Adaptive finite element strategies for shell structures
Stanley, G.; Levit, I.; Stehlin, B.; Hurlbut, B.
1992-01-01
The present paper extends existing finite element adaptive refinement (AR) techniques to shell structures, which have heretofore been neglected in the AR literature. Specific challenges in applying AR to shell structures include: (1) physical discontinuities (e.g., stiffener intersections); (2) boundary layers; (3) sensitivity to geometric imperfections; (4) the sensitivity of most shell elements to mesh distortion, constraint definition and/or thinness; and (5) intrinsic geometric nonlinearity. All of these challenges but (5) are addressed here.
Adaptive finite element methods for differential equations
Bangerth, Wolfgang
2003-01-01
These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...
Adaptive finite element method for shape optimization
Morin, Pedro
2012-01-16
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Adaptive Finite Element Approximations for Kohn-Sham Models
Chen, Huajie; Dai, Xiaoying; Gong, Xingao; He, Lianhua; Zhou, Aihui
2013-01-01
The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element approximations for the Kohn-Sham model. Based on the residual type a posteriori error estimators proposed in this paper, we introduce an adaptive finite element algorithm with a quite general marking strategy and prove the convergence of the adaptive finite el...
An adaptive finite element strategy for complex flow problems
Oden, J. T.; Strouboulis, T.; Devloo, PH.; Spradley, L. W.; Price, J.
1987-01-01
Adaptive finite element methods for steady and unsteady flow problems in two-dimensional domains are described. Details of a data management scheme are given that provide for the rapid implementation of various CFD algorithms on changing unstructured meshes. The results of several numerical experiments on subsonic and supersonic flow problems are discussed.
An adaptive finite element approach for neutron transport equation
Highlights: → Using uniform grid solution gives high local residuals errors. → Element refinement in the region where the flux gradient is large improves accuracy of results. → It is not necessary to use high density element throughout problem domain. → The method provides great geometrical flexibility. → Implementation of different density of elements lowers computational cost. - Abstract: In this paper, we develop an adaptive element refinement strategy that progressively refines the elements in appropriate regions of domain to solve even-parity Boltzmann transport equation. A posteriori error approach has been used for checking the approximation solutions for various sizes of elements. The local balance of neutrons in elements is utilized as an error assessment. To implement the adaptive approach a new neutron transport code FEMPT, finite element modeling of particle transport, for arbitrary geometry has been developed. This code is based on even-parity spherical harmonics and finite element method. A variational formulation is implemented for the even-parity neutron transport equation for the general case of anisotropic scattering and sources. High order spherical harmonic functions expansion for angle and finite element method in space is used as trial function. This code can be used to solve the multi-group neutron transport equation in highly complex X-Y geometries with arbitrary boundary condition. Due to powerful element generator tools of FEMPT, the description of desired and complicated 2D geometry becomes quite convenient. The numerical results show that the locally adaptive element refinement approach enhances the accuracy of solution in comparison with uniform meshing approach.
Adaptive Finite Element Methods for Continuum Damage Modeling
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.
Parallel, adaptive finite element methods for conservation laws
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 Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea
2013-01-01
Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.
On Round-off Error for Adaptive Finite Element Methods
Alvarez-Aramberri, J.
2012-06-02
Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called ‘radical meshes’. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.
An adaptive finite element procedure for crack propagation analysis
ALSHOAIBI Abdulnaser M.; HADI M.S.A.; ARIFFIN A.K.
2007-01-01
This paper presents the adaptive mesh finite element estimation method for analyzing 2D linear elastic fracture problems. The mesh is generated by the advancing front method and the norm stress error is taken as a posteriori error estimator for the h-type adaptive refinement. The stress intensity factors are estimated by a displacement extrapolation technique. The near crack tip displacements used are obtained from specific nodes of natural six-noded quarter-point elements which are generated around the crack tip defined by the user. The crack growth and its direction are determined by the calculated stress intensity factors.The maximum circumference theory is used for the latter. In evaluating the accuracy of the estimated stress intensity factors, four cases are tested consisting of compact tension specimen, three-point bending specimen, central cracked plate and double edge notched plate. These were carried out and compared to the results from other studies. The crack trajectories of these specimen tests are also illustrated.
Essentials of finite element modeling and adaptive refinement
Dow, John O
2012-01-01
Finite Element Analysis is a very popular, computer-based tool that uses a complex system of points called nodes to make a grid called a ""mesh. "" The mesh contains the material and structural properties that define how the structure will react to certain loading conditions, allowing virtual testing and analysis of stresses or changes applied to the material or component design. This groundbreaking text extends the usefulness of finite element analysis by helping both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method while at the same t
Adaptive grid finite element model of the tokamak scrapeoff layer
Kuprat, A.P.; Glasser, A.H. [Los Alamos National Lab., NM (United States)
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.
Adaptive finite element methods for two-dimensional problems in computational fracture mechanics
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.
ADAPTIVE FINITE ELEMENT METHOD FOR HIGH-SPEED FLOW-STRUCTURE INTERACTION
Wiroj LIMTRAKARN; Pramote DECHAUMPHAI
2004-01-01
An adaptive finite element method for high-speed flow-structure interaction is presented. The cell-centered finite element method is combined with an adaptive meshing technique to solve the Navier-Stokes equations for high-speed compressible flow behavior. The energy equation and the quasi-static structural equations for aerodynamically heated structures are solved by applying the Galerkin finite element method. The finite element formulation and computational procedure are described. Interactions between the high-speed flow, structural heat transfer, and deformation are studied by two applications of Mach 10 flow over an inclined plate, and Mach 4 flow in a channel.
Contaminated groundwater transport using an adaptive 3-D finite element model
A three-dimensional, h-adapting finite element model has been developed to calculate subsurface transport and dispersion of contaminant. The model is based on a hybrid finite element scheme previously developed for two-dimensional groundwater and species transport
Si YUAN; Yan DU; Qin-yan XING; Kang-sheng YE
2014-01-01
The element energy projection (EEP) method for computation of super-convergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton’s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re-sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation (ODE) of second-order as the model problem, this paper describes the related fundamental idea, the imple-mentation strategy, and the computational algorithm. Representative numerical exam-ples are given to show the eﬃciency, stability, versatility, and reliability of the proposed approach.
Convergence of a simple adaptive finite element method for optimal control
Becker, Roland; Karim, Hafida; Mao, Shipeng
2008-01-01
We prove convergence and optimal complexity of an adaptive finite element algorithm for a model problem of optimal control. Following previous work, our algorithm is based on an adaptive marking strategy which compares a simple edge estimator with an oscillation term in each step of the algorithm in order to adapt the marking of cells.
An adaptative finite element method for turbulent flow simulations
After outlining the space and time discretization methods used in the N3S thermal hydraulic code developed at EDF/NHL, we describe the possibilities of the peripheral version, the Adaptative Mesh, which comprises two separate parts: the error indicator computation and the development of a module subdividing elements usable by the solid dynamics code ASTER and the electromagnetism code TRIFOU also developed by R and DD. The error indicators implemented in N3S are described. They consist of a projection indicator quantifying the space error in laminar or turbulent flow calculations and a Navier-Stokes residue indicator calculated on each element. The method for subdivision of triangles into four sub-triangles and tetrahedra into eight sub-tetrahedra is then presented with its advantages and drawbacks. It is illustrated by examples showing the efficiency of the module. The last concerns the 2 D case of flow behind a backward-facing step. (authors). 9 refs., 5 figs., 1 tab
A Schroedinger eigenvalue problem is solved for the 2D quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, (i) an application of the Kelly error estimator, and (ii) a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver. (general)
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.
Adaptive implicit-explicit finite element algorithms for fluid mechanics problems
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.
Adaptive Finite Element Methods for Computing Nonstationary Incompressible Flows
Schmich, Michael
2009-01-01
Subject of this work is the development of numerical methods for efficiently solving nonstationary incompressible flow problems. In contrast to stationary flow problems, here errors due to discretization in time and space occur. Furthermore, especially three-dimensional simulations lead to huge computational costs. Thus, adaptive discretization methods have to be used in order to reduce the computational costs while still maintaining a certain accuracy. The main focus of this thesis is the de...
Algorithms and data structures for massively parallel generic adaptive finite element codes
Bangerth, Wolfgang
2011-12-01
Today\\'s largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions of unknowns. However, the complexity of scaling to such large machines and problem sizes has so far prevented the emergence of generic software libraries that support such computations, although these would lower the threshold of entry and enable many more applications to benefit from large-scale computing. We are concerned with providing this functionality for mesh-adaptive finite element computations. We assume the existence of an "oracle" that implements the generation and modification of an adaptive mesh distributed across many processors, and that responds to queries about its structure. Based on querying the oracle, we develop scalable algorithms and data structures for generic finite element methods. Specifically, we consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing. Our algorithms remove the bottlenecks that typically limit large-scale adaptive finite element analyses. We demonstrate scalability of complete finite element workflows on up to 16,384 processors. An implementation of the proposed algorithms, based on the open source software p4est as mesh oracle, is provided under an open source license through the widely used deal.II finite element software library. © 2011 ACM 0098-3500/2011/12-ART10 $10.00.
An adaptive hybrid stress transition quadrilateral finite element method for linear elasticity
Huang, Feiteng; Xie, Xiaoping; Zhang, Chen-Song
2014-01-01
In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid stress quadrilateral elements with 5 to 7 nodes. In particular, we derive a priori error estimation for the 5-node transition hybrid stress element to show that it is free from Poisson-locking, in the sense that the error bound in the a priori estimate is i...
Kou, Jisheng
2014-01-01
The gradient theory for the surface tension of simple fluids and mixtures is rigorously analyzed based on mathematical theory. The finite element approximation of surface tension is developed and analyzed, and moreover, an adaptive finite element method based on a physical-based estimator is proposed and it can be coupled efficiently with Newton\\'s method as well. The numerical tests are carried out both to verify the proposed theory and to demonstrate the efficiency of the proposed method. © 2013 Elsevier B.V. All rights reserved.
ADAPTIVE FINITE ELEMENT METHOD FOR ANALYSIS OF POLLUTANT DISPERSION IN SHALLOW WATER
Somboon Otarawanna; Pramote Dechaumphai
2005-01-01
A finite element method for analysis of pollutant dispersion in shallow water is presented. The analysis is divided into two parts: ( 1 ) computation of the velocity flow field and water surface elevation, and (2) computation of the pollutant concentration field from the dispersion model. The method was combined with an adaptive meshing technique to increase the solution accuracy ,as well as to reduce the computational time and computer memory. The finite element formulation and the computer programs were validated by several examples that have known solutions. In addition, the capability of the combined method was demonstrated by analyzing pollutant dispersion in Chao Phraya River near the gulf of Thailand.
Adaptive finite element strategies for solution of two dimensional elasticity problems
Vasiliauskienė, Lina
2006-01-01
The advent of modern computer technologies provided a powerful tool in numerical simulations. One of the most frequently used method for the discretization of the physical domain is Finite element Method (FEM). One of the main problems in a finite element analysis is the adequacy of the finite element mesh. Since the quality of the finite element solution directly depends on the quality of meshes, the additional process to improve the quality of meshes is necessary for reliable finite element...
Herath, Manudha T; Natarajan, Sundararajan; Prusty, B Gangadhara; John, Nigel St
2013-01-01
An optimization scheme using the Cell-based Smoothed Finite Element Method (CS-FEM) combined with a Genetic Algorithm (GA) framework is proposed in this paper to design shape adaptive laminated composite marine propellers. The proposed scheme utilise the bend-twist coupling characteristics of the composites to achieve the required performance. An iterative procedure to evaluate the unloaded shape of the propeller blade is proposed, confirming the manufacturing requirements at the initial stag...
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.
Using Multi-threading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes
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.
Finite element model for linear-elastic mixed mode loading using adaptive mesh strategy
无
2008-01-01
An adaptive mesh finite element model has been developed to predict the crack propagation direction as well as to calculate the stress intensity factors (SIFs), under linear-elastic assumption for mixed mode loading application. The finite element mesh is generated using the advancing front method. In order to suit the requirements of the fracture analysis, the generation of the background mesh and the construction of singular elements have been added to the developed program. The adaptive remeshing process is carried out based on the posteriori stress error norm scheme to obtain an optimal mesh. Previous works of the authors have proposed techniques for adaptive mesh generation of 2D cracked models. Facilitated by the singular elements, the displacement extrapolation technique is employed to calculate the SIF. The fracture is modeled by the splitting node approach and the trajectory follows the successive linear extensions of each crack increment. The SIFs values for two different case studies were estimated and validated by direct comparisons with other researchers work.
Adaptive finite element simulation of flow and transport applications on parallel computers
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
Zanotti, Olindo; Dumbser, Michael; Hidalgo, Arturo
2015-01-01
In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space-time adaptive Cartesian meshes (AMR) for hyperbolic conservation laws in multiple space dimensions, using a high order \\aposteriori sub-cell ADER-WENO finite volume \\emph{limiter}. Notoriously, the original DG method produces strong oscillations in the presence of discontinuous solutions and several types of limiters have been introduced over the years to cope with this problem. Following the innovative idea recently proposed in \\cite{Dumbser2014}, the discrete solution within the troubled cells is \\textit{recomputed} by scattering the DG polynomial at the previous time step onto a suitable number of sub-cells along each direction. Relying on the robustness of classical finite volume WENO schemes, the sub-cell averages are recomputed and then gathered back into the DG polynomials over the main grid. In this paper this approach is implemented for the first time within a space-time adaptive ...
