance of the two procedures is compared for the analysis of a problem involving a moving heat source applied to a convectively cooled cylindrical leading edge.
NASA Astrophysics Data System (ADS)
Hoppe, R. H. W.; Linsenmann, C.
2012-05-01
The immersed boundary method (IB) is known as a powerful technique for the numerical solution of fluid-structure interaction problems as, for instance, the motion and deformation of viscoelastic bodies immersed in an external flow. It is based on the treatment of the flow equations within an Eulerian framework and of the equations of motion of the immersed bodies with respect to a Lagrangian coordinate system including interaction equations providing the transfer between both frames. The classical IB uses finite differences, but the IBM can be set up within a finite element approach in the spatial variables as well (FE-IB). The discretization in time usually relies on the Backward Euler (BE) method for the semidiscretized flow equations and the Forward Euler (FE) method for the equations of motion of the immersed bodies. The BE/FE FE-IB is subject to a CFL-type condition, whereas the fully implicit BE/BE FE-IB is unconditionally stable. The latter one can be solved numerically by Newton-type methods whose convergence properties are dictated by an appropriate choice of the time step size, in particular, if one is faced with sudden changes in the total energy of the system. In this paper, taking advantage of the well developed affine covariant convergence theory for Newton-type methods, we study a predictor-corrector continuation strategy in time with an adaptive choice of the continuation steplength. The feasibility of the approach and its superiority to BE/FE FE-IB is illustrated by two representative numerical examples.
A p-adaptive stabilized finite element method for fluid dynamics
NASA Astrophysics Data System (ADS)
Karanam, Anil Kumar
2008-10-01
Stabilized finite element methods have been shown to yield robust, accurate numerical solutions to both the compressible and incompressible Navier-Stokes equations for laminar and turbulent flows. This work presents an application of mesh entity based, hierarchical basis functions to a new stabilized finite element formulation, exploiting the capability to grade polynomial order while maintaining C0 continuity while using traditional finite element data structures. The hierarchical basis accomplishes this by starting with vertex interpolants (a linear basis) and then allowing the polynomial order to vary on each entity (edges, faces, and regions) in the mesh which are then multiplied by blends within each element to build a composite function that is locally higher order but still globally continuous. Details of this formulation and its efficient implementation will be presented. Partition weighting schemes were developed to achieve optimal load balance and scalability for parallel simulations. An application is presented, of p-refinement applied to a laminar flow past a surface mounted unit cube placed in a channel. Finally, post-processing techniques are also described for the effective visualization of higher order solutions.
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 Astrophysics Data System (ADS)
Davies, D. R.; Davies, J. H.; Hassan, O.; Morgan, K.; Nithiarasu, P.
2007-05-01
An adaptive finite element procedure is presented for improving the quality of solutions to convection-dominated problems in geodynamics. The method adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver, and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code ConMan. An unstructured quadrilateral mesh generator is utilized, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation-based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermochemical problems with well-established benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy while increasing computational efficiency. For thermochemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid-based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies.
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 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).
NASA Astrophysics Data System (ADS)
Jeshvaghani, Mehdi Shahmirzae; Darijani, Mehrdad
2014-06-01
Forward modeling approach is a major concept in geophysical exploration and also a key factor in the development of inversion algorithms. Finite element method for two-dimensional (2-D) geomagnetic forward modeling is based on numerical solution of the Laplace equation. In this paper we present a fast and accurate adaptive finite element algorithm for forward modeling of 2-D geomagnetic structures. Our method is stable and is reliable to recover 2-D magnetization distribution with complex shapes. It uses an unstructured triangular grid which allows modeling the complex geometry with the presence of topography. The Galerkin's method is used to derive the systems of equations. Then, the conjugate gradient solver with incomplete LU decomposition as the pre-conditioner is used to solve the system of equations. To ensure numerical accuracy, iterative mesh refinement is guided by a posteriori error estimator. We validate our algorithm in simple geometry by analytical technique. The tests on synthetic data illustrate a good performance of the method in mapping the complex geometry of the magnetic sources with topography. The magnetic responses of the model have proved to be different in the presence of topography. Therefore, it is highly recommended to consider the effects of topography on interpretation. Finally, we applied numerical FEM algorithm to real data set providing fine recovery model of the shallow high mineralized crustal setting of Soltanieh region, Iran.
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.
Finite element methods in numerical relativity.
NASA Astrophysics Data System (ADS)
Mann, P. J.
The finite element method is very successful in Newtonian fluid simulations, and can be extended to relativitstic fluid flows. This paper describes the general method, and then outlines some preliminary results for spherically symmetric geometries. The mixed finite element - finite difference scheme is introduced, and used for the description of spherically symmetric collapse. Baker's (Newtonian) shock modelling method and Miller's moving finite element method are also mentioned. Collapse in double-null coordinates requires non-constant time slicing, so the full finite element method in space and time is described.
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.
Shape optimization including finite element grid adaptation
NASA Technical Reports Server (NTRS)
Kikuchi, N.; Taylor, J. E.
1984-01-01
The prediction of optimal shape design for structures depends on having a sufficient level of precision in the computation of structural response. These requirements become critical in situations where the region to be designed includes stress concentrations or unilateral contact surfaces, for example. In the approach to shape optimization discussed here, a means to obtain grid adaptation is incorporated into the finite element procedures. This facility makes it possible to maintain a level of quality in the computational estimate of response that is surely adequate for the shape design problem.
The finite element method in thermomechanics
Hsu, T.
1986-01-01
Thermal stress analysis is critical in the design and operation of energy-efficient power plant components and engines as well as in nuclear and aerospace systems. The Finite Element Method in Thermomechanics attempts to embrace a wide range of topics in the nonlinear thermomechanical analysis. The book covers the basic principles of the finite element method: the formulations for the base thermomechanical analysis, including thermoelastic-plastic-creep stress analysis; the use of Fourier series for nonaxisymmetric loadings, and stress waves in solids in thermal environments; and the base finite element code called TEPSAC.
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)
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.
Finite element methods in probabilistic mechanics
NASA Technical Reports Server (NTRS)
Liu, Wing Kam; Mani, A.; Belytschko, Ted
1987-01-01
Probabilistic methods, synthesizing the power of finite element methods with second-order perturbation techniques, are formulated for linear and nonlinear problems. Random material, geometric properties and loads can be incorporated in these methods, in terms of their fundamental statistics. By construction, these methods are applicable when the scale of randomness is not too large and when the probabilistic density functions have decaying tails. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. Applications showing the effects of combined random fields and cyclic loading/stress reversal are studied and compared with Monte Carlo simulation results.
Auto-adaptive finite element meshes
NASA Technical Reports Server (NTRS)
Richter, Roland; Leyland, Penelope
1995-01-01
Accurate capturing of discontinuities within compressible flow computations is achieved by coupling a suitable solver with an automatic adaptive mesh algorithm for unstructured triangular meshes. The mesh adaptation procedures developed rely on non-hierarchical dynamical local refinement/derefinement techniques, which hence enable structural optimization as well as geometrical optimization. The methods described are applied for a number of the ICASE test cases are particularly interesting for unsteady flow simulations.
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.
Iterative methods for mixed finite element equations
NASA Technical Reports Server (NTRS)
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
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
Quantum algorithms and the finite element method
NASA Astrophysics Data System (ADS)
Montanaro, Ashley; Pallister, Sam
2016-03-01
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretizes the parameter space and finds an approximate solution by solving a large system of linear equations. Here we investigate the extent to which the finite element method can be accelerated using an efficient quantum algorithm for solving linear equations. We consider the representative general question of approximately computing a linear functional of the solution to a boundary value problem and compare the quantum algorithm's theoretical performance with that of a standard classical algorithm—the conjugate gradient method. Prior work claimed that the quantum algorithm could be exponentially faster but did not determine the overall classical and quantum run times required to achieve a predetermined solution accuracy. Taking this into account, we find that the quantum algorithm can achieve a polynomial speedup, the extent of which grows with the dimension of the partial differential equation. In addition, we give evidence that no improvement of the quantum algorithm can lead to a superpolynomial speedup when the dimension is fixed and the solution satisfies certain smoothness properties.
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.
3D Finite Element Trajectory Code with Adaptive Meshing
NASA Astrophysics Data System (ADS)
Ives, Lawrence; Bui, Thuc; Vogler, William; Bauer, Andy; Shephard, Mark; Beal, Mark; Tran, Hien
2004-11-01
Beam Optics Analysis, a new, 3D charged particle program is available and in use for the design of complex, 3D electron guns and charged particle devices. The code reads files directly from most CAD and solid modeling programs, includes an intuitive Graphical User Interface (GUI), and a robust mesh generator that is fully automatic. Complex problems can be set up, and analysis initiated in minutes. The program includes a user-friendly post processor for displaying field and trajectory data using 3D plots and images. The electrostatic solver is based on the standard nodal finite element method. The magnetostatic field solver is based on the vector finite element method and is also called during the trajectory simulation process to solve for self magnetic fields. The user imports the geometry from essentially any commercial CAD program and uses the GUI to assign parameters (voltages, currents, dielectric constant) and designate emitters (including work function, emitter temperature, and number of trajectories). The the mesh is generated automatically and analysis is performed, including mesh adaptation to improve accuracy and optimize computational resources. This presentation will provide information on the basic structure of the code, its operation, and it's capabilities.
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.
NASA Astrophysics Data System (ADS)
Zolotareva, N. D.; Nikolaev, E. S.
2016-05-01
An iterative process implementing an adaptive hp-version of the finite element method (FEM) previously proposed by the authors for the approximate solution of boundary value problems for the stationary reaction-diffusion equation is described. The method relies on piecewise polynomial basis functions and makes use of an adaptive strategy for constructing a sequence of finite-dimensional subspaces based on the computation of correction indicators. Singularly perturbed boundary value test problems with smooth and not very smooth solutions are used to analyze the efficiency of the method in the situation when an approximate solution has to be found with high accuracy. The convergence of the approximate solution to the exact one is investigated depending on the value of the small parameter multiplying the highest derivative, on the family of basis functions and the quadrature formulas used, and on the internal parameters of the method. The method is compared with an adaptive h-version of FEM that also relies on correction indicators and with its nonadaptive variant based on the bisection of grid intervals.
Finite element error estimation and adaptivity based on projected stresses
Jung, J.
1990-08-01
This report investigates the behavior of a family of finite element error estimators based on projected stresses, i.e., continuous stresses that are a least squared error fit to the conventional Gauss point stresses. An error estimate based on element force equilibrium appears to be quite effective. Examples of adaptive mesh refinement for a one-dimensional problem are presented. Plans for two-dimensional adaptivity are discussed. 12 refs., 82 figs.
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.
Highly accurate adaptive finite element schemes for nonlinear hyperbolic problems
NASA Astrophysics Data System (ADS)
Oden, J. T.
1992-08-01
This document is a final report of research activities supported under General Contract DAAL03-89-K-0120 between the Army Research Office and the University of Texas at Austin from July 1, 1989 through June 30, 1992. The project supported several Ph.D. students over the contract period, two of which are scheduled to complete dissertations during the 1992-93 academic year. Research results produced during the course of this effort led to 6 journal articles, 5 research reports, 4 conference papers and presentations, 1 book chapter, and two dissertations (nearing completion). It is felt that several significant advances were made during the course of this project that should have an impact on the field of numerical analysis of wave phenomena. These include the development of high-order, adaptive, hp-finite element methods for elastodynamic calculations and high-order schemes for linear and nonlinear hyperbolic systems. Also, a theory of multi-stage Taylor-Galerkin schemes was developed and implemented in the analysis of several wave propagation problems, and was configured within a general hp-adaptive strategy for these types of problems. Further details on research results and on areas requiring additional study are given in the Appendix.
Modular Finite Element Methods Library Version: 1.0
2010-06-22
MFEM is a general, modular library for finite element methods. It provides a variety of finite element spaces and bilinear/linear forms in 2D and 3D. MFEM also includes classes for dealing with various types of meshes and their refinement.
Seakeeping with the semi-Lagrangian particle finite element method
NASA Astrophysics Data System (ADS)
Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio
2016-07-01
The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.
NASA Astrophysics Data System (ADS)
Paszyński, Maciej; Gurgul, Piotr; Sieniek, Marcin; Pardo, David
2010-06-01
In the first part of the paper we present the multi-scale simulation of the Step-and-Flash Imprint Lithography (SFIL), a modern patterning process. The simulation utilizes the hp adaptive Finite Element Method (hp-FEM) coupled with Molecular Statics (MS) model. Thus, we consider the multi-scale problem, with molecular statics applied in the areas of the mesh where the highest accuracy is required, and the continuous linear elasticity with thermal expansion coefficient applied in the remaining part of the domain. The degrees of freedom from macro-scale element's nodes located on the macro-scale side of the interface have been identified with particles from nano-scale elements located on the nano-scale side of the interface. In the second part of the paper we present Unified Modeling Language (UML) description of the resulting multi-scale application (hp-FEM coupled with MS). We investigated classical, procedural codes from the point of view of the object-oriented (O-O) programming paradigm. The discovered hierarchical structure of classes and algorithms makes the UML project as independent on the spatial dimension of the problem as possible. The O-O UML project was defined at an abstract level, independent on the programming language used.
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.
Large spatial, temporal, and algorithmic adaptivity for implicit nonlinear finite element analysis
Engelmann, B.E.; Whirley, R.G.
1992-07-30
The development of effective solution strategies to solve the global nonlinear equations which arise in implicit finite element analysis has been the subject of much research in recent years. Robust algorithms are needed to handle the complex nonlinearities that arise in many implicit finite element applications such as metalforming process simulation. The authors experience indicates that robustness can best be achieved through adaptive solution strategies. In the course of their research, this adaptivity and flexibility has been refined into a production tool through the development of a solution control language called ISLAND. This paper discusses aspects of adaptive solution strategies including iterative procedures to solve the global equations and remeshing techniques to extend the domain of Lagrangian methods. Examples using the newly developed ISLAND language are presented to illustrate the advantages of embedding temporal, algorithmic, and spatial adaptivity in a modem implicit nonlinear finite element analysis code.
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.
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.
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.
Generalized multiscale finite element method. Symmetric interior penalty coupling
NASA Astrophysics Data System (ADS)
Efendiev, Y.; Galvis, J.; Lazarov, R.; Moon, M.; Sarkis, M.
2013-12-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the “mass” matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples.
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.
Interpolation functions in the immersed boundary and finite element methods
NASA Astrophysics Data System (ADS)
Wang, Xingshi; Zhang, Lucy T.
2010-03-01
In this paper, we review the existing interpolation functions and introduce a finite element interpolation function to be used in the immersed boundary and finite element methods. This straightforward finite element interpolation function for unstructured grids enables us to obtain a sharper interface that yields more accurate interfacial solutions. The solution accuracy is compared with the existing interpolation functions such as the discretized Dirac delta function and the reproducing kernel interpolation function. The finite element shape function is easy to implement and it naturally satisfies the reproducing condition. They are interpolated through only one element layer instead of smearing to several elements. A pressure jump is clearly captured at the fluid-solid interface. Two example problems are studied and results are compared with other numerical methods. A convergence test is thoroughly conducted for the independent fluid and solid meshes in a fluid-structure interaction system. The required mesh size ratio between the fluid and solid domains is obtained.
Mathematical aspects of finite element methods for incompressible viscous flows
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.
1986-01-01
Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.
NASA Astrophysics Data System (ADS)
Chung, T. J.; Karr, Gerald R.
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.
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.
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.
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.
Electrical and Joule heating relationship investigation using Finite Element Method
NASA Astrophysics Data System (ADS)
Thangaraju, S. K.; Munisamy, K. M.
2015-09-01
The finite element method is vastly used in material strength analysis. The nature of the finite element solver, which solves the Fourier equation of stress and strain analysis, made it possible to apply for conduction heat transfer Fourier Equation. Similarly the Current and voltage equation is also liner Fourier equation. The nature of the governing equation makes it possible to numerical investigate the electrical joule heating phenomena in electronic component. This paper highlights the Finite Element Method (FEM) application onto semiconductor interconnects to determine the specific contact resistance (SCR). Metal and semiconductor interconnects is used as model. The result confirms the possibility and validity of FEM utilization to investigate the Joule heating due electrical resistance.
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.
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.
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.
Spanwise variation of potential form drag. [finite element method
NASA Technical Reports Server (NTRS)
Clever, W. C.
1977-01-01
The finite element method is used to calculate the spanwise variation of potential form drag of a wing at subsonic and supersonic speeds using linearly varying panels. The wing may be of arbitrary planform and nonplanar provided the wing panels are parallel to the aircraft axis.
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.
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
The finite element method: Is weighted volume integration essential?
NASA Astrophysics Data System (ADS)
Narasimhan, T. N.
In developing finite element equations for steady state and transient diffusion-type processes, weighted volume integration is generally assumed to be an intrinsic requirement. It is shown that such finite element equations can be developed directly and with ease on the basis of the elementary notion of a surface integral. Although weighted volume integration is mathematically correct, the algebraic equations stemming from it are no more informative than those derived directly on the basis of a surface integral. An interesting upshot is that the derivation based on surface integration does not require knowledge of a partial differential equation but yet is logically rigorous. It is commonly stated that weighted volume integration of the differential equation helps one carry out analyses of errors, convergence and existence, and therefore, weighted volume integration is preferable. It is suggested that because the direct derivation is logically consistent, numerical solutions emanating from it must be testable for accuracy and internal consistency in ways that the style of which may differ from the classical procedures of error- and convergence-analysis. In addition to simplifying the teaching of the finite element method, the thoughts presented in this paper may lead to establishing the finite element method independently in its own right, rather than it being a surrogate of the differential equation. The purpose of this paper is not to espouse any one particular way of formulating the finite element equations. Rather, it is one of introspection. The desire is to critically examine our traditional way of doing things and inquire whether alternate approaches may reveal to us new and interesting insights.
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.
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.
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.
[Whiplash injury analysis of cervical vertebra by finite element method].
Wang, Tao; Li, Zheng-Dong; Shao, Yu; Chen, Yi-Jiu
2015-02-01
Finite element method (FEM) is an effective mathematical method for stress analysis, and has been gradually applied in the study of biomechanics of human body structures. This paper reviews the construction, development, materials assignment and verification of FEM model of cervical vertebra, and it also states the research results of injury mechanism of whiplash injury and biomechanical response analysis of the cervical vertebra using FEM by researchers at home and abroad. PMID:26058135
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.
Phased array antenna analysis using hybrid finite element methods
NASA Astrophysics Data System (ADS)
McGrath, Daniel T.
1993-06-01
This research in computational electromagnetics developed a new method for predicting the near-field mutual coupling effects in phased array antennas, using the finite element method (FEM) in combination with integral equations. Accurate feed modeling is accomplished by enforcing continuity between the FEM solution and an arbitrary number of wave guide models across a ground plane aperture. A periodic integral equation is imposed above the antenna's physical structure in order to enforce the radiation condition and to confine the analysis to an array unit cell. The electric field is expanded in terms of vector finite elements, and Galerkin's method is used to write the problem as a matrix equation. A general-purpose computer code was developed and validated by comparing its results to published data for several array types. Its versatility was demonstrated with predictions of the scanning properties of arrays of printed dipoles and printed flared notches.
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.
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.
Material nonlinear analysis via mixed-iterative finite element method
NASA Technical Reports Server (NTRS)
Sutjahjo, Edhi; Chamis, Christos C.
1992-01-01
The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.
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.
The finite element method for calculating the marine structural design
NASA Astrophysics Data System (ADS)
Ion, A.; Ticu, I.
2015-11-01
The aim of this paper is to optimally design and dimension marine structures in order for them to fulfil both functional and safety requirements. A master level of structural mechanics is vital in order to check tests and analysis and to develop new structures. This study can improve the calculation and estimation of the effects of hydrodynamics and of other loads; movements, strains and internal forces in fixed and floating platforms and ships. The finite element method (FEM) ensures basic understanding of the finite element model as applied on static cases including beam and plate elements, experience with static analysis of marine structures like platforms and ships, along with the basic understanding of dynamic response of systems with one degree of freedom and simple continuous beams, and also how analysis models can be established for real structures by the use of generalized coordinates and superposition.
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.
Spectral finite-element methods for parametric constrained optimization problems.
Anitescu, M.; Mathematics and Computer Science
2009-01-01
We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
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.
Weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
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.
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.
Finite element and finite difference methods in electromagnetic scattering
NASA Astrophysics Data System (ADS)
Morgan, Michael A.
Finite-difference and finite-element methods for the computational analysis of EM scattering phenomena are examined in chapters contributed by leading experts. Topics addressed include an FEM for composite scatterers, coupled finite- and boundary-element methods for EM scattering, absorbing boundary conditions for the direct solution PDEs arising in EM scattering problems, application of the control-region approximation to two-dimensional EM scattering, coupled potentials for EM fields in inhomogeneous media, the method of conforming boundary elements for transient electromagnetics, and the finite-difference time-domain method for numerical modeling of EM wave interactions with arbitrary structures. Extensive diagrams and graphs of typical results are provided.
Residual-driven online generalized multiscale finite element methods
NASA Astrophysics Data System (ADS)
Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat
2015-12-01
The construction of local reduced-order models via multiscale basis functions has been an area of active research. In this paper, we propose online multiscale basis functions which are constructed using the offline space and the current residual. Online multiscale basis functions are constructed adaptively in some selected regions based on our error indicators. We derive an error estimator which shows that one needs to have an offline space with certain properties to guarantee that additional online multiscale basis function will decrease the error. This error decrease is independent of physical parameters, such as the contrast and multiple scales in the problem. The offline spaces are constructed using Generalized Multiscale Finite Element Methods (GMsFEM). We show that if one chooses a sufficient number of offline basis functions, one can guarantee that additional online multiscale basis functions will reduce the error independent of contrast. We note that the construction of online basis functions is motivated by the fact that the offline space construction does not take into account distant effects. Using the residual information, we can incorporate the distant information provided the offline approximation satisfies certain properties. In the paper, theoretical and numerical results are presented. Our numerical results show that if the offline space is sufficiently large (in terms of the dimension) such that the coarse space contains all multiscale spectral basis functions that correspond to small eigenvalues, then the error reduction by adding online multiscale basis function is independent of the contrast. We discuss various ways computing online multiscale basis functions which include a use of small dimensional offline spaces.
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.
Dual Formulations of Mixed Finite Element Methods with Applications
Gillette, Andrew; Bajaj, Chandrajit
2011-01-01
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail. PMID:21984841
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.
Turbomachinery flow calculation on unstructured grids using finite element method
NASA Astrophysics Data System (ADS)
Koschel, W.; Vornberger, A.
An explicit finite-element scheme based on a two-step Taylor-Galerkin algorithm allows the solution of the Euler and Navier-Stokes equations on unstructured grids. Mesh generation methods for unstructured grids are described which lead to efficient flow calculations. Turbulent flow is calculated by using an algebraic turbulence model. To test the numerical accuracy, a laminar and turbulent flow over a flat plate and the supersonic flow in a corner has been calculated. For validation the method is applied to the simulation of the inviscid flow through a transonic turbine cascade and the viscous flow through a subsonic turbine cascade.
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.
Scientific use of the finite element method in Orthodontics
Knop, Luegya; Gandini, Luiz Gonzaga; Shintcovsk, Ricardo Lima; Gandini, Marcia Regina Elisa Aparecida Schiavon
2015-01-01
INTRODUCTION: The finite element method (FEM) is an engineering resource applied to calculate the stress and deformation of complex structures, and has been widely used in orthodontic research. With the advantage of being a non-invasive and accurate method that provides quantitative and detailed data on the physiological reactions possible to occur in tissues, applying the FEM can anticipate the visualization of these tissue responses through the observation of areas of stress created from applied orthodontic mechanics. OBJECTIVE: This article aims at reviewing and discussing the stages of the finite element method application and its applicability in Orthodontics. RESULTS: FEM is able to evaluate the stress distribution at the interface between periodontal ligament and alveolar bone, and the shifting trend in various types of tooth movement when using different types of orthodontic devices. Therefore, it is necessary to know specific software for this purpose. CONCLUSIONS: FEM is an important experimental method to answer questions about tooth movement, overcoming the disadvantages of other experimental methods. PMID:25992996
Immersed finite element method and its applications to biological systems
Liu, Wing Kam; Liu, Yaling; Farrell, David; Zhang, Lucy; Wang, X. Sheldon; Fukui, Yoshio; Patankar, Neelesh; Zhang, Yongjie; Bajaj, Chandrajit; Lee, Junghoon; Hong, Juhee; Chen, Xinyu; Hsu, Huayi
2009-01-01
This paper summarizes the newly developed immersed finite element method (IFEM) and its applications to the modeling of biological systems. This work was inspired by the pioneering work of Professor T.J.R. Hughes in solving fluid–structure interaction problems. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans the entire computational domain. Hence, mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element method and the continuity between the fluid and solid subdomains is enforced via the interpolation of the velocities and the distribution of the forces with the reproducing Kernel particle method (RKPM) delta function. The proposed method is used to study the fluid–structure interaction problems encountered in human cardiovascular systems. Currently, the heart modeling is being constructed and the deployment process of an angioplasty stent has been simulated. Some preliminary results on monocyte and platelet deposition are presented. Blood rheology, in particular, the shear-rate dependent de-aggregation of red blood cell (RBC) clusters and the transport of deformable cells, are modeled. Furthermore, IFEM is combined with electrokinetics to study the mechanisms of nano/bio filament assembly for the understanding of cell motility. PMID:20200602
Immersed finite element method and its applications to biological systems.