Adaptive finite element solution for the heat conduction with a moving heat source
We have demonstrated that some of the parabolic type problems encountered in such branches of engineering as heat conductions with a moving source can be analyzed successfully by means of the finite element method. Adapted mesh generation technique is implemented for solving heat transfer involving a moving heat source so that small elements can be used in areas of large time rates of change of temperature. It has been adjusted to steep gradients of the solution with respect to the relatively large time interval. A program has been developed for the case of two-dimensional triangular elements, and algorithm is possessed a number of usual advantages that made solutions very divergent. Numerical results have shown that the adaptive gridding scheme is effective in localizing oscillations due to the sharp gradients or discontinuities in the solution. Furthermore, the numerical results near the region of moving source from the present method are under and over estimated the solution of traditional finite element method by almost 3% respectively. The several examples are given to illustrate the validity and practicality of the method. The results of various sample solutions are evaluated and discussed
Dyja, Robert; van der Zee, Kristoffer G
2016-01-01
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. This methodology enables, in principle, simultaneous adaptivity in both space and time (within the block) domains. We explore this basic concept in the context of a variety of time-steppers including $\\Theta$-schemes and Backward Differentiate Formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear and semi-linear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial adaptivity. Final...
An h-adaptive finite element method for turbulent heat transfer
Carriington, David B [Los Alamos National Laboratory
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.
2.5D induced polarization forward modeling using the adaptive finite-element method
Ye Yi-Xin; Li Yu-Guo; Deng Ju-Zhi; Li Ze-Lin
2014-01-01
The conventional finite-element (FE) method often uses a structured mesh, which is designed according to the user’s experience, and it is not sufficiently accurate and flexible to accommodate complex structures such as dipping interfaces and rough topography. We present an adaptive FE method for 2.5D forward modeling of induced polarization (IP). In the presented method, an unstructured triangulation mesh that allows for local mesh refinement and flexible description of arbitrary model geometries is used. Furthermore, the mesh refinement process is guided by dual error estimate weighting to bias the refinement towards elements that affect the solution at the receiver locations. After the final mesh is generated, the Jacobian matrix is used to obtain the IP response on 2D structure models. We validate the adaptive FE algorithm using a vertical contact model. The validation shows that the elements near the receivers are highly refined and the average relative error of the potentials converges to 0.4%and 1.2%for the IP response. This suggests that the numerical solution of the adaptive FE algorithm converges to an accurate solution with the refined mesh. Finally, the accuracy and flexibility of the adaptive FE procedure are also validated using more complex models.
Advanced finite element technologies
Wriggers, Peter
2016-01-01
The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.
Development of an adaptive hp-version finite element method for computational optimal control
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.
Mohan, Ram V.; Tamma, Kumar K.
1993-01-01
An adaptive time stepping strategy for transient thermal analysis of engineering systems is described which computes the time step based on the local truncation error with a good global error control and obtains optimal time steps to be used during the analysis. Combined mesh partitionings involving FEM/FVM meshes based on physical situations to obtain numerically improved physical representations are also proposed. Numerical test cases are described and comparative pros and cons are identified for practical situations.
DISCONTINUITY-CAPTURING FINITE ELEMENT COMPUTATION OF UNSTEADY FLOW WITH ADAPTIVE UNSTRUCTURED MESH
DONG Genjin; LU Xiyun; ZHUANG Lixian
2004-01-01
A discontinuity-capturing scheme of finite element method (FEM) is proposed. The unstructured-grid technique combined with a new type of adaptive mesh approach is developed for both compressible and incompressible unsteady flows, which exhibits the capability of capturing the shock waves and/or thin shear layers accurately in an unsteady viscous flow at high Reynolds number.In particular, a new testing variable, i.e., the disturbed kinetic energy E, is suggested and used in the adaptive mesh computation, which is universally applicable to the capturing of both shock waves and shear layers in the inviscid flow and viscous flow at high Reynolds number. Based on several calculated examples, this approach has been proved to be effective and efficient for the calculations of compressible and incompressible flows.
无
2011-01-01
The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdomain,all fields of state variables including displacement,stress,velocity and acceleration are semi-analytical,and the kinetic energy,strain energy and energy error are all integrated semi-analytically.These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains.Because only a small number of subdomains are subdivided,mesh refinement is very simple and efficient,and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate.Two 2D examples with stress wave propagation were modelled.The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses,using only a fraction of degrees of freedom required by adaptive finite element method.
ERROR REDUCTION IN ADAPTIVE FINITE ELEMENT APPROXIMATIONS OF ELLIPTIC OBSTACLE PROBLEMS
Dietrich Braess; Carsten Carstensen; Ronald H.W. Hoppe
2009-01-01
We consider an adaptive finite element method (AFEM) for obstacle problems associated with linear second order elliptic boundary value problems and prove a reduction in the energy norm of the discretization error which leads to R-linear convergence. This result is shown to hold up to a consistency error due to the extension of the discrete multipliers (point functionals) to H-1 and a possible mismatch between the continuous and discrete coincidence and noncoincidence sets. The AFEM is based on a residual-type error estimator consisting of element and edge residuals. The a posteriori error analysis reveals that the significant difference to the unconstrained case lies in the fact that these residuals only have to be taken into account within the discrete noncoincidence set. The proof of the error reduction property uses the reliability and the discrete local efficiency of the estimator as well as a perturbed Galerkin orthogonality. Numerical results are given illustrating the performance of the AFEM.
Moving finite elements: A continuously adaptive method for computational fluid dynamics
Moving Finite Elements (MFE), a recently developed method for computational fluid dynamics, promises major advances in the ability of computers to model the complex behavior of liquids, gases, and plasmas. Applications of computational fluid dynamics occur in a wide range of scientifically and technologically important fields. Examples include meteorology, oceanography, global climate modeling, magnetic and inertial fusion energy research, semiconductor fabrication, biophysics, automobile and aircraft design, industrial fluid processing, chemical engineering, and combustion research. The improvements made possible by the new method could thus have substantial economic impact. Moving Finite Elements is a moving node adaptive grid method which has a tendency to pack the grid finely in regions where it is most needed at each time and to leave it coarse elsewhere. It does so in a manner which is simple and automatic, and does not require a large amount of human ingenuity to apply it to each particular problem. At the same time, it often allows the time step to be large enough to advance a moving shock by many shock thicknesses in a single time step, moving the grid smoothly with the solution and minimizing the number of time steps required for the whole problem. For 2D problems (two spatial variables) the grid is composed of irregularly shaped and irregularly connected triangles which are very flexible in their ability to adapt to the evolving solution. While other adaptive grid methods have been developed which share some of these desirable properties, this is the only method which combines them all. In many cases, the method can save orders of magnitude of computing time, equivalent to several generations of advancing computer hardware
Jingjing Yu
2013-01-01
Full Text Available 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.
Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
Cotter, Simon L.
2013-01-01
Stochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with nonnegligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods. © 2013 Society for Industrial and Applied Mathematics.
Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation
Holst, Michael; Yu, Zeyun; Zhou, Yongcheng; Zhu, Yunrong
2010-01-01
We develop an efficient and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the regularization technique of Chen, Holst, and Xu; this technique made possible the first a priori pointwise estimates and the first complete solution and approximation theory for the Poisson-Boltzmann equation. It also made possible the first provably convergent discretization of the PBE, and allowed for the development of a provably convergent AFEM for the PBE. However, in practice the regularization turns out to be numerically ill-conditioned. In this article, we examine a second regularization, and establish a number of basic results to ensure that the new approach produces the same mathematical advantages of the original regularization, without the ill-conditioning property. We then design an AFEM scheme based on the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This res...
A parallel direct solver for the self-adaptive hp Finite Element Method
Paszyński, Maciej R.
2010-03-01
In this paper we present a new parallel multi-frontal direct solver, dedicated for the hp Finite Element Method (hp-FEM). The self-adaptive hp-FEM generates in a fully automatic mode, a sequence of hp-meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs an initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows us to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p-FEM, with finite elements of various sizes and polynomial orders of approximation varying from p = 1 to p = 9. From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizations over the longest path, coming from the root of the elimination tree down to the deepest leaf. © 2009 Elsevier Inc. All rights reserved.
Adaptive Finite-element Analysis of Plastic Deformation of Plates under Projectile Impact
T. Prakash
2003-01-01
Full Text Available This paper deals with the finite-element analysis of plastic deformation of plates during normal impact of projectile on plates, The finite element method implemented here is based on the flow formulation of plasticity. During projectile impact the geometrical configuration of domain is progressively altered that generally causes distortion of mesh. It affects the accuracy of finite-element solution, Hence, a posteriori error estimation for the computed finite-element solution has been incorporated to capture the zones of high stress and strain gradients. The h-refinement of the mesh is carried out over such domain to limit the solution error, Two projectile impact problems on a circular aluminium plate-one by a blunt-end projectile and another by a hemi-spherical-headed projectile-are analysed to illustrate the proposed method.
Wind Forecasting Based on the HARMONIE Model and Adaptive Finite Elements
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/.
As a molecular imaging technique, bioluminescence tomography (BLT) with its highly sensitive detection and facile operation can significantly reveal molecular and cellular information in vivo at the whole-body small animal level. However, because of complex photon transportation in biological tissue and boundary detection data with high noise, bioluminescent sources in deeper positions generally cannot be localized. In our previous work, we used achromatic or monochromatic measurements and an a priori permissible source region strategy to develop a multilevel adaptive finite-element algorithm. In this paper, we propose a spectrally solved tomographic algorithm with a posteriori permissible source region selection. Multispectral measurements, and anatomical and optical information first deal with the nonuniqueness of BLT and constrain the possible solution of source reconstruction. The use of adaptive mesh refinement and permissible source region based on a posteriori measures not only avoids the dimension disaster arising from the multispectral measured data but also reduces the ill-posedness of BLT and therefore improves the reconstruction quality. Reconsideration of the optimization method and related modifications further enhance reconstruction robustness and efficiency. We also incorporate into the method some improvements for reducing computational burdens. Finally, using a whole-body virtual mouse phantom, we demonstrate the capability of the proposed BLT algorithm to reconstruct accurately bioluminescent sources in deeper positions. In terms of optical property errors and two sources of discernment in deeper positions, this BLT algorithm represents the unique predominance for BLT reconstruction
S. D. Parkinson
2014-09-01
Full Text Available High-resolution direct numerical simulations (DNSs are an important tool for the detailed analysis of turbidity current dynamics. Models that resolve the vertical structure and turbulence of the flow are typically based upon the Navier–Stokes equations. Two-dimensional simulations are known to produce unrealistic cohesive vortices that are not representative of the real three-dimensional physics. The effect of this phenomena is particularly apparent in the later stages of flow propagation. The ideal solution to this problem is to run the simulation in three dimensions but this is computationally expensive. This paper presents a novel finite-element (FE DNS turbidity current model that has been built within Fluidity, an open source, general purpose, computational fluid dynamics code. The model is validated through re-creation of a lock release density current at a Grashof number of 5 × 106 in two and three dimensions. Validation of the model considers the flow energy budget, sedimentation rate, head speed, wall normal velocity profiles and the final deposit. Conservation of energy in particular is found to be a good metric for measuring model performance in capturing the range of dynamics on a range of meshes. FE models scale well over many thousands of processors and do not impose restrictions on domain shape, but they are computationally expensive. The use of adaptive mesh optimisation is shown to reduce the required element count by approximately two orders of magnitude in comparison with fixed, uniform mesh simulations. This leads to a substantial reduction in computational cost. The computational savings and flexibility afforded by adaptivity along with the flexibility of FE methods make this model well suited to simulating turbidity currents in complex domains.
Higher-order adaptive finite-element methods for orbital-free density functional theory
In the present work, we study various numerical aspects of higher-order finite-element discretizations of the non-linear saddle-point formulation of orbital-free density-functional theory. We first investigate the robustness of viable solution schemes by analyzing the solvability conditions of the discrete problem. We find that a staggered solution procedure where the potential fields are computed consistently for every trial electron-density is a robust solution procedure for higher-order finite-element discretizations. We next study the convergence properties of higher-order finite-element discretizations of orbital-free density functional theory by considering benchmark problems that include calculations involving both pseudopotential as well as Coulomb singular potential fields. Our numerical studies suggest close to optimal rates of convergence on all benchmark problems for various orders of finite-element approximations considered in the present study. We finally investigate the computational efficiency afforded by various higher-order finite-element discretizations, which constitutes the main aspect of the present work, by measuring the CPU time for the solution of discrete equations on benchmark problems that include large Aluminum clusters. In these studies, we use mesh coarse-graining rates that are derived from error estimates and an a priori knowledge of the asymptotic solution of the far-field electronic fields. Our studies reveal a significant 100–1000 fold computational savings afforded by the use of higher-order finite-element discretization, alongside providing the desired chemical accuracy. We consider this study as a step towards developing a robust and computationally efficient discretization of electronic structure calculations using the finite-element basis.
Node-based finite element method for large-scale adaptive fluid analysis in parallel environments
In this paper, a FEM-based (finite element method) mesh free method with a probabilistic node generation technique is presented. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed fluently in parallel in terms of nodes. Local finite element mesh is generated robustly around each node, even for harsh boundary shapes such as cracks. The algorithm and the data structure of finite element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. In addition, the node-based finite element method is accompanied by a probabilistic node generation technique, which generates good-natured points for nodes of finite element mesh. Furthermore, the probabilistic node generation technique can be performed in parallel environments. As a numerical example of the proposed method, we perform a compressible flow simulation containing strong shocks. Numerical simulations with frequent mesh refinement, which are required for such kind of analysis, can effectively be performed on parallel processors by using the proposed method. (authors)
Stresses in faulted tunnel models by photoelasticity and adaptive finite element
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 ampersand 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
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.
S. D. Parkinson
2014-05-01
Full Text Available 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.
3D adaptive finite element method for a phase field model for the moving contact line problems
Shi, Yi
2013-08-01
In this paper, we propose an adaptive finite element method for simulating the moving contact line problems in three dimensions. The model that we used is the coupled Cahn-Hilliard Navier-Stokes equations with the generalized Navier boundary condition(GNBC) proposed in [18]. In our algorithm, to improve the efficiency of the simulation, we use the residual type adaptive finite element algorithm. It is well known that the phase variable decays much faster away from the interface than the velocity variables. There- fore we use an adaptive strategy that will take into account of such difference. Numerical experiments show that our algorithm is both efficient and reliable. © 2013 American Institute of Mathematical Sciences.
A spatially adaptive grid-refinement approach has been investigated to solve the even-parity Boltzmann transport equation. A residual based a posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local particle balance has been considered as an error assessment criterion. To implement the adaptive approach, a computer program ADAFENT (adaptive finite elements for neutron transport) has been developed to solve the second order even-parity Boltzmann transport equation using K+ variational principle for slab geometry. The program has a core K+ module which employs Lagrange polynomials as spatial basis functions for the finite element formulation and Legendre polynomials for the directional dependence of the solution. The core module is called in by the adaptive grid generator to determine local gradients and residuals to explore the possibility of grid refinements in appropriate regions of the problem. The a posteriori error estimation scheme has been implemented in the outer grid refining iteration module. Numerical experiments indicate that local errors are large in regions where the flux gradients are large. A comparison of the spatially adaptive grid-refinement approach with that of uniform meshing approach for various benchmark cases confirms its superiority in greatly enhancing the accuracy of the solution without increasing the number of unknown coefficients. A reduction in the local errors of the order of 102 has been achieved using the new approach in some cases
Janssen, Bärbel
2011-01-01
A multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has optimal computational complexity. When applied to conforming finite element discretizations of elliptic problems and Maxwell equations, the method\\'s convergence rates are very close to those for the nonadaptive version. Furthermore, the smoothers remain efficient for high order finite elements. We discuss the implementation in a general finite element code using the example of the deal.II library. © 2011 Societ y for Industrial and Applied Mathematics.
Li, Xianping
2010-01-01
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numerical solution validates the discrete counterpart (DMP) of the maximum principle satisfied by the continuous solution. A well known mesh condition for the DMP satisfaction by the linear finite element solution of isotropic diffusion problems is the non-obtuse angle condition that requires the dihedral angles of mesh elements to be non-obtuse. In this paper, a generalization of the condition, the so-called anisotropic non-obtuse angle condition, is developed for the finite element solution of heterogeneous anisotropic diffusion problems. The new condition is essentially the same as the existing one except that the dihedral ...
Higher-order adaptive finite-element methods for orbital-free density functional theory
Motamarri, Phani; Iyer, Mrinal; Knap, Jaroslaw; Gavini, Vikram
2011-01-01
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable solution schemes by analyzing the solvability conditions of the discrete problem. We find that a staggered solution procedure where the potential fields are computed consistently for every trial electron-density is a robust solution procedure for higher-or...
Goal-Oriented Self-Adaptive hp Finite Element Simulation of 3D DC Borehole Resistivity Simulations
Calo, Victor M.
2011-05-14
In this paper we present a goal-oriented self-adaptive hp Finite Element Method (hp-FEM) with shared data structures and a parallel multi-frontal direct solver. The algorithm automatically generates (without any user interaction) a sequence of meshes delivering exponential convergence of a prescribed quantity of interest with respect to the number of degrees of freedom. The sequence of meshes is generated from a given initial mesh, by performing h (breaking elements into smaller elements), p (adjusting polynomial orders of approximation) or hp (both) refinements on the finite elements. The new parallel implementation utilizes a computational mesh shared between multiple processors. All computational algorithms, including automatic hp goal-oriented adaptivity and the solver work fully in parallel. We describe the parallel self-adaptive hp-FEM algorithm with shared computational domain, as well as its efficiency measurements. We apply the methodology described to the three-dimensional simulation of the borehole resistivity measurement of direct current through casing in the presence of invasion.
An efficient solution-adaptive implicit finite element CFD Navier-Stokes algorithm
A finite-element CFD aerodynamics algorithm is developed for the compressible Navier-Stokes and Euler equations. The derived companion conservation-law system yields a continuum stability mechanism statement which is appropriate for arbitrary discretizations. Boundary-condition specifications are thoroughly analyzed, with special consideration for mixed subsonic-supersonic outflow. Metric data handling is organized for consistent-order quadrature-rule replacement that leads to a robust and efficient procedure on absolutely arbitrary meshes. Essentially nonoscillatory solutions are uniformly attained for a wide range of transonic/supersonic inviscid and laminar viscous benchmark problems with shocks in two dimensions. 24 refs
Norapat Noilublao
2013-01-01
Full Text Available This paper proposes a novel integrated design strategy to accomplish simultaneous topology shape and sizing optimisation of a two-dimensional (2D truss. An optimisation problem is posed to find a structural topology, shape, and element sizes of the truss such that two objective functions, mass and compliance, are minimised. Design constraints include stress, buckling, and compliance. The procedure for an adaptive ground elements approach is proposed and its encoding/decoding process is detailed. Two sets of design variables defining truss layout, shape, and element sizes at the same time are applied. A number of multiobjective evolutionary algorithms (MOEAs are implemented to solve the design problem. Comparative performance based on a hypervolume indicator shows that multiobjective population-based incremental learning (PBIL is the best performer. Optimising three design variable types simultaneously is more efficient and effective.
Adaptive mesh refinement and automatic remeshing in crystal plasticity finite element simulations
In finite element simulations dedicated to the modelling of microstructure evolution, the mesh has to be fine enough to: (i) accurately describe the geometry of the constituents; (ii) capture local strain gradients stemming from the heterogeneity in material properties. In this paper, 3D polycrystalline aggregates are discretized into unstructured meshes and a level set framework is used to represent the grain boundaries. The crystal plasticity finite element method is used to simulate the plastic deformation of these aggregates. A mesh sensitivity analysis based on the deformation energy distribution shows that the predictions are, on average, more sensitive near grain boundaries. An anisotropic mesh refinement strategy based on the level set description is introduced and it is shown that it offers a good compromise between accuracy requirements on the one hand and computation time on the other hand. As the aggregates deform, mesh distortion inevitably occurs and ultimately causes the breakdown of the simulations. An automatic remeshing tool is used to periodically reconstruct the mesh and appropriate transfer of state variables is performed. It is shown that the diffusion related to data transfer is not significant. Finally, remeshing is performed repeatedly in a highly resolved 500 grains polycrystal subjected to about 90% thickness reduction in rolling. The predicted texture is compared with the experimental data and with the predictions of a standard Taylor model
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
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
2010-01-01
Finite element analysis is an engineering method for the numerical analysis of complex structures. This book provides a bird's eye view on this very broad matter through 27 original and innovative research studies exhibiting various investigation directions. Through its chapters the reader will have access to works related to Biomedical Engineering, Materials Engineering, Process Analysis and Civil Engineering. The text is addressed not only to researchers, but also to professional engineers, engineering lecturers and students seeking to gain a better understanding of where Finite Element Analysis stands today.
无
2006-01-01
@@ Scientific computation is widely used in multiple cross-disciplinary areas. Most of the issues coming from this area finally result in solving PDE. In the process of solving PDE, the meshes are firstly generated within the area where PDE is functional; then, the methods of FE,Finite Difference (FD), and Finite Volume (FV) are applied on the meshes to solve the PDE.
Hugger, Jens
1992-01-01
Matematik, numerisk analyse, den endelige element metode, fejlestimering, tæthedsfunktion, netgenerering......Matematik, numerisk analyse, den endelige element metode, fejlestimering, tæthedsfunktion, netgenerering...
Adaptive Kronrod-Patterson integration of non-linear finite-element matrices
Janssen, Hans
2010-01-01
inappropriate discretization. In response, this article develops adaptive integration, based on nested Kronrod-Patterson-Gauss integration schemes: basically, the integration order is adapted to the locally observed grade of non-linearity. Adaptive integration is developed based on a standard infiltration...
Weiser, Martin
2016-01-01
All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms. Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.
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.
Paszyński, Maciej R.
2013-04-01
This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.
This book discusses the topics in the general field of finite element analysis of flow problems and describes the major advances over the last two years and introduces new powerful methods for high-speed and free-surface flows, and discusses applications. The contents include: General Topics, Computational and Mathematical Aspects. High-speed and Transonic flows. Hydraulics, Viscous Flow, Boundary-Layers, MHD. Free Surface Flow. Index
Adaptive finite element method assisted by stochastic simulation of chemical systems
Cotter, S.L.; Vejchodský, Tomáš; Erban, R.
2013-01-01
Roč. 35, č. 1 (2013), B107-B131. ISSN 1064-8275 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional support: RVO:67985840 Keywords : chemical Fokker-Planck * adaptive meshes * stochastic simulation algorithm Subject RIV: BA - General Mathematics Impact factor: 1.940, year: 2013 http://epubs.siam.org/doi/abs/10.1137/120877374
Dolejší, V.; Kůs, Pavel
2008-01-01
Roč. 73, č. 12 (2008), s. 1739-1766. ISSN 0029-5981 Keywords : backward difference formula * discontinuous Galerkin method * adaptive choice of the time step Subject RIV: BA - General Mathematics Impact factor: 2.229, year: 2008 http://onlinelibrary.wiley.com/doi/10.1002/nme.2143/abstract
Kreuzer, Christian; Schedensack, Mira
2014-01-01
We extend the ideas of Diening, Kreuzer, and Stevenson [Instance optimality of the adaptive maximum strategy, Found. Comput. Math. (2015)], from conforming approximations of the Poisson problem to nonconforming Crouzeix-Raviart approximations of the Poisson and the Stokes problem in 2D. As a consequence, we obtain instance optimality of an AFEM with a modified maximum marking strategy.
Vey, Simon
2008-01-01
In the recent past, the field of scientific computing has become of more and more importance for scientific as well as for industrial research, playing a comparable role as experiment and theory do. This success of computational methods in scientific and engineering research is next to the enormous improvement of computer hardware to a large extend due to contributions from applied mathematicians, who have developed algorithms which make real life applications feasible. Examples are adaptive ...
Lipnikov, Konstantin [Los Alamos National Laboratory; Agouzal, Abdellatif [UNIV DE LYON; Vassilevski, Yuri [Los Alamos National Laboratory
2009-01-01
We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N{sub h} triangles, the error is proportional to N{sub h}{sup -1} and the gradient of error is proportional to N{sub h}{sup -1/2} which are optimal asymptotics. The methodology is verified with numerical experiments.
无
2002-01-01
This paper discusses the validity of (adaptive) Lagrange generalized plain finite element method(FEM) and plate element method for accurate analysis of acoustic waves in multi-layered piezoelectric structures with tiny interfaces between metal electrodes and surface mounted piezoelectric substrates. We have come to conclusion that the quantitative relationships between the acoustic and electric fields in a piezoelectric structure can be accurately determined through the proposed finite element methods. The higher-order Lagrange FEM proposed for dynamic piezoelectric computation is proved to be very accurate (prescribed relative error 0.02%-0.04%) and a great improvement in convergence accuracy over the higher order Mindlin plate element method for piezoelectric structural analysis due to the assumptions and corrections in the plate theories. The converged Lagrange finite element methods are compared with the plate element methods and the computed results are in good agreement with available exact and experimental data. The adaptive Lagrange finite element methods and a new FEA computer program developed for macro- and micro-scale analyses are reviewed, and recently extended with great potential to high-precision nano-scale analysis in this paper and the similarities between piezoelectric and seismic wave propagations in layered structures and plates are stressed.
The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems. While FEM is commonly used to solve solid mechanics equations, it can be applied to a large range of BVPs from many different fields. FEM has been used for reactor fuels modelling for many years. It is most often used for fuel performance modelling at the pellet and pin scale, however, it has also been used to investigate properties of the fuel material, such as thermal conductivity and fission gas release. Recently, the United Stated Department Nuclear Energy Advanced Modelling and Simulation Program has begun using FEM as the basis of the MOOSE-BISON-MARMOT Project that is developing a multi-dimensional, multi-physics fuel performance capability that is massively parallel and will use multi-scale material models to provide a truly predictive modelling capability. (authors)
Space and Time Adaptive Two-Mesh hp-Finite Element Method for Transient Microwave Heating Problems
Dubcová, Lenka; Šolín, Pavel; Červený, Jakub; Kůs, Pavel
1-2, č. 30 (2010), s. 23-40. ISSN 0272-6343 R&D Projects: GA ČR(CZ) GA102/07/0496; GA AV ČR IAA100760702 Institutional research plan: CEZ:AV0Z20570509 Keywords : hp-finite element method * microwave heating * edge elements Subject RIV: JA - Electronics ; Optoelectronics, Electric al Engineering Impact factor: 0.844, year: 2010
Mixed finite element-finite volume methods
Zine Dine, Khadija; Achtaich, Naceur; Chagdali, Mohamed
2010-01-01
This paper is devoted to present a numerical methods for a model of incompressible and miscible flow in porous media. We analyze a numerical scheme combining a mixed finite element method (MFE) and finite volume scheme (FV) for solving a coupled system includes an elliptic equation (pressure and velocity) and a linear convection-diffusion equation (concentration). The (FV) scheme considered is "vertex centered" type semi implicit. We show that this scheme is $L^{\\infty...
Pardo, David
2011-07-01
The paper introduces a high-order, adaptive finite-element method for simulation of sonic measurements acquired with borehole-eccentered logging instruments. The resulting frequency-domain based algorithm combines a Fourier series expansion in one spatial dimension with a two-dimensional high-order adaptive finite-element method (FEM), and incorporates a perfectly matched layer (PML) for truncation of the computational domain. The simulation method was verified for various model problems, including a comparison to a semi-analytical solution developed specifically for this purpose. Numerical results indicate that for a wireline sonic tool operating in a fast formation, the main propagation modes are insensitive to the distance from the center of the tool to the center of the borehole (eccentricity distance). However, new flexural modes arise with an increase in eccentricity distance. In soft formations, we identify a new dipole tool mode which arises as a result of tool eccentricity. © 2011 Elsevier Inc.