Liu, Wing Kam; Liu, Yaling; Farrell, David; Zhang, Lucy; Wang, X Sheldon; Fukui, Yoshio; Patankar, Neelesh; Zhang, Yongjie; Bajaj, Chandrajit; Lee, Junghoon; Hong, Juhee; Chen, Xinyu; Hsu, Huayi
2006-02-15
This paper summarizes the newly developed immersed finite element method (IFEM) and its applications to the modeling of biological systems. This work was inspired by the pioneering work of Professor T.J.R. Hughes in solving fluid-structure interaction problems. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans the entire computational domain. Hence, mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element method and the continuity between the fluid and solid subdomains is enforced via the interpolation of the velocities and the distribution of the forces with the reproducing Kernel particle method (RKPM) delta function. The proposed method is used to study the fluid-structure interaction problems encountered in human cardiovascular systems. Currently, the heart modeling is being constructed and the deployment process of an angioplasty stent has been simulated. Some preliminary results on monocyte and platelet deposition are presented. Blood rheology, in particular, the shear-rate dependent de-aggregation of red blood cell (RBC) clusters and the transport of deformable cells, are modeled. Furthermore, IFEM is combined with electrokinetics to study the mechanisms of nano/bio filament assembly for the understanding of cell motility. PMID:20200602
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.
Hybrid finite element and Brownian dynamics method for charged particles
NASA Astrophysics Data System (ADS)
Huber, Gary A.; Miao, Yinglong; Zhou, Shenggao; Li, Bo; McCammon, J. Andrew
2016-04-01
Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.
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.
Progress on hybrid finite element methods for scattering by bodies of revolution
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Volakis, John L.
1992-01-01
Progress on the development and implementation of hybrid finite element methods for scattering by bodies of revolution are described. It was found that earlier finite element-boundary integral formulations suffered from convergence difficulties when applied to large and thin bodies of revolution. An alternative implementation is described where the finite element method is terminated with an absorbing termination boundary. In addition, an alternative finite element-boundary integral implementation is discussed for improving the convergence of the original code.
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.
Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration
NASA Astrophysics Data System (ADS)
Zhang, Y.; Key, K.; Ovall, J.; Holst, M.
2014-12-01
We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented
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.
Discussion of the finite element method in optical diffraction tomography
NASA Astrophysics Data System (ADS)
Lobera, Julia; Coupland, Jeremy
2006-04-01
In Optical Diffraction Tomography (ODT) the refractive index is reconstructed from images with different illuminating wavefronts. In most cases the Born approximation is assumed, although this limits the applicability of the technique to weak-scattering problems. In this work we examine the scattering problem from first principles beginning from the Helmholtz equation that governs scalar diffraction and wave propagation. We demonstrate the use of the Born approximation and show typical errors when it is applied in practice. Solution of the Helmholtz equation using a Finite Element Method (FEM) with an appropriate Absorbing Boundary Condition (ABC) is described, and a non-linear optimization technique, the Conjugate Gradient Method (CGM), previously proposed for microwave imaging, is applied to the inverse problem.
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.
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.
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.
An analytically enriched finite element method for cohesive crack modeling.
Cox, James V.
2010-04-01
Meaningful computational investigations of many solid mechanics problems require accurate characterization of material behavior through failure. A recent approach to fracture modeling has combined the partition of unity finite element method (PUFEM) with cohesive zone models. Extension of the PUFEM to address crack propagation is often referred to as the extended finite element method (XFEM). In the PUFEM, the displacement field is enriched to improve the local approximation. Most XFEM studies have used simplified enrichment functions (e.g., generalized Heaviside functions) to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. As such, the mesh had to be sufficiently fine for the FEM basis functions to capture these gradients.In this study enrichment functions based upon two analytical investigations of the cohesive crack problem are examined. These functions have the potential of representing displacement gradients in the vicinity of the cohesive crack with a relatively coarse mesh and allow the crack to incrementally advance across each element. Key aspects of the corresponding numerical formulation are summarized. Analysis results for simple model problems are presented to evaluate if quasi-static crack propagation can be accurately followed with the proposed formulation. A standard finite element solution with interface elements is used to provide the accurate reference solution, so the model problems are limited to a straight, mode I crack in plane stress. Except for the cohesive zone, the material model for the problems is homogenous, isotropic linear elasticity. The effects of mesh refinement, mesh orientation, and enrichment schemes that enrich a larger region around the cohesive crack are considered in the study. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are presented. The analysis
Valuing Asian options using the finite element method and duality techniques
NASA Astrophysics Data System (ADS)
Foufas, Georgios; Larson, Mats G.
2008-12-01
The main objective of this paper is to develop an adaptive finite element method for computation of the values, and different sensitivity measures, of the Asian option with both fixed and floating strike. The pricing is based on Black-Scholes PDE-model and a method developed by Vecer where the resulting PDEs are of parabolic type in one spatial dimension and can be applied to both continuous and discrete Asian options. We propose using an adaptive finite element method which is based on a posteriori estimates of the error in desired quantities, which we derive using duality techniques. The a posteriori error estimates are tested and verified, and are used to calculate optimal meshes for each type of option. The use of adapted meshes gives superior accuracy and performance with less degrees of freedom than using uniform meshes. The suggested adaptive finite element method is stable, gives fast and accurate results, and can be applied to other types of options as well.
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.
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.
Finite element method application for turbulent and transitional flow
NASA Astrophysics Data System (ADS)
Sváček, Petr
2016-03-01
This paper is interested in numerical simulations of the interaction of the fluid flow with an airfoil. Particularly, the problem of the turbulent flow around the airfoil with elastic support is considered. The main attention is paid to the numerical approximation of the flow problem using the finite element approximations. The laminar - turbulence transition of the flow on the surface airfoil is considered. The chois of the transition model is discussed. The transition model based on the two equation k-ω turbulence model is used. The structure motion is described with the aid of two degrees of freedom. The motion of the computational domain is treated with the aid of the arbitrary Lagrangian-Eulerian method. Numerical results are shown.
NASA Astrophysics Data System (ADS)
Burman, E.; Jacot, A.; Picasso, M.
2004-03-01
A multiphase-field model for the description of coalescence in a binary alloy is solved numerically using adaptive finite elements with high aspect ratio. The unknown of the multiphase-field model are the three phase fields (solid phase 1, solid phase 2, and liquid phase), a Lagrange multiplier and the concentration field. An Euler implicit scheme is used for time discretization, together with continuous, piecewise linear finite elements. At each time step, a linear system corresponding to the three phases plus the Lagrange multiplier has to be solved. Then, the linear system pertaining to concentration is solved. An adaptive finite element algorithm is proposed. In order to reduce the number of mesh vertices, the generated meshes contain elements with high aspect ratio. The refinement and coarsening criteria are based on an error indicator which has already been justified theoretically for simpler problems. Numerical results on two test cases show the efficiency of the method.
Finite-element methods for spatially resolved mesoscopic electron transport
NASA Astrophysics Data System (ADS)
Kramer, Stephan
2013-09-01
A finite-element method is presented for calculating the quantum conductance of mesoscopic two-dimensional electron devices of complex geometry attached to semi-infinite leads. For computational purposes, the leads must be cut off at some finite length. To avoid spurious, unphysical reflections, this is modeled by transparent boundary conditions. We introduce the Hardy space infinite-element technique from acoustic scattering as a way of setting up transparent boundary conditions for transport computations spanning the range from the quantum mechanical to the quasiclassical regime. These boundary conditions are exact even for wave packets and thus are especially useful in the limit of high energies with many excited modes. Yet, they possess a memory-friendly sparse matrix representation. In addition to unbounded domains, Hardy space elements allow us to truncate those parts of the computational domain which are irrelevant for the calculation of the transport properties. Thus, the computation can be done only on the region that is essential for a physically meaningful simulation of the scattering states. The benefits of the method are demonstrated by three examples. The convergence properties are tested on the transport through a quasi-one-dimensional quantum wire. It is shown that higher-order finite elements considerably improve current conservation and establish the correct phase shift between the real and the imaginary parts of the electron wave function. The Aharonov-Bohm effect demonstrates that characteristic features of quantum interference can be assessed. A simulation of electron magnetic focusing exemplifies the capability of the computational framework to study the crossover from quantum to quasiclassical behavior.
Multiphase flow through porous media: an adaptive control volume finite element formulation
NASA Astrophysics Data System (ADS)
Mostaghimi, P.; Tollit, B.; Gorman, G.; Neethling, S.; Pain, C.
2012-12-01
Accurate modeling of multiphase flow in porous media is of great importance in a wide range of applications in science and engineering. We have developed a numerical scheme which employs an implicit pressure explicit saturation (IMPES) algorithm for the temporal discretization of the governing equations. The saturation equation is spatially discretized using a node centered control volume method on an unstructured finite element mesh. The face values are determined through an upwind scheme. The pressure equation is spatially discretized using a continuous control volume finite element method (CV-FEM) to achieve consistency with the discrete saturation equation. The numerical simulation is implemented in Fluidity, an open source and general purpose fluid simulator capable of solving a number of different governing equations for fluid flow and accompanying field equations on arbitrary unstructured meshes. The model is verified against the Buckley-Leverett problem where a quasi-analytical solution is available. We discuss the accuracy and the order of convergence of the scheme. We demonstrate the scheme for modeling multiphase flow in a synthetic heterogeneous porous medium along with the use of anisotropic mesh adaptivity to control local solution errors and increase computational efficiency. The adaptive method is also used to simulate two-phase flow in heap leaching, an industrial mining process, where the flow of the leaching solution is gravitationally dominated. Finally we describe the extension of the developed numerical scheme for simulation of flow in multiscale fractured porous media and its capability to model the multiscale characterization of flow in full scale.
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.
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.
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. PMID:25202164
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
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
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
Numerical performance of projection methods in finite element consolidation models
NASA Astrophysics Data System (ADS)
Gambolati, Giuseppe; Pini, Giorgio; Ferronato, Massimiliano
2001-12-01
Projection, or conjugate gradient like, methods are becoming increasingly popular for the efficient solution of large sparse sets of unsymmetric indefinite equations arising from the numerical integration of (initial) boundary value problems. One such problem is soil consolidation coupling a flow and a structural model, typically solved by finite elements (FE) in space and a marching scheme in time (e.g. the Crank-Nicolson scheme). The attraction of a projection method stems from a number of factors, including the ease of implementation, the requirement of limited core memory and the low computational cost if a cheap and effective matrix preconditioner is available. In the present paper, biconjugate gradient stabilized (Bi- CGSTAB) is used to solve FE consolidation equations in 2-D and 3-D settings with variable time integration steps. Three different nodal orderings are selected along with the preconditioner ILUT based on incomplete triangular factorization and variable fill-in. The overall cost of the solver is made up of the preconditioning cost plus the cost to converge which is in turn related to the number of iterations and the elementary operations required by each iteration. The results show that nodal ordering affects the perfor mance of Bi-CGSTAB. For normally conditioned consolidation problems Bi-CGSTAB with the best ILUT preconditioner may converge in a number of iterations up to two order of magnitude smaller than the size of the FE model and proves an accurate, cost-effective and robust alternative to direct methods.
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
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
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.
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.
Nonlinear stress analysis of titanium implants by finite element method.
Nagasawa, Sakae; Hayano, Keigo; Niino, Tooru; Yamakura, Kazunori; Yoshida, Takamitsu; Mizoguchi, Toshihide; Terashima, Nobuyosi; Tamura, Kaoru; Ito, Michio; Yagasaki, Hiroshi; Kubota, Osamu; Yoshimura, Masayuki
2008-07-01
With use of dental implants on the rise, there is also a tandem increase in the number of implant fracture reports. To the end of investigating the stress occurring in implants, elasticity and plasticity analyses were performed using the finite element method. The following results were obtained: (1) With one-piece type of implants of 3.3 mm diameter, elasticity analysis showed that after applying 500 N in a 45-degree direction, stress exceeding 500 MPa which is the proof stress of grade 4 pure titanium - occurred. This suggested the possibility of fatigue destruction due to abnormal occlusal force, such as during bruxism. (2) With two-piece type of implants that can tolerate vertical loading of 5,000 N, plasticity analysis suggested the possibility of screw area fracture after applying 500 N in a 45-degree direction. (3) On the combined use of an abutment and a fixture from different manufacturers, fracture destruction of even Ti-6Al-4V, which has a high degree of strength, was predicted. PMID:18833779
Structured Extended Finite Element Methods of Solids Defined by Implicit Surfaces
Belytschko, T; Mish, K; Moes, N; Parimi, C
2002-11-17
A paradigm is developed for generating structured finite element models from solid models by means of implicit surface definitions. The implicit surfaces are defined by radial basis functions. Internal features, such as material interfaces, sliding interfaces and cracks are treated by enrichment techniques developed in the extended finite element method (X-FEM). Methods for integrating the weak form for such models are proposed. These methods simplify the generation of finite element models. Results presented for several examples show that the accuracy of this method is comparable to standard unstructured finite element methods.
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.
New Application of Finite Element Method to Seamount Magnetism
NASA Astrophysics Data System (ADS)
HA, G.; Kim, S. S.; So, B. D.
2015-12-01
Geomagnetic method can be utilized in a wide range of applications, including investigation of small-scale near-surface targets and characterization of large-scale geologic structures. In particular, marine magnetic studies involve with various interpretation approaches to constrain geophysical information regarding the depth of a particular seamount, its size and shape, and the orientation and magnitude of its magnetization. The accuracy of the estimated information is normally governed by the quality and amount of available data and by the sophistication of the employed modeling techniques. Here we aim to advance geomagnetic modeling approaches using the interactive finite element solver, COMSOL Multiphysics, and improve the degree of detail that can be obtained from the measured magnetic field. First, we carried out benchmark tests by comparing the computed results using the analytic solutions for simple bodies. We built two types of synthetic models with rectangular and sphere shaped ore bodies having high intensity of magnetization and we changed magnetized direction in each calculation. Comparisons of FEM-based results with the analytic ones exhibited good agreement in general. Second, marine magnetic data obtained at seamounts can be very crucial to determine the age and location of seamount formation. Traditional magnetic methods often assume the uniformly magnetized seamounts to simplify computational efforts. However, the inner structures of seamounts constrained by seismic data show a clear distinction between the dense core and edifice layers. Here we divide the seamount into the dense core and edifice layers in a synthetic model, assign different magnetization direction and intensity to them, and optimize these parameters by minimizing differences between the observed and numerical computed data. These examined results will be valuable to understand seamount formation processes in detail. In addition, we discuss FEM-based magnetic models to mimic the
Witteveen, Jeroen A.S. Bijl, Hester
2009-10-01
The Unsteady Adaptive Stochastic Finite Elements (UASFE) method resolves the effect of randomness in numerical simulations of single-mode aeroelastic responses with a constant accuracy in time for a constant number of samples. In this paper, the UASFE framework is extended to multi-frequency responses and continuous structures by employing a wavelet decomposition pre-processing step to decompose the sampled multi-frequency signals into single-frequency components. The effect of the randomness on the multi-frequency response is then obtained by summing the results of the UASFE interpolation at constant phase for the different frequency components. Results for multi-frequency responses and continuous structures show a three orders of magnitude reduction of computational costs compared to crude Monte Carlo simulations in a harmonically forced oscillator, a flutter panel problem, and the three-dimensional transonic AGARD 445.6 wing aeroelastic benchmark subject to random fields and random parameters with various probability distributions.
Yu, Jingjing; He, Xiaowei; Geng, Guohua; Liu, Fang; Jiao, L C
2013-01-01
Quantitative reconstruction of bioluminescent sources from boundary measurements is a challenging ill-posed inverse problem owing to the high degree of absorption and scattering of light through tissue. We present a hybrid multilevel reconstruction scheme by combining the ability of sparse regularization with the advantage of adaptive finite element method. In view of the characteristics of different discretization levels, two different inversion algorithms are employed on the initial coarse mesh and the succeeding ones to strike a balance between stability and efficiency. Numerical experiment results with a digital mouse model demonstrate that the proposed scheme can accurately localize and quantify source distribution while maintaining reconstruction stability and computational economy. The effectiveness of this hybrid reconstruction scheme is further confirmed with in vivo experiments. PMID:23533542
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
Basis Functions With Divergence Constraints For The Finite Element Method
NASA Astrophysics Data System (ADS)
Pinciuc, Christopher Michael
Maxwell's equations are a system of partial differential equations of vector fields. Imposing the constitutive relations for material properties yields equations for the curl and divergence of the electric and magnetic fields. The curl and divergence equations must be solved simultaneously, which is not the same as solving three separate scalar problems in each component of the vector field. This thesis describes a new method for solving partial differential equations of vector fields using the finite element method. New basis functions are used to solve the curl equation while allowing the divergence to be set as a constraint. The basis functions are defined on a mesh of bricks and the method is applicable for geometries that conform to a Cartesian coordinate system. The basis functions are a combination of cubic Hermite splines and second order Lagrange interpolation polynomials. The method yields a linearly independent set of constraints for the divergence, which is modelled to second order accuracy within each brick. Mesh refinement is accomplished by dividing selected bricks into 2 x 2 x 2 smaller bricks of equal size. The change in the node pattern at an interface where mesh refinement occurs necessitates a modified implementation of the divergence constraints as well as additional constraints for hanging nodes. The mesh can be refined to an arbitrary number of levels. The basis functions can exactly model the discontinuity in the normal component of the field at a planar interface. The method is modified to solve problems with singularities at material boundaries that form 90° edges and corners. The primary test problem of the new basis functions is to obtain the resonant frequencies and fields of three-dimensional cavities. The new basis functions can resolve physical solutions and non-physical, spurious modes. The eigenvalues obtained with the new method are in good agreement with exact solutions and experimental values in cases where they exist. There is
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.
A Dynamic Finite Element Method for Simulating the Physics of Faults Systems
NASA Astrophysics Data System (ADS)
Saez, E.; Mora, P.; Gross, L.; Weatherley, D.
2004-12-01
We introduce a dynamic Finite Element method using a novel high level scripting language to describe the physical equations, boundary conditions and time integration scheme. The library we use is the parallel Finley library: a finite element kernel library, designed for solving large-scale problems. It is incorporated as a differential equation solver into a more general library called escript, based on the scripting language Python. This library has been developed to facilitate the rapid development of 3D parallel codes, and is optimised for the Australian Computational Earth Systems Simulator Major National Research Facility (ACcESS MNRF) supercomputer, a 208 processor SGI Altix with a peak performance of 1.1 TFlops. Using the scripting approach we obtain a parallel FE code able to take advantage of the computational efficiency of the Altix 3700. We consider faults as material discontinuities (the displacement, velocity, and acceleration fields are discontinuous at the fault), with elastic behavior. The stress continuity at the fault is achieved naturally through the expression of the fault interactions in the weak formulation. The elasticity problem is solved explicitly in time, using the Saint Verlat scheme. Finally, we specify a suitable frictional constitutive relation and numerical scheme to simulate fault behaviour. Our model is based on previous work on modelling fault friction and multi-fault systems using lattice solid-like models. We adapt the 2D model for simulating the dynamics of parallel fault systems described to the Finite-Element method. The approach uses a frictional relation along faults that is slip and slip-rate dependent, and the numerical integration approach introduced by Mora and Place in the lattice solid model. In order to illustrate the new Finite Element model, single and multi-fault simulation examples are presented.
Finite element method - A companion in experimental mechanics
NASA Technical Reports Server (NTRS)
Kobayashi, A. S.
1984-01-01
The hybrid experimental-numerical procedure for structural analysis is described by its applications in fracture mechanics. The procedure was first verified by the excellent agreements between the dynamic stress intensity factors obtained directly by dynamic photoelasticity and those generated by the hybrid procedure where a dynamic finite element code was executed in its generation mode. The hybrid procedure was then used to determine the dynamic fracture toughness of reaction bonded silicon nitride.
Stress Recovery Based h-Adaptive Finite Element Simulation of Sheet Forming Operations
NASA Astrophysics Data System (ADS)
Ahmed, Mohd.; Singh, Devinder
2016-05-01
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.
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.
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
NASA Astrophysics Data System (ADS)
Beilina, Larisa
2016-08-01
We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the computational domain: finite difference method is used on the structured part of the computational domain and finite elements on the unstructured part of the domain. Explicit discretizations for both methods are constructed such that the finite element and the finite difference schemes coincide on the common structured overlapping layer between computational subdomains. Then the resulting approach can be considered as a pure finite element scheme which avoids instabilities at the interfaces. We derive an energy estimate for the underlying hyperbolic equation with absorbing boundary conditions and illustrate efficiency of the domain decomposition method on the reconstruction of the conductivity function in three dimensions.
Non-conforming finite element methods for transmission eigenvalue problem
NASA Astrophysics Data System (ADS)
Yang, Yidu; Han, Jiayu; Bi, Hai
2016-08-01
The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem, we give a weak formulation which is a nonselfadjoint linear eigenvalue problem. Based on the weak formulation, we first discuss the non-conforming finite element approximation, and prove the error estimates of the discrete eigenvalues obtained by the Adini element, Morley-Zienkiewicz element, modified-Zienkiewicz element et. al. And we report some numerical examples to validate the efficiency of our approach for solving transmission eigenvalue problem.
A Method of Modeling Fabric Shear using Finite Element Analysis
NASA Astrophysics Data System (ADS)
Chichani, Swapnil; Guha, Anirban
2015-04-01
Fabric modeling may be attempted by modeling fibres or yarns or small fabric units. The first is computationally intensive while the third does not allow relationships between the fabric's structure and its mechanical properties to be predicted. The second approach has been the most widely used so far. Out of the various ways in which this has been attempted, the finite element approach offers high flexibility while allowing the procedure to be relatively simple because of the availability of user-friendly softwares. This work explores a two-step finite element approach for modeling in-plane fabric shear. A major innovation of the modeling process was that the path of yarns in the fabric was allowed to evolve through the modeling process rather than being pre-defined. The relationship between shear angle and shear stress predicted by this model was compared with that obtained from a picture frame shear experiment. It was found that modeling the yarn with a set of anisotropic properties, gave very good correlation with experimental results.
Wind Forecasting Based on the HARMONIE Model and Adaptive Finite Elements
NASA Astrophysics Data System (ADS)
Oliver, Albert; Rodríguez, Eduardo; Escobar, José María; Montero, Gustavo; Hortal, Mariano; Calvo, Javier; Cascón, José Manuel; Montenegro, Rafael
2015-01-01
In this paper, we introduce a new method for wind field forecasting over complex terrain. The main idea is to use the predictions of the HARMONIE meso-scale model as the input data for an adaptive finite element mass-consistent wind model. The HARMONIE results (obtained with a maximum resolution of about 1 km) are refined in a local scale (about a few metres). An interface between both models is implemented in such a way that the initial wind field is obtained by a suitable interpolation of the HARMONIE results. Genetic algorithms are used to calibrate some parameters of the local wind field model in accordance to the HARMONIE data. In addition, measured data are considered to improve the reliability of the simulations. An automatic tetrahedral mesh generator, based on the meccano method, is applied to adapt the discretization to complex terrains. The main characteristic of the framework is a minimal user intervention. The final goal is to validate our model in several realistic applications on Gran Canaria island, Spain, with some experimental data obtained by the AEMET in their meteorological stations. The source code of the mass-consistent wind model is available online at http://www.dca.iusiani.ulpgc.es/Wind3D/.
Integrated force method versus displacement method for finite element analysis
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Berke, L.; Gallagher, R. H.
1991-01-01
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 (EEs) are integrated with the global compatibility conditions (CCs) to form the governing set of equations. In IFM the CCs 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.
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.
NASA Astrophysics Data System (ADS)
Yan, Bo; Li, Yuguo; Liu, Ying
2016-07-01
In this paper, we present an adaptive finite element (FE) algorithm for direct current (DC) resistivity modeling in 2-D generally anisotropic conductivity structures. Our algorithm is implemented on an unstructured triangular mesh that readily accommodates complex structures such as topography and dipping layers and so on. We implement a self-adaptive, goal-oriented grid refinement algorithm in which the finite element analysis is performed on a sequence of refined grids. The grid refinement process is guided by an a posteriori error estimator. The problem is formulated in terms of total potentials where mixed boundary conditions are incorporated. This type of boundary condition is superior to the Dirichlet type of conditions and improves numerical accuracy considerably according to model calculations. We have verified the adaptive finite element algorithm using a two-layered earth with azimuthal anisotropy. The FE algorithm with incorporation of mixed boundary conditions achieves high accuracy. The relative error between the numerical and analytical solutions is less than 1% except in the vicinity of the current source location, where the relative error is up to 2.4%. A 2-D anisotropic model is used to demonstrate the effects of anisotropy upon the apparent resistivity in DC soundings.
Quadratic Finite Element Method for 1D Deterministic Transport
Tolar, Jr., D R; Ferguson, J M
2004-01-06
In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.
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)
Danilov, D.; Nestler, B.
2005-02-01
We present adaptive finite element simulations of dendritic and eutectic solidification in binary and ternary alloys. The computations are based on a recently formulated phase-field model that is especially appropriate for modelling non-isothermal solidification in multicomponent multiphase systems. In this approach, a set of governing equations for the phase-field variables, for the concentrations of the alloy components and for the temperature has to be solved numerically, ensuring local entropy production and the conservation of mass and inner energy. To efficiently perform numerical simulations, we developed a numerical scheme to solve the governing equations using a finite element method on an adaptive non-uniform mesh with highest resolution in the regions of the phase boundaries. Simulation results of the solidification in ternary Ni60Cu40-xCrx alloys are presented investigating the influence of the alloy composition on the growth morphology and on the growth velocity. A morphology diagram is obtained that shows a transition from a dendritic to a globular structure with increasing Cr concentrations. Furthermore, we comment on 2D and 3D simulations of binary eutectic phase transformations. Regular oscillatory growth structures are observed combined with a topological change of the matrix phase in 3D. An outlook for the application of our methods to describe AlCu eutectics is given.
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.
Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method
NASA Astrophysics Data System (ADS)
Yang, Zailin; Wang, Yao; Hei, Baoping
2013-12-01
The dynamic inhomogeneous finite element method is studied for use in the transient analysis of onedimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.
Numerical simulation of fluid-structure interactions with stabilized finite element method
NASA Astrophysics Data System (ADS)
Sváček, Petr
2016-03-01
This paper is interested to the interactions of the incompressible flow with a flexibly supported airfoil. The bending and the torsion modes are considered. The problem is mathematically described. The numerical method is based on the finite element method. A combination of the streamline-upwind/Petrov-Galerkin and pressure stabilizing/Petrov-Galerkin method is used for the stabilization of the finite element method. The numerical results for a three-dimensional problem of flow over an airfoil are shown.