Stabilized Finite Elements with Matlab
Asensio, M. I.; A. Russo
2002-01-01
The purpose of this note is to explain the MATLAB code developed to solve an advection diffusion-reaction problem, with different Finite Element Methods: Standard Galerkin [7], Streamline Upwind/ Petrov-Galerkin (SUPG) [6], Unsual Stabilized [8, 9] and Residual-Free Bubbles [3, 4, 5], for both linear (P1) (see [1]) and quadratic (P2) (see [2]) triangular finite elements.
Solution of Finite Element Equations
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...
Massively Parallel Finite Element Programming
Heister, Timo
2010-01-01
Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Rapolder, M.
2000-07-01
This thesis deals with the derivation of efficient and robust algorithms for the dynamic analysis of coupled structures with a large number of degrees of freedom. The numerical simulations are based on a modified time integration scheme combined with an adaptive time step control. The algorithms are optimized for the numerical treatment of interaction effects and contact simulations. Parallel computing of the semi-analytical Finite Element model accelerates the numerical process. Calculations of unanchored liquid filled storage tanks under earthquake excitation exhibit the efficiency of the derived algorithms. (orig.) [German] In der vorliegenden Arbeit werden Methoden zur effizienten und robusten nichtlinearen dynamischen Berechnung von gekoppelten Systemen mit sehr vielen Freiheitsgraden vorgestellt. Die numerische Simulation erfolgt mit einem modifizierten Zeitintegrationsverfahren sowie einer adaptiven Schrittweitensteuerung. Die Algorithmen werden insbesondere fuer die numerische Behandlung von Interaktionsvorgaengen und fuer die Kontaktsimulation optimiert. Mit Hilfe der Paralellisierung auf Elementebene kann die verwendete semi-analytische Finite-Element-Berechnung beschleunigt werden. Die Leistungsfaehigkeit der entwickelten Verfahren wird mit der Simulation von unverankerten, fluessigkeitsgefuellten Behaeltern unter Erdbebeneinwirkung demonstriert. (orig.)
Finite element computational fluid mechanics
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
Finite Element Method: An Overview
Vishal JAGOTA
2013-02-01
Full Text Available The finite element method (FEM is a numerical analysis technique for obtaining approximate solutions to a wide variety of engineering problems. A finite element model of a problem gives a piecewise approximation to the governing equations. The basic premise of the FEM is that a solution region can be analytically modeled or approximated by replacing it with an assemblage of discrete elements (discretization. Since these elements can be put together in a variety of ways, they can be used to represent exceedingly complex shapes.
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.
Finite element methods for engineers
Fenner, Roger T
2013-01-01
This book is intended as a textbook providing a deliberately simple introduction to finite element methods in a way that should be readily understandable to engineers, both students and practising professionals. Only the very simplest elements are considered, mainly two dimensional three-noded “constant strain triangles”, with simple linear variation of the relevant variables. Chapters of the book deal with structural problems (beams), classification of a broad range of engineering into harmonic and biharmonic types, finite element analysis of harmonic problems, and finite element analysis of biharmonic problems (plane stress and plane strain). Full Fortran programs are listed and explained in detail, and a range of practical problems solved in the text. Despite being somewhat unfashionable for general programming purposes, the Fortran language remains very widely used in engineering. The programs listed, which were originally developed for use on mainframe computers, have been thoroughly updated for use ...
Higher-Order Finite Element Modeling with Curvilinear Elements
Karban, P.; Mach, F.; Doležel, Ivo
Gliwice : Silesian University of Technology, 2011, s. 5-6. ISBN 978-83-85940-33-3. [INTERNATIONAL CONFERENCE ON FUNDAMENTALS OF ELECTROTECHNICS AND CIRCUIT THEORY /34./. Ustroň (PL), 18.05.2011-21.05.2011] R&D Projects: GA ČR(CZ) GAP102/11/0498 Institutional research plan: CEZ:AV0Z20570509 Keywords : automatic adaptivity * higher-order finite element method * curvilinear elements Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering
Finite elements of nonlinear continua
Oden, J T
2000-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
Fadhil Mezghani
2015-01-01
Full Text Available The optical properties of metallic nanoparticles are well known, but the study of their thermal behavior is in its infancy. However the local heating of surrounding medium, induced by illuminated nanostructures, opens the way to new sensors and devices. Consequently the accurate calculation of the electromagnetically induced heating of nanostructures is of interest. The proposed multiphysics problem cannot be directly solved with the classical refinement method of Comsol Multiphysics and a 3D adaptive remeshing process based on an a posteriori error estimator is used. In this paper the efficiency of three remeshing strategies for solving the multiphysics problem is compared. The first strategy uses independent remeshing for each physical quantity to reach a given accuracy. The second strategy only controls the accuracy on temperature. The third strategy uses a linear combination of the two normalized targets (the electric field intensity and the temperature. The analysis of the performance of each strategy is based on the convergence of the remeshing process in terms of number of elements. The efficiency of each strategy is also characterized by the number of computation iterations, the number of elements, the CPU time, and the RAM required to achieve a given target accuracy.
A Finite Element Framework for Some Mimetic Finite Difference Discretizations
Rodrigo, Carmen; Gaspar, Francisco; Hu, Xiaozhe; Zikatanov, Ludmil
2015-01-01
In this work we derive equivalence relations between mimetic finite difference schemes on simplicial grids and modified N\\'ed\\'elec-Raviart-Thomas finite element methods for model problems in $\\mathbf{H}(\\operatorname{\\mathbf{curl}})$ and $H(\\operatorname{div})$. This provides a simple and transparent way to analyze such mimetic finite difference discretizations using the well-known results from finite element theory. The finite element framework that we develop is also crucial for the design...
Stochastic finite element method with simple random elements
Starkloff, Hans-Jörg
2008-01-01
We propose a variant of the stochastic finite element method, where the random elements occuring in the problem formulation are approximated by simple random elements, i.e. random elements with only a finite number of possible values.
Solid finite elements through three decades
Venkatesh, DN; Shrinivasa, U
1994-01-01
conventionally, solid finite elements have been looked upon as just generalizations of two-dimensional finite elements. In this article we trace their development starting from the days of their inception. Keeping in tune with our perceptions on developing finite elements, without taking recourse to any extra variational techniques, we discuss a few of the techniques which have been applied to solid finite elements. Finally we critically examine our own work on formulating solid finite elemen...
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
Nonlinear, finite deformation, finite element analysis
Nguyen, Nhung; Waas, Anthony M.
2016-06-01
The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli ( C e ) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated
ANSYS duplicate finite-element checker routine
Ortega, R.
1995-01-01
An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.
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.
Quantum Finite Elements for Lattice Field Theory
Brower, Richard C; Gasbarro, Andrew; Raben, Timothy; Tan, Chung-I; Weinberg, Evan
2016-01-01
Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element (QFE) Lagrangian is constructed for fields on a smooth Riemann manifold. To reach the continuum limit additional counter terms must be constructed to cancel the ultraviolet distortions. This is tested by the comparison of phi 4-th theory at the Wilson-Fisher fixed point with the exact Ising (c =1/2) CFT on a 2D Riemann sphere. The Dirac equation is also constructed on a simplicial lattice approximation to a Riemann manifold by introducing a lattice vierbein and spin connection on each link. Convergence of the QFE Dirac equation is tested against the exact solution for the 2D Riemann sphere. Future directions and applications to Conformal Field Theories are suggested.
Peridynamic Multiscale Finite Element Methods
Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
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
Flux-conserving finite element methods
Zhang, Shangyou; Zhang, Zhimin; Zou, Qingsong
2012-01-01
We analyze the flux conservation property of the finite element method. It is shown that the finite element solution does approximate the flux locally in the optimal order, i.e., the same order as that of the nodal interpolation operator. We propose two methods, post-processing the finite element solutions locally. The new solutions, remaining as optimal-order solutions, are flux-conserving elementwise. In one of our methods, the processed solution also satisfies the original finite element e...
The UNCLE finite element scheme
A completely general finite element scheme, implemented in the UKAEA Reactor Group is outlined. UNCLE is not a complete, self-contained program. It is a framework of routines that provide the common services required by all general purpose finite element programs, whether for heat transfer, stress analysis or any other linear (or piece-wise linear) problem. These services are: input of mesh, geometry, loads (etc) and material data: matrix and load vector calculation and assembly (including handling of standard boundary conditions); solution of global matrix (elimination and conjugate gradient methods); output (printed and graphical) of initial geometry, displacements, stresses, final geometry etc; facilities for iteration for non-linear problems and time integration; mass matrix reduction, dynamic analysis of reduced problem and expansion of displacements to full problem. The framework is written to handle 1, 2, 3 or more dimensions equally efficiently. To produce a general purpose program for a particular range of applications it is only necessary to provide a set of element subroutines specialised to the application (heat transfer, framework analysis, continuum stress analysis etc)
Schmidt, M.
2001-07-01
Finding robust, reliable and therefore secure solutions for the given tasks has always been the engineer's goal. In the beginning, engineering concentrated on the pure functionality of the technical construction. Soon it became clear that also economic aspects had to be considered. Constructions have to be efficient regarding the costs for the material, building and maintenance. Therefore it must be able to test construction elements before expensive prototypes are built. Especially in the area of mechanics, predictions of the behavior of an assembly became possible in the design phase. While only elastic material behavior could be simulated at first, the rapid development of both available computer power and new theories in mechanics allowed for better and more exact computations. In particular, the use of adaptive procedures made for a leap in quality, although error measures defined for elasticity were used for elasto-plastic materials as well. So the solutions found were insecure in spite of the error control. This thesis gives an overview of FE-computations for mechanical systems showing elastoplastic behavior with error-controlled adaptivity in space and pseudo-time. Spanning from the mathematical foundations of elasto-plasticity over the selection of a suitable error measure to adapt the chosen discretizations of the space and time domains to the visualization of the results on parallel computers. A special emphasis is put on error estimators and error indicators for elasto-plasticity. (orig.) [German] Im Bereich der technischen Mechanik konnten bereits im Entwurfsstadium Aussagen ueber die Belastbarkeit getroffen werden. Beschraenkte man sich zunaechst auf die Simulation elastischer Materialien, so ermoeglichte die rasante Entwicklung sowohl der zur Verfuegung stehenden Rechenleistung als auch der mechanischen Theorien schnell wesentlich genauere Betrachtungsweisen. Insbesondere die aufkommenden fehlerkontrollierten, adaptiven Techniken trugen zu einem
Infinite to finite: An overview of finite element analysis
Srirekha A; Bashetty Kusum
2010-01-01
The method of finite elements was developed at perfectly right times; growing computer capacities, growing human skills and industry demands for ever faster and cost effective product development providing unlimited possibilities for the researching community. This paper reviews the basic concept, current status, advances, advantages, limitations and applications of finite element method (FEM) in restorative dentistry and endodontics. Finite element method is able to reveal the otherwise inac...
BERSAFE: (BERkeley Structural Analysis by Finite Elements)
BERSAFE is a well-known finite element system which has been under continuous use and development for over 20 years. The BERSAFE system comprises an inter-compatible set of program modules covering static stress analysis, linear dynamics and thermal analysis. Data generation and results presentation modules are also available, along with special supporting functions including automatic crack growth through a model with adaptive meshing. The functionality of BERSAFE, is nowadays very advanced, both in engineering scope and finite element technology. It has seen many firsts, including the front solution and Virtual Crack Extension methods (VCE). More recent additions which have developed out of the Power Industry's requirements are a finite element computational fluid dynamics code, FEAT, and engineering design assessment procedures. These procedures include R6 and R5 for the assessment of the integrity of structures containing defects below and within the creep regime. To use all this software in a user-friendly manner, a new computational environment has been developed, called 'The Harness' which takes advantage of modern hardware and software philosophies. This provides the tool-kit to undertake complete problems, covering determination of fluid loads, structural analysis and failure assessment. In the following sections we describe briefly various components of the BERSAFE suite. (author)
Elements with Square Roots in Finite Groups
M.S. Lucido; M.R. Pournaki
2005-01-01
In this paper, we study the probability that a randomly chosen element in a finite group has a square root, in particular the simple groups of Lie type of rank 1, the sporadic finite simple groups and the alternating groups.
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.
Unified Framework for Finite Element Assembly
Alnæs, Martin Sandve; Mardal, Kent-Andre; Skavhaug, Ola; Langtangen, Hans Petter; 10.1504/IJCSE.2009.029160
2012-01-01
At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain.
A first course in finite elements
Fish, Jacob
2007-01-01
Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations. Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements:Adopts
Šolín, Pavel; Korous, L.
2012-01-01
Roč. 231, č. 4 (2012), s. 1635-1649. ISSN 0021-9991 R&D Projects: GA AV ČR IAA100760702 Institutional research plan: CEZ:AV0Z20760514 Keywords : Runge-Kutta method * Butcher's table * finite element method Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 2.138, year: 2012
Finite element coiled cochlea model
Isailovic, Velibor; Nikolic, Milica; Milosevic, Zarko; Saveljic, Igor; Nikolic, Dalibor; Radovic, Milos; Filipović, Nenad
2015-12-01
Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers - scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experimental measurements. Future work is needed for more realistic geometry model. Coiled model of the cochlea was created and results are compared with initial simplified coiled model of the cochlea.
Continuous finite element methods for Hamiltonian systems
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
Dimmler, G.; Weidinger, Th.; Cerjak, H. [Inst. fuer Werkstoffkunde, Schweisstechnik und Spanlose Formgebungsverfahren (IWS), Technische Univ. Graz, Graz (Austria)
2005-03-01
The fact that it is possible to directly trace timed materials science related processes in the SEM with no need to interrupt the variety of loads (''in-situ examinations'') by means of a high-temperature loading device opens up new horizons for the more profound comprehension of the phenomena of materials. This article aims at conceiving a suitable sample geometry with regard to temperature and stress distributions with a support by finite element modelling. The comprehension gained for the different interactions between the loading device and the scanning electron microscope forms an important basis here to further optimize the performance of tests. Currently, it is possible to examine kinetic processes on specific samples at temperatures up to 650 C and under a tensile and compression load which theoretically is up to 10.000 N. In addition, a simulation is possible for any stress and temperature profile via a fully digitized micro-processor control. The loading device allows to make short-time creep tests while continuously measuring strains and studying the structure of the surfaces at a constant and freely selectable temperature. A short-time creep test, when performed, is intended to prepare future in-situ damage examinations at 9-12% Cr steels here. (orig.)
Finite-Element Composite-Analysis Program
Bowles, David E.
1990-01-01
Finite Element Composite Analysis Program, FECAP, special-purpose finite-element program for analyzing behavior of composite material with microcomputer. Procedure leads to set of linear simultaneous equations relating unknown nodal displacement to applied loads. Written in HP BASIC 3.0.
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS
李宏; 刘儒勋
2001-01-01
Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L∞ (L2) norm, that is maximum-norm in time, L2norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.
Rotationally invariant distortion resistant finite-elements.
Cowan, T.; Coombs, W.M.
2014-01-01
The predictive capability of conventional iso-parametric finite-elements deteriorates with mesh distortion. In the case of geometrically non-linear analysis, changes in geometry causing severe distortion can result in negative Jacobian mapping between the local and global systems resulting in numerical breakdown. This paper presents a finite-element formulation that is resistant to irregular mesh geometries and large element distortions whilst remaining invariant to rigid body motion. The pre...
Achatz, Stefan
2007-01-01
Auf Grund ihrer hervorragenden Approximationseigenschaften bieten sich Funktionenräume über dünnen Gittern zur numerischen Lösung von partiellen Differentialgleichungen im Rahmen der Finite-Elemente-Methode (FEM) an. Seit einem Jahrzehnt werden sie erfolgreich eingesetzt, wobei polynomiale Basisfunktionen und lokale Gitterverfeinerungen als die wichtigsten Erweiterungen des Konzepts zu nennen sind. Allerdings ergeben sich für Differentialoperatoren mit variablen Koeffizienten und nicht-rechte...
Electrical machine analysis using finite elements
Bianchi, Nicola
2005-01-01
OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I
Superconvergence of tricubic block finite elements
2009-01-01
In this paper, we first introduce interpolation operator of projection type in three dimen- sions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W 2, 1-seminorm of the discrete derivative Green’s function and the weak estimates, we show that the tricubic block finite element solution uh and the tricubic interpolant of projection type Πh3u have superclose gradient in the pointwise sense of the L∞-norm. Finally, this supercloseness is applied to superconvergence analysis, and the global superconvergence of the finite element approximation is derived.
Will Finite Elements Replace Structural Mechanics?
Ojalvo, I. U.
1984-01-01
This paper presents a personal view regarding the need for a continued interest and activity in structural methods in general, while viewing finite elements and the computer as simply two specific tools for assisting in this endeavor. An attempt is made to provide some insight as to why finite element methods seem to have "won the war," and to give examples of their more (and less) intelligent use. Items addressed include a highlight of unnecessary limitations of many existing standard finite element codes and where it is felt that further development work is needed.
Finite element analysis of piezoelectric materials
This guide is intended to help people wanting to do finite element analysis of piezoelectric materials by answering some of the questions that are peculiar to piezoelectric materials. The document is not intended as a complete beginners guide for finite element analysis in general as this is better dealt with by the individual software producers. The guide is based around the commercial package ANSYS as this is a popular package amongst piezoelectric material users, however much of the information will still be useful to users of other finite element codes. (author)
Climbing elements in finite coxeter groups
Brady, Thomas; Kenny, Aisling; Watt, And Colum
2010-01-01
We define the notion of a climbing element in a finite real reflection group relative to a total order on the reflection set and we characterise these elements in the case where the total order arises from a bipartite Coxeter element.
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
Discrete mechanics Based on Finite Element Methods
Chen, Jing-Bo; Guo, Han-Ying; Wu, Ke
2002-01-01
Discrete Mechanics based on finite element methods is presented in this paper. We also explore the relationship between this discrete mechanics and Veselov discrete mechanics. High order discretizations are constructed in terms of high order interpolations.
Efficient Finite Element Analysis of Inelastic Structures with Iterative Solvers
Quint, K.J.; Hartmann, S.; Duintjer Tebbens, Jurjen; Meister, A.
2008-01-01
Roč. 8, č. 1 (2008), s. 10331-10332. ISSN 1617-7061 R&D Projects: GA AV ČR KJB100300703 Institutional research plan: CEZ:AV0Z10300504 Keywords : inexact multilevel- Newton * diagonally implicit Runge-Kutta * finite element analysis * linear solver * preconditioning * adaptive stopping criterion Subject RIV: BA - General Mathematics
Aranha: a 2D mesh generator for triangular finite elements
A method for generating unstructured meshes for linear and quadratic triangular finite elements is described in this paper. Some topics on the C language data structure used in the development of the program Aranha are also presented. The applicability for adaptive remeshing is shown and finally several examples are included to illustrate the performance of the method in irregular connected planar domains. (author)
Finite element modeling of the human pelvis
Carlson, B.
1995-11-01
A finite element model of the human pelvis was created using a commercial wire frame image as a template. To test the final mesh, the model`s mechanical behavior was analyzed through finite element analysis and the results were displayed graphically as stress concentrations. In the future, this grid of the pelvis will be integrated with a full leg model and used in side-impact car collision simulations.
Finite-Element Modeling For Structural Analysis
Min, J. B.; Androlake, S. G.
1995-01-01
Report presents study of finite-element mathematical modeling as used in analyzing stresses and strains at joints between thin, shell-like components (e.g., ducts) and thicker components (e.g., flanges or engine blocks). First approach uses global/local model to evaluate system. Provides correct total response and correct representation of stresses away from any discontinuities. Second approach involves development of special transition finite elements to model transitions between shells and thicker structural components.
Nonconforming finite element methods on quadrilateral meshes
Hu, Jun; Zhang, Shangyou
2013-01-01
It is well-known that it is comparatively difficult to design nonconforming finite elements on quadrilateral meshes by using Gauss-Legendre points on each edge of triangulations. One reason lies in that these degrees of freedom associated to these Gauss-Legendre points are not all linearly independent for usual expected polynomial spaces, which explains why only several lower order nonconforming quadrilateral finite elements can be found in literature. The present paper proposes two families ...
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
Surgery simulation using fast finite elements
Bro-Nielsen, Morten
1996-01-01
This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism......This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism...
Finite Element Analysis of Deep Excavations
Bentler, David J.
1998-01-01
This dissertation describes enhancements made to the finite element program, SAGE, and research on the performance of deep excavations This dissertation describes enhancements made to the finite element program, SAGE, and research on the performance of deep excavations. SAGE was developed at Virginia Tech for analysis of soil-structure interaction problems (Morrison, 1995). The purpose of the work described in this text with SAGE was to increase the capabilities o...
Parallel adaptive finite state automata
Rocha, Ricardo L.; Garanhani, César E.C.
2006-01-01
The interest on parallelism has grown in many areas of technology. Hardware development has evolved greatly in the last years, leaving to software developers the goal of building better tools and compilers for parallel computation. Also, symbolic computation must take advantage of parallel computation. The proposal contained in this paper is to use functional languages as a tool to implement adaptive automata using the concepts of symbolic computation
The strong formulation finite element method: stability and accuracy
Francesco Tornabene
2014-07-01
Full Text Available The Strong Formulation Finite Element Method (SFEM is a numerical solution technique for solving arbitrarily shaped structural systems. This method uses a hybrid scheme given by the Differential Quadrature Method (DQM and the Finite Element Method (FEM. The SFEM takes the best from DQM and FEM giving a highly accurate strong formulation based technique with the adaptability of finite elements. The present study investigates the stability and accuracy of SFEM when applied to 1D and 2D structural components, such as rods, beams, membranes and plates using analytical and semi-analytical well-known solutions. The numerical results show that the present approach can be very accurate using a small number of grid points and elements, when it is compared to standard FEM.
A finite element for plates and shells
A simple triangular finite element for plates and shells, is presented. Since the rotation fields are assumed independent of the displacement fields, the element allows one to solve thick shells problems. In the limit for thin shell, the Kirchoff-Love hypothesis is automatically satisfied, thus enlarging its range of application. (Author)
Finite Element Computational Dynamics of Rotating Systems
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element analysis of rotor dynamics problems that were published in 1994–1998. It contains 319 citations. Also included, as separate subsections, are finite element analyses of rotor elements – discs, shafts, spindles, and blades. Topics dealing with fracture mechanics, contact and stability problems of rotating machinery are also considered in specific sections. The last part of the bibliography presents papers dealing with specific industrial applications.
Finite-element models of continental extension
Lynch, H. David; Morgan, Paul
1990-01-01
Numerical models of the initial deformation of extending continental lithosphere, computed to investigate the control of preexisting thermal and mechanical heterogeneities on the style of deformation, are presented. The finite element method is used to calculate deformation with a viscoelastic-plastic model for the lithosphere. Comparisons of the results of analytic models and finite-element models using this method show that good results may be obtained by the numerical technique, even with elements containing both brittle and viscoelastic sampling points. It is shown that the gross style of initial extensional deformation is controlled by the depth and width of the initial heterogeneity which localizes deformation.
Finite element analysis of tibial fractures
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner; Darvann, Tron; Gebuhr, Peter Henrik
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... bony healing. The biomechanical results are the basis for fracture healing, biomechanical fall analysis and stability analysis of osteosynthesis. MATERIAL AND METHODS: A finite element model of the bony part of the lower leg was generated on the basis of computed tomography data from the Visible Human...... Project. The data consisted of 21,219 3D elements with a cortical shell and a trabecular core. Three types of load of torsion, a direct lateral load and axial compression were applied. RESULTS: The finite element linear static analysis resulted in relevant fracture localizations and indicated relevant...
Coupled finite-difference/finite-element approach for wing-body aeroelasticity
Guruswamy, Guru P.
1992-01-01
Computational methods using finite-difference approaches for fluids and finite-element approaches for structures have individually advanced to solve almost full-aircraft configurations. However, coupled approaches to solve fluid/structural interaction problems are still in their early stages of development, particularly for complex geometries using complete equations such as the Euler/Navier-Stokes equations. Earlier work demonstrated the success of coupling finite-difference and finite-element methods for simple wing configurations using the Euler/Navier-Stokes equations. In this paper, the same approach is extended for general wing-body configurations. The structural properties are represented by beam-type finite elements. The flow is modeled using the Euler/Navier-Stokes equations. A general procedure to fully couple structural finite-element boundary conditions with fluid finite-difference boundary conditions is developed for wing-body configurations. Computations are made using moving grids that adapt to wing-body structural deformations. Results are illustrated for a typical wing-body configuration.
Finite element methods for sea ice modeling
Lietaer, Olivier
2011-01-01
In order to study and understand the behavior of sea ice, numerical sea ice models have been developed since the early seventies and have traditionally been based on structured grids and finite difference schemes. This doctoral research is part of the Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM) project whose objective is to bring to oceanography modern numerical techniques. The motivation for this thesis is therefore to investigate the potential of finite element methods and uns...
Finite-Element Software for Conceptual Design
Lindemann, J.; Sandberg, G.; Damkilde, Lars
2010-01-01
and research. Forcepad is an effort to provide a conceptual design and teaching tool in a finite-element software package. Forcepad is a two-dimensional finite-element application based on the same conceptual model as image editing applications such as Adobe Photoshop or Microsoft Paint. Instead of using......Using finite-element analysis in conceptual design and teaching has quite different software requirements to that in engineering and research. In teaching and conceptual design the focus is on speed, interactivity and ease of use, whereas accuracy and precision are needed in engineering...... success in teaching as well as in conceptual design environments such as architecture, industrial design and engineering. The addition of an optimisation algorithm and tablet PC support makes the software even more interesting as a tool for conceptual design....
Finite element radiation transport in one dimension
A new physics package solves radiation transport equations in one space dimension, multiple energy groups and directions. A discontinuous finite element method discretizes radiation intensity with respect to space and angle, and a continuous finite element method discretizes electron temperature 'in space. A splitting method solves the resulting linear equations. This is a one-dimensional analog of Kershaw and Harte's two-dimensional package. This package has been installed in a two-dimensional inertial confinement fusion code, and has given excellent results for both thermal waves and highly directional radiation. In contrast, the traditional discrete ordinate and spherical harmonic methods show less accurate results in both cases
Non-linear finite element modeling
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University of the...... Southern Denmark and in Medicine and Technology at the Technical University of Denmark. The note focus on the applicability to actually code routines with the purpose to analyze a geometrically or material non-linear problem. The note is tried to be kept on so brief a form as possible, with the main focus...
Finite elements for analysis and design
Akin, J E; Davenport, J H
1994-01-01
The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.Key Features* Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing* Basic theory has bee
Simplicial Finite Elements in Higher Dimensions
Brandts, J.; Korotov, S.; Křížek, Michal
2007-01-01
Roč. 52, č. 3 (2007), s. 251-265. ISSN 0862-7940 R&D Projects: GA ČR GA201/04/1503 Institutional research plan: CEZ:AV0Z10190503 Keywords : n- simplex * finite element method * superconvergence Subject RIV: BA - General Mathematics
Fast finite elements for surgery simulation
Bro-Nielsen, Morten
1997-01-01
This paper discusses volumetric deformable models for modeling human body parts and organs in surgery simulation systems. These models are built using finite element models for linear elastic materials. To achieve real-time response condensation has been applied to the system stiffness matrix...