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.
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)
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.
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.
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.
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)
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.
Fotos, P G; Spyrakos, C C; Bernard, D O
1990-01-01
The finite element method has been used to determine the stress distribution generated by the initial placement of a simulated preset bracket-type orthodontic appliance utilizing titanium-nickel alloy archwire. PMID:2256565
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.
The hp-MITC finite element method for the Reissner-Mindlin plate problem
NASA Astrophysics Data System (ADS)
Ainsworth, Mark; Pinchedez, Katia
2002-11-01
The popular MITC finite elements used for the approximation of the Reissner-Mindlin plate are extended to the case where elements of non-uniform degree p distribution are used on locally refined meshes. Such an extension is of particular interest to the hp-version and hp-adaptive finite element methods. A priori error bounds are provided showing that the method is locking-free. The analysis is based on new approximation theoretic results for non-uniform Brezzi-Douglas-Fortin-Marini spaces, and extends the results obtained in the case of uniform order approximation on globally quasi-uniform meshes presented by Stenberg and Suri (SIAM J. Numer. Anal. 34 (1997) 544). Numerical examples illustrating the theoretical results and comparing the performance with alternative standard Galerkin approaches are presented for two new benchmark problems with known analytic solution, including the case where the shear stress exhibits a boundary layer. The new method is observed to be locking-free and able to provide exponential rates of convergence even in the presence of boundary layers.
Stresses in faulted tunnel models by photoelasticity and adaptive finite element
Ladkany, S.G.; Huang, Y.
1995-12-01
Research efforts in this area continue to investigate the development of a proper technique to analyze the stresses in the Ghost Dance fault and the effect of the fault on the stability of drifts in the proposed repository. Results from two parallel techniques are being compared to each other - Photoelastic models and Finite Element (FE) models. The Photoelastic plexiglass model (88.89 mm thick & 256.1 mm long and wide) has two adjacent spare openings (57.95 mm long and wide) and a central round opening (57.95 mm diameter) placed at a clear distance approximately equal to its diameter from the square openings. The vertical loading on top of the model is 2269 N (500 lb.). Saw cuts (0.5388 mm wide), representing a fault, are being propagated from the tunnels outward with stress measurements taken at predefined locations, as the saw cuts increase in length. The FE model duplicates exactly the Photoelastic models. The adaptive mesh generation method is used to refine the FE grid at every step of the analysis. This nonlinear interactive computational techniques uses various uses various percent tolerance errors in the convergence of stress values as a measure in ending the iterative process.
A knowledge-based approach to the adaptive finite element analysis
Haghighi, K.; Kang, E.
1995-12-31
An automatic and knowledge-based finite element mesh generator (INTELMESH), which makes extensive use of interactive computer graphics techniques, has been developed. INTELMESH is designed for planar domains and axisymmetric 3-D structures of elasticity and heat transfer subjected to mechanical and thermal loading. It intelligently identifies the critical regions/points in the problem domain and utilizes the new concepts of substructuring and wave propagation to choose the proper mesh size for them. INTELMESH generates well-shaped triangular elements by applying triangulation and Laplacian smoothing procedures. The adaptive analysis involves the initial finite element analysis and an efficient a-posteriori error analysis and estimation. Once a problem is defined, the system automatically builds a finite element model and analyzes the problem through an automatic iterative process until the error reaches a desired level. It has been shown that the proposed approach which initiates the process with an a-priori, and near optimum mesh of the object, converges to the desired accuracy in less time and at less cost.
NASA Astrophysics Data System (ADS)
Ying, Jinyong; Xie, Dexuan
2015-10-01
The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.
Advanced finite element method for nano-resonators
NASA Astrophysics Data System (ADS)
Zschiedrich, Lin; Burger, Sven; Kettner, Benjamin; Schmidt, Frank
2006-02-01
Miniaturized optical resonators with spatial dimensions of the order of the wavelength of the trapped light offer prospects for a variety of new applications like quantum processing or construction of meta-materials. Light propagation in these structures is modelled by Maxwell's equations. For a deeper numerical analysis one may compute the scattered field when the structure is illuminated or one may compute the resonances of the structure. We therefore address in this paper the electromagnetic scattering problem as well as the computation of resonances in an open system. For the simulation effcient and reliable numerical methods are required which cope with the infinite domain. We use transparent boundary conditions based on the Perfectly Matched Layer Method (PML) combined with a novel adaptive strategy to determine optimal discretization parameters like the thickness of the sponge layer or the mesh width. Further a novel iterative solver for time-harmonic Maxwell's equations is presented.
NOTE: Solving the ECG forward problem by means of a meshless finite element method
NASA Astrophysics Data System (ADS)
Li, Z. S.; Zhu, S. A.; He, Bin
2007-07-01
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.
Design of an Electrostatic Comb Actuator Based on Finite Element Method
NASA Astrophysics Data System (ADS)
Mon, Thet Thet; Ghazalli, Zakri; Ahmad, Asnul Hadi; Ismail, Mohd Fazli; Muhamad, Khairul Fikri
2011-05-01
Electrostatic comb actuators were designed using finite element modeling and analysis, so-called finite element method (FEM). Design objective was to generate maximum actuating force within the constraints. 2D and 3D FE models of the comb structures were developed in general-purpose FE code. The element geometries were 4-node plate element for 2D model and 8-node brick element for 3D models. Electrostatic field strength and voltage analysis of the FE models were performed to compute generated voltage and electrostatic force in the structure. Subsequently done was the structural analysis to examine structural response to the electrostatic force. The initial finite element model was verified with the published experimental result. Based on the amount of force generated and lateral deflection of the comb fingers, the best possible design of choice was determined. The finite element computations show that the comb structure having high aspect ratio with smaller gaps can provide higher actuation force.
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.
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.
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
Toward automatic finite element analysis
NASA Technical Reports Server (NTRS)
Kela, Ajay; Perucchio, Renato; Voelcker, Herbert
1987-01-01
Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.
Using Multithreading 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.; Bailey, David H. (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 question phase of FE applications on 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 on EARTH-SP2, an implementation of EARTH on the IBM SP2, with different load balancing strategies that are built into the runtime system.
Three-dimensional crack growth with hp-generalized finite element and face offsetting methods
NASA Astrophysics Data System (ADS)
Pereira, J. P.; Duarte, C. A.; Jiao, X.
2010-08-01
A coupling between the hp-version of the generalized finite element method ( hp-GFEM) and the face offsetting method (FOM) for crack growth simulations is presented. In the proposed GFEM, adaptive surface meshes composed of triangles are utilized to explicitly represent complex three-dimensional (3-D) crack surfaces. By applying the hp-GFEM at each crack growth step, high-order approximations on locally refined meshes are automatically created in complex 3-D domains while preserving the aspect ratio of elements, regardless of crack geometry. The FOM is applied to track the evolution of the crack front in the explicit crack surface representation. The FOM provides geometrically feasible crack front descriptions based on hp-GFEM solutions. The coupling of hp-GFEM and FOM allows the simulation of arbitrary crack growth with concave crack fronts independent of the volume mesh. Numerical simulations illustrate the robustness and accuracy of the proposed methodology.
Finite-element-method expectation values for correlated two-electron wave functions
Ackermann, J.
1995-09-01
The Schroedinger equation for the ground state of correlated two-electron atoms is treated by an accurate finite-element method (FEM) yielding energy eigenvalues of {minus}2.903 724 377 021 a.u. for the helium atom and {minus}0.527 751 016 532 a.u. for the hydrogen ion H{sup {minus}}. By means of an adaptive multilevel grid refinement the FEM energy eigenvalue is improved to a precision of 1{times}10{sup {minus}11} a.u., which is comparable to results obtained with sophisticated global basis sets. The local and overall precision of the FEM wave function approximation is studied and discussed. Benchmark values for the expectation values {l_angle}{ital r}{sup 2}{r_angle}, {l_angle}{ital r}{r_angle}, {l_angle}1/{ital r}{r_angle}, and {l_angle}1/{ital r}{sub 12}{r_angle} are presented.
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.
Review of correlation methods for evaluating finite element simulations of impact injury risk.
Wang, Qian; Gabler, Hampton C
2008-01-01
Finite element models have been used to understand human injury responses in various crash configurations. Most of the model validations were limited to qualitative descriptions. Quantitative analysis was needed for the validation of finite element models against experimental results. The purpose of this study is to compare the existing correlation techniques and to determine the best method to use for evaluating finite element simulations of impact injury risk in vehicle crashes. Five correlation methods in the literature were reviewed for systematic comparisons between simulations and tests. A full frontal impact test of a 1997 Geo Metro was simulated. The finite element model of a 1997 Geo Metro was obtained from NCAC finite element model archive. The acceleration and velocity responses of the vehicle seat were extracted from the simulation and compared to the test data. Evaluations of the validation methods were based on the analysis results compared to the suggested criteria. Performance of the different methods showed that the Comprehensive Error Factor method was the best overall correlation method, and therefore was recommended for assessing occupant injury potentials in vehicle accidents. PMID:19141927
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.
An Imbricate Finite Element Method (I-FEM) using full, reduced, and smoothed integration
NASA Astrophysics Data System (ADS)
Cazes, Fabien; Meschke, Günther
2013-11-01
A method to design finite elements that imbricate with each other while being assembled, denoted as imbricate finite element method, is proposed to improve the smoothness and the accuracy of the approximation based upon low order elements. Although these imbricate elements rely on triangular meshes, the approximation stems from the shape functions of bilinear quadrilateral elements. These elements satisfy the standard requirements of the finite element method: continuity, delta function property, and partition of unity. The convergence of the proposed approximation is investigated by means of two numerical benchmark problems comparing three different schemes for the numerical integration including a cell-based smoothed FEM based on a quadratic shape of the elements edges. The method is compared to related existing methods.
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.
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.
Iterative methods for elliptic finite element equations on general meshes
NASA Technical Reports Server (NTRS)
Nicolaides, R. A.; Choudhury, Shenaz
1986-01-01
Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.
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)
NASA Astrophysics Data System (ADS)
Zhang, H. W.; Fu, Z. D.; Wu, J. K.
2009-02-01
The multiscale finite element method is developed for solving the coupling problems of consolidation of heterogeneous saturated porous media under external loading conditions. Two sets of multiscale base functions are constructed, respectively, for the pressure field of fluid flow and the displacement field of solid skeleton. The coupling problems are then solved with a multiscale numerical procedure in space and time domain. The heterogeneities induced by permeabilities and mechanical parameters of the saturated porous media are both taken into account. Numerical experiments are carried out for different cases in comparison with the standard finite element method. The numerical results show that the coupling multiscale finite element method can be successfully used for solving the complicated coupling problems. It reduces greatly the computing effort in both memory and time for transient problems.
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.
Petrov-galerkin finite element method for solving the neutron transport equation
Greenbaum, A.; Ferguson, J.M.
1986-05-01
A finite element using different trial and test spaces in introduced for solving the neutron transport equation in spherical geometry. It is shown that the widely used discrete ordinates method can also be thought of as such a finite element technique, in which integrals appearing in the difference equations are replaced by one-point Gauss quadrature formulas (midpoint rule). Comparison of accuracy between the new method and the discrete ordinates method is discussed, and numerical examples are given to illustrate the greater accuracy of the new technique.
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.
Nonlinear Schwarz-Fas Methods for Unstructured Finite Element Elliptic Problems
Jones, J E; Vassilevski, P S; Woodward, C S
2002-09-30
This paper provides extensions of an element agglomeration AMG method to nonlinear elliptic problems discretized by the finite element method on general unstructured meshes. The method constructs coarse discretization spaces and corresponding coarse nonlinear operators as well as their Jacobians. We introduce both standard (fairly quasi-uniformly coarsened) and non-standard (coarsened away) coarse meshes and respective finite element spaces. We use both kind of spaces in FAS type coarse subspace correction (or Schwarz) algorithms. Their performance is illustrated on a number of model problems. The coarsened away spaces seem to perform better than the standard spaces for problems with nonlinearities in the principal part of the elliptic operator.
Finite element methods and Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Cuvelier, C.; Segal, A.; van Steenhoven, A. A.
This book is devoted to two and three-dimensional FEM analysis of the Navier-Stokes (NS) equations describing one flow of a viscous incompressible fluid. Three different approaches to the NS equations are described: a direct method, a penalty method, and a method that constructs discrete solenoidal vector fields. Subjects of current research which are important from the industrial/technological viewpoint are considered, including capillary-free boundaries, nonisothermal flows, turbulence, and non-Newtonian fluids.
NASA Astrophysics Data System (ADS)
Casadei, F.; Ruzzene, M.
2011-04-01
This work illustrates the possibility to extend the field of application of the Multi-Scale Finite Element Method (MsFEM) to structural mechanics problems that involve localized geometrical discontinuities like cracks or notches. The main idea is to construct finite elements with an arbitrary number of edge nodes that describe the actual geometry of the damage with shape functions that are defined as local solutions of the differential operator of the specific problem according to the MsFEM approach. The small scale information are then brought to the large scale model through the coupling of the global system matrices that are assembled using classical finite element procedures. The efficiency of the method is demonstrated through selected numerical examples that constitute classical problems of great interest to the structural health monitoring community.
Finite element method for optimal guidance of an advanced launch vehicle
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.; Calise, Anthony J.; Leung, Martin
1992-01-01
A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.
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.
A finite element method for active vibration control of uncertain structures
NASA Astrophysics Data System (ADS)
Morales, A. L.; Rongong, J. A.; Sims, N. D.
2012-10-01
This work introduces a fuzzy design method using the finite element procedure to simulate and analyze active vibration control of structures subjected to uncertain parameters. The purpose of this work is to provide a tool for studying the influence of uncertainty propagation on both stability and performance of a vibration control system, whilst avoiding the need for computationally expensive probabilistic methods or complex robust control techniques. The proposed procedure applies a general and efficient strategy for computing fuzzy results to a sequence of finite element calculations. Finally, the applicability of the methodology is illustrated through some realistic case studies related to structural control where spillover instability may arise.
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
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
Ma Xiang; Zabaras, Nicholas
2011-06-01
A computational methodology is developed to efficiently perform uncertainty quantification for fluid transport in porous media in the presence of both stochastic permeability and multiple scales. In order to capture the small scale heterogeneity, a new mixed multiscale finite element method is developed within the framework of the heterogeneous multiscale method (HMM) in the spatial domain. This new method ensures both local and global mass conservation. Starting from a specified covariance function, the stochastic log-permeability is discretized in the stochastic space using a truncated Karhunen-Loeve expansion with several random variables. Due to the small correlation length of the covariance function, this often results in a high stochastic dimensionality. Therefore, a newly developed adaptive high dimensional stochastic model representation technique (HDMR) is used in the stochastic space. This results in a set of low stochastic dimensional subproblems which are efficiently solved using the adaptive sparse grid collocation method (ASGC). Numerical examples are presented for both deterministic and stochastic permeability to show the accuracy and efficiency of the developed stochastic multiscale method.
Singularity computations. [finite element methods for elastoplastic flow
NASA Technical Reports Server (NTRS)
Swedlow, J. L.
1978-01-01
Direct descriptions of the structure of a singularity would describe the radial and angular distributions of the field quantities as explicitly as practicable along with some measure of the intensity of the singularity. This paper discusses such an approach based on recent development of numerical methods for elastoplastic flow. Attention is restricted to problems where one variable or set of variables is finite at the origin of the singularity but a second set is not.
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.
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.
An exact zooming method for finite element analyses
NASA Technical Reports Server (NTRS)
Hirai, I.; Wang, B. P.; Pilkey, W. D.
1982-01-01
An exact zooming technique which employs static condensation and exact structural reanalysis methods was developed. Successive application of static condensation reduces the system to one that is only associated with the degrees of freedom (dof) of the original model. Application of an exact static reanalysis technique permits the displacements at the dof of the original model that are contained in the zoomed portion of the structure to be obtained first. The response external to the zoom, as well as the response of additional dof within various levels of zooming, is computed. With the triangular factor of the stiffness matrix of the original system available, this approach involves only the solution of a system of equations of small order.
An explicit Lagrangian finite element method for free-surface weakly compressible flows
NASA Astrophysics Data System (ADS)
Cremonesi, Massimiliano; Meduri, Simone; Perego, Umberto; Frangi, Attilio
2016-07-01
In the present work, an explicit finite element approach to the solution of the Lagrangian formulation of the Navier-Stokes equations for weakly compressible fluids or fluid-like materials is investigated. The introduction of a small amount of compressibility is shown to allow for the formulation of a fast and robust explicit solver based on a particle finite element method. Newtonian and Non-Newtonian Bingham laws are considered. A barotropic equation of state completes the model relating pressure and density fields. The approach has been validated through comparison with experimental tests and numerical simulations of free surface fluid problems involving water and water-soil mixtures.
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.
Axisymmetric analysis of a tube-type acoustic levitator by a finite element method.
Hatano, H
1994-01-01
A finite element approach was taken for the study of the sound field and positioning force in a tube-type acoustic levitator. An axisymmetric model, where a rigid sphere is suspended on the tube axis, was introduced to model a cylindrical chamber of a levitation tube furnace. Distributions of velocity potential, magnitudes of positioning force, and resonance frequency shifts of the chamber due to the presence of the sphere were numerically estimated in relation to the sphere's position and diameter. Experiments were additionally made to compare with the simulation. The finite element method proved to be a useful tool for analyzing and designing the tube-type levitator. PMID:18263265
Research of carbon composite material for nonlinear finite element method
NASA Astrophysics Data System (ADS)
Kim, Jung Ho; Garg, Mohit; Kim, Ji Hoon
2011-11-01
Works on the absorption of collision energy in the structural members are carried out widely with various material and cross-sections. And, with ever increasing safety concerns, they are presently applied in various fields including railroad trains, air crafts and automobiles. In addition to this, problem of lighting structural members became important subject by control of exhaust gas emission, fuel economy and energy efficiency. CFRP(Carbon Fiber Reinforced Plastics) usually is applying the two primary structural members because of different result each design parameter as like stacking thickness, stacking angle, moisture absorption ect. We have to secure the data for applying primary structural members. But it always happens to test design parameters each for securing the data. So, it has much more money and time. We can reduce the money and the time, if can ensure the CFRP material properties each design parameters. In this study, we experiment the coupon test each tension, compression and shear using CFRP prepreg sheet and simulate non-linear analyze at the sources - test result, Caron longitudinal modulus and matrix poisson's ratio using GENOAMQC is specialized at Composite analysis. And then we predict the result that specimen manufacture changing stacking angle and experiment in such a way of test method using GENOA-MCQ.
Research of carbon composite material for nonlinear finite element method
NASA Astrophysics Data System (ADS)
Kim, Jung Ho; Garg, Mohit; Kim, Ji Hoon
2012-04-01
Works on the absorption of collision energy in the structural members are carried out widely with various material and cross-sections. And, with ever increasing safety concerns, they are presently applied in various fields including railroad trains, air crafts and automobiles. In addition to this, problem of lighting structural members became important subject by control of exhaust gas emission, fuel economy and energy efficiency. CFRP(Carbon Fiber Reinforced Plastics) usually is applying the two primary structural members because of different result each design parameter as like stacking thickness, stacking angle, moisture absorption ect. We have to secure the data for applying primary structural members. But it always happens to test design parameters each for securing the data. So, it has much more money and time. We can reduce the money and the time, if can ensure the CFRP material properties each design parameters. In this study, we experiment the coupon test each tension, compression and shear using CFRP prepreg sheet and simulate non-linear analyze at the sources - test result, Caron longitudinal modulus and matrix poisson's ratio using GENOAMQC is specialized at Composite analysis. And then we predict the result that specimen manufacture changing stacking angle and experiment in such a way of test method using GENOA-MCQ.
An implicit finite element method for discrete dynamic fracture
Jobie M. Gerken
1999-12-01
A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The resulting stiffness matrix is that of a standard plane element. The resulting load vector is that of a standard plane element with an additional term that includes the externally applied strain field. Except for the crack strain field equations, all terms of the stiffness matrix and load vector are integrated symbolically in Maple V so that fully integrated plane stress and plane strain elements are constructed. The crack strain field equations are integrated numerically. The modeling of dynamic behavior of simple structures was demonstrated within acceptable engineering accuracy. In the model of axial and transverse vibration of a beam and the breathing mode of vibration of a thin ring, the dynamic characteristics were shown to be within expected limits. The models dominated by tensile forces (the axially loaded beam and the pressurized ring) were within 0.5% of the theoretical values while the shear dominated model (the transversely loaded beam) is within 5% of the calculated theoretical value. The constant strain field of the tensile problems can be modeled exactly by the numerical model. The numerical results should therefore, be exact. The discrepancies can be accounted for by errors in the calculation of frequency from the numerical results. The linear strain field of the transverse model must be modeled by a series of constant strain elements. This is an approximation to the true strain field, so some
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.
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.
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.
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.
FEMSECT: An inverse section model based on the finite element method
NASA Astrophysics Data System (ADS)
Losch, M.; Sidorenko, D.; Beszczynska-MöLler, A.
2005-12-01
A new inverse model is presented for the analysis of hydrographic section data in conjunction with velocity measurements. The model offers advantages over commonly applied interpolation techniques because it combines data and physical assumptions such as geostrophic balance in the framework of a finite element discretization. Specifically, a quadratic objective function of model-data misfits is minimized to give estimates of transports together with formal error estimates. The finite element method allows the accurate representation of highly irregular bottom topography and ensures consistent interpolation of model variables to measurement points. The model is called Finite Element Method Section model (FEMSECT). FEMSECT also gives improved flexibility and performance over standard box models by allowing dynamic adjustment of the model variables temperature and salinity. Idealized test cases illustrate that the finite element methods solve the thermal wind equations far more accurately than standard finite difference methods, especially in the presence of steep topography. For a more realistic test, FEMSECT is applied to hydrographic conductivity-temperature-depth section data and moored instrument current meter measurements from an array in the Fram Strait. Transport estimates by FEMSECT prove to be more robust and less sensitive to the spatial data resolution than estimates by a conventional interpolation method that only uses information from moored instruments. FEMSECT is available as a highly portable Matlab code and can be run on an ordinary desktop computer.
Compressible seal flow analysis using the finite element method with Galerkin solution technique
NASA Technical Reports Server (NTRS)
Zuk, J.
1974-01-01
A finite element method with a Galerkin solution (FEMGS) technique is formulated for the solution of nonlinear problems in high-pressure compressible seal flow analyses. An example of a three-dimensional axisymmetric flow having nonlinearities, due to compressibility, area expansion, and convective inertia, is used for illustrating the application of the technique.
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;…
Goiato, Marcelo Coelho; Tonella, Bianca Piccolotto; Ribeiro, Paula do Prado; Ferraço, Renato; Pellizzer, Eduardo Piza
2009-03-01
The authors describe a literature revision on assessing stresses in buccomaxillary prostheses photoelasticity, finite element technique, and extensometry. They describe the techniques and the importance for use of each method in buccomaxillary prostheses with implants and the need of accomplishing more studies in this scarce literary area. PMID:19305257
NASA Astrophysics Data System (ADS)
Bouklas, Nikolaos; Landis, Chad M.; Huang, Rui
2015-06-01
Hydrogels are capable of coupled mass transport and large deformation in response to external stimuli. In this paper, a nonlinear, transient finite element formulation is presented for initial boundary value problems associated with swelling and deformation of hydrogels, based on a nonlinear continuum theory that is consistent with classical theory of linear poroelasticity. A mixed finite element method is implemented with implicit time integration. The incompressible or nearly incompressible behavior at the initial stage imposes a constraint to the finite element discretization in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for stability of the mixed method, similar to linear poroelasticity as well as incompressible elasticity and Stokes flow; failure to choose an appropriate discretization would result in locking and numerical oscillations in transient analysis. To demonstrate the numerical method, two problems of practical interests are considered: constrained swelling and flat-punch indentation of hydrogel layers. Constrained swelling may lead to instantaneous surface instability for a soft hydrogel in a good solvent, which can be regulated by assuming a stiff surface layer. Indentation relaxation of hydrogels is simulated beyond the linear regime under plane strain conditions, in comparison with two elastic limits for the instantaneous and equilibrium states. The effects of Poisson's ratio and loading rate are discussed. It is concluded that the present finite element method is robust and can be extended to study other transient phenomena in hydrogels.
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.
Simulation of wind effects on tall structures by finite element method
NASA Astrophysics Data System (ADS)
Ebrahimi, Masood
2015-07-01
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.
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.
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.
Automatic data generation scheme for finite-element method /FEDGE/ - Computer program
NASA Technical Reports Server (NTRS)
Akyuz, F.
1970-01-01
Algorithm provides for automatic input data preparation for the analysis of continuous domains in the fields of structural analysis, heat transfer, and fluid mechanics. The computer program utilizes the natural coordinate systems concept and the finite element method for data generation.
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.
NASA Astrophysics Data System (ADS)
Kergrene, Kenan; Babuška, Ivo; Banerjee, Uday
2016-06-01
The Generalized Finite Element Method (GFEM) is an extension of the Finite Element Method (FEM), where the standard finite element space is augmented with a space of non-polynomial functions, called the enrichment space. The functions in the enrichment space mimic the local behavior of the unknown solution of the underlying variational problem. GFEM has been successfully applied to a wide range of problems. However, it often suffers from bad conditioning, i.e., its conditioning may not be robust with respect to the mesh and in fact, the conditioning could be much worse than that of the standard FEM. In this paper, we present a numerical study that shows that if the "angle" between the finite element space and the enrichment space is bounded away from 0, uniformly with respect to the mesh, then the GFEM is stable, i.e., the conditioning of GFEM is not worse than that of the standard FEM. A GFEM with this property is called a Stable GFEM (SGFEM). The last part of the paper is devoted to the derivation of a robust iterative solver exploiting this angle condition. It is shown that the required "wall-clock" time is greatly reduced compared to popular GFEMs used in the literature.
Kuramae, Hiroyuki; Okada, Kenji; Uetsuji, Yasutomo; Nakamachi, Eiji; Tam, Nguyen Ngoc; Nakamura, Yasunori
2005-08-05
Since the multi-scale finite element analysis (FEA) requires large computation time, development of the parallel computing technique for the multi-scale analysis is inevitable. A parallel elastic/crystalline viscoplastic FEA code based on a crystallographic homogenization method has been developed using PC cluster. The homogenization scheme is introduced to compute macro-continuum plastic deformations and material properties by considering a polycrystal texture. Since the dynamic explicit method is applied to this method, the analysis using micro crystal structures computes the homogenized stresses in parallel based on domain partitioning of macro-continuum without solving simultaneous linear equations. The micro-structure is defined by the Scanning Electron Microscope (SEM) and the Electron Back Scan Diffraction (EBSD) measurement based crystal orientations. In order to improve parallel performance of elastoplasticity analysis, which dynamically and partially increases computational costs during the analysis, a dynamic workload balancing technique is introduced to the parallel analysis. The technique, which is an automatic task distribution method, is realized by adaptation of subdomain size for macro-continuum to maintain the computational load balancing among cluster nodes. The analysis code is applied to estimate the polycrystalline sheet metal formability.
Jia, Zhiheng; Du, Zhijiang; Monan, Wang
2006-01-01
To build a biomechanical human model can make much sense for surgical training and surgical rehearse. Especially, it will be more meaningful to develop a biomechanical model to guide the control strategy for the medical robots in HIT-Robot Assisted Orthopedic Surgery System (HIT-RAOS). In this paper, based the successful work of others, a novel reliable finite element method based biomechanical model for HIT-RAOS was developed to simulate the force needed in reposition procedure. Geometrical model was obtained from 3D reconstruction from CT images of a just died man. Using this boundary information, the finite element model of the leg including part of femur, broken upper tibia, broken lower tibia, talus, calcaneus, Kirschner nail, muscles and other soft tissues was created in ANSYS. Furthermore, as it was too difficult to reconstruct the accurate geometry model from CT images, a new simplified muscle model was presented. The bony structures and tendons were defined as linearly elastic, while soft tissues and muscle fibers were assumed to be hyper elastic. To validate this model, the same dead man was involved to simulate the patient, and a set of data of the force needed to separate the two broken bones and the distance between them in reposition procedure was recorded. Then, another set of data was acquired from the finite element analysis. After comparison, the two sets of data matched well. The Finite Element model was proved to be acceptable. PMID:17945663
Jia, Zhiheng; Du, Zhijiang; Wang, Monan
2006-01-01
To build a biomechanical human model can make much sense for surgical training and surgical rehearse. Especially, it will be more meaningful to develop a biomechanical model to guide the control strategy for the medical robots in HIT-Robot Assisted Orthopedic Surgery System (HIT-RAOS). In this paper, based the successful work of others, a novel reliable finite element method based biomechanical model for HIT-RAOS was developed to simulate the force needed in reposition procedure. Geometrical model was obtained from 3D reconstruction from CT images of a just died man. Using this boundary information, the finite element model of the leg including part of femur, broken upper tibia, broken lower tibia, talus, calcaneus, Kirschner nail, muscles and other soft tissues was created in ANSYS. Furthermore, as it was too difficult to reconstruct the accurate geometry model from CT images, a new simplified muscle model was presented. The bony structures and tendons were defined as linearly elastic, while soft tissues and muscle fibers were assumed to be hyper elastic. To validate this model, the same dead man was involved to simulate the patient, and a set of data of the force needed to separate the two broken bones and the distance between them in reposition procedure was recorded. Then, another set of data was acquired from the finite element analysis. After comparison, the two sets of data matched well. The Finite Element model was proved to be acceptable. PMID:17959437
A semi-implicit finite element method for viscous lipid membranes
NASA Astrophysics Data System (ADS)
Rodrigues, Diego; Ausas, Roberto; Mut, Fernando; Buscaglia, Gustavo
2014-11-01
We propose a robust simulation method for phospholipid membranes. It is based on a mixed three-field formulation that accounts for tangential fluidity (Boussinesq-Scriven law), bending elasticity (Canham-Helfrich model) and inextensibility. The unknowns are the velocity, vector curvature and surface pressure fields, all of which are interpolated with linear continuous finite elements. The method is semi-implicit, it requires the solution of a single linear system per time step. Conditional time stability is observed, with a time step restriction that scales as the square of the mesh size. Mesh quality and refinement are maintained by adaptively remeshing. Another ingredient is a numerical force that emulates the action of an optical tweezer, allowing for virtual interaction with the membrane. Extensive relaxation experiments are reported. Comparisons to exact shapes reveal the orders of convergence for position (5/3), vector curvature (3/2), surface pressure (1) and bending energy (2). Tweezing experiments are also presented. Convergence to the exact dynamics of a cylindrical tether is confirmed. Further tests illustrate the robustness of the method (six tweezers acting simultaneously) and the significance of viscous effects on membrane's deformation under external forces. The authors acknowledge the financial support received from Grants #11/01800-5, #12/14481-8 and #12/23383-0, São Paulo Research Foundation (FAPESP).
Song, Yuhua; Zhang, Yongjie; Bajaj, Chandrajit L.; Baker, Nathan A.
2004-01-01
As described previously, continuum models, such as the Smoluchowski equation, offer a scalable framework for studying diffusion in biomolecular systems. This work presents new developments in the efficient solution of the continuum diffusion equation. Specifically, we present methods for adaptively refining finite element solutions of the Smoluchowski equation based on a posteriori error estimates. We also describe new, molecular-surface-based models, for diffusional reaction boundary criteria and compare results obtained from these models with the traditional spherical criteria. The new methods are validated by comparison of the calculated reaction rates with experimental values for wild-type and mutant forms of mouse acetylcholinesterase. The results show good agreement with experiment and help to define optimal reactive boundary conditions. PMID:15345536
Probabilistic Finite Element: Variational Theory
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.
1985-01-01
The goal of this research is to provide techniques which are cost-effective and enable the engineer to evaluate the effect of uncertainties in complex finite element models. Embedding the probabilistic aspects in a variational formulation is a natural approach. In addition, a variational approach to probabilistic finite elements enables it to be incorporated within standard finite element methodologies. Therefore, once the procedures are developed, they can easily be adapted to existing general purpose programs. Furthermore, the variational basis for these methods enables them to be adapted to a wide variety of structural elements and to provide a consistent basis for incorporating probabilistic features in many aspects of the structural problem. Tasks concluded include the theoretical development of probabilistic variational equations for structural dynamics, the development of efficient numerical algorithms for probabilistic sensitivity displacement and stress analysis, and integration of methodologies into a pilot computer code.
Lu, Yujie; Zhu, Banghe; Shen, Haiou; Rasmussen, John C; Wang, Ge; Sevick-Muraca, Eva M
2010-08-21
Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP(N)) approximations. To fully evaluate the performance of the SP(N) approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP(N) can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation. PMID:20671350
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.
Pipe crack identification based on finite element method of second generation wavelets
NASA Astrophysics Data System (ADS)
Ye, Junjie; He, Yumin; Chen, Xuefeng; Zhai, Zhi; Wang, Youming; He, Zhengjia
2010-02-01
In this paper, a new method is presented to identify crack location and size, which is based on stress intensity factor suitable for pipe structure and finite element method of second generation wavelets (SGW-FEM). Pipe structure is dispersed into a series of nested thin-walled pipes. By making use of stress intensity factor of the thin-walled pipe, a new calculation method of crack equivalent stiffness is proposed to solve the stress intensity factor of the pipe structure. On this basis, finite element method of second generation wavelets is used to establish the dynamic model of cracked pipe. Then we combine forward problem with inverse problem in order to establish quantitative identification method of the crack based on frequency change, which provides a non-destructive testing technology with vibration for the pipe structure. The efficiency of the proposed method is verified by experiments.
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.
Gaussian and finite-element Coulomb method for the fast evaluation of Coulomb integrals
NASA Astrophysics Data System (ADS)
Kurashige, Yuki; Nakajima, Takahito; Hirao, Kimihiko
2007-04-01
The authors propose a new linear-scaling method for the fast evaluation of Coulomb integrals with Gaussian basis functions called the Gaussian and finite-element Coulomb (GFC) method. In this method, the Coulomb potential is expanded in a basis of mixed Gaussian and finite-element auxiliary functions that express the core and smooth Coulomb potentials, respectively. Coulomb integrals can be evaluated by three-center one-electron overlap integrals among two Gaussian basis functions and one mixed auxiliary function. Thus, the computational cost and scaling for large molecules are drastically reduced. Several applications to molecular systems show that the GFC method is more efficient than the analytical integration approach that requires four-center two-electron repulsion integrals. The GFC method realizes a near linear scaling for both one-dimensional alanine α-helix chains and three-dimensional diamond pieces.
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 Review on the Finite Element Methods for Heat Conduction in Functionally Graded Materials
NASA Astrophysics Data System (ADS)
Sharma, R.; Jadon, V. K.; Singh, B.
2015-01-01
The review presented in this paper focuses mainly on the application of finite element methods for investigating the effect of heat transfer, variation of temperature and other parameters in the functionally graded materials. Different methods have been investigated for thermal conduction in functionally graded materials. The use of FEM for steady state heat transfer has been addressed in this work. The authors have also discussed the utilization of FEM based shear deformation theories and FEM in combination with other methods for the problems involving complexity of the shape and geometry of functionally graded materials. Finite element methods proved to be effective for the solution of heat transfer problem in functionally graded materials. These methods can be used for steady state heat transfer and as well as for transient state.
Gaussian and finite-element Coulomb method for the fast evaluation of Coulomb integrals.
Kurashige, Yuki; Nakajima, Takahito; Hirao, Kimihiko
2007-04-14
The authors propose a new linear-scaling method for the fast evaluation of Coulomb integrals with Gaussian basis functions called the Gaussian and finite-element Coulomb (GFC) method. In this method, the Coulomb potential is expanded in a basis of mixed Gaussian and finite-element auxiliary functions that express the core and smooth Coulomb potentials, respectively. Coulomb integrals can be evaluated by three-center one-electron overlap integrals among two Gaussian basis functions and one mixed auxiliary function. Thus, the computational cost and scaling for large molecules are drastically reduced. Several applications to molecular systems show that the GFC method is more efficient than the analytical integration approach that requires four-center two-electron repulsion integrals. The GFC method realizes a near linear scaling for both one-dimensional alanine alpha-helix chains and three-dimensional diamond pieces. PMID:17444700
Piras, Paolo; Sansalone, Gabriele; Teresi, Luciano; Moscato, Marco; Profico, Antonio; Eng, Ronald; Cox, Timothy C; Loy, Anna; Colangelo, Paolo; Kotsakis, Tassos
2015-10-01
The enigmatic Early Miocene fossorial mammal Mesoscalops montanensis shows one of the most modified humeri among terrestrial mammals. It has been suggested, on qualitative considerations, that this species has no extant homologues for humerus kinematics and that, functionally, the closest extant group is represented by Chrysochloridae. We combine here three dimensional geometric morphometrics, finite element analysis and phylogenetic comparative methods to explore the shape and mechanical stress states of Mesoscalops montanensis as well as of extant and extinct Talpidae and Chrysochloridae under realistic digging simulations. Evolutionary convergence analyses reveal that the shape of Mesoscalops montanensis represents a unique morphology in the context of fossorial mammals and that its functional performance, albeit superficially similar to that of extant Chrysochloridae, still represents a nonconvergent optimum for adaptation to digging. PMID:26134243
Numerical Quadrature and Operator Splitting in Finite Element Methods for Cardiac Electrophysiology
Krishnamoorthi, Shankarjee; Sarkar, Mainak; Klug, William S.
2015-01-01
SUMMARY We examine carefully the numerical accuracy and computational efficiency of alternative formulations of the finite-element solution procedure for the mono-domain equations of cardiac electrophysiology (EP), focusing on the interaction of spatial quadrature implementations with operator splitting, 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 EP 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 non-uniform meshes having a large distribution of element sizes. PMID:23873868
A fictitious domain approach for the Stokes problem based on the extended finite element method
NASA Astrophysics Data System (ADS)
Court, Sébastien; Fournié, Michel; Lozinski, Alexei
2014-01-01
In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries do not match. A mixed finite element method is used for fluid flow. The interface between the fluid and the structure is localized by a level-set function. Dirichlet boundary conditions are taken into account using Lagrange multiplier. A stabilization term is introduced to improve the approximation of the normal trace of the Cauchy stress tensor at the interface and avoid the inf-sup condition between the spaces for velocity and the Lagrange multiplier. Convergence analysis is given and several numerical tests are performed to illustrate the capabilities of the method.
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.
NASA Astrophysics Data System (ADS)
Chen, De-Xiang; Xu, Zi-Li; Liu, Shi; Feng, Yong-Xin
2014-03-01
Modern least squares finite element method (LSFEM) has advantage over mixed finite element method for non-self-adjoint problem like Navier-Stokes equations, but has problem to be norm equivalent and mass conservative when using C0 type basis. In this paper, LSFEM with non-uniform B-splines (NURBS) is proposed for Navier-Stokes equations. High order continuity NURBS is used to construct the finite-dimensional spaces for both velocity and pressure. Variational form is derived from the governing equations with primitive variables and the DOFs due to additional variables are not necessary. There is a novel k-refinement which has spectral convergence of least squares functional. The method also has same advantages as isogeometric analysis like automatic mesh generation and exact geometry representation. Several benchmark problems are solved using the proposed method. The results agree well with the benchmark solutions available in literature. The results also show good performance in mass conservation.
Numerical solution of 3-D magnetotelluric using vector finite element method
NASA Astrophysics Data System (ADS)
Prihantoro, Rudy; Sutarno, Doddy; Nurhasan
2015-09-01
Magnetotelluric (MT) is a passive electromagnetic (EM) method which measure natural variations of electric and magnetic vector fields at the Earth surface to map subsurface electrical conductivity/resistivity structure. In this study, we obtained numerical solution of three-dimensional (3-D) MT using vector finite element method by solving second order Maxwell differential equation describing diffusion of plane wave through the conductive earth. Rather than the nodes of the element, the edges of the element is used as a vector basis to overcome the occurrence of nonphysical solutions that usually faced by scalar (node based) finite element method. Electric vector fields formulation was used and the resulting system of equation was solved using direct solution method to obtain the electric vector field distribution throughout the earth resistivity model structure. The resulting MT response functions was verified with 1-D layered Earth and 3-D2 COMMEMI outcropping structure. Good agreement is achieved for both structure models.
NASA Technical Reports Server (NTRS)
Strong, Stuart L.; Meade, Andrew J., Jr.
1992-01-01
Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.
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
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.
NASA Astrophysics Data System (ADS)
Zhang, H. W.; Fu, Z. D.
2010-01-01
The coupling upscaling finite element method is developed for solving the coupling problems of deformation and consolidation of heterogeneous saturated porous media under external loading conditions. The method couples two kinds of fully developed methodologies together, i.e., the numerical techniques developed for calculating the apparent and effective physical properties of the heterogeneous media and the upscaling techniques developed for simulating the fluid flow and mass transport properties in heterogeneous porous media. Equivalent permeability tensors and equivalent elastic modulus tensors are calculated for every coarse grid block in the coarse-scale model of the heterogeneous saturated porous media. Moreover, an oversampling technique is introduced to improve the calculation accuracy of the equivalent elastic modulus tensors. A numerical integration process is performed over the fine mesh within every coarse grid element to capture the small scale information induced by non-uniform scalar field properties such as density, compressibility, etc. Numerical experiments are carried out to examine the accuracy of the developed method. It shows that the numerical results obtained by the coupling upscaling finite element method on the coarse-scale models fit fairly well with the reference solutions obtained by traditional finite element method on the fine-scale models. Moreover, this method gets more accurate coarse-scale results than the previously developed coupling multiscale finite element method for solving this kind of coupling problems though it cannot recover the fine-scale solutions. At the same time, the method developed reduces dramatically the computing effort in both CPU time and memory for solving the transient problems, and therefore more large and computational-demanding coupling problems can be solved by computers.
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.
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.
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.
Evolutionary topology optimization using the extended finite element method and isolines
NASA Astrophysics Data System (ADS)
Abdi, Meisam; Wildman, Ricky; Ashcroft, Ian
2014-05-01
This study presents a new algorithm for structural topological optimization of two-dimensional continuum structures by combining the extended finite element method (X-FEM) with an evolutionary optimization algorithm. Taking advantage of an isoline design approach for boundary representation in a fixed grid domain, X-FEM can be implemented to improve the accuracy of finite element solutions on the boundary during the optimization process. Although this approach does not use any remeshing or moving mesh algorithms, final topologies have smooth and clearly defined boundaries which need no further interpretation. Numerical comparisons of the converged solutions with standard bi-directional evolutionary structural optimization solutions show the efficiency of the proposed method, and comparison with the converged solutions using MSC NASTRAN confirms the high accuracy of this method.
NASA Technical Reports Server (NTRS)
Jin, Jian-Ming; Volakis, John L.
1992-01-01
A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite element and boundary integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate gradient method in conjunction with the Fast Fourier Transform (FFT) thus achieving an O(N) storage requirement. By virtue of the finite element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique.
Reliability of the finite element method for calculating free edge stresses in composite laminates
NASA Technical Reports Server (NTRS)
Whitcomb, J. D.; Raju, I. S.; Goree, J. G.
1982-01-01
The interlaminar normal stress distributions along the interface between the +45 deg and -45 deg plies of a graphite/epoxy laminate, obtained by various investigators, were found to disagree in both magnitude and sign. The reliability of the displacement-formulated finite element method in analyzing the edge-stress problem of a composite laminate is investigated. The history of the edge-stress problem is reviewed, and two well-known elasticity problems, one involving a stress discontinuity and one a singularity, are analyzed. The finite element analysis in these problems yields accurate stress distributions everywhere except in two elements closest to the stress discontinuity or singularity. Stress distributions for a + or -45 deg ply laminate near the singularity were similar to those of the two elasticity problems, demonstrating the methods, accuracy for calculating interlaminar stresses in composite laminates. The disagreement between the numerical methods was attributed to the unsymmetric stress tensor at singularity.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Ziemys, A.; Kojic, M.; Milosevic, M.; Kojic, N.; Hussain, F.; Ferrari, M.; Grattoni, A.
2011-06-01
We present a successful hierarchical modeling approach which accounts for interface effects on diffusivity, ignored in classical continuum theories. A molecular dynamics derived diffusivity scaling scheme is incorporated into a finite element method to model transport through a nanochannel. In a 5 nm nanochannel, the approach predicts 2.2 times slower mass release than predicted by Fick's law by comparing time spent to release 90% of mass. The scheme was validated by predicting experimental glucose diffusion through a nanofluidic membrane with a correlation coefficient of 0.999. Comparison with experiments through a nanofluidic membrane showed interface effects to be crucial. We show robustness of our discrete continuum model in addressing complex diffusion phenomena in biomedical and engineering applications by providing flexible hierarchical coupling of molecular scale effects and preserving computational finite element method speed.
Three dimensional finite element methods: Their role in the design of DC accelerator systems
Podaru, Nicolae C.; Gottdang, A.; Mous, D. J. W.
2013-04-19
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 Multiplication-Sign 300 mm{sup 2}. 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.
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.
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
Simulation of 3D tumor cell growth using nonlinear finite element method.
Dong, Shoubing; Yan, Yannan; Tang, Liqun; Meng, Junping; Jiang, Yi
2016-06-01
We propose a novel parallel computing framework for a nonlinear finite element method (FEM)-based cell model and apply it to simulate avascular tumor growth. We derive computation formulas to simplify the simulation and design the basic algorithms. With the increment of the proliferation generations of tumor cells, the FEM elements may become larger and more distorted. Then, we describe a remesh and refinement processing of the distorted or over large finite elements and the parallel implementation based on Message Passing Interface to improve the accuracy and efficiency of the simulation. We demonstrate the feasibility and effectiveness of the FEM model and the parallelization methods in simulations of early tumor growth. PMID:26213205
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.
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.
NASA Astrophysics Data System (ADS)
Zhang, Jiaping; Zhao, Xuanhe; Suo, Zhigang; Jiang, Hanqing
2009-05-01
A gel is an aggregate of polymers and solvent molecules. The polymers crosslink into a three-dimensional network by strong chemical bonds and enable the gel to retain its shape after a large deformation. The solvent molecules, however, interact among themselves and with the network by weak physical bonds and enable the gel to be a conduit of mass transport. The time-dependent concurrent process of large deformation and mass transport is studied by developing a finite element method. We combine the kinematics of large deformation, the conservation of the solvent molecules, the conditions of local equilibrium, and the kinetics of migration to evolve simultaneously two fields: the displacement of the network and the chemical potential of the solvent. The finite element method is demonstrated by analyzing several phenomena, such as swelling, draining and buckling. This work builds a platform to study diverse phenomena in gels with spatial and temporal complexity.
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
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. PMID:10949130
Calculations of the polycentric linear molecule H 32+ with the finite element method
NASA Astrophysics Data System (ADS)
Hackel, S.; Heinemann, D.; Kolb, D.; Fricke, B.
1993-04-01
A fully numerical two-dimensional solution of the Schrödinger equation is presented for the linear polyatomic molecule H 32+ using the finite element method (FEM). The Coulomb singularities at the nuclei are rectified by using both a condensed element distribution around the singularities and special elements. The accuracy of the results for the lσ and 2σ orbitals is of the order of 10 -7 au.
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.
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.
Calculation by the finite element method of 3-D turbulent flow in a centrifugal pump
NASA Astrophysics Data System (ADS)
Combes, J. F.
1992-02-01
In order to solve industrial flow problems in complex geometries, a finite element code, N3S, was developed. It allows the computation of a wide variety of 2-D or 3-D unsteady incompressible flows, by solving the Reynolds averaged Navier-Stokes equations together with a k-epsilon turbulence model. Some recent developments of this code concern turbomachinery flows, where one has to take into account periodic boundary conditions, as well as Coriolis and centrifugal forces. The numerical treatment is based on a fractional step method: at each time step, an advection step is solved successively by means of a characteristic method; a diffusion step for the scalar terms; and finally, a Generalized Stokes Problem by using a preconditioned Uzawa algorithm. The space discretization uses a standard Galerkin finite element method with a mixed formulation for the velocity and pressure. An application is presented of this code to the flow inside a centrifugal pump which was extensively tested on several air and water test rigs, and for which many quasi-3-D or Euler calculations were reported. The present N3S calculation is made on a finite element mesh comprising about 28000 tetrahedrons and 43000 nodes.
Toparli, M; Aykul, H; Aksoy, T
2002-11-01
The axisymmetrical finite element method (FEM) was used to compare stress distribution in a maxillary second premolar restored tooth. The three models were evaluated by crowning the tooth with Au-Pd alloy, Ni-Cr alloy and Ti alloy with acrylic. A longitudinal static force, 200 N in magnitude at an angle of 45 degrees was applied on the occlusal margin of each model. The tooth was assumed isotropic, homogenous and elastic. This numerical study was carried out using axisymmetric finite element models and calculation programmes were prepared by the authors using FORTRAN 77. Comparison of stress distributions was made in four regions of apex, cole, dentin-metal interface and metal-acrylic interface. The highest stress values were obtained when NiCr alloy with acrylic was used. PMID:12453266
NASA Astrophysics Data System (ADS)
Wang, Yajun; Liu, Yang; Li, Hong; Wang, Jinfeng
2016-03-01
In this article, a Galerkin finite element method combined with second-order time discrete scheme for finding the numerical solution of nonlinear time fractional Cable equation is studied and discussed. At time t_{k-α/2} , a second-order two step scheme with α -parameter is proposed to approximate the first-order derivative, and a weighted discrete scheme covering second-order approximation is used to approximate the Riemann-Liouville fractional derivative, where the approximate order is higher than the obtained results by the L1-approximation with order (2-α in the existing references. For the spatial direction, Galerkin finite element approximation is presented. The stability of scheme and the rate of convergence in L^2 -norm with O(Δ t^2+(1+Δ t^{-α})h^{m+1}) are derived in detail. Moreover, some numerical tests are shown to support our theoretical results.
Strain energy release rate determination of stress intensity factors by finite element methods
NASA Technical Reports Server (NTRS)
Walsh, R. M., Jr.; Pipes, R. B.
1985-01-01
The stiffness derivative finite element technique is used to determine the Mode I stress intensity factors for three-crack configurations. The geometries examined include the double edge notch, single edge notch, and the center crack. The results indicate that when the specified guidelines of the Stiffness Derivative Method are used, a high degree of accuracy can be achieved with an optimized, relatively coarse finite element mesh composed of standard, four-node, plane strain, quadrilateral elements. The numerically generated solutions, when compared with analytical ones, yield results within 0.001 percent of each other for the double edge crack, 0.858 percent for the single edge crack, and 2.021 percent for the center crack.
Dacles-Mariani, J; Rodrigue, G
2005-05-11
We study the effects of macroscopic bends and twists in an optical waveguide and how they influence the transmission capabilities of a waveguide. These mechanical stresses and strains distort the optical indicatrix of the medium producing optical anisotropy. The spatially varying refractive indices are incorporated into the full-wave Maxwell's equations. The governing equations are discretized using a vector finite element method cast in a high-order finite element approximation. This approach allows us to study the complexities of the mechanical deformation within a framework of a high-order formulation which can in turn, reduce the computational requirement without degrading its performance. The optical activities generated, total energy produced and power loss due to the mechanical stresses and strains are reported and discussed.
GPU-Accelerated Finite Element Method for Modelling Light Transport in Diffuse Optical Tomography
Schweiger, Martin
2011-01-01
We introduce a GPU-accelerated finite element forward solver for the computation of light transport in scattering media. The forward model is the computationally most expensive component of iterative methods for image reconstruction in diffuse optical tomography, and performance optimisation of the forward solver is therefore crucial for improving the efficiency of the solution of the inverse problem. The GPU forward solver uses a CUDA implementation that evaluates on the graphics hardware the sparse linear system arising in the finite element formulation of the diffusion equation. We present solutions for both time-domain and frequency-domain problems. A comparison with a CPU-based implementation shows significant performance gains of the graphics accelerated solution, with improvements of approximately a factor of 10 for double-precision computations, and factors beyond 20 for single-precision computations. The gains are also shown to be dependent on the mesh complexity, where the largest gains are achieved for high mesh resolutions. PMID:22013431
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.