Finite element method - theory and applications
This paper summarizes the mathematical basis of the finite element method. Attention is drawn to the natural development of the method from an engineering analysis tool into a general numerical analysis tool. A particular application to the stress analysis of rubber materials is presented. Special advantages and issues associated with the method are mentioned. (author). 4 refs., 3 figs
Minimal length elements of finite Coxeter groups
He, Xuhua; Nie, Sian
2012-01-01
We give a geometric proof that any minimal length element in a (twisted) conjugacy class of a finite Coxeter group $W$ has remarkable properties with respect to conjugation, taking powers in the associated braid monoid and taking the centralizer in $W$ .
Image segmentation with a finite element method
Bourdin, Blaise
1999-01-01
regularization results, make possible to imagine a finite element resolution method.In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its $\\Gamma$-convergence is proved. Finally, some...
Finite element simulation of asphalt fatigue testing
Ullidtz, Per; Kieler, Thomas Lau; Kargo, Anders
damage mechanics.The paper describes how continuum damage mechanics may be used with a finite element program to explain the progressive deterioration of asphalt mixes under laboratory fatigue testing. Both constant stress and constant strain testing are simulated, and compared to the actual results from...
Finite element analysis of photonic crystal fibers
Uranus, H.P.; Hoekstra, H.J.W.M.; Groesen, van E.
2005-01-01
A finite-element-based vectorial optical mode solver, furnished with Bayliss-Gunzburger-Turkel-like transparent boundary conditions, is used to rigorously analyze photonic crystal fibers (PCFs). Both the real and imaginary part of the modal indices can be computed in a relatively small computational
Orthodontic treatment: Introducing finite element analysis
Driel, W.D. van; Leeuwen, E.J. van
1998-01-01
The aim of orthodontic treatment is the displacement of teeth by means ofspecial appliances, like braces and brackets. Through these appliances the orthodontist can apply a set of forces to the teeth which wilt result in its displacement through the jawbone. Finite Element analysis of this process e
Four levels of hydrologic models have been categorized to handle varying complexities and degrees of available input parameters. The first level is for the simplest one-dimensional models having analytical solutions; the second level includes idealized analytic or hybrid analytic models for single aquifer systems with scanty input data; the third level deals with more complex single or quasi-multilayered systems; and the fourth level is for complex multilayered systems. The three-dimensional finite element ground-water model described in this report falls under the fourth level of hydrologic models. This model is capable of simulating single-layered systems having variable thickness or multilayered systems where not only thickness can be varied, but the number of layers can be changed to agree with the vertical geologic section. Supporting programs have been developed to plot grid values, contour maps and three-dimensional graphics of the input data used in simulation as well as the results obtained. At present, the model considers only confined aquifers. The capabilities of the model were demonstrated by using a test case consisting of the multilayered ground-water system beneath Long Island, New York
SURFACE FINITE ELEMENTS FOR PARABOLIC EQUATIONS
G. Dziuk; C.M. Elliott
2007-01-01
In this article we define a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces Γ in (R)n+1. The key idea is based on the approximation of Γ by a polyhedral surface Γh consisting of a union of simplices (triangles for n = 2, intervals for n = 1) with vertices on Γ. A finite element space of functions is then defined by taking the continuous functions on Γh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Γ. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward.We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.
Diagonal multisoliton matrix elements in finite volume
Pálmai, T.; Takács, G.
2013-02-01
We consider diagonal matrix elements of local operators between multisoliton states in finite volume in the sine-Gordon model and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Takács which were only valid for diagonal scattering. In order to test the conjecture, we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.
Finite element analysis of tibial fractures
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner;
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... analysis of the bones of the lower leg to examine if such a model is adequate for prediction of fracture locations and patterns. In future studies, we aim to use these biomechanical results to examine fracture prevention, among others, and to simulate different types of osteosynthesis and the process of...... bony healing. The biomechanical results are the basis for fracture healing, biomechanical fall analysis and stability analysis of osteosynthesis. MATERIAL AND METHODS: A finite element model of the bony part of the lower leg was generated on the basis of computed tomography data from the Visible Human...
Finite Element Analysis of Honeycomb Impact Attenuator
Yang, Seung-Yong; Choi, Seung-Kyu; Kim, Nohyu
To participate in Student Formula Society of Automotive Engineers (SAE) competitions, it is necessary to build an impact attenuator that would give an average deceleration not to exceed 20g when it runs into a rigid wall. Students can use numerical simulations or experimental test data to show that their car satisfies this safety requirement. A student group to study formula cars at the Korea University of Technology and Education has designed a vehicle to take part in a SAE competition, and a honeycomb structure was adopted as the impact attenuator. In this paper, finite element calculations were carried out to investigate the dynamic behavior of the honeycomb attenuator. Deceleration and deformation behaviors were studied. Effect of the yield strength was checked by comparing the numerical results. ABAQUS/Explicit finite element code was used.
Finite element analysis of human joints
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described
Finite element simulations with ANSYS workbench 16
Lee , Huei-Huang
2015-01-01
Finite Element Simulations with ANSYS Workbench 16 is a comprehensive and easy to understand workbook. It utilizes step-by-step instructions to help guide readers to learn finite element simulations. Twenty seven real world case studies are used throughout the book. Many of these cases are industrial or research projects the reader builds from scratch. All the files readers may need if they have trouble are available for download on the publishers website. Companion videos that demonstrate exactly how to preform each tutorial are available to readers by redeeming the access code that comes in the book. Relevant background knowledge is reviewed whenever necessary. To be efficient, the review is conceptual rather than mathematical. Key concepts are inserted whenever appropriate and summarized at the end of each chapter. Additional exercises or extension research problems are provided as homework at the end of each chapter. A learning approach emphasizing hands-on experiences spreads through this entire book. A...
Finite element modelling of solidification phenomena
K N Seetharamu; R Paragasam; Ghulam A Quadir; Z A Zainal; B Sathya Prasad; T Sundararajan
2001-02-01
The process of solidification process is complex in nature and the simulation of such process is required in industry before it is actually undertaken. Finite element method is used to simulate the heat transfer process accompanying the solidification process. The metal and the mould along with the air gap formation is accounted in the heat transfer simulation. Distortion of the casting is caused due to non-uniform shrinkage associated with the process. Residual stresses are induced in the final castings. Simulation of the shrinkage and the thermal stresses are also carried out using finite element methods. The material behaviour is considered as visco-plastic. The simulations are compared with available experimental data and the comparison is found to be good. Special considerations regarding the simulation of solidification process are also brought out.
Discontinuous finite element methods for reactor calculations
Variational principles which employ discontinuous shape functions for the angular and/or the spatial component of the neutron flux are established to obtain numerical solutions for neutron diffusion and transport equations. Implementing discontinuous finite element methods reduces the total nodal unknowns and hence the over all computational efforts. This reduction varies from one problem to another. In this paper one group neutron transport problems are solved by varying only the order of spherical harmonic expansion for the angular component of the flux. A comparison of the solutions obtained from the discontinuous approach with either a published solutions or a conventional finite element solutions shows that the method is a very effective tool for reactor calculations
Introduction to nonlinear finite element analysis
Kim, Nam-Ho
2015-01-01
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: · Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems · Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory · ...
Finite Element Simulation of Metal Quenching
方刚; 曾攀
2004-01-01
The evolution of the phase transformation and the resulting internal stresses and strains in metallic parts during quenching were modeled numerically. The numerical simulation of the metal quenching process was based on the metallo-thermo-mechanical theory using the finite element method to couple the temperature, phase transformation, and stress-strain fields. The numerical models are presented for the heat treatment and kinetics of the phase transformation. The finite element models and the phase transition kinetics accurately predict the distribution of the microstructure volume fractions, the temperature, the distortion, and the stress-strain relation during quenching. The two examples used to validate the models are the quenching of a small gear and of a large turbine rotor. The simulation results for the martensite phase volume fraction, the stresses, and the distortion in the gear agree well with the experimental data. The models can be used to optimize the quenching conditions to ensure product quality.
Multiphase Transformer Modelling using Finite Element Method
Nor Azizah Mohd Yusoff
2015-03-01
Full Text Available In the year of 1970 saw the starting invention of the five-phase motor as the milestone in advanced electric motor. Through the years, there are many researchers, which passionately worked towards developing for multiphase drive system. They developed a static transformation system to obtain a multiphase supply from the available three-phase supply. This idea gives an influence for further development in electric machines as an example; an efficient solution for bulk power transfer. This paper highlighted the detail descriptions that lead to five-phase supply with fixed voltage and frequency by using Finite-Element Method (FEM. Identifying of specification on a real transformer had been done before applied into software modeling. Therefore, Finite-Element Method provides clearly understandable in terms of visualize the geometry modeling, connection scheme and output waveform.
On the Finite Volume Reformulation of the Mixed Finite Elements Method on Triangles
Chavent, Guy; Younès, Anis; Mosé, Robert; Ackerer, Philippe
1999-01-01
We analyse the finite volume reformulation of the triangular mixed finite element approximation for the porous flow equation, as proposed in [10] [9]. We show that the finite volumes are obtained by aggregation of finite elements (usually one, sometimes two or more), that the matrix of the finite volume equations is regular, but generally not symmetrical, and that the finite volume formulation is algebraically equivalent to the mixed approximation. The finite volume matrix becomes symmetrical...
Finite element analysis of nonlinear creeping flows
Steady-state creep problems with monotone constitutive laws are studied. Finite element approximations are constructed based on mixed Petrov-Galerkin formulations for constrained problems. Stability, convergence and a priori error estimates are proved for equal-order discontinuous stress and continuous velocity interpolations. Numerical results are presented confirming the rates of convergence predicted in the analysis and the good performance of this formulation. (author)
Finite Element Reconstruction of Craniocerebral Injury
Jiroušek, Ondřej; Brichtová, E.; Jírová, Jitka
Praha: IT ASc. CzR,v.v ,, 2007 - (Zolotarev, I.), s. 107-108. (Inženýrská mechanika. 14). ISBN 978-80-87012-06-2. [Enginnering mechanics. Svratka (CZ), 14.05.2007-17.05.2007] R&D Projects: GA ČR(CZ) GA103/05/1020 Institutional research plan: CEZ:AV0Z20710524 Keywords : Craniocerebral Injury * Finite Element Method * Sport Accident Subject RIV: FI - Traumatology, Orthopedics
Quick finite elements for electromagnetic waves
Pelosi, Giuseppe; Selleri, Stefano
2009-01-01
This practical book and accompanying software enables you to quickly and easily work out challenging microwave engineering and high-frequency electromagnetic problems using the finite element method (FEM) Using clear, concise text and dozens of real-world application examples, the book provides a detailed description of FEM implementation, while the software provides the code and tools needed to solve the three major types of EM problems: guided propagation, scattering, and radiation.
Finite element model of needle electrode sensitivity
Høyum, P.; Kalvøy, H.; Martinsen, Ø. G.; Grimnes, S.
2010-04-01
We used the Finite Element (FE) Method to estimate the sensitivity of a needle electrode for bioimpedance measurement. This current conducting needle with insulated shaft was inserted in a saline solution and current was measured at the neutral electrode. FE model resistance and reactance were calculated and successfully compared with measurements on a laboratory model. The sensitivity field was described graphically based on these FE simulations.
Finite element analysis of centrifugal impellers
Sham Sunder, K.
1981-01-01
A three-dimensional method of stress analysis using finite element techniques is presented for determining the stress distribution in centrifugal impellers. It can treat all of the three types of loading possible in an inpeller, viz centrifugal, thermal and fluid. The method has no known limitations with regards to the geometric factors such as asymnetry of disk, blade curvature, presence of a cover disk or shroud, single or double sided impeller etc. A comparison of r...
FINELM: a multigroup finite element diffusion code
FINELM is a FORTRAN IV program to solve the Neutron Diffusion Equation in X-Y, R-Z, R-theta, X-Y-Z and R-theta-Z geometries using the method of Finite Elements. Lagrangian elements of linear or higher degree to approximate the spacial flux distribution have been provided. The method of dissections, coarse mesh rebalancing and Chebyshev acceleration techniques are available. Simple user defined input is achieved through extensive input subroutines. The input preparation is described followed by a program structure description. Sample test cases are provided. (Auth.)
FESDIF -- Finite Element Scalar Diffraction theory code
This document describes the theory and use of a powerful scalar diffraction theory based computer code for calculation of intensity fields due to diffraction of optical waves by two-dimensional planar apertures and lenses. This code is called FESDIF (Finite Element Scalar Diffraction). It is based upon both Fraunhofer and Kirchhoff scalar diffraction theories. Simplified routines for circular apertures are included. However, the real power of the code comes from its basis in finite element methods. These methods allow the diffracting aperture to be virtually any geometric shape, including the various secondary aperture obstructions present in telescope systems. Aperture functions, with virtually any phase and amplitude variations, are allowed in the aperture openings. Step change aperture functions are accommodated. The incident waves are considered to be monochromatic. Plane waves, spherical waves, or Gaussian laser beams may be incident upon the apertures. Both area and line integral transformations were developed for the finite element based diffraction transformations. There is some loss of aperture function generality in the line integral transformations which are typically many times more computationally efficient than the area integral transformations when applicable to a particular problem
Finite Element Method in Machining Processes
Markopoulos, Angelos P
2013-01-01
Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...
HANGING NODES IN THE UNIFYING THEORY OF A POSTERIORI FINITE ELEMENT ERROR CONTROL
C.Carstensen; Jun Hu
2009-01-01
A unified a posteriori error analysis has been developed in [18,21-23] to analyze the finite element error a posteriori under a universal roof.This paper contributes to the finite element meshes with hanging nodes which are required for local mesh-refining.The twodimensional 1-irregular triangulations into triangles and parallelograms and their combinations are considered with conforming and nonconforming finite element methods named after or by Courant,Q1,Crouzeix-Raviart,Han,Rannacher-Turek,and others for the a posteriori error analysis for triangulations with hanging nodes of degree≤1 which are fundamental for local mesh refinement in self-adaptive finite element discretisations.