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.
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 was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was 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. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements.
A weak Hamiltonian finite element method for optimal guidance of an advanced launch vehicle
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Calise, Anthony J.; Bless, Robert R.; Leung, Martin
1989-01-01
A temporal finite-element method based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables, which are expanded in terms of nodal values and simple shape functions. Time derivatives of the states and costates do not appear in the governing variational equation; the only quantities whose time derivatives appear therein are virtual states and virtual costates. Numerical results are presented for an elementary trajectory optimization problem; they show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The feasibility of this approach for real-time guidance applications is evaluated. A simplified model for an advanced launch vehicle application that is suitable for finite-element solution is presented.
NASA Astrophysics Data System (ADS)
Wu, Xian-Qian; Wang, Xi; Wei, Yan-Peng; Song, Hong-Wei; Huang, Chen-Guang
2012-06-01
Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and resistance to corrosion fatigue, cracking, etc. Compressive residual stress and dent profile are important factors to evaluate the effectiveness of shot peening process. In this paper, the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated. Firstly, dimensionless relations of processing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were deduced by dimensional analysis method. Secondly, the influence of each dimensionless parameter on dimensionless variables was investigated by the finite element method. Furthermore, related empirical formulas were given for each dimensionless parameter based on the simulation results. Finally, comparison was made and good agreement was found between the simulation results and the empirical formula, which shows that a useful approach is provided in this paper for analyzing the influence of each individual parameter.
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.
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.
Application of finite-element method to three-dimensional nuclear reactor analysis
Cheung, K.Y.
1985-01-01
The application of the finite element method to solve a realistic one-or-two energy group, multiregion, three-dimensional static neutron diffusion problem is studied. Linear, quadratic, and cubic serendipity box-shape elements are used. The resulting sets of simultaneous algebraic equations with thousands of unknowns are solved by the conjugate gradient method, without forming the large coefficient matrix explicitly. This avoids the complicated data management schemes to store such a large coefficient matrix. Three finite-element computer programs: FEM-LINEAR, FEM-QUADRATIC and FEM-CUBIC were developed, using the linear, quadratic, and cubic box-shape elements respectively. They are self-contained, using simple nodal labeling schemes, without the need for separate finite element mesh generating routines. The efficiency and accuracy of these computer programs are then compared among themselves, and with other computer codes. The cubic element model is not recommended for practical usage because it gives almost identical results as the quadratic model, but it requires considerably longer computation time. The linear model is less accurate than the quadratic model, but it requires much shorter computation time. For a large 3-D problem, the linear model is to be preferred since it gives acceptable accuracy. The quadratic model may be used if improved accuracy is desired.
A finite element method for solving the shallow water equations on the sphere
NASA Astrophysics Data System (ADS)
Comblen, Richard; Legrand, Sébastien; Deleersnijder, Eric; Legat, Vincent
Within the framework of ocean general circulation modeling, the present paper describes an efficient way to discretize partial differential equations on curved surfaces by means of the finite element method on triangular meshes. Our approach benefits from the inherent flexibility of the finite element method. The key idea consists in a dialog between a local coordinate system defined for each element in which integration takes place, and a nodal coordinate system in which all local contributions related to a vectorial degree of freedom are assembled. Since each element of the mesh and each degree of freedom are treated in the same way, the so-called pole singularity issue is fully circumvented. Applied to the shallow water equations expressed in primitive variables, this new approach has been validated against the standard test set defined by [Williamson, D.L., Drake, J.B., Hack, J.J., Jakob, R., Swarztrauber, P.N., 1992. A standard test set for numerical approximations to the shallow water equations in spherical geometry. Journal of Computational Physics 102, 211-224]. Optimal rates of convergence for the P1NC-P1 finite element pair are obtained, for both global and local quantities of interest. Finally, the approach can be extended to three-dimensional thin-layer flows in a straightforward manner.
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
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. PMID:25616741
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. PMID:26727401
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.
Consistent linearization method for finite-element analysis of viscoelastic materials
Smith, P.D.; Pelessone, D.
1983-05-01
A method of formulating material models for viscoelastic analysis using the finite-element method is presented. The method, named consistent linearization, includes the influence of creep in the material stiffness in a theoretically ideal manner. This method has been applied to the linear viscoelastic analysis of graphite subject to irradiation. Previously, using the initial strain method, short time steps had been required to avoid a numerical instability associated with the rapid transient creep. Using the consistent linearization method a factor of 15 reduction in computer time was achieved for the same accuracy.
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. PMID:23804949
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.
Use of adjoint methods in the probabilistic finite element approach to fracture mechanics
NASA Technical Reports Server (NTRS)
Liu, Wing Kam; Besterfield, Glen; Lawrence, Mark; Belytschko, Ted
1988-01-01
The adjoint method approach to probabilistic finite element methods (PFEM) is presented. When the number of objective functions is small compared to the number of random variables, the adjoint method is far superior to the direct method in evaluating the objective function derivatives with respect to the random variables. The PFEM is extended to probabilistic fracture mechanics (PFM) using an element which has the near crack-tip singular strain field embedded. Since only two objective functions (i.e., mode I and II stress intensity factors) are needed for PFM, the adjoint method is well suited.
A comparison of the finite difference and finite element methods for heat transfer calculations
NASA Technical Reports Server (NTRS)
Emery, A. F.; Mortazavi, H. R.
1982-01-01
The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined.
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 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.
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.
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 Astrophysics Data System (ADS)
Zirari, M.; Abdellah El-Hadj, A.; Bacha, N.
2010-03-01
A finite element method is used to simulate the deposition of the thermal spray coating process. A set of governing equations is solving by a volume of fluid method. For the solidification phenomenon, we use the specific heat method (SHM). We begin by comparing the present model with experimental and numerical model available in the literature. In this study, completely molten or semi-molten aluminum particle impacts a H13 tool steel substrate is considered. Next we investigate the effect of inclination of impact of a partially molten particle on flat substrate. It was found that the melting state of the particle has great effects on the morphologies of the splat.
A Lagrange-Galerkin hp-Finite Element Method for a 3D Nonhydrostatic Ocean Model
NASA Astrophysics Data System (ADS)
Galán del Sastre, Pedro; Bermejo, Rodolfo
2016-03-01
We introduce in this paper a Lagrange-Galerkin hp-finite element method to calculate the numerical solution of a nonhydrostatic ocean model. The Lagrange-Galerkin method yields a Stokes-like problem the solution of which is computed by a second-order rotational splitting scheme that separates the calculation of the velocity and pressure, the latter is decomposed into hydrostatic and nonhydrostatic components. We have tested the method in flows where the nonhydrostatic effects are important. The results are very encouraging.
Petrov-Galerkin's method hybrid with finite element into the Helmholtz equation solution. Part II
NASA Astrophysics Data System (ADS)
Rabadan Malda, Itzala; Salazar Cordero, Emigdio; Ortega Herrera, Jose Angel
2002-11-01
This work proposes a hybridization between Petrov-Galerkins numeric method and finite element method (FEM) to resolve Helmholtz equation when dominion is an open or semiopen tube-shaped configuration and with determinate number of holes over cylindrical surface. It's pretended to solve these kind of cavities, thereby it allows us to obtain very important design parameters like: cavity length, quantity, size and distance between toneholes, form and size of mouthpiece or outlet. These parameters are design basis into acoustic and musical instrumentation: baffles outlet pipes, diffusers, silencers, flutes, oboes, saxophones, trumpets, quenas, and many more. In this way it's expected to determine advantages of this numeric method above another using actually.
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.
NASA Astrophysics Data System (ADS)
Li, L.; Wang, K.; Li, H.; Eibert, T. F.
2014-11-01
A hybrid higher-order finite element boundary integral (FE-BI) technique is discussed where the higher-order FE matrix elements are computed by a fully analytical procedure and where the gobal matrix assembly is organized by a self-identifying procedure of the local to global transformation. This assembly procedure applys to both, the FE part as well as the BI part of the algorithm. The geometry is meshed into three-dimensional tetrahedra as finite elements and nearly orthogonal hierarchical basis functions are employed. The boundary conditions are implemented in a strong sense such that the boundary values of the volume basis functions are directly utilized within the BI, either for the tangential electric and magnetic fields or for the asssociated equivalent surface current densities by applying a cross product with the unit surface normals. The self-identified method for the global matrix assembly automatically discerns the global order of the basis functions for generating the matrix elements. Higher order basis functions do need more unknowns for each single FE, however, fewer FEs are needed to achieve the same satisfiable accuracy. This improvement provides a lot more flexibility for meshing and allows the mesh size to raise up to λ/3. The performance of the implemented system is evaluated in terms of computation time, accuracy and memory occupation, where excellent results with respect to precision and computation times of large scale simulations are found.
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.
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.
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.
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.
Homogenization of Periodic Masonry Using Self-Consistent Scheme and Finite Element Method
NASA Astrophysics Data System (ADS)
Kumar, Nitin; Lambadi, Harish; Pandey, Manoj; Rajagopal, Amirtham
2016-01-01
Masonry is a heterogeneous anisotropic continuum, made up of the brick and mortar arranged in a periodic manner. Obtaining the effective elastic stiffness of the masonry structures has been a challenging task. In this study, the homogenization theory for periodic media is implemented in a very generic manner to derive the anisotropic global behavior of the masonry, through rigorous application of the homogenization theory in one step and through a full three-dimensional behavior. We have considered the periodic Eshelby self-consistent method and the finite element method. Two representative unit cells that represent the microstructure of the masonry wall exactly are considered for calibration and numerical application of the theory.
NASA Astrophysics Data System (ADS)
Kraczek, B.
2005-03-01
We present a means for coupling dynamic atomistic and continuum simulations via a spacetime discontinuous Galerkin (SDG) finite element method. Our scheme allows the SDG method to couple a general MD simulation using Verlet time-stepping through the flux conditions on the element boundaries at the interface. These flux conditions ensure weak balance of momentum and energy to achieve reflection-free transfer of disturbance across the interface. Our work is supported by the National Science Foundation (ITR grant DMR-0121695) on Process Simulation and Design and, in part, by the Materials Computation Center (FRG grant DMR-99-76550)
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. PMID:22587208
Finite-size scaling for quantum criticality using the finite-element method
NASA Astrophysics Data System (ADS)
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.
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
A multiscale modeling technique for bridging molecular dynamics with finite element method
Lee, Yongchang Basaran, Cemal
2013-11-15
In computational mechanics, molecular dynamics (MD) and finite element (FE) analysis are well developed and most popular on nanoscale and macroscale analysis, respectively. MD can very well simulate the atomistic behavior, but cannot simulate macroscale length and time due to computational limits. FE can very well simulate continuum mechanics (CM) problems, but has the limitation of the lack of atomistic level degrees of freedom. Multiscale modeling is an expedient methodology with a potential to connect different levels of modeling such as quantum mechanics, molecular dynamics, and continuum mechanics. This study proposes a new multiscale modeling technique to couple MD with FE. The proposed method relies on weighted average momentum principle. A wave propagation example has been used to illustrate the challenges in coupling MD with FE and to verify the proposed technique. Furthermore, 2-Dimensional problem has also been used to demonstrate how this method would translate into real world applications. -- Highlights: •A weighted averaging momentum method is introduced for bridging molecular dynamics (MD) with finite element (FE) method. •The proposed method shows excellent coupling results in 1-D and 2-D examples. •The proposed method successfully reduces the spurious wave reflection at the border of MD and FE regions. •Big advantages of the proposed method are simplicity and inexpensive computational cost of multiscale analysis.
Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2005-10-01
A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility. PMID:16383571
A method of coupling discrete dislocation plasticity to the crystal plasticity finite element method
NASA Astrophysics Data System (ADS)
Xu, Y.; Balint, D. S.; Dini, D.
2016-05-01
A method of concurrent coupling of planar discrete dislocation plasticity (DDP) and a crystal plasticity finite element (CPFE) method was devised for simulating plastic deformation in large polycrystals with discrete dislocation resolution in a single grain or cluster of grains for computational efficiency; computation time using the coupling method can be reduced by an order of magnitude compared to DDP. The method is based on an iterative scheme initiated by a sub-model calculation, which ensures displacement and traction compatibility at all nodes at the interface between the DDP and CPFE domains. The proposed coupling approach is demonstrated using two plane strain problems: (i) uniaxial tension of a bi-crystal film and (ii) indentation of a thin film on a substrate. The latter was also used to demonstrate that the rigid substrate assumption used in earlier DDP studies is inadequate for indentation depths that are large compared to the film thickness, i.e. the effect of the plastic substrate modelled using CPFE becomes important. The coupling method can be used to study a wider range of indentation depths than previously possible using DDP alone, without sacrificing the indentation size effect regime captured by DDP. The method is general and can be applied to any problem where finer resolution of dislocation mediated plasticity is required to study the mechanical response of polycrystalline materials, e.g. to capture size effects locally within a larger elastic/plastic boundary value problem.
Dynamic Analysis of 2D Electromagnetic Resonant Optical Scanner Using 3D Finite Element Method
NASA Astrophysics Data System (ADS)
Hirata, Katsuhiro; Hong, Sara; Maeda, Kengo
The optical scanner is a scanning device in which a laser beam is reflected by a mirror that can be rotated or oscillated. In this paper, we propose a new 2D electromagnetic resonant optical scanner that employs electromagnets and leaf springs. Torque characteristics and resonance characteristics of the scanner are analyzed using the 3D finite element method. The validity of the analysis is shown by comparing the characteristics inferred from the analysis with the characteristics of the prototype. Further, 2D resonance is investigated by introducing a superimposed-frequency current in a single coil.
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.
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.
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.
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.
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
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.
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.
NASA Astrophysics Data System (ADS)
Abbas, Ibrahim A.; Youssef, Hamdy M.
2012-07-01
In this article, a general finite element method (FEM) is proposed to analyze transient phenomena in a thermoelastic model in the context of the theory of generalized thermoelasticity with one relaxation time. The exact solution of the nonlinear model of the thermal shock problem of a generalized thermoelastic half-space of temperature-dependent materials exists only for very special and simple initial- and boundary problems. In view of calculating general problems, a numerical solution technique is to be used. For this reason, the FEM is chosen. The results for the temperature increment, the stress components, and the displacement component are illustrated graphically with some comparisons.
Sensitivity Analysis of Linear Elastic Cracked Structures Using Generalized Finite Element Method
NASA Astrophysics Data System (ADS)
Pal, Mahendra Kumar; Rajagopal, Amirtham
2014-09-01
In this work, a sensitivity analysis of linear elastic cracked structures using two-scale Generalized Finite Element Method (GFEM) is presented. The method is based on computation of material derivatives, mutual potential energies, and direct differentiation. In a computational setting, the discrete form of the mutual potential energy release rate is simple and easy to calculate, as it only requires the multiplication of the displacement vectors and stiffness sensitivity matrices. By judiciously choosing the velocity field, the method only requires displacement response in a sub-domain close to the crack tip, thus making the method computationally efficient. The method thus requires an exact computation of displacement response in a sub-domain close to the crack tip. To this end, in this study we have used a two-scale GFEM for sensitivity analysis. GFEM is based on the enrichment of the classical finite element approximation. These enrichment functions incorporate the discontinuity response in the domain. Three numerical examples which comprise mode-I and mixed mode deformations are presented to evaluate the accuracy of the fracture parameters calculated by the proposed method.
Comparison of Two Methods of Finite Element Modeling for Elbows with Unequal Wall Thickness
NASA Astrophysics Data System (ADS)
Dong, Junhua; Bao, Xiangfu; Zheng, Xize
In Finite Element Stress Analysis of elbow, its unequal wall thickness can be obtained by two methods: eccentric circle method and multi-spot spline curve drawed according to wall thickness of elbow. In this work, an elbow with constant inner diameter was taken as an illustration and its simulation results based on these two modeling methods were compared under different ratios of central line bend radius to mean diameter of pipe R/D. It is found that modeling method has no effect on the stress analysis results of elbows. But eccentric circle method has the virtue of being easier to implement and can be used without restriction of R/D, so it is an ideal method of finite element modeling for unequal wall thickness elbows. Because the FEA results of equal thickness elbows are recognizably higher than those of elbows with unequal wall thickness, considering non-uniform thickness of elbows is necessary to set up a reasonable safety evaluation for elbows.
NASA Astrophysics Data System (ADS)
Sotokoba, Yasumasa; Okajima, Kenji; Iida, Toshiaki; Tanaka, Tadatsugu
We propose the trenchless box culvert construction method to construct box culverts in small covering soil layers while keeping roads or tracks open. When we use this construction method, it is necessary to clarify deformation and shear failure by excavation of grounds. In order to investigate the soil behavior, model experiments and elasto-plactic finite element analysis were performed. In the model experiments, it was shown that the shear failure was developed from the end of the roof to the toe of the boundary surface. In the finite element analysis, a shear band effect was introduced. Comparing the observed shear bands in model experiments with computed maximum shear strain contours, it was found that the observed direction of the shear band could be simulated reasonably by the finite element analysis. We may say that the finite element method used in this study is useful tool for this construction method.
Robust and scalable 3-D geo-electromagnetic modelling approach using the finite element method
NASA Astrophysics Data System (ADS)
Grayver, Alexander V.; Bürg, Markus
2014-07-01
We present a robust and scalable solver for time-harmonic Maxwell's equations for problems with large conductivity contrasts, wide range of frequencies, stretched grids and locally refined meshes. The solver is part of the fully distributed adaptive 3-D electromagnetic modelling scheme which employs the finite element method and unstructured non-conforming hexahedral meshes for spatial discretization using the open-source software deal.II. We use the complex-valued electric field formulation and split it into two real-valued equations for which we utilize an optimal block-diagonal pre-conditioner. Application of this pre-conditioner requires the solution of two smaller real-valued symmetric problems. We solve them by using either a direct solver or the conjugate gradient method pre-conditioned with the recently introduced auxiliary space technique. The auxiliary space pre-conditioner reformulates the original problem in form of several simpler ones, which are then solved using highly efficient algebraic multigrid methods. In this paper, we consider the magnetotelluric case and verify our numerical scheme by using COMMEMI 3-D models. Afterwards, we run a series of numerical experiments and demonstrate that the solver converges in a small number of iterations for a wide frequency range and variable problem sizes. The number of iterations is independent of the problem size, but exhibits a mild dependency on frequency. To test the stability of the method on locally refined meshes, we have implemented a residual-based a posteriori error estimator and compared it with uniform mesh refinement for problems up to 200 million unknowns. We test the scalability of the most time consuming parts of our code and show that they fulfill the strong scaling assumption as long as each MPI process possesses enough degrees of freedom to alleviate communication overburden. Finally, we refer back to a direct solver-based pre-conditioner and analyse its complexity in time. The results show
Space-time discontinuous Galerkin finite element method for two-fluid flows
NASA Astrophysics Data System (ADS)
Sollie, W. E. H.; Bokhove, O.; van der Vegt, J. J. W.
2011-02-01
A novel numerical method for two-fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local hp-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative. The numerical method is applied to one and two dimensional two-fluid test problems using the Euler equations.
A cut finite element method for coupled bulk-surface problems on time-dependent domains
NASA Astrophysics Data System (ADS)
Hansbo, Peter; Larson, Mats G.; Zahedi, Sara
2016-08-01
In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous piecewise linear elements in space on a fixed background mesh. The domain is represented using a piecewise linear level set function on the background mesh and a cut finite element method is used to discretize the bulk and surface problems. In the cut finite element method the bilinear forms associated with the weak formulation of the problem are directly evaluated on the bulk domain and the surface defined by the level set, essentially using the restrictions of the piecewise linear functions to the computational domain. In addition a stabilization term is added to stabilize convection as well as the resulting algebraic system that is solved in each time step. We show in numerical examples that the resulting method is accurate and stable and results in well conditioned algebraic systems independent of the position of the interface relative to the background mesh.
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.
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.
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.
Nonlinear bend stiffener analysis using a simple formulation and finite element method
NASA Astrophysics Data System (ADS)
Tong, Dong Jin; Low, Ying Min; Sheehan, John M.
2011-12-01
Flexible marine risers are commonly used in deepwater floating systems. Bend stiffeners are designed to protect flexible risers against excessive bending at the connection with the hull. The structure is usually analyzed as a cantilever beam subjected to an inclined point load. As deflections are large and the bend stiffener material exhibits nonlinear stress-strain characteristics, geometric and material nonlinearities are important considerations. A new approach has been developed to solve this nonlinear problem. Its main advantage is its simplicity; in fact the present method can be easily implemented on a spreadsheet. Finite element analysis using ABAQUS is performed to validate the method. Solid elements are used for the bend stiffener and flexible pipe. To simulate the near inextensibility of flexible risers, a simple and original idea of using truss elements is proposed. Through a set of validation studies, the present method is found to be in a good agreement with the finite element analysis. Further, parametric studies are performed by using both methods to identify the key parameters and phenomena that are most critical in design. The most important finding is that the common practice of neglecting the internal steel sleeve in the bend stiffener analysis is non-conservative and therefore needs to be reassessed.
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.
2D-3D hybrid stabilized finite element method for tsunami runup simulations
NASA Astrophysics Data System (ADS)
Takase, S.; Moriguchi, S.; Terada, K.; Kato, J.; Kyoya, T.; Kashiyama, K.; Kotani, T.
2016-09-01
This paper presents a two-dimensional (2D)-three-dimensional (3D) hybrid stabilized finite element method that enables us to predict a propagation process of tsunami generated in a hypocentral region, which ranges from offshore propagation to runup to urban areas, with high accuracy and relatively low computational costs. To be more specific, the 2D shallow water equation is employed to simulate the propagation of offshore waves, while the 3D Navier-Stokes equation is employed for the runup in urban areas. The stabilized finite element method is utilized for numerical simulations for both of the 2D and 3D domains that are independently discretized with unstructured meshes. The multi-point constraint and transmission methods are applied to satisfy the continuity of flow velocities and pressures at the interface between the resulting 2D and 3D meshes, since neither their spatial dimensions nor node arrangements are consistent. Numerical examples are presented to demonstrate the performance of the proposed hybrid method to simulate tsunami behavior, including offshore propagation and runup to urban areas, with substantially lower computation costs in comparison with full 3D computations.
2D-3D hybrid stabilized finite element method for tsunami runup simulations
NASA Astrophysics Data System (ADS)
Takase, S.; Moriguchi, S.; Terada, K.; Kato, J.; Kyoya, T.; Kashiyama, K.; Kotani, T.
2016-05-01
This paper presents a two-dimensional (2D)-three-dimensional (3D) hybrid stabilized finite element method that enables us to predict a propagation process of tsunami generated in a hypocentral region, which ranges from offshore propagation to runup to urban areas, with high accuracy and relatively low computational costs. To be more specific, the 2D shallow water equation is employed to simulate the propagation of offshore waves, while the 3D Navier-Stokes equation is employed for the runup in urban areas. The stabilized finite element method is utilized for numerical simulations for both of the 2D and 3D domains that are independently discretized with unstructured meshes. The multi-point constraint and transmission methods are applied to satisfy the continuity of flow velocities and pressures at the interface between the resulting 2D and 3D meshes, since neither their spatial dimensions nor node arrangements are consistent. Numerical examples are presented to demonstrate the performance of the proposed hybrid method to simulate tsunami behavior, including offshore propagation and runup to urban areas, with substantially lower computation costs in comparison with full 3D computations.
Free-Vibration Analysis of Rotating Beams by a Variable-Order Finite-Element Method
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Rutkowski, Michael J.
1981-01-01
The free vibration of rotating beams is analyzed by means of a finite-element method of variable order. This method entails displacement functions that are a complete power series of a variable number of terms. The terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and, additionally, displacements at certain points within the element. The displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series. Numerical results are presented for uniform beams with zero and nonzero hub radii, tapered beams, and a nonuniform beam with discontinuities. Since the present method reduces to a conventional beam finite-element method for a cubic displacement function, the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom. Indeed, essentially exact eigenvalues and eigenvectors are obtained with this technique, which is far more rapidly convergent than other approaches in the literature.
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
Efficient evaluation of the Coulomb force in the Gaussian and finite-element Coulomb method
NASA Astrophysics Data System (ADS)
Kurashige, Yuki; Nakajima, Takahito; Sato, Takeshi; Hirao, Kimihiko
2010-06-01
We propose an efficient method for evaluating the Coulomb force in the Gaussian and finite-element Coulomb (GFC) method, which is a linear-scaling approach for evaluating the Coulomb matrix and energy in large molecular systems. The efficient evaluation of the analytical gradient in the GFC is not straightforward as well as the evaluation of the energy because the SCF procedure with the Coulomb matrix does not give a variational solution for the Coulomb energy. Thus, an efficient approximate method is alternatively proposed, in which the Coulomb potential is expanded in the Gaussian and finite-element auxiliary functions as done in the GFC. To minimize the error in the gradient not just in the energy, the derived functions of the original auxiliary functions of the GFC are used additionally for the evaluation of the Coulomb gradient. In fact, the use of the derived functions significantly improves the accuracy of this approach. Although these additional auxiliary functions enlarge the size of the discretized Poisson equation and thereby increase the computational cost, it maintains the near linear scaling as the GFC and does not affects the overall efficiency of the GFC approach.
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.
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.
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.
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.
Sever, Martin; Krč, Janez; Čampa, Andrej; Topič, Marko
2015-11-30
Finite element method is coupled with Huygens' expansion to determine light intensity distribution of scattered light in solar cells and other optoelectronic devices. The rigorous foundation of the modelling enables calculation of the light intensity distribution at a chosen distance and surface of observation in chosen material in reflection or in transmission for given wavelength of the incident light. The calculation of scattering or anti-reflection properties is not limited to a single textured interface, but can be done above more complex structures with several scattering interfaces or even with particles involved. Both scattering at periodic and at random textures can be efficiently handled with the modelling approach. A procedure for minimisation of the effect of small-area sample, which is considered in the finite element method calculation, is proposed and implemented into the modelling. Angular distribution function, total transmission and total reflection of the scattering interface or structure can be determined using the model. Furthermore, a method for calculation of the haze parameter of reflected or transmitted light is proposed. The modelling approach is applied to periodic and random nano-textured samples for photovoltaic applications, showing good agreement with measured data. PMID:26698803
NASA Astrophysics Data System (ADS)
Zhu, Yu; Cangellaris, Andreas C.