Least-squares finite element methods for quantum chromodynamics
Ketelsen, Christian [Los Alamos National Laboratory; Brannick, J [PENN STATE UNIV; Manteuffel, T [UNIV OF CO.; Mccormick, S [UNIV OF CO.
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.
Finite Element Analysis of the Crack Propagation for Solid Materials
Miloud Souiyah
2009-01-01
Full Text Available Problem statement: The use of fracture mechanics techniques in the assessment of performance and reliability of structure is on increase and the prediction of crack propagation in structure play important part. The finite element method is widely used for the evaluation of SIF for various types of crack configurations. Source code program of two-dimensional finite element model had been developed, to demonstrate the capability and its limitations, in predicting the crack propagation trajectory and the SIF values under linear elastic fracture analysis. Approach: Two different geometries were used on this finite element model in order, to analyze the reliability of this program on the crack propagation in linear and nonlinear elastic fracture mechanics. These geometries were namely; a rectangular plate with crack emanating from square-hole and Double Edge Notched Plate (DENT. Where, both geometries are in tensile loading and under mode I conditions. In addition, the source code program of this model was written by FORTRAN language. Therefore, a Displacement Extrapolation Technique (DET was employed particularly, to predict the crack propagations directions and to, calculate the Stress Intensity Factors (SIFs. Furthermore, the mesh for the finite elements was the unstructured type; generated using the advancing front method. And, the global h-type adaptive mesh was adopted based on the norm stress error estimator. While, the quarter-point singular elements were uniformly generated around the crack tip in the form of a rosette. Moreover, make a comparison between this current study with other relevant and published research study. Results: The application of the source code program of 2-D finite element model showed a significant result on linear elastic fracture mechanics. Based on the findings of the two different geometries from the current study, the result showed a good agreement. And, it seems like very close compare to the other published
Finite Element Based Design and Optimization for Piezoelectric Accelerometers
Liu, Bin; Kriegbaum, B.; Yao, Q.
1998-01-01
A systematic Finite Element design and optimisation procedure is implemented for the development of piezoelectric accelerometers. Most of the specifications of accelerometers can be obtained using the Finite Element simulations. The deviations between the simulated and calibrated sensitivities...
Application of finite-element-methods in food processing
Risum, Jørgen
Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given.......Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given....
Convergence of finite elements enriched with meshless methods
Fernandez Mendez, Sonia; Díez, Pedro; Huerta, Antonio
2003-01-01
A combined hierarchical approximation based on finite elements and mesh-less methods is proposed and studied. Finite Elements are enriched adding hierarchical shape functions based on a particle distribution. Convergence results are presented and proved.
Modelling bucket excavation by finite element
Pecingina, O. M.
2015-11-01
Changes in geological components of the layers from lignite pits have an impact on the sustainability of the cup path elements and under the action of excavation force appear efforts leading to deformation of the entire assembly. Application of finite element method in the optimization of components leads to economic growth, to increase the reliability and durability of the studied machine parts thus the machine. It is obvious usefulness of knowledge the state of mechanical tensions that the designed piece or the assembly not to break under the action of tensions that must cope during operation. In the course of excavation work on all bucket cutting force components, the first coming into contact with the material being excavated cutting edge. Therefore in the study with finite element analysis is retained only cutting edge. To study the field of stress and strain on the cutting edge will be created geometric patterns for each type of cup this will be subject to static analysis. The geometric design retains the cutting edge shape and on this on the tooth cassette location will apply an areal force on the abutment tooth. The cutting edge real pattern is subjected to finite element study for the worst case of rock cutting by symmetrical and asymmetrical cups whose profile is different. The purpose of this paper is to determine the displacement and tensions field for both profiles considering the maximum force applied on the cutting edge and the depth of the cutting is equal with the width of the cutting edge of the tooth. It will consider the worst case when on the structure will act both the tangential force and radial force on the bucket profile. For determination of stress and strain field on the form design of cutting edge profile will apply maximum force assuming uniform distribution and on the edge surface force will apply a radial force. After geometric patterns discretization on the cutting knives and determining stress field, can be seen that at the
Pseudo-conforming polynomial finite elements on quadrilaterals
Dubach, Eric; Luce, Robert; Thomas, Jean-Marie
2008-01-01
The aim of this paper is to present a new class of finite elements on quadrilaterals where the approximation is polynomial on each element K. In the case of Lagrange finite elements, the degrees of freedom are the values at the vertices and in the case of mixed finite elements the degrees of freedom are the mean values of the fluxes on each side. The degres of freedom are the same as those of classical finite elements. However, in general, with this kind of finite elements,the resolution of s...
Finite element simulation and testing of ISW CFRP anchorage
Schmidt, Jacob Wittrup; Goltermann, Per; Hertz, Kristian Dahl
2013-01-01
modelled in the 3D finite Element program ABAQUS, just as digital image correlation (DIC) testing was performed to verify the finite element simulation. Also a new optimized design was produced to ensure that the finite element simulation and anchorage behaviour correlated well. It is seen that the...
Vemaganti, Gururaja R.; Wieting, Allan R.
1990-01-01
A higher-order streamline upwinding Petrov-Galerkin finite element method is employed for high speed viscous flow analysis using structured and unstructured meshes. For a Mach 8.03 shock interference problem, successive mesh adaptation was performed using an adaptive remeshing method. Results from the finite element algorithm compare well with both experimental data and results from an upwind cell-centered method. Finite element results for a Mach 14.1 flow over a 24 degree compression corner compare well with experimental data and two other numerical algorithms for both structured and unstructured meshes.
The main goal of this research is to establish a methodology of finite element analysis of containment building predicting not only global behaviour but also local failure mode. In this report, we summerize some existing numerical analysis techniques to be improved for containment building. In other words, a complete description of the standard degenerated shell finite element formulation is provided for nonlinear stress analysis of nuclear containment structure. A shell finite element is derived using the degenerated solid concept which does not rely on a specific shell theory. Reissner-Mindlin assumptions are adopted to consider the transverse shear deformation effect. In order to minimize the sensitivity of the constitutive equation to structural types, microscopic material model is adopted. The four solution algorithms based on the standard Newton-Raphson method are discussed. Finally, two numerical examples are carried out to test the performance of the adopted shell medel
Finite element analysis of permanent magnet motors
The analysis of permanent magnet D.C. brushless motors, supplied by current control inverters, is developed employing a finite element package tailored for such devices. The study is devoted to predicting the performance of a set of four poles machines, under different operating conditions (no-load, rated load). The over-load conditions are also considered including the saturation effect. Moreover the influence of such design parameters, as the tooth shape and the number of magnet segments, is investigated. Computed results are found in satisfactory agreement with experimental ones
Finite element modeling methods for photonics
Rahman, B M Azizur
2013-01-01
The term photonics can be used loosely to refer to a vast array of components, devices, and technologies that in some way involve manipulation of light. One of the most powerful numerical approaches available to engineers developing photonic components and devices is the Finite Element Method (FEM), which can be used to model and simulate such components/devices and analyze how they will behave in response to various outside influences. This resource provides a comprehensive description of the formulation and applications of FEM in photonics applications ranging from telecommunications, astron
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
Finite element solutions of free surface flows
Zarda, P. R.; Marcus, M. S.
1977-01-01
A procedure is presented for using NASTRAN to determine the flow field about arbitrarily shaped bodies in the presence of a free surface. The fundamental unknown of the problem is the velocity potential which must satisfy Laplace's equation in the fluid region. Boundary conditions on the free surface may involve second order derivatives in space and time. In cases involving infinite domains either a tractable radiation condition is applied at a truncated boundary or a series expansion is used and matched to the local finite elements. Solutions are presented for harmonic, transient, and steady state problems and compared to either exact solutions or other numerical solutions.
Image segmentation with a finite element method
Bourdin, Blaise
1999-01-01
The Mumford-Shah functional for image segmentation is an original approach of the image segmentation problem, based on a minimal energy criterion. Its minimization can be seen as a free discontinuity problem and is based on \\Gamma-convergence and bounded variation functions theories.Some new...... regularization results, make possible to imagine a finite element resolution method.In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its $\\Gamma$-convergence is proved. Finally, some...
Finite element methods in probabilistic mechanics
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.
Finite Element analysis of jar connections
Kristensen, A.; Toor, Kashif; Solem, Sigurd
A new tool joint system is considered. Traditionally these rotary connections have been designed with only one shoulder geometry. However, in order to increase the torque rating of the tool joint, a new design is introduced using two shoulders. This design allow reduced tool joint dimensions wher...... whereby down-hole equipment more easily can be fitted. In order to evaluate the validity of the design, finite element analysis have been performed in ANSYS. The results obtained indicate that the new design is valid and further tests can be performed....
TITUS: a general finite element system
TITUS is a general finite element structural analysis system which performs linear/non-linear, static/dynamic analyses of heat-transfer/thermo-mechanical problems. One of the major features of TITUS is that it was designed by engineers, to address engineers in an industrial environment. This has resulted in an easy to use system, with a high-level free-formatted problem oriented language, a large selection of pre- and post processors and sophisticated graphic capabilities. TITUS has many references in civil, mechanical and nuclear engineering applications. The TITUS system is available on various types of machines, from large mainframes to mini computers
Iterative methods for mixed finite element equations
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.
Quadrature representation of finite element variational forms
Ølgaard, Kristian Breum; Wells, Garth N.
2012-01-01
This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations. An...... alternative to the run-time quadrature approach is the tensor representation presented in Chapter 8. Both the quadrature and tensor approaches are implemented in FFC (see Chapter 11). In this chapter we discuss four strategies for optimizing the quadrature representation for run-time performance of the...... generated code and show that optimization strategies lead to a dramatic improvement in run-time performance over a naive implementation. We also examine performance aspects of the quadrature and tensor approaches for different equations, and this will motivate the desirability of being able to choose...
A finite element model for ultrasonic cutting.
Lucas, Margaret; MacBeath, Alan; McCulloch, Euan; Cardoni, Andrea
2006-12-22
Using a single-blade ultrasonic cutting device, a study of ultrasonic cutting of three very different materials is conducted using specimens of cheese, polyurethane foam and epoxy resin. Initial finite element models are created, based on the assumption that the ultrasonic blade causes a crack to propagate in a controlled mode 1 opening, and these are validated against experimental data from three point bend fracture tests and ultrasonic cutting experiments on the materials. Subsequently, the finite element model is developed to represent ultrasonic cutting of a multi-layered material. Materials are chosen whose properties allow a model to be developed that could represent a multi-layer food product or biological structure, to enable ultrasonic cutting systems to be designed for applications both in the field of food processing and surgical procedures. The model incorporates an estimation of the friction condition between the cutting blade and the material to be cut and allows adjustment of the frequency, cutting amplitude and cutting speed. PMID:16814351
Finite element analysis of multilayer coextrusion.
Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A. (Proctor & Gamble Company, West Chester, OH); Mrozek, Randy A. (Army Research Laboratory, Adelphi, MD); Lenhart, Joseph Ludlow (Army Research Laboratory, Adelphi, MD); Rao, Rekha Ranjana; Collins, Robert (Oak Ridge National Laboratory); Mondy, Lisa Ann
2011-09-01
Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.
Finite elements in engineering applications. Proceedings
1990-01-01
This volume contains 16 papers presented on the conference 'Finite Elements in Engineering Applications' in Strasbourg, 26th and 27th April 1990, which was organized on the occasion of the fifth anniversary of the FE-software system PERMAS. The presentation comprised particular applications and problem solutions from industry and research. The papers deal with the following subjects: Present status and future aspects of the PERMAS development; Simulation of discrete void formation in a WC-Co microstructure; Dynamic investigation of PORSCHE Carrera 4 using FEM; Linear dynamics analysis of a coarse-pointing-mechanism; The optimization of PERMAS on the IBM 3090-vector facility; Two examples of PERMAS application in defense industry; The CONLIN program: A new capability for structural optimization within PERMAS; An application of PERMAS to some flattening problems; Reliability of uncertain structural systems; Fracture mechanics analyses with PERMAS for high temperature applications; Elastic-plastic analysis of a quick-acting gate valve; The influence of creep-fatigue interaction on incipient cracking of thermally loaded turbine shafts; Integrated MCAE-rnvironment at Daimler-Benz; Sizing and application of composite components; Solution of coupled piezoelectric-solid-fluid problems with PERMAS; Finite element models of the ARIANE launchers prediction of the flight dynamic environment. (orig./MM).
Impeller deflection and modal finite element analysis.
Spencer, Nathan A.
2013-10-01
Deflections of an impeller due to centripetal forces are calculated using finite element analysis. The lateral, or out of plane, deflections are an important design consideration for this particular impeller because it incorporates an air bearing with critical gap tolerances. The target gap distance is approximately 10 microns at a rotational velocity of 2500 rpm. The centripetal forces acting on the impeller cause it deflect in a concave fashion, decreasing the initial gap distance as a function of radial position. This deflection is characterized for a previous and updated impeller design for comparative purposes. The impact of design options such as material selection, geometry dimensions, and operating rotational velocity are also explored, followed by a sensitivity study with these parameters bounded by specific design values. A modal analysis is also performed to calculate the impeller's natural frequencies which are desired to be avoided during operation. The finite element modeling techniques continue to be exercised by the impeller design team to address specific questions and evaluate conceptual designs, some of which are included in the Appendix.
Stable Generalized Finite Element Method (SGFEM)
Babuska, I
2011-01-01
The Generalized Finite Element Method (GFEM) is a Partition of Unity Method (PUM), where the trial space of standard Finite Element Method (FEM) is augmented with non-polynomial shape functions with compact support. These shape functions, which are also known as the enrichments, mimic the local behavior of the unknown solution of the underlying variational problem. GFEM has been successfully used to solve a variety of problems with complicated features and microstructure. However, the stiffness matrix of GFEM is badly conditioned (much worse compared to the standard FEM) and there could be a severe loss of accuracy in the computed solution of the associated linear system. In this paper, we address this issue and propose a modification of the GFEM, referred to as the Stable GFEM (SGFEM). We show that the conditioning of the stiffness matrix of SGFEM is not worse than that of the standard FEM. Moreover, SGFEM is very robust with respect to the parameters of the enrichments. We show these features of SGFEM on se...