2002-05-01
A new finite element methodology is presented for fast and robust numerical simulation of three-dimensional electromagnetic wave phenomena. The new methodology combines nested multigrid techniques with the ungauged vector and scalar potential formulation of the finite element method. The finite element modeling is performed on nested meshes over the computational domain of interest. The iterative solution of the finite element matrix on the finest mesh is performed using the conjugate gradient method, while the nested multigrid vector and scalar potential algorithm acts as the preconditioner for the iterative solver. Numerical experiments from the application of the new methodology to three-dimensional electromagnetic scattering are used to demonstrate its superior numerical convergence and efficient memory usage.
Massively parallel multifrontal methods for finite element analysis on MIMD computer systems
Benner, R.E.
1993-03-01
The development of highly parallel direct solvers for large, sparse linear systems of equations (e.g. for finite element or finite difference models) is lagging behind progress in parallel direct solvers for dense matrices and iterative methods for sparse matrices. We describe a massively parallel (MP) multifrontal solver for the direct solution of large sparse linear systems, such as those routinely encountered in finite element structural analysis, in an effort to address concerns about the viability of scalable, MP direct methods for sparse systems and enhance the software base for MP applications. Performance results are presented and future directions are outlined for research and development efforts in parallel multifrontal and related solvers. In particular, parallel efficiencies of 25% on 1024 nCUBE 2 nodes and 36% on 64 Intel iPSCS60 nodes have been demonstrated, and parallel efficiencies of 60--85% are expected when a severe load imbalance is overcome by static mapping and dynamic load balance techniques previously developed for other parallel solvers and application codes.
Stability analysis of flexible wind-turbine blades using finite-element method
Kamoulakos, A.
1982-08-01
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 a 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.
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.
Vibro-acoustic modelling of the outer and middle ear using the finite-element method.
Prendergast, P J; Ferris, P; Rice, H J; Blayney, A W
1999-01-01
In this study, a computer-based method called finite-element analysis is used to predict the forced-frequency response of the ear, with and without an ossicular replacement prosthesis (PORP 0362, Xomed Surgical Products). The method allows visualisation of the dynamical behaviour of the tympanic membrane (TM) and of the ossicles. The finite-element model is fully three-dimensional and includes both ligaments and muscles, and accounts for damping caused by the TM, ligaments, incudostapedial joint and the fluids of the inner ear. For validation, comparison is made with experimental measurements of umbo displacement taken from the literature. The translation and rotation (both anterior-posterior and inferior-superior) of the stapedial footplate are investigated. It is predicted that the translatory motion of the footplate decreases with increasing frequency, except when the frequency of the acoustic signal matches the natural frequencies of the ossicular chain or outer ear canal. The tilting motion of the stapedial footplate is also predicted to depend on frequency of excitation. The presence of a prosthesis changes the dynamical response considerably by shifting the natural frequencies of the ossicular chain. Ratios of stapes motion with and without the prostheses are plotted as a function of frequency allowing this effect to be clearly observed. PMID:10187928
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.
NASA Technical Reports Server (NTRS)
Nakazawa, Shohei
1989-01-01
The internal structure is discussed of the MHOST finite element program designed for 3-D inelastic analysis of gas turbine hot section components. The computer code is the first implementation of the mixed iterative solution strategy for improved efficiency and accuracy over the conventional finite element method. The control structure of the program is covered along with the data storage scheme and the memory allocation procedure and the file handling facilities including the read and/or write sequences.
NASA Astrophysics Data System (ADS)
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
Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation
Chen, Zhangxin; Cockburn, Bernardo; Jerome, Joseph W.; Shu, Chi-Wang
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
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.
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.
Finite element method for conserved phase fields: Stress-mediated diffusional phase transformation
NASA Astrophysics Data System (ADS)
Zaeem, Mohsen Asle; Mesarovic, Sinisa Dj.
2010-12-01
Phase-field models with conserved phase-field variables result in a 4th order evolution partial differential equation (PDE). When coupled with the usual 2nd order thermo-mechanics equations, such problems require special treatment. In the past, the finite element method (FEM) has been successfully applied to non-conserved phase fields, governed by a 2nd order PDE. For higher order equations, the convergence of the standard Galerkin FEM requires that the interpolation functions belong to a higher continuity class. We consider the Cahn-Hilliard phase-field model for diffusion-controlled solid state phase transformation in binary alloys, coupled with elasticity of the solid phases. A Galerkin finite element formulation is developed, with mixed-order interpolation: C 0 interpolation functions for displacements, and C 1 interpolation functions for the phase-field variable. To demonstrate convergence of the mixed interpolation scheme, we first study a one-dimensional problem - nucleation and growth of the intermediate phase in a thin-film diffusion couple with elasticity effects. Then, we study the effects of completeness of C 1 interpolation on parabolic problems in two space dimensions by considering the growth of the intermediate phase in a binary system. Quadratic convergence, expected for conforming elements, is achieved for both one- and two-dimensional systems.
A-priori analysis and the finite element method for a class of degenerate elliptic equations
NASA Astrophysics Data System (ADS)
Li, Hengguang
2009-06-01
Consider the degenerate elliptic operator mathcal{L_delta} := -partial^2_x-frac{delta^2}{x^2}partial^2_y on Omega:= (0, 1)times(0, l) , for delta>0, l>0 . We prove well-posedness and regularity results for the degenerate elliptic equation mathcal{L_delta} u=f in Omega , u\\vert _{partialOmega}=0 using weighted Sobolev spaces mathcal{K}^m_a . In particular, by a proper choice of the parameters in the weighted Sobolev spaces mathcal{K}^m_a , we establish the existence and uniqueness of the solution. In addition, we show that there is no loss of mathcal{K}^m_a -regularity for the solution of the equation. We then provide an explicit construction of a sequence of finite dimensional subspaces V_n for the finite element method, such that the optimal convergence rate is attained for the finite element solution u_nin V_n , i.e., \\vert\\vert u-u_n\\vert\\vert _{H^1(Omega)}leq C{dim}(V_n)^{-frac{m}{2}}\\vert\\vert f\\vert\\vert _{H^{m-1}(Omega)} with C independent of f and n .
NASA Astrophysics Data System (ADS)
Li, Jiaqian; Shen, Haijun
2015-12-01
The longitudinal vibration band gaps in periodic (n, 0)-(2n, 0) single-walled carbon nanotube(SWCNT) intramolecular junctions(IMJs) are investigated based on the finite element calculation. The frequency ranges of band gaps in frequency response functions(FRF) simulated by finite element method (FEM) show good agreement with those in band structure obtained by simple spring-mass model. Moreover, a comprehensive parametric study is also conducted to highlight the influences of the geometrical parameters such as the size of unit cell, component ratios of the IMJs and diameters of the CNT segments as well as geometric imperfections on the first band gap. The results show that the frequency ranges and the bandwidth of the gap strongly depend on the geometrical parameters. Furthermore, the influences of geometrical parameters on gaps are nuanced in IMJs with different topological defects. The existence of vibration band gaps in periodic IMJs lends a new insight into the development of CNT-based nano-devices in application of vibration isolation.
Modelling the core convection using finite element and finite difference methods
NASA Astrophysics Data System (ADS)
Chan, K. H.; Li, Ligang; Liao, Xinhao
2006-08-01
Applications of both parallel finite element and finite difference methods to thermal convection in a rotating spherical shell modelling the fluid dynamics of the Earth's outer core are presented. The numerical schemes are verified by reproducing the convection benchmark test by Christensen et al. [Christensen, U.R., Aubert, J., Cardin, P., Dormy, E., Gibbons, S., Glatzmaier, G.A., Grote, E., Honkura, Y., Jones, C., Kono, M., Matsushima, M., Sakuraba, A., Takahashi, F., Tilgner, A., Wilcht, J., Zhang, K., 2001. A numerical dynamo benchmark. Phys. Earth Planet. Interiors 128, 25-34.]. Both global average and local characteristics agree satisfactorily with the benchmark solution. With the element-by-element (EBE) parallelization technique, the finite element code demonstrates nearly optimal linear scalability in computational speed. The finite difference code is also efficient and scalable by utilizing a parallel library Aztec [Tuminaro, R.S., Heroux, M., Hutchinson, S.A., Shadid, J.N., 1999. Official AZTEC User's Guide: Version 2.1.].
Stress analysis of ceramic, polymeric, and metallic composite systems by the finite-element method
Min, B.J.
1987-01-01
In this thesis, with the help of the finite-element method based on the concept of the elasto-viscoplastic approach, the residual stresses in ceramic/metal composite systems resulting from differences between the thermophysical and mechanical properties of the ceramic and metal components were analyzed. This study focuses on the inclusion of the variation of elastic properties of both metal and ceramics with temperature. From results, variation of material properties with temperature is found to produce higher tensile residual stresses in the ceramic as well as in the alloy. Also, it was observed that inclusion of variation of the coefficient of thermal expansion (..cap alpha..) is more important for residual-stress calculations than the effect of the variation of the modulus of elasticity (E) with temperature. A finite-element study was done for Cement Bonded Porcelain-Fused-to-Metal (PFM) restorative systems. From this study, it is found that the value of the stresses can be reduced significantly if the cement layer is considered.
Dynamic Analysis of Flexible Slider-Crank Mechanisms with Non-Linear Finite Element Method
NASA Astrophysics Data System (ADS)
CHEN, J.-S.; HUANG, C.-L.
2001-09-01
Previous research in finite element formulation of flexible mechanisms usually neglected high order terms in the strain-energy function. In particular, the quartic term of the displacement gradient is always neglected due to the common belief that it is not important in the dynamic analysis. In this paper, we show that this physical intuition is not always valid. By retaining all the high order terms in the strain-energy function the equations of motion naturally become non-linear, which can then be solved by the Newmark method. In the low-speed range it is found that the dynamic responses predicted by non-linear and linear approaches indeed make no significant difference. However, when the rotation speed increases up to about one-fifth of the fundamental bending natural frequency of the connecting rod, simplified approaches begin to incur noticeable error. Specifically, for a connecting rod with a slenderness ratio of 0·01 the conventional simplified approaches overestimate the vibration amplitude almost 10-fold when the rotation speed is comparable to the fundamental natural frequency of the connecting rod. Therefore, non-linear finite element formulation taking into account the complete non-linear strain is needed in analyzing high-speed flexible mechnisms with slender links.
Safety assessment of a shallow foundation using the random finite element method
NASA Astrophysics Data System (ADS)
Zaskórski, Łukasz; Puła, Wojciech
2015-04-01
A complex structure of soil and its random character are reasons why soil modeling is a cumbersome task. Heterogeneity of soil has to be considered even within a homogenous layer of soil. Therefore an estimation of shear strength parameters of soil for the purposes of a geotechnical analysis causes many problems. In applicable standards (Eurocode 7) there is not presented any explicit method of an evaluation of characteristic values of soil parameters. Only general guidelines can be found how these values should be estimated. Hence many approaches of an assessment of characteristic values of soil parameters are presented in literature and can be applied in practice. In this paper, the reliability assessment of a shallow strip footing was conducted using a reliability index β. Therefore some approaches of an estimation of characteristic values of soil properties were compared by evaluating values of reliability index β which can be achieved by applying each of them. Method of Orr and Breysse, Duncan's method, Schneider's method, Schneider's method concerning influence of fluctuation scales and method included in Eurocode 7 were examined. Design values of the bearing capacity based on these approaches were referred to the stochastic bearing capacity estimated by the random finite element method (RFEM). Design values of the bearing capacity were conducted for various widths and depths of a foundation in conjunction with design approaches DA defined in Eurocode. RFEM was presented by Griffiths and Fenton (1993). It combines deterministic finite element method, random field theory and Monte Carlo simulations. Random field theory allows to consider a random character of soil parameters within a homogenous layer of soil. For this purpose a soil property is considered as a separate random variable in every element of a mesh in the finite element method with proper correlation structure between points of given area. RFEM was applied to estimate which theoretical
Crane, N K; Parsons, I D; Hjelmstad, K D
2002-03-21
Adaptive mesh refinement selectively subdivides the elements of a coarse user supplied mesh to produce a fine mesh with reduced discretization error. Effective use of adaptive mesh refinement coupled with an a posteriori error estimator can produce a mesh that solves a problem to a given discretization error using far fewer elements than uniform refinement. A geometric multigrid solver uses increasingly finer discretizations of the same geometry to produce a very fast and numerically scalable solution to a set of linear equations. Adaptive mesh refinement is a natural method for creating the different meshes required by the multigrid solver. This paper describes the implementation of a scalable adaptive multigrid method on a distributed memory parallel computer. Results are presented that demonstrate the parallel performance of the methodology by solving a linear elastic rocket fuel deformation problem on an SGI Origin 3000. Two challenges must be met when implementing adaptive multigrid algorithms on massively parallel computing platforms. First, although the fine mesh for which the solution is desired may be large and scaled to the number of processors, the multigrid algorithm must also operate on much smaller fixed-size data sets on the coarse levels. Second, the mesh must be repartitioned as it is adapted to maintain good load balancing. In an adaptive multigrid algorithm, separate mesh levels may require separate partitioning, further complicating the load balance problem. This paper shows that, when the proper optimizations are made, parallel adaptive multigrid algorithms perform well on machines with several hundreds of processors.
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.
NASA Astrophysics Data System (ADS)
Lavery, N.; Taylor, C.
1999-07-01
Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright
A finite element method for the statistics of non-linear random vibration
NASA Astrophysics Data System (ADS)
Langley, R. S.
1985-07-01
The transitional probability density function for the random response of a certain class of non-linear system satisfies the Fokker-Planck-Kolmogorov equation. This paper concerns the numerical solution of the stationary form of this equation, yielding the stationary probability density function of response. The weighted residual statement for the problem is integrated by parts to yield the weak form of the equations, which are then solved by the finite element method. The method is applied to a Duffing oscillator and good agreement is found with the exact result, and the method is compared favourably with a Galerkin solution method given by Bhandari and Sherrer [1]. Also, the method is applied to the ship rolling problem and good agreement is found with an approximate analytical result due to Roberts [2].
Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity
Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu
2014-10-11
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.
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. PMID:19773193
NASA Astrophysics Data System (ADS)
Bailey, Teresa S.
In this dissertation we discuss the development, implementation, analysis and testing of the Piecewise Linear Discontinuous Finite Element Method (PWLD) applied to the particle transport equation in two-dimensional cylindrical (RZ) and three-dimensional Cartesian (XYZ) geometries. We have designed this method to be applicable to radiative-transfer problems in radiation-hydrodynamics systems for arbitrary polygonal and polyhedral meshes. For RZ geometry, we have implemented this method in the Capsaicin radiative-transfer code being developed at Los Alamos National Laboratory. In XYZ geometry, we have implemented the method in the Parallel Deterministic Transport code being developed at Texas A&M University. We discuss the importance of the thick diffusion limit for radiative-transfer problems, and perform a thick diffusion-limit analysis on our discretized system for both geometries. This analysis predicts that the PWLD method will perform well in this limit for many problems of physical interest with arbitrary polygonal and polyhedral cells. Finally, we run a series of test problems to determine some useful properties of the method and verify the results of our thick diffusion limit analysis. Finally, we test our method on a variety of test problems and show that it compares favorably to existing methods. With these test problems, we also show that our method performs well in the thick diffusion limit as predicted by our analysis. Based on PWLD's solid finite-element foundation, the desirable properties it shows under analysis, and the excellent performance it demonstrates on test problems even with highly distorted spatial grids, we conclude that it is an excellent candidate for radiative-transfer problems that need a robust method that performs well in thick diffusive problems or on distorted grids.
Linear-scaling multipole-accelerated Gaussian and finite-element Coulomb method
NASA Astrophysics Data System (ADS)
Watson, Mark A.; Kurashige, Yuki; Nakajima, Takahito; Hirao, Kimihiko
2008-02-01
A linear-scaling implementation of the Gaussian and finite-element Coulomb (GFC) method is presented for the rapid computation of the electronic Coulomb potential. The current work utilizes the fast multipole method (FMM) for the evaluation of the Poisson equation boundary condition. The FMM affords significant savings for small- and medium-sized systems and overcomes the bottleneck in the GFC method for very large systems. Compared to an exact analytical treatment of the boundary, more than 100-fold speedups are observed for systems with more than 1000 basis functions without any significant loss of accuracy. We present CPU times to demonstrate the effectiveness of the linear-scaling GFC method for both one-dimensional polyalanine chains and the challenging case of three-dimensional diamond fragments.
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.
NASA Astrophysics Data System (ADS)
Arbatani, Siamak; Callejo, Alfonso; Kövecses, József; Kalantari, Masoud; Marchand, Nick R.; Dargahi, Javad
2016-03-01
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.
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.
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.
Finite element modified method of characteristics for the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Allievi, Alejandro; Bermejo, Rodolfo
2000-02-01
An algorithm based on the finite element modified method of characteristics (FEMMC) is presented to solve convection-diffusion, Burgers and unsteady incompressible Navier-Stokes equations for laminar flow. Solutions for these progressively more involved problems are presented so as to give numerical evidence for the robustness, good error characteristics and accuracy of our method. To solve the Navier-Stokes equations, an approach that can be conceived as a fractional step method is used. The innovative first stage of our method is a backward search and interpolation at the foot of the characteristics, which we identify as the convective step. In this particular work, this step is followed by a conjugate gradient solution of the remaining Stokes problem. Numerical results are presented for:aConvection-diffusion equation. Gaussian hill in a uniform rotating field.bBurgers equations with viscosity.
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.
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
Prediction of metallic nano-optical trapping forces by finite element-boundary integral method.
Pan, Xiao-Min; Xu, Kai-Jiang; Yang, Ming-Lin; Sheng, Xin-Qing
2015-03-01
The hybrid of finite element and boundary integral (FE-BI) method is employed to predict nano-optical trapping forces of arbitrarily shaped metallic nanostructures. A preconditioning strategy is proposed to improve the convergence of the iterative solution. Skeletonization is employed to speed up the design and optimization where iteration has to be repeated for each beam configuration. The radiation pressure force (RPF) is computed by vector flux of the Maxwell's stress tensor. Numerical simulations are performed to validate the developed method in analyzing the plasmonic effects as well as the optical trapping forces. It is shown that the proposed method is capable of predicting the trapping forces of complex metallic nanostructures accurately and efficiently. PMID:25836836
Exact finite element method analysis of viscoelastic tapered structures to transient loads
NASA Technical Reports Server (NTRS)
Spyrakos, Constantine Chris
1987-01-01
A general method is presented for determining the dynamic torsional/axial response of linear structures composed of either tapered bars or shafts to transient excitations. The method consists of formulating and solving the dynamic problem in the Laplace transform domain by the finite element method and obtaining the response by a numerical inversion of the transformed solution. The derivation of the torsional and axial stiffness matrices is based on the exact solution of the transformed governing equation of motion, and it consequently leads to the exact solution of the problem. The solution permits treatment of the most practical cases of linear tapered bars and shafts, and employs modeling of structures with only one element per member which reduces the number of degrees of freedom involved. The effects of external viscous or internal viscoelastic damping are also taken into account.
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
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.
The dual variable method for finite element discretizations of Navier/Stokes equations
NASA Astrophysics Data System (ADS)
Hall, C. A.; Peterson, J. S.; Porsching, T. A.; Sledge, F. R.
1985-05-01
The dual-variable method of Amit et al. (1981) and Hall et al. (1980) is applied to the numerical solution of the transient Navier-Stokes equations for two-dimensional incompressible flows. The basic procedures of the method are reviewed, including determining the rank of the discrete divergence matrix, obtaining a particular solution of the discrete continuity equation, and defining the null space of the discrete divergence operator. Finite-element algorithms based on quadrilateral piecewise-bilateral-velocity/constant-pressure elements are developed and demonstrated for Poiseuille flow, a lid-driven cavity, and flow past a semicircular obstacle. The results are presented in tables and graphs and compared with those of a primitive-variable method, and the dual-variable approach is found to yield significant savings in dynamic memory and computation time.
Applying Padé via Lanczos to the finite element method for electromagnetic radiation problems
NASA Astrophysics Data System (ADS)
Slone, Rodney Daryl; Lee, Robert
2000-03-01
Recently there has been a great deal of interest in using the Padé via Lanczos (PVL) technique to analyze the transfer functions and impulse responses of large-scale linear circuits. In this paper, matrix-Padé via Lanczos (MPVL), which can be used on multiple-input multiple-output systems, is applied to solve models resulting from applying the finite element method (FEM) to electromagnetic wave propagation problems in the frequency domain. The resulting solution procedure of using MPVL to solve FEM equations allows for wideband frequency simulations with a reduction in total computation time. Several issues arise during this application, and each is addressed in detail. Numerical simulations using this method are shown along with traditional methods using an LU decomposition at each frequency point of interest. Comparisons in accuracy as well as computation time are also given.
Phenomenological model of diffuse global and regional atrophy using finite-element methods.
Camara, Oscar; Schweiger, Martin; Scahill, Rachael I; Crum, William R; Sneller, Beatrix I; Schnabel, Julia A; Ridgway, Gerard R; Cash, David M; Hill, Derek L G; Fox, Nick C
2006-11-01
The main goal of this work is the generation of ground-truth data for the validation of atrophy measurement techniques, commonly used in the study of neurodegenerative diseases such as dementia. Several techniques have been used to measure atrophy in cross-sectional and longitudinal studies, but it is extremely difficult to compare their performance since they have been applied to different patient populations. Furthermore, assessment of performance based on phantom measurements or simple scaled images overestimates these techniques' ability to capture the complexity of neurodegeneration of the human brain. We propose a method for atrophy simulation in structural magnetic resonance (MR) images based on finite-element methods. The method produces cohorts of brain images with known change that is physically and clinically plausible, providing data for objective evaluation of atrophy measurement techniques. Atrophy is simulated in different tissue compartments or in different neuroanatomical structures with a phenomenological model. This model of diffuse global and regional atrophy is based on volumetric measurements such as the brain or the hippocampus, from patients with known disease and guided by clinical knowledge of the relative pathological involvement of regions and tissues. The consequent biomechanical readjustment of structures is modelled using conventional physics-based techniques based on biomechanical tissue properties and simulating plausible tissue deformations with finite-element methods. A thermoelastic model of tissue deformation is employed, controlling the rate of progression of atrophy by means of a set of thermal coefficients, each one corresponding to a different type of tissue. Tissue characterization is performed by means of the meshing of a labelled brain atlas, creating a reference volumetric mesh that will be introduced to a finite-element solver to create the simulated deformations. Preliminary work on the simulation of acquisition
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.
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.
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.
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
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)
Puzyrev, Vladimir; Koldan, Jelena; de la Puente, Josep; Houzeaux, Guillaume; Vázquez, Mariano; Cela, José María
2013-05-01
We present a nodal finite-element method that can be used to compute in parallel highly accurate solutions for 3-D controlled-source electromagnetic forward-modelling problems in anisotropic media. Secondary coupled-potential formulation of Maxwell's equations allows to avoid the singularities introduced by the sources, while completely unstructured tetrahedral meshes and mesh refinement support an accurate representation of geological and bathymetric complexity and improve the solution accuracy. Different complex iterative solvers and an efficient pre-conditioner based on the sparse approximate inverse are used for solving the resulting large sparse linear system of equations. Results are compared with the ones of other researchers to check the accuracy of the method. We demonstrate the performance of the code in large problems with tens and even hundreds of millions of degrees of freedom. Scalability tests on massively parallel computers show that our code is highly scalable.
NASA Astrophysics Data System (ADS)
Darrall, Bradley T.
For the first time true variational principles are formulated for the analysis of the continuum problems of heat diffusion, dynamic thermoelasticity, poroelasticity, and time-dependent quantum mechanics. This is accomplished by considering the stationarity of a mixed convolved action, which can be seen as a modern counterpart to the original actions posed in Hamilton's principle and its many extensions. By including fractional derivatives, convolution integrals, and mixed variables into the definition of the action these new variational principles overcome the shortcomings of the many other variational methods based on Hamilton's principle, namely the inability to include dissipation in a consistent manner and the unjustified need to constrain variations on the primary unknowns of a system at the end of the time interval. These new variational principles then provide ideal weak forms from which novel time-space finite element methods having certain attractive properties are formulated.
NASA Astrophysics Data System (ADS)
Nanda, Namita; Bandyopadhyay, J. N.
2009-08-01
The nonlinear transient response of composite shells with/without cutouts and initial geometric imperfection is investigated using the finite element method. The present formulation considers doubly curved shells incorporating von Kármán type nonlinear strains into the first order shear deformation theory. The analysis is carried out using quadratic C0 eight-noded isoparametric element. The governing nonlinear equations are solved by using the Newmark average acceleration method in the time integration in conjunction with modified Newton-Raphson iteration scheme. The validity of the model is demonstrated by comparing the present results with those available in the literature. Parametric studies are carried out varying the radius of curvature to width ratio and amplitude of initial geometric imperfection of laminated composite cylindrical, spherical and hyperbolic paraboloid shells with/without cutouts.
Modelling the transport of ionizing radiation using the finite element method.
Boman, E; Tervo, J; Vauhkonen, M
2005-01-21
Radiation therapy treatment planning is based on the calculation of the absorbed dose in the patient domain. For exact dose calculations, the solution of three coupled Boltzmann transport equations (BTEs) is needed to cover the transport of photons, electrons and positrons. In many situations, however, two coupled systems for photons and electrons are enough. The use of numerical methods in finding the exact solution of the unknown particle fluxes is necessary. In the stationary case, the BTE has six variables, three spatial, two directional and one energy variable. In this paper, we describe an approach in which the finite element method (FEM) is used to solve the six-dimensional problem. For the coupled photon-electron system, the variational formulation and the existence and uniqueness of the solution are derived. We simulate the solution of two coupled BTEs describing the travelling of photons and electrons in two spatial dimensions. The results are compared to Monte Carlo calculations with good agreement. PMID:15742943
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.
Charged-particle Gun Design with 3D Finite-element Methods
NASA Astrophysics Data System (ADS)
Humphries, Stanley
2002-04-01
The DARHT second-axis injector poses a major challenge for computer simulation. The relativistic electrons are subject to strong beam-generated electric and magnetic forces. The beam and applied fields are fully three-dimensional. Furthermore, accurate field calculations at surfaces are critical to model Child-law emission. Although several 2D relativistic beam codes are available, there is presently no 3D tool that can address all important processes in the DARHT injector. As a result, we created the OmniTrak 3D finite-element code suite. This talk gives a basic tutorial on finite-element methods with emphasis on electron gun design via the ray-tracing technique. Four main areas are covered: 1) the mesh as a tool to organize space, 2) transformation of the Poisson equation through the minimum residual principle, 3) orbit tracking in a complex environment and 4) handling self-consistent beam-generated fields. The components of a volume mesh (elements, nodes and facets) are reviewed. We consider motivations for choosing a 3D mesh style: structured versus unstructured, tetrahedrons versus hexahedrons. We discuss methods for taking volume integrals over arbitrary hexahedrons through normal coordinates and shape functions, leading to the fundamental field equations. The special problems of 3D magnetic field solutions and the advantages of the reduced potential method are outlined. Accurate field interpolations for orbit calculations require fast identification of occupied elements. A method for fast element identification that also yields the orbit penetration point on the element surface is described. The final topics are the assignment of charge and current to meshes from calculated orbits and techniques for space-charge-limited emission from multiple arbitrary 3D surfaces.
The finite element method: a tool to study orthodontic tooth movement.
Cattaneo, P M; Dalstra, M; Melsen, B
2005-05-01
Orthodontic tooth movement is achieved by (re)modeling processes of the alveolar bone, which are triggered by changes in the stress/strain distribution in the periodontium. In the past, the finite element (FE) method has been used to describe the stressed situation within the periodontal ligament (PDL) and surrounding alveolar bone. The present study sought to determine the impact of the modeling process on the outcome from FE analyses and to relate these findings to the current theories on orthodontic tooth movement. In a series of FE analyses simulating teeth subjected to orthodontic loading, the influence of geometry/morphology, material properties, and boundary conditions was evaluated. The accurate description of alveolar bone morphology and the assignment of non-linear mechanical properties for the PDF elements demonstrate that loading of the periodontium cannot be explained in simple terms of compression and tension along the loading direction. Tension in the alveolar bone was far more predominant than compression. PMID:15840778
Aerodynamic study of three-dimensional larynx models using finite element methods
NASA Astrophysics Data System (ADS)
de Oliveira Rosa, Marcelo; Pereira, José Carlos
2008-03-01
The airflow velocities and pressures are calculated from a three-dimensional model of the human larynx by using the finite element method. The laryngeal airflow is assumed to be incompressible, isothermal, steady, and created by fixed pressure drops. The influence of different laryngeal profiles (convergent, parallel, and divergent), glottal area, and dimensions of false vocal folds in the airflow are investigated. The results indicate that vertical and horizontal phase differences in the laryngeal tissue movements are influenced by the nonlinear pressure distribution across the glottal channel, and the glottal entrance shape influences the air pressure distribution inside the glottis. Additionally, the false vocal folds increase the glottal duct pressure drop by creating a new constricted channel in the larynx, and alter the airflow vortexes formed after the true vocal folds.
Birefringence analysis of a two elliptical cores hollow fiber based on finite element method
NASA Astrophysics Data System (ADS)
Tian, Fengjun; Yuan, Libo; Dai, Qian; Liu, Zhihai; Zhang, Jianzhong
2012-02-01
We design and fabricate a two elliptical cores hollow optical fiber, which has an about 60μm diameter hollow air hole centrally, a 125μm diameter cladding, two 8μm/4μm (major axis/minor axis) elliptical cores, and a 2μm thickness silica cladding between core layer and air hole. Its mode birefringence is consisted of geometry birefringence and self-stress birefringence. Based on the finite element method the birefringence characteristics are analyzed numerically at 200nm- 1800nm wavelength. We expect that the two elliptical cores hollow fiber has some potential applications in in-fiber interferometers with polarization maintaining, poling fiber and Bio-sensor based on evanescent wave field.
The solution of non-linear hyperbolic equation systems by the finite element method
NASA Technical Reports Server (NTRS)
Loehner, R.; Morgan, K.; Zienkiewicz, O. C.
1984-01-01
A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.
NASA Technical Reports Server (NTRS)
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.
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.
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.
Dunn, T.A.; McCallen, R.C.
2000-10-17
The Galerkin Finite Element Method was used to predict a natural convection flow in an enclosed cavity. The problem considered was a differentially heated, tall (8:1), rectangular cavity with a Rayleigh number of 3.4 x 10{sup 5} and Prandtl number of 0.71. The incompressible Navier-Stokes equations were solved using a Boussinesq approximation for the buoyancy force. The algorithm was developed for efficient use on massively parallel computer systems. Emphasis was on time-accurate simulations. It was found that the average temperature and velocity values can be captured with a relatively coarse grid, while the oscillation amplitude and period appear to be grid sensitive and require a refined computation.
NASA Astrophysics Data System (ADS)
Aya Baquero, H.
2015-01-01
The Finite Element Method FEM can be used in the context of physics engineering education, particularly in nanotechnology training. Cantilevers and cantilevers arrays have been implemented as sensors within lots of applications. In the present paper, FEM was used to assess validity of basic models where cantilevers are used as mass sensors. Resonance frequency of a cantilever transversal vibration was found; this was a silicon one-side clamped cantilever. A number of minor mass elements Am was added on the cantilever's free side. Then in each case, a new resonance frequency was found; this led to obtain the Am values from shifts of resonance frequencies. Finally, those values were compared with CAD model values.
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.
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.
Birkholzer, J.; Karasaki, K.
1996-09-01
Fracture network simulators have been extensively used in the past for obtaining a better understanding of flow and transport processes in fractured rock. However, most of these models do not account for fluid or solute exchange between the fractures and the porous matrix, although diffusion into the matrix pores can have a major impact on the spreading of contaminants. In the present paper a new finite element code TRIPOLY is introduced which combines a powerful Lagrangian-Eulerian approach for solving flow and transport in networks of discrete fractures with an efficient method to account for the diffusive interaction between the fractures and the adjacent matrix blocks. The code is capable of handling large-scale fracture-matrix systems comprising individual fractures and matrix blocks of arbitrary size, shape, and dimension.
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.
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.
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
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.
NASA Astrophysics Data System (ADS)
Emamzadeh, Seyed Shahab; Ahmadi, Mohammad Taghi; Mohammadi, Soheil; Biglarkhani, Masoud
2015-07-01
In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes: a) calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b) fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c) adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.
Giambini, Hugo; Qin, Xiaoliang; Dragomir-Daescu, Dan; An, Kai-Nan; Nassr, Ahmad
2016-04-01
Osteoporotic vertebral body fractures are an increasing clinical problem among the aging population. Specimen-specific finite element models, derived from quantitative computed tomography (QCT), have the potential to more accurately predict failure loads in the vertebra. Additionally, the use of extended finite element modeling (X-FEM) allows for a detailed analysis of crack initiation and propagation in various materials. Our aim was to study the feasibility of QCT/X-FEM analysis to predict fracture properties of vertebral bodies. Three cadaveric specimens were obtained, and the L3 vertebrae were excised. The vertebrae were CT scanned to develop computational models and mechanically tested in compression to measure failure load, stiffness and to observe crack location. One vertebra was used for calibration of the material properties from experimental results and CT gray-scale values. The two additional specimens were used to assess the model prediction. The resulting QCT/X-FEM model of the specimen used for calibration had 2 and 4 % errors in stiffness and failure load, respectively, compared with the experiment. The predicted failure loads of the additional two vertebrae were larger by about 41-44 % when compared to the measured values, while the stiffness differed by 129 and 40 %. The predicted fracture patterns matched fairly well with the visually observed experimental cracks. Our feasibility study indicated that the QCT/X-FEM method used to predict vertebral compression fractures is a promising tool to consider in future applications for improving vertebral fracture risk prediction in the elderly. PMID:26239163
A parallel geometric multigrid method for finite elements on octree meshes
Sampath, Rahul S; Biros, George
2010-01-01
In this article, we present a parallel geometric multigrid algorithm for solving variable-coefficient elliptic partial differential equations on the unit box (with Dirichlet or Neumann boundary conditions) using highly nonuniform, octree-based, conforming finite element discretizations. Our octrees are 2:1 balanced, that is, we allow no more than one octree-level difference between octants that share a face, edge, or vertex. We describe a parallel algorithm whose input is an arbitrary 2:1 balanced fine-grid octree and whose output is a set of coarser 2:1 balanced octrees that are used in the multigrid scheme. Also, we derive matrix-free schemes for the discretized finite element operators and the intergrid transfer operations. The overall scheme is second-order accurate for sufficiently smooth right-hand sides and material properties; its complexity for nearly uniform trees is {Omicron}(N/n{sub p} log N/n{sub p}) + {Omicron}(n{sub p} log n{sub p}), where N is the number of octree nodes and n{sub p} is the number of processors. Our implementation uses the Message Passing Interface standard. We present numerical experiments for the Laplace and Navier (linear elasticity) operators that demonstrate the scalability of our method. Our largest run was a highly nonuniform, 8-billion-unknown, elasticity calculation using 32,000 processors on the Teragrid system, 'Ranger,' at the Texas Advanced Computing Center. Our implementation is publically available in the Dendro library, which is built on top of the PETSc library from Argonne National Laboratory.
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. PMID:26520450
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.
A Simulation of crustal deformation around sourthwest Japan using 3D Finite Element Method
NASA Astrophysics Data System (ADS)
Oma, T.; Ito, T.; Sasajima, R.
2015-12-01
In southwest Japan, the Philippine Sea plate is subducting beneath the Amurian plate at the Nankai Trough. Megathrust earthquakes have been occurred with recurrence intervals of about 100-150 years. Previous studies have estimated co-seismic slip distribution at the 1944 Tokankai and the 1946 Nankai earthquakes and interplate plate coupling along the Nankai Trough. Many of previous studies employed a homogeneous elastic half space or elastic and viscoelastic layers structure. However, these assumptions as mentioned above are inadequate, since inhomogeneous structure is exceled in the real earth result from subducting plate. Therefore, in order to estimate the effect of inhomogeneous structure on the crustal deformation, we calculate crustal deformation due to Megathrust earthquake using 3-dimensional Finite Element Method (FEM). We use FEM software PyLith v2.1. In this study, we construct a finite element mesh with the region of 3000km(SW) × 2300km(NS) × 400km(depth) cover Japanese Islands, using Cubit 13.0. This mesh is considered topography, the Philippine Sea plate, the Pacific plate, Moho discontinuity, and curvature of the earth. In order to examine differences of surface displacement between inhomogeneous and homogeneous structures, we use co-seismic slip distribution of the 1944 and 1946 earthquakes estimated by Sagiya and Thatcher (1999). In result, surface elastic response under inhomogeneous structure becomes 30% larger than it's homogeneous structure at the Muroto cape. This difference indicates that co-seismic slip or plate coupling distribution estimated from Green's function under an assumption of homogeneous structure is overestimated. Then, we calculate viscoelastic response assuming Maxwell rheology model and viscosity as 1×1019. As a result, predicted horizontal velocity of viscoelastic response due to the events corresponds to 10 % of observed present deformation. It suggest that spatial pattern of plate coupling might be change when we
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)
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 Technical Reports Server (NTRS)
Zhao, W.; Newman, J. C., Jr.; Sutton, M. A.; Wu, X. R.; Shivakumar, K. N.
1995-01-01
Stress intensity factors for quarter-elliptical corner cracks emanating from a circular hole are determined using a 3-D weight function method combined with a 3-D finite element method. The 3-D finite element method is used to analyze uncracked configuration and provide stress distribution in the region where crack is to occur. Using this stress distribution as input, the 3-D weight function method is used to determine stress intensity factors. Three different loading conditions, i.e. remote tension, remote bending and wedge loading, are considered for a wide range in geometrical parameters. The significance in using 3-D uncracked stress distribution and the difference between single and double corner cracks are studied. Typical crack opening displacements are also provided. Comparisons are made with solutions available in the literature.
NASA Technical Reports Server (NTRS)
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 Astrophysics Data System (ADS)
Atkins, Carolyn; Wang, Hongchang; Doel, Peter; Brooks, David; Thompson, Samantha; Feldman, Charlotte; Willingale, Richard; Button, Tim; Rodriguez Sanmartin, Daniel; Zhang, Dou; James, Ady; Theobald, Craig
2008-07-01
The Smart X-ray Optics (SXO) project is a UK based consortium consisting of several institutions investigating the application of active/adaptive optics to both large and small scale grazing incidence x-ray optics. University College London presents work relating to the large scale x-ray optics that is geared towards the next generation of x-ray space telescopes. It is proposed that through the addition of piezoelectric actuators, an active x-ray telescope with a resolution better than that currently achieved (e.g. Chandra 0.5") could be realised. An immediate aim of the SXO project is to produce an operational active ellipsoidal segment prototype, with point-to- point focusing and with the intention of being tested at the University of Leicester's x-ray beam source. Work relating to the fabrication of the prototype will be presented, including shell replication via a nickel sulphamate electroforming process, piezoelectric actuators and prototype assembly and operation. Results from finite element analysis modelling will be discussed; these relate primarily to gravitational distortion effects and the plating tank electrostatics.
Modelling The Bending Test Behaviour Of Carbon Fibre Reinforced SiC By Finite Element Method
NASA Astrophysics Data System (ADS)
Hofmann, S.; Koch, D.; Voggenreiter, H.
2012-07-01
Liquid silicon infiltrated carbon fibre reinforced SiC, has shown to be a high-potential material for thermal protection systems. The tensile and bending behaviour of the ceramic-matrix composite, C/C-SiC, were investigated in varying orientations relative to the 0/90° woven carbon fibres. The ratio of bending to tensile strength was about 1.7 to 2 depending on the loading direction. With the goal to understand this large difference finite element analyses (FEA) of the bending tests were performed. The different stress-strain behaviour of C/C-SiC under tensile and compression load were included in the FEA. Additionally the bending failure of the CMC-material was modelled by Cohesive Zone Elements (CZE) accounting for the directional tensile strength and Work of Fracture (WOF). The WOF was determined by Single Edge Notched Bending (SENB) tests. Comparable results from FEA and bending test were achieved. The presented approach could also be adapted for the design of C/C-SiC-components and structures.
Finnveden, Svante; Hörlin, Nils-Erik; Barbagallo, Mathias
2014-04-01
Viscoelastic properties of porous materials, typical of those used in vehicles for noise insulation and absorption, are estimated from measurements and inverse finite element procedures. The measurements are taken in a near vacuum and cover a broad frequency range: 20 Hz to 1 kHz. The almost cubic test samples were made of 25 mm foam covered by a "heavy layer" of rubber. They were mounted in a vacuum chamber on an aluminum table, which was excited in the vertical and horizontal directions with a shaker. Three kinds of response are measured allowing complete estimates of the viscoelastic moduli for isotropic materials and also providing some information on the degree of material anisotropicity. First, frequency independent properties are estimated, where dissipation is described by constant loss factors. Then, fractional derivative models that capture the variation with frequency of the stiffness and damping are adapted. The measurement setup is essentially two-dimensional and calculations are three-dimensional and for a state of plane strain. The good agreement between measured and calculated response provides some confidence in the presented procedures. If, however, the material model cannot fit the measurements well, the inverse procedure yields a certain degree of arbitrariness to the parameter estimation. PMID:25234982
NASA Technical Reports Server (NTRS)
Coy, J. J.; Chao, C. H. C.
1981-01-01
A method of selecting grid size for the finite element analysis of gear tooth deflection is presented. The method is based on a finite element study of two cylinders in line contact, where the criterion for establishing element size was that there be agreement with the classical Hertzian solution for deflection. The results are applied to calculate deflection for the gear specimen used in the NASA spur gear test rig. Comparisons are made between the present results and the results of two other methods of calculation. The results have application in design of gear tooth profile modifications to reduce noise and dynamic loads.
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 Astrophysics Data System (ADS)
Zeng, X.; Scovazzi, G.
2016-06-01
We present a monolithic arbitrary Lagrangian-Eulerian (ALE) finite element method for computing highly transient flows with strong shocks. We use a variational multiscale (VMS) approach to stabilize a piecewise-linear Galerkin formulation of the equations of compressible flows, and an entropy artificial viscosity to capture strong solution discontinuities. Our work demonstrates the feasibility of VMS methods for highly transient shock flows, an area of research for which the VMS literature is extremely scarce. In addition, the proposed monolithic ALE method is an alternative to the more commonly used Lagrangian+remap methods, in which, at each time step, a Lagrangian computation is followed by mesh smoothing and remap (conservative solution interpolation). Lagrangian+remap methods are the methods of choice in shock hydrodynamics computations because they provide nearly optimal mesh resolution in proximity of shock fronts. However, Lagrangian+remap methods are not well suited for imposing inflow and outflow boundary conditions. These issues offer an additional motivation for the proposed approach, in which we first perform the mesh motion, and then the flow computations using the monolithic ALE framework. The proposed method is second-order accurate and stable, as demonstrated by extensive numerical examples in two and three space dimensions.
A High-order Eulerian-Lagrangian Finite Element Method for Coupled Electro-mechanical Systems
NASA Astrophysics Data System (ADS)
Brandstetter, Gerd
The main focus of this work is on the development of a high-order Eulerian-Lagrangian finite element method for the simulation of electro-mechanical systems. The coupled problem is solved by a staggered scheme, where the mechanical motion is discretized by standard Lagrangian finite elements, and the electrical field is solved on a fixed Eulerian grid with embedded boundary conditions. Traditional Lagrangian-Lagrangian or arbitrary Lagrangian-Eulerian (ALE) methods encounter deficiencies, for example, when dealing with mesh distortion due to large deformations, or topology changes due to contacting bodies. The presented Eulerian-Lagrangian approach addresses these issues in a natural way. Within this context we develop a high-order immersed boundary discontinuous-Galerkin (IB-DG) method, which is shown to be necessary for (i) the accurate representation of the electrical gradient along nonlinear boundary features such as singular corners, and (ii) to achieve full convergence during the iterative global solution. We develop an implicit scheme based on the mid-point rule, as well as an explicit scheme based on the centered-difference method, with the incorporation of energy conserving, frictionless contact algorithms for an elastic-to-rigid-surface contact. The performance of the proposed method is assessed for several benchmark tests: the electro-static force vector around a singular corner, the quasi-static pull-in of an electro-mechanically actuated switch, the excitation of a carbon nanotube at resonance, and the cyclic impact simulation of a micro-electro-mechanical resonant-switch. We report improved accuracy for the high-order method as compared to low-order methods, and linear convergence in the iterative solution of the staggered scheme. Additionally, we investigate a Newton-Krylov shooting scheme in order to directly find cyclic steady states of electro-mechanical devices excited at resonance-- as opposed to a naive time-stepping from zero initial
NASA Astrophysics Data System (ADS)
Saeedifar, Milad; Fotouhi, Mohamad; Najafabadi, Mehdi Ahmadi; Toudeshky, Hossein Hosseini
2015-01-01
Delamination is one of the most common modes of failure in laminated composites and it leads to the loss of structural strength and stiffness. In this paper, mode I, mode II, and mixed of these pure modes were investigated using mechanical data, Finite Element Method (FEM) and Acoustic Emission (AE) signals. Experimental data were obtained from in situ monitoring of glass/epoxy laminated composites with different lay-ups when subjected to different modes of failure. The main objective was to investigate the behavior of delamination propagation and to evaluate the critical value of the strain energy which is required for onset of the delamination ( G C). For the identification of interlaminar fracture toughness of the specimens, four methods were used: (a) ASTM standard methods, (b) FEM analysis, (c) AE method, and (d) sentry function method which is a function of mechanical and AE behaviors of the specimens. The results showed that the G C values obtained by the sentry function method and FEM analysis were in a close agreement with the results of nonlinearity methods which is recommended in the ASTM standards. It was also found that the specimens under different loading conditions and various lay-up have different G C values. These differences are related to different stress components distribution in the specimens which induce various damage mechanisms. Accordingly, stress components distribution obtained from FEM analyses were in agreement with SEM observations of the damaged surfaces of the specimens.
NASA Astrophysics Data System (ADS)
Koval, L. R.; Motamedi, S.; Ramakrishnan, J. V.
1985-09-01
This investigation represents an extension of a study of Roussos (1985) who considered the noise transmission loss of a rectangular plate in an infinite baffle. Roussos, who employed an analytical formulation, considered an unstiffened plate. While it is difficult to consider stiffeners by means of analytical methods, the difficulties can be avoided by employing a finite element procedure. For this reason, the present study is concerned with the implementation of a finite element method. The representation of the panel transmission loss is discussed, and the determination of the panel motion by means of the finite element technique is described, taking into account an isotropic flat panel, the exciting force, an eigenvalue problem, the radiation pressure, a plate element, and a cylindrical shell element. Numerical results are considered for a flat panel, a curved panel, and a stiffened flat panel.
A finite element computational method for high Reynolds number laminar flows
NASA Technical Reports Server (NTRS)
Kim, Sang-Wook
1987-01-01
A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.
NASA Technical Reports Server (NTRS)
Dubowsky, Steven
1989-01-01
An approach is described to modeling the flexibility effects in spatial mechanisms and manipulator systems. The method is based on finite element representations of the individual links in the system. However, it should be noted that conventional finite element methods and software packages will not handle the highly nonlinear dynamic behavior of these systems which results form their changing geometry. In order to design high-performance lightweight systems and their control systems, good models of their dynamic behavior which include the effects of flexibility are required.
ten Broeke, René H M; Tarala, Maria; Arts, Jacobus J; Janssen, Dennis W; Verdonschot, Nico; Geesink, Rudolph G T
2014-03-01
This study assessed whether the Symax™ implant, a modification of the Omnifit(®) stem (in terms of shape, proximal coating and distal surface treatment), would yield improved bone remodelling in a clinical DEXA study, and if these results could be predicted in a finite element (FE) simulation study. In a randomized clinical trial, 2 year DEXA measurements between the uncemented Symax™ and Omnifit(®) stem (both n=25) showed bone mineral density (BMD) loss in Gruen zone 7 of 14% and 20%, respectively (p<0.05). In contrast, the FE models predicted a 28% (Symax™) and 26% (Omnifit(®)) bone loss. When the distal treatment to the Symax™ was not modelled in the simulation, bone loss of 35% was predicted, suggesting the benefit of this surface treatment for proximal bone maintenance. The theoretical concept for enhanced proximal bone loading by the Symax™, and the predicted remodelling pattern were confirmed by DEXA-results, but there was no quantitative match between clinical and FE findings. This was due to a simulation based on incomplete assumptions concerning the yet unknown biological and mechanical effects of the new coating and surface treatment. Study listed under ClinicalTrials.gov with number NCT01695213. PMID:24378381
NASA Astrophysics Data System (ADS)
Zhang, Zhiqiang; Geng, Dalong; Wang, Xudong
2016-04-01
A simple and effective decoupled finite element analysis method was developed for simulating both the piezoelectric and flexoelectric effects of zinc oxide (ZnO) and barium titanate (BTO) nanowires (NWs). The piezoelectric potential distribution on a ZnO NW was calculated under three deformation conditions (cantilever, three-point, and four-point bending) and compared to the conventional fully coupled method. The discrepancies of the electric potential maximums from these two methods were found very small, validating the accuracy and effectiveness of the decoupled method. Both ZnO and BTO NWs yielded very similar potential distributions. Comparing the potential distributions induced by the piezoelectric and flexoelectric effects, we identified that the middle segment of a four-point bending NW beam is the ideal place for measuring the flexoelectric coefficient, because the uniform parallel plate capacitor-like potential distribution in this region is exclusively induced by the flexoelectric effect. This decoupled method could provide a valuable guideline for experimental measurements of the piezoelectric effects and flexoelectric effects in the nanometer scale.
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.
NASA Astrophysics Data System (ADS)
Kouhi, Mohammad; Oñate, Eugenio
2015-07-01
A new implicit stabilized formulation for the numerical solution of the compressible Navier-Stokes equations is presented. The method is based on the finite calculus (FIC) scheme using the Galerkin finite element method (FEM) on triangular grids. Via the FIC formulation, two stabilization terms, called streamline term and transverse term, are added to the original conservation equations in the space-time domain. The non-linear system of equations resulting from the spatial discretization is solved implicitly using a damped Newton method benefiting from the exact Jacobian matrix. The matrix system is solved at each iteration with a preconditioned GMRES method. The efficiency of the proposed stabilization technique is checked out in the solution of 2D inviscid and laminar viscous flow problems where appropriate solutions are obtained especially near the boundary layer and shock waves. The work presented here can be considered as a follow up of a previous work of the authors Kouhi, Oñate (Int J Numer Methods Fluids 74:872-897, 2014). In that paper, the stabilized Galerkin FEM based on the FIC formulation was derived for the Euler equations together with an explicit scheme. In the present paper, the extension of this work to the Navier-Stokes equations using an implicit scheme is presented.
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.
Ragusa, Jean C.
2015-01-01
In this paper, we propose a piece-wise linear discontinuous (PWLD) finite element discretization of the diffusion equation for arbitrary polygonal meshes. It is based on the standard diffusion form and uses the symmetric interior penalty technique, which yields a symmetric positive definite linear system matrix. A preconditioned conjugate gradient algorithm is employed to solve the linear system. Piece-wise linear approximations also allow a straightforward implementation of local mesh adaptation by allowing unrefined cells to be interpreted as polygons with an increased number of vertices. Several test cases, taken from the literature on the discretization of the radiation diffusion equation, are presented: random, sinusoidal, Shestakov, and Z meshes are used. The last numerical example demonstrates the application of the PWLD discretization to adaptive mesh refinement.
A simple adaptive mesh generator for 2-D finite element calculations
Fernandez, F.A.; Yong, Y.C.; Ettinger, R.D. )
1993-03-01
A strategy for adaptive mesh generation is proposed. The method consists of the use of a suitably defined density function', which can either be defined by the user or be calculated from a previous approximate solution, to guide the generation of a new mesh. This new mesh is built starting from a minimal number of triangular elements which are then in several sweeps, repeatedly refined according to the density function. The Delaunay algorithm is used in each stage to keep the shape of the triangles as equilateral as possible.
NASA Astrophysics Data System (ADS)
Ding, Yan; Kawahara, Mutsuto
1999-09-01
The linear stability of incompressible flows is investigated on the basis of the finite element method. The two-dimensional base flows computed numerically over a range of Reynolds numbers are perturbed with three-dimensional disturbances. The three-dimensionality in the flow associated with the secondary instability is identified precisely. First, by using linear stability theory and normal mode analysis, the partial differential equations governing the evolution of perturbation are derived from the linearized Navier-Stokes equation with slight compressibility. In terms of the mixed finite element discretization, in which six-node quadratic Lagrange triangular elements with quadratic interpolation for velocities (P2) and three-node linear Lagrange triangular elements for pressure (P1) are employed, a non-singular generalized eigenproblem is formulated from these equations, whose solution gives the dispersion relation between complex growth rate and wave number. Then, the stabilities of two cases, i.e. the lid-driven cavity flow and flow past a circular cylinder, are examined. These studies determine accurately stability curves to identify the critical Reynolds number and the critical wavelength of the neutral mode by means of the Krylov subspace method and discuss the mechanism of instability. For the cavity flow, the estimated critical results are Rec=920.277+/-0.010 for the Reynolds number and kc=7.40+/-0.02 for the wave number. These results are in good agreement with the observation of Aidun et al. and are more accurate than those by the finite difference method. This instability in the cavity is associated with absolute instability [Huerre and Monkewitz, Annu. Rev. Fluid Mech., 22, 473-537 (1990)]. The Taylor-Göertler-like vortices in the cavity are verified by means of the reconstruction of three-dimensional flows. As for the flow past a circular cylinder, the primary instability result shows that the flow has only two-dimensional characteristics at the
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.
NASA Astrophysics Data System (ADS)
Matandirotya, Electdom; Cilliers, Pierre J.; Van Zyl, Robert R.
2015-03-01
Geomagnetically induced currents (GIC) are a result of time variations of the geomagnetic field, which induce a geoelectric field at the Earth's surface. Geomagnetic perturbations are enhanced during adverse space weather events called geomagnetic storms. All ground-based conductor networks can be affected by GIC during such events. As a way of assessing the magnitude of GIC expected in a particular technological system, models are developed, in which the computation of the induced geoelectric field is a key step. Computation of GIC in the South African power transmission network has so far been done using a uniform Earth model and improved using a layered Earth conductivity profile. In this work we present geoelectric field results obtained by using the finite element method (FEM) and improved GIC estimates using a realistic conductivity profile, magnetic field data interpolated from two South African observatories, and a new method for estimating the network coefficients, a and b, which map the north-south and east-west electric fields to their respective GIC components. The performance of the chosen FEM model demonstrates that it is an effective tool for GIC modeling. Unlike previous engineering techniques, our method for estimating the a and b coefficients from GIC and measured magnetic field data gives results that are independent of prior knowledge of the network configuration. The GIC estimated using the a and b coefficients obtained from the proposed method compares well with the measured GIC during the late October 2003 geomagnetic storm.
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.
NASA Astrophysics Data System (ADS)
Key, K.
2013-12-01
This work announces the public release of an open-source inversion code named MARE2DEM (Modeling with Adaptively Refined Elements for 2D Electromagnetics). Although initially designed for the rapid inversion of marine electromagnetic data, MARE2DEM now supports a wide variety of acquisition configurations for both offshore and onshore surveys that utilize electric and magnetic dipole transmitters or magnetotelluric plane waves. The model domain is flexibly parameterized using a grid of arbitrarily shaped polygonal regions, allowing for complicated structures such as topography or seismically imaged horizons to be easily assimilated. MARE2DEM efficiently solves the forward problem in parallel by dividing the input data parameters into smaller subsets using a parallel data decomposition algorithm. The data subsets are then solved in parallel using an automatic adaptive finite element method that iterative solves the forward problem on successively refined finite element meshes until a specified accuracy tolerance is met, thus freeing the end user from the burden of designing an accurate numerical modeling grid. Regularized non-linear inversion for isotropic or anisotropic conductivity is accomplished with a new implementation of Occam's method referred to as fast-Occam, which is able to minimize the objective function in much fewer forward evaluations than the required by the original method. This presentation will review the theoretical considerations behind MARE2DEM and use a few recent offshore EM data sets to demonstrate its capabilities and to showcase the software interface tools that streamline model building and data inversion.
Material characterization of open-cell foams by finite element based micromechanics methods
NASA Astrophysics Data System (ADS)
Thiyagasundaram, Prasanna
Finite element based micromechanics methods have been used for predicting elastic properties, failure strengths, mode-I, mode-II and mixed mode fracture toughness of open-cell foams. In predicting the orthotropic elastic properties, foams with both equisided and Kelvin-elongated tetrakaidecahedron unit cells are studied. Periodic Boundary Conditions (PBCs) exploiting the special repeating microstructural geometry for these materials have been derived and have been applied on the micromechanical model to calculate the elastic properties. It is shown that the results for the elastic constants from these finite element based models agree well with the available analytical models. Further studies such as effect of a varying strut cross-section over a uniform strut cross-section on the elastic properties are also done in the same context. Next, the procedures used for predicting the above elastic properties are extended to predict multi-axial failure strengths of these low density open cell foams with a microstructure made out of tetrakaidecahedral unit cells. Again, foams with both equisided tetrakaidecahedron and Kelvin-elongated tetrakaidecahedron as unit cells are studied. Failure strengths in different material directions are computed using direct Micromechanics based Methods (DMM). Further, the effect of a varying strut cross section over a uniform strut cross section on failure strengths is also presented. Bi-axial failure envelopes for foams with equisided tetrakaidecahedron unit cells are shown to take the shape of a regular hexagon in the hydrostatic plane. The tri-axial failure envelope for foams made out of equisided tetrakaidecahedron unit cells is shown to have a shape of a double hexagonal pyramid. The bi-axial and tri-axial failure envelopes of foams with elongated tetrakaidecahedron unit cells are also plotted and the effect of anisotropy in foams with these unit cells on the failure envelopes is also discussed. Next, global-local models are developed
Modeling slot die coatings of magnetic inks using finite element methods
NASA Astrophysics Data System (ADS)
Hawkins, Michael
Finite element methods were used to model the slot die coating of cobalt gamma modified iron oxide magnetic inks with a polymeric binder in an organic solvent. The slot die included an upstream seal, which prevented the formation of an upstream meniscus and some recirculations. The shear-thinning characteristics of the ink were modeled with the Carreau equation. The viscoelastic characteristics of the ink were fit to the Giesekus equation. The results of the single coating models indicate that the shear thinning characteristics have only slight effects on the velocity, shear rate, and vorticity between the die and the substrate, but the viscosity and stresses were affected by the degree of shear-thinning. As the power-law index of the coating fluid was decreased, the viscosity and shear stress between the die and the substrate decreased. For a lower power-law index, the viscosity of the ink increased more sharply as the free surface formed. The distribution of the shear rate and vorticity of the double layer coatings was primarily affected by the ratio of the power-law index of the top layer to the power-law index of the bottom layer. When the power-law index of the top layer was greater than the power law index of the bottom layer, the shear rate and vorticity of the top layer were much lower than those of the bottom layer. When the situation was reversed and the ratio was less than one, the shear rate and vorticity were much higher in the top layer than in the bottom layer. When the ratio was approximately equal to one the shear rate distribution was more even and resembled the single coating process. The angle formed by the initial free surface and the die was also affected by the ratio of the power-law indices. In fact, the angle was linearly dependent on the ratio of the power-law indices. It was determined that the distribution of the shear rate and other properties could be manipulated by choosing the appropriate fluid for the bottom layer, which would
Wave properties in poroelastic media using a Wave Finite Element Method
NASA Astrophysics Data System (ADS)
Serra, Q.; Ichchou, M. N.; Deü, J.-F.
2015-01-01
The application of the bidirectional Wave Finite Element Method (WFE) to Biot-Allard's theory of poroelasticity is investigated. This method has been successfully used in previous elastodynamics studies. In the case of porous media, the rigidity of the layer is very low, leading to very small wavelengths, and a high dissipation rate occurs within the pores. These differences with the elastic case justify a study of their consequences on numerical results. In this paper, it is shown that despite these difficulties, the WFE provides an efficient tool to compute the waves propagating through poroelastic media. The influence of boundary conditions on wave propagation is discussed, as well as the convergence of the numerical results, depending on the spatial discretization, the order of shape functions, and the choice of the formulation. Finally, the wavenumbers predicted with this method are compared with some simplified models such as equivalent fluid models or equivalent plate models. It is shown that the WFE can be used to validate the assumptions made by the simplified models.
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.
Simulation of plasmonic and photonic crystal structures using finite-element method
NASA Astrophysics Data System (ADS)
Yang, Sen
In this thesis, the Finite-Element Method (FEM) was utilized to simulate and design the optimal nanostructures for better performances of Surface-Enhanced Raman Scattering (SERS) and lasing. FEM proved its effectiveness in the calculations of target physical models to optimize the model geometry or theoretically validate experimental observations. In chapter 1 and 2, the fundamental theorem of SERS and photonic crystal cavity were introduced and discussed. The most used optical structures for the two effects, metal/dielectric SPP structure and dielectric photonic crystal structure, were introduced as examples. Equations stem from Maxwell equations were derived and discussed to clarify the concepts of SERS and PCC. In chapter 3, the FEM method was carried out to simulate the SERS performance of Au nano-bowl/SiO2/Au nanoparticle structure. The electric field distributions and Raman enhancement factors of models in real experiments were calculated and analyzed theoretically. The simulation result on Raman enhancement factors showed consistency with the experimental observations. In chapter 4, the design process of silicon nitride photonic crystal cavity was introduced and the simulation results were discussed. Using L3 geometrical model, the FEM method successfully revealed the relations between key optical properties, such as quality factor and resonant wavelength, and geometrical parameter selections. The simulations were also helpful in determination of the optimal parameter selection in L3 PCC model for further experimental fabrication.
A time-domain finite element boundary integration method for ultrasonic nondestructive evaluation.
Shi, Fan; Choi, Wonjae; Skelton, Elizabeth A; Lowe, Michael J S; Craster, Richard V
2014-12-01
A 2-D and 3-D numerical modeling approach for calculating the elastic wave scattering signals from complex stress-free defects is evaluated. In this method, efficient boundary integration across the complex boundary of the defect is coupled with a time-domain finite element (FE) solver. The model is designed to simulate time-domain ultrasonic nondestructive evaluation in bulk media. This approach makes use of the hybrid concept of linking a local numerical model to compute the near-field scattering behavior and theoretical mathematical formulas for postprocessing to calculate the received signals. It minimizes the number of monitoring signals from the FE calculation so that the computation effort in postprocessing decreases significantly. In addition, by neglecting the conventional regular monitoring box, the region for FE calculation can be made smaller. In this paper, the boundary integral method is implemented in a commercial FE code, and it is validated by comparing the scattering signals with results from corresponding full FE models. The coupled method is then implemented in real inspection scenarios in both 2-D and 3-D, and the accuracy and the efficiency are demonstrated. The limitations of the proposed model and future works are also discussed. PMID:25474780
A mixed-grid finite element method with PML absorbing boundary conditions for seismic wave modelling
NASA Astrophysics Data System (ADS)
Liu, Shaolin; Li, Xiaofan; Wang, Wenshuai; Liu, Youshan
2014-10-01
We have developed a mixed-grid finite element method (MGFEM) to simulate seismic wave propagation in 2D structurally complex media. This method divides the physical domain into two subdomains. One subdomain covering the major part of the physical domain is divided by regular quadrilateral elements, while the other subdomain uses triangular elements to correctly fit a rugged free surface topography. The local stiffness matrix of any quadrilateral element is identical and matrix-vector production is calculated using an element-by-element technique, which avoids assembling a huge global stiffness matrix. As only a few triangular elements exist in the subdomain containing the rugged free surface topography, the memory requirements for storing the assembled subdomain global stiffness matrix are significantly reduced. To eliminate artificial boundary reflections, the MGFEM is also implemented to solve the system equations of PML absorbing boundary conditions (PML ABC). The accuracy and efficiency of the MGFEM is tested in numerical experiments by comparing it with conventional methods, and numerical comparisons also indicate its tremendous ability to describe rugged surfaces.
Geometrically non-linear vibration of spinning structures by finite element method
NASA Astrophysics Data System (ADS)
Leung, A. Y. T.; Fung, T. C.
1990-05-01
The geometrically non-linear steady state vibration of spinning structures is studied. Full flap-lag-torsional gyroscopic coupling effects are considered. The non-linearity arises mainly from the non-linear axial strain-displacement relation. The equations of motion are derived from Lagrangian equations. Spatial discretization is achieved by the finite element method and steady state nodal displacements are expanded into Fourier series. The harmonic balance method gives a set of non-linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns. The non-linear algebraic equations are solved by a Newtonian algorithm iteratively. The importance of the conditions of completeness and balanceability in choosing the number of harmonic terms to be used is discussed. General frame structures with arbitrary orientation in a rotating frame can be investigated by the present method. Rotating blades and shafts are treated as special cases. Examples of a rotating ring with different orientations are given. The non-linear amplitude-frequency relation can be constructed parametrically.
A coupled finite-element, boundary-integral method for simulating ultrasonic flowmeters.
Bezdĕk, Michal; Landes, Hermann; Rieder, Alfred; Lerch, Reinhard
2007-03-01
Today's most popular technology of ultrasonic flow measurement is based on the transit-time principle. In this paper, a numerical simulation technique applicable to the analysis of transit-time flowmeters is presented. A flowmeter represents a large simulation problem that also requires computation of acoustic fields in moving media. For this purpose, a novel boundary integral method, the Helmholtz integral-ray tracing method (HIRM), is derived and validated. HIRM is applicable to acoustic radiation problems in arbitrary mean flows at low Mach numbers and significantly reduces the memory demands in comparison with the finite-element method (FEM). It relies on an approximate free-space Green's function which makes use of the ray tracing technique. For simulation of practical acoustic devices, a hybrid simulation scheme consisting of FEM and HIRM is proposed. The coupling of FEM and HIRM is facilitated by means of absorbing boundaries in combination with a new, reflection-free, acoustic-source formulation. Using the coupled FEM-HIRM scheme, a full three-dimensional (3-D) simulation of a complete transit-time flowmeter is performed for the first time. The obtained simulation results are in good agreement with measurements both at zero flow and under flow conditions. PMID:17375833
Hybrid finite volume/ finite element method for radiative heat transfer in graded index media
NASA Astrophysics Data System (ADS)
Zhang, L.; Zhao, J. M.; Liu, L. H.; Wang, S. Y.
2012-09-01
The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89-101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.
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.
Automatic finite element generators
NASA Technical Reports Server (NTRS)
Wang, P. S.
1984-01-01
The design and implementation of a software system for generating finite elements and related computations are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and element stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions are discussed. Automatic FORTRAN code generation is described with emphasis on improving the efficiency of the resultant code.
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...
Application of equivalent elastic methods in three-dimensional finite element structural analysis
Jones, D.P.; Gordon, J.L.; Hutula, D.N.; Holliday, J.E.; Jandrasits, W.G.
1998-02-01
This paper describes use of equivalent solid (EQS) modeling to obtain efficient solutions to perforated material problems using three-dimensional finite element analysis (3D-FEA) programs. It is shown that the accuracy of EQS methods in 3D-FEA depends on providing sufficient equivalent elastic properties to allow the EQS material to respond according to the elastic symmetry of the pattern. Peak stresses and ligament stresses are calculated from the EQS stresses by an appropriate 3D-FEA submodel approach. The method is demonstrated on the problem of a transversely pressurized simply supported plate with a central divider lane separating two perforated regions with circular penetrations arranged in a square pattern. A 3D-FEA solution for a model that incorporates each penetration explicitly is used for comparison with results from an EQS solution for the plate. Results for deflection and stresses from the EQS solution are within 3% of results from the explicit 3D-FE model. A solution to the sample problem is also provided using the procedures in the ASME B and PV Code. The ASME B and PV Code formulas for plate deflection were shown to overestimate the stiffening effects of the divider lane and the outer stiffening ring.
Finite element method-simulation of the human lens during accommodation
NASA Astrophysics Data System (ADS)
Breitenfeld, P.; Ripken, T.; Lubatschowski, H.
2005-08-01
A finite-element-method model with ANSYS 8.0 of a 29 year old human lens during accommodation will be presented. The required data, to draw and calculate a two dimensional, axis-symmetric model of the human lens is inherited from various sources. Furthermore the analysis premises all lens materials to be linear elastic and allows large displacements. A first analysis of a possible method for the treatment of presbyopia by fs-laser induced microcuts is accomplished. Therefore a mechanical analysis of an untreated and a treated lens are compared. As a result an improvement of the flexibility of the lens tissue is found and as its consequence a change of the lens' radii of curvature is established. After a suitable processing of the output data a linear Gaussian ray trace is performed and a minor change in the optical power between the untreated and treaded human lens is perceived. By calculation of the discrete optical power of the anterior and posterior surface on the one hand and the overall optical power on the other hand an interpretation of the effectiveness resulting from the treatment is offered. It is ascertained that the change in optical power of the anterior lens surface is increased while the optical power of the posterior lens surface is decreased, almost compensating each other. A possible explanation for this phenomenon is given and a suggestion of how to increase the effectiveness of the treatment is discussed.
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
Possibilities of the particle finite element method for fluid-soil-structure interaction problems
NASA Astrophysics Data System (ADS)
Oñate, Eugenio; Celigueta, Miguel Angel; Idelsohn, Sergio R.; Salazar, Fernando; Suárez, Benjamín
2011-09-01
We present some developments in the particle finite element method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the later including soil/rock and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The stabilization for dealing with an incompressibility continuum is introduced via the finite calculus method. An incremental iterative scheme for the solution of the non linear transient coupled FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid-solid and solid-solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of a river bed adjacent to a bridge foundation, the stability of breakwaters and constructions sea waves and the study of landslides.
Strong tangential discontinuity modeling of shear bands using the extended finite element method
NASA Astrophysics Data System (ADS)
Daneshyar, Alireza; Mohammadi, Soheil
2013-11-01
A method is developed for modeling of shear band with strong tangential discontinuity by means of cohesive surfaces within the extended finite element method (XFEM). A rate-independent non-associated plasticity model is incorporated along the strong discontinuity to consider the highly localized regions. Once the localization is occurred, tangential enrichment degrees of freedom are added to the localized elements, and the discontinuity is captured regardless of mesh resolution and alignment. By introducing the tangential enrichment function, the discontinuity is only imposed in the tangential direction, while the continuity across the shear band is automatically fulfilled. Adopting bilinear quadrilateral elements within the context of XFEM allows for the plastic deformation of shear band to be obtained with quadratic distribution within an enriched element. Since the strong discontinuity approach is employed, the singularity of strain field at the position of displacement jump is attained through a Dirac delta distribution. By means of this singularity, the cohesive shear traction is derived for the J2 plasticity model and is applied onto the band interfaces in order to reproduce the dissipative mechanism of the band. Several numerical examples are analyzed to assess the accuracy and robustness of the proposed approach.
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.
Free vibration analysis of a cracked beam by finite element method
NASA Astrophysics Data System (ADS)
Zheng, D. Y.; Kessissoglou, N. J.
2004-06-01
In this paper, the natural frequencies and mode shapes of a cracked beam are obtained using the finite element method. An 'overall additional flexibility matrix', instead of the 'local additional flexibility matrix', is added to the flexibility matrix of the corresponding intact beam element to obtain the total flexibility matrix, and therefore the stiffness matrix. Compared with analytical results, the new stiffness matrix obtained using the overall additional flexibility matrix can give more accurate natural frequencies than those resulted from using the local additional flexibility matrix. All the elements in the overall additional flexibility matrix are computed by 128-point (1D) or (128×128)-point (2D) Gauss quadrature, and then further best fitted using the least-squares method. The explicit form best-fitted formulas agree very well with the numerical integration results, and are very convenient for use and valuable for further reference. In addition, the authors constructed a shape function that can perfectly satisfy the local flexibility conditions at the crack locations, which can give more accurate vibration modes.
Schmidt, Sebastian; Hudde, Herbert
2009-06-01
Acoustic impedances measured at the entrance of the ear canal provide information on both the ear canal geometry and the terminating impedance at the eardrum, in principle. However, practical experience reveals that measured results in the audio frequency range up to 20 kHz are frequently not very accurate. Measurement methods successfully tested in artificial tubes with varying area functions often fail when applied to real ear canals. The origin of these errors is investigated in this paper. To avoid mixing of systematical and other errors, no real measurements are performed. Instead finite element simulations focusing on the coupling between a connecting tube and the ear canal are regarded without simulating a particular measuring method in detail. It turns out that realistic coupling between the connecting tube and the ear canal causes characteristic shifts of the frequencies of measured pressure minima and maxima. The errors in minima mainly depend on the extent of the area discontinuity arising at the interface; the errors in maxima are determined by the alignment of the tube with respect to the ear canal. In summary, impedance measurements using coupling tubes appear questionable beyond 3 kHz. PMID:19507964
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. PMID:23113651
Use of the Vector Finite Element Method for the Solution of Electromagnetic Problems
NASA Astrophysics Data System (ADS)
Polycarpou, A. C.
2010-11-01
The vector finite element method (VFEM) is formulated for the time-harmonic Maxwell's equations to model microwave integrated circuits and electronic packages at high frequencies. A number of computational challenges often appear during the formulation of these problems ranging from proper excitation of the input ports and reflection-free truncation of the unbounded infinite domain to accurate modeling of material interfaces and anisotropies. To deal with the challenge of proper excitation/termination of the ports, a generalized eigenvalue problem is formulated at each of the ports in order to obtain the dispersive propagation characteristics and governing modes of the 2-D structure; these modal characteristics are subsequently used to properly excite and terminate the input and output ports of the 3-D structure under investigation. In the case where scattering is involved, the unbounded infinite domain is properly truncated using first-, second-, or even higher-order absorbing boundary conditions (ABCs), a perfectly matched layer (PML), or an exact radiation condition based on a boundary-integral (BI) method. Numerical results on a number of practical engineering applications illustrate the power and effectiveness of the VFEM in solving complex electromagnetic problems.
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
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.
A coupled/uncoupled deformation and fatigue damage algorithm utilizing the finite element method
Wilt, T.E.; Arnold, S.M.
1994-03-01
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Prévost, Jean H.; Sukumar, N.
2016-01-01
Faults are geological entities with thicknesses several orders of magnitude smaller than the grid blocks typically used to discretize reservoir and/or over-under-burden geological formations. Introducing faults in a complex reservoir and/or geomechanical mesh therefore poses significant meshing difficulties. In this paper, we consider the strong-coupling of solid displacement and fluid pressure in a three-dimensional poro-mechanical (reservoir-geomechanical) model. We introduce faults in the mesh without meshing them explicitly, by using the extended finite element method (X-FEM) in which the nodes whose basis function support intersects the fault are enriched within the framework of partition of unity. For the geomechanics, the fault is treated as an internal displacement discontinuity that allows slipping to occur using a Mohr-Coulomb type criterion. For the reservoir, the fault is either an internal fluid flow conduit that allows fluid flow in the fault as well as to enter/leave the fault or is a barrier to flow (sealing fault). For internal fluid flow conduits, the continuous fluid pressure approximation admits a discontinuity in its normal derivative across the fault, whereas for an impermeable fault, the pressure approximation is discontinuous across the fault. Equal-order displacement and pressure approximations are used. Two- and three-dimensional benchmark computations are presented to verify the accuracy of the approach, and simulations are presented that reveal the influence of the rate of loading on the activation of faults.
Radiative transfer in the atmosphere-ocean system: the finite-element method.
Bulgarelli, B; Kisselev, V B; Roberti, L
1999-03-20
The finite-element method has been applied to solving the radiative-transfer equation in a layered medium with a change in the refractive index, such as the atmosphere-ocean system. The physical processes that are included in the algorithm are multiple scattering, bottom-boundary bidirectional reflectivity, and refraction and reflection at the interface between the media with different refractive properties. The incident radiation is a parallel flux on the top boundary that is characteristic of illumination of the atmosphere by the Sun in the UV, visible, and near-IR regions of the electromagnetic spectrum. The necessary changes, compared with the case of a uniformly refracting layered medium, are described. An energy-conservation test has been performed on the model. The algorithm has also been validated through comparison with an equivalent backward Monte Carlo code and with data taken from the literature, and optimal agreement was shown. The results show that the model allows energy conservation independently of the adopted phase function, the number of grid points, and the relative refractive index. The radiative-transfer model can be applied to any other layered system with a change in the refractive index. The fortran code for this algorithm is documented and is available for applications. PMID:18305777
Finite element method for a class of viscoelastic flows in deforming domains applied to jet breakup
NASA Astrophysics Data System (ADS)
Keunings, R.
1984-05-01
A numerical method for solving a class of transient viscoelastic flows in domains with free boundaries which is based on a Galerkin finite element technique combined with a predictor/corrector scheme that allows for the prediction of stress field, velocity field and flow domain as a function of time is presented. The numerical procedure is applied to the analysis of surface tension driven breakup of liquid jets. The nonlinear growth of a periodic disturbance imposed on an infinitely long jet and leading to breakup was studied. It is predicted that in the Newtonian case the birth of satellite drops when inertia forces are present. It is shown that elasticity accelerates the breakup process at short times for an Oldroyd fluid which is consistent with linear stability analyses. This tendency however, is reversed at later times when a pattern of drops connected by stable filaments is obtained. The stabilizing effect of elastic forces, known experimentally for any years, and are predicted shown it is that the breakup mechanism of a viscoelastic jet cannot be described by linearized dynamics.