Continuous Finite Element Methods of Molecular Dynamics Simulations
Qiong Tang; Luohua Liu; Yujun Zheng
2015-01-01
Molecular dynamics simulations are necessary to perform very long integration times. In this paper, we discuss continuous finite element methods for molecular dynamics simulation problems. Our numerical results about AB diatomic molecular system and A2B triatomic molecules show that linear finite element and quadratic finite element methods can better preserve the motion characteristics of molecular dynamics, that is, properties of energy conservation and long-term stability. So finite elemen...
A multigrid solution method for mixed hybrid finite elements
Schmid, W. [Universitaet Augsburg (Germany)
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.
Finite element analysis enhancement of cryogenic testing
Thiem, Clare D.; Norton, Douglas A.
1991-12-01
Finite element analysis (FEA) of large space optics enhances cryogenic testing by providing an analytical method by which to ensure that a test article survives proposed testing. The analyses presented in this paper were concerned with determining the reliability of a half meter mirror in an environment where the exact environmental profile was unknown. FEA allows the interaction between the test object and the environment to be simulated to detect potential problems prior to actual testing. These analyses examined worse case scenerios related to cooling the mirror, its structural integrity for the proposed test environment, and deformation of the reflective surface. The FEA was conducted in-house on the System's Reliability Division's VAX 11-750 and Decstation 3100 using Engineering Mechanics Research Corporation's numerically integrated elements for systems analysis finite element software. The results of the analyses showed that it would take at least 48 hours to cool the mirror to its desired testing temperature. It was also determined that the proposed mirror mount would not cause critical concentrated thermal stresses that would fracture the mirror. FEA and actual measurements of the front reflective face were compared and good agreement between computer simulation and physical tests were seen. Space deployment of large optics requires lightweight mirrors which can perform under the harsh conditions of space. The physical characteristics of these mirrors must be well understood in order that their deployment and operation are successful. Evaluating design approaches by analytical simulation, like FEA, verifies the reliability and structural integrity of a space optic during design prior to prototyping and testing. Eliminating an optic's poor design early in its life saves money, materials, and human resources while ensuring performance.
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.
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.
Primitive elements in finite fields with arbitrary trace
Çoban, Mustafa; Coban, Mustafa
2003-01-01
Arithmetic of finite fields is not only important for other branches of mathematics but also widely used in applications such as coding and cryptography. A primitive element of a finite field is of particular interest since it enables one to represent all other elements of the field. Therefore an extensive research has been done on primitive elements, especially those satisfying extra conditions. We are interested in the existence of primitive elements in extensions of finite fields with pres...
A set of pathological tests to validate new finite elements
Rao, Mallikarjuna K; Shrinivasa, U
2001-01-01
The finite element method entails several approximations. Hence it is essential to subject all new finite elements to an adequate set of pathological tests in order to assess their performance. Many such tests have been proposed by researchers from time to time. We present an adequate set of tests, which every new finite element should pass. A thorough account of the patch test is also included in view of its significance in the validation of new elements.
Finite-Element Modelling of Biotransistors
Selvaganapathy PR
2010-01-01
Full Text Available Abstract Current research efforts in biosensor design attempt to integrate biochemical assays with semiconductor substrates and microfluidic assemblies to realize fully integrated lab-on-chip devices. The DNA biotransistor (BioFET is an example of such a device. The process of chemical modification of the FET and attachment of linker and probe molecules is a statistical process that can result in variations in the sensed signal between different BioFET cells in an array. In order to quantify these and other variations and assess their importance in the design, complete physical simulation of the device is necessary. Here, we perform a mean-field finite-element modelling of a short channel, two-dimensional BioFET device. We compare the results of this model with one-dimensional calculation results to show important differences, illustrating the importance of the molecular structure, placement and conformation of DNA in determining the output signal.
Finite element program Lamcal. (User's manual)
The present user's manual gives the input formats, job control and an input example for the finite element part of the Lamcal program. The input data have been organized in a more or less self explaining way, using keywords and standard input formats and is printed at the beginning of every run. To simplify the use of the whole program and to avoid unecessary data handling, all three parts of the Lamcal program, meshgeneration, plotting and, FE, are combined into one load module. This setup allows to do all calculations in one single run. However, preprocessing, postprocessing and restarts can be made in separate runs as well. The same reserved space for the dynamic core storage is used in all three parts, if the available space is not sufficient the FE program will stop
Computational structural analysis and finite element methods
Kaveh, A
2014-01-01
Graph theory gained initial prominence in science and engineering through its strong links with matrix algebra and computer science. Moreover, the structure of the mathematics is well suited to that of engineering problems in analysis and design. The methods of analysis in this book employ matrix algebra, graph theory and meta-heuristic algorithms, which are ideally suited for modern computational mechanics. Efficient methods are presented that lead to highly sparse and banded structural matrices. The main features of the book include: application of graph theory for efficient analysis; extension of the force method to finite element analysis; application of meta-heuristic algorithms to ordering and decomposition (sparse matrix technology); efficient use of symmetry and regularity in the force method; and simultaneous analysis and design of structures.
Finite element simulation of asphalt fatigue testing
Ullidtz, Per; Kieler, Thomas Lau; Kargo, Anders
1997-01-01
The traditional interpretation of fatigue tests on asphalt mixes has been in terms of a logarithmic linear relationship between the constant stress or strain amplitude and the number of load repetitions to cause failure, often defined as a decrease in modulus to half the initial value. To...... accomodate non-constant stress or strain, a mode factor may be introduced or the dissipated energy may be used instead of stress or strain.Cracking of asphalt (or other materials) may be described as a process consisting of three phases. In phase one diffuse microcracking is formed in the material. In the...... damage mechanics.The paper describes how continuum damage mechanics may be used with a finite element program to explain the progressive deterioration of asphalt mixes under laboratory fatigue testing. Both constant stress and constant strain testing are simulated, and compared to the actual results from...
Finite Element Analysis of a Contactless Transformer
Jianyu Lan
2013-10-01
Full Text Available Inductively coupling power transfer is an emerging technique, which enables power transfer to loads through air. The contactless transformer is the key component of it, and the design of a transformer is a time-consuming work with a large number of tests. In this paper, a design method of contactless transformer with finite element analysis is presented. First the contactless transformer model is deduced from Maxwell Equations, and the self inductance and mutual inductance computational equations are given as well. Then the magnetic field distributions of contactless transformer with different air gaps are presented by simulation of MAXWELL ANSOFT. Furthermore, the skin and proximity effects are analyzed as well. At last, the results are compared with the experimental results with the same dimension and material. The analyses show that there has a good agreement with each other. So by this method, the design period of a contactless transformer will be shorter than before
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.
Finite element analyses of CCAT preliminary design
Sarawit, Andrew T.; Kan, Frank W.
2014-07-01
This paper describes the development of the CCAT telescope finite element model (FEM) and the analyses performed to support the preliminary design work. CCAT will be a 25 m diameter telescope operating in the 0.2 to 2 mm wavelength range. It will be located at an elevation of 5600 m on Cerro Chajnantor in Northern Chile, near ALMA. The telescope will be equipped with wide-field cameras and spectrometers mounted at the two Nasmyth foci. The telescope will be inside an enclosure to protect it from wind buffeting, direct solar heating, and bad weather. The main structures of the telescope include a steel Mount and a carbon-fiber-reinforced-plastic (CFRP) primary truss. The finite element model developed in this study was used to perform modal, frequency response, seismic response spectrum, stress, and deflection analyses of telescope. Modal analyses of telescope were performed to compute the structure natural frequencies and mode shapes and to obtain reduced order modal output at selected locations in the telescope structure to support the design of the Mount control system. Modal frequency response analyses were also performed to compute transfer functions at these selected locations. Seismic response spectrum analyses of the telescope subject to the Maximum Likely Earthquake were performed to compute peak accelerations and seismic demand stresses. Stress analyses were performed for gravity load to obtain gravity demand stresses. Deflection analyses for gravity load, thermal load, and differential elevation drive torque were performed so that the CCAT Observatory can verify that the structures meet the stringent telescope surface and pointing error requirements.
Finite element simulation of wheel impact test
S.H. Yang
2008-06-01
Full Text Available Purpose: In order to achieve better performance and quality, the wheel design and manufacturing use a number of wheel tests (rotating bending test, radial fatigue test, and impact test to insure that the wheel meets the safety requirements. The test is very time consuming and expensive. Computer simulation of these tests can significantly reduce the time and cost required to perform a wheel design. In this study, nonlinear dynamic finite element is used to simulate the SAE wheel impact test.Design/methodology/approach: The test fixture used for the impact test consists of a striker with specified weight. The test is intended to simulate actual vehicle impact conditions. The tire-wheel assembly is mounted at 13° angle to the vertical plane with the edge of the weight in line with outer radius of the rim. The striker is dropped from a specified height above the highest point of the tire-wheel assembly and contacts the outboard flange of the wheel.Because of the irregular geometry of the wheel, the finite element model of an aluminium wheel is constructed by tetrahedral element. A mesh convergence study is carried out to ensure the convergence of the mesh model. The striker is assumed to be rigid elements. Initially, the striker contacts the highest area of the wheel, and the initial velocity of the striker is calculated from the impact height. The simulated strains at two locations on the disc are verified by experimental measurements by strain gages. The damage parameter of a wheel during the impact test is a strain energy density from the calculated result.Findings: The prediction of a wheel failure at impact is based on the condition that fracture will occur if the maximum strain energy density of the wheel during the impact test exceeds the total plastic work of the wheel material from tensile test. The simulated results in this work show that the total plastic work can be effectively employed as a fracture criterion to predict a wheel
Interpolation theory of anisotropic finite elements and applications
2008-01-01
Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error of anisotropic elements based on Newton’s formula of polynomial interpolation as well as its applications.
Interpolation theory of anisotropic finite elements and applications
CHEN ShaoChun; XIAO LiuChao
2008-01-01
Interpolation theory is the foundation of finite element methods. In this paper, after reviewing some existed interpolation theorems of anisotropic finite element methods, we present a new way to analyse the interpolation error of anisotropic elements based on Newton's formula of polynomial interpolation as well as its applications.
Finite-state machines as elements in control systems.
Burgin, G. H.; Walsh, M. J.
1971-01-01
Demonstration that approximate solutions to certain classes of differential and difference equations can be expressed in form of finite state machines. Based on this result, a finite-state machine model of an adaptive gain changer in an aircraft stability augmentation system is developed. Results of simulated flights using the finite-state machine gain changer are presented.
An efficient wavelet finite element method in fault prognosis of incipient crack
无
2006-01-01
The method of constructing any scale wavelet finite element (WFE) based on the one-dimensional or two-dimensional Daubechies scaling functions was presented, and the corresponding WFE adaptive lifting algorithm was given. In order to obtain the nested increasing approximate subspaces of multiscale finite element, the Daubechies scaling functions with the properties of multi-resolution analysis were employed as the finite element interpolating functions. Thus, the WFE could adaptively mesh the singularity domain caused by local cracks, which resulted in better approximate solutions than the traditional finite element methods. The calculations of natural frequencies of cracked beam were used to check the accuracy of given methods. In addition, the results of cracked cantilever beam and engineering application were satisfied. So, the current methods can provide effective tools in the numerical modeling of the fault prognosis of incipient crack.
Finite element analysis theory and application with ANSYS
Moaveni, Saeed
2015-01-01
For courses in Finite Element Analysis, offered in departments of Mechanical or Civil and Environmental Engineering. While many good textbooks cover the theory of finite element modeling, Finite Element Analysis: Theory and Application with ANSYS is the only text available that incorporates ANSYS as an integral part of its content. Moaveni presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively. Teaching and Learning Experience This program will provide a better teaching and learning experience-for you and your students. It will help: *Present the Theory of Finite Element Analysis: The presentation of theoretical aspects of finite element analysis is carefully designed not to overwhelm students. *Explain How to Use ANSYS Effectively: ANSYS is incorporated as an integral part of the content throughout the book. *Explore How to Use FEA as a Design/Modeling Tool: Open-ended design problems help stude...
Finite Element Method (Chapter from "Gratings: Theory and Numeric Applications")
Demésy, Guillaume; Nicolet, André; Vial, Benjamin
2013-01-01
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack lightened by a plane wave of arbitrary incidence and polarization angle. It relies on a rigorous treatment of the plane wave sources problem through an equivalent radiation problem with localized sources. Bloch conditions and a new Adaptative Perfectly Matched Layer have been implemented in order to truncate the computational domain. We derive this formulation for both mono-dimensional gratings in TE/TM polarization cases (2D or scalar case) and for the most general bidimensional or crossed gratings (3D or vector case). The main advantage of this formulation is its complete generality with respect to the studied geometries and the material properties. Its principle remains independent of both the number of diffractive elements by period and number of stack layers. The flexi...
Adaptive Through-Thickness Integration Strategy for Shell Elements
Burchitz, I.A.; Meinders, T.; Huetink, J.
2007-01-01
Reliable numerical prediction of springback in sheet metal forming is essential for the automotive industry. There are numerous factors that influence the accuracy of springback prediction by using the finite element method. One of the reasons is the through-thickness numerical integration of shell elements. It is known that even for simple problems the traditional integration schemes may require up to 50 integration points to achieve a high accuracy of springback analysis. An adaptive throug...
Numerical Analysis of Higher Order Discontinuous Galerkin Finite Element methods
Hartmann, Ralf
2008-01-01
After the introduction in Section 1 this lecture starts off with recalling well-known results from the numerical analysis of the continuous finite element methods. In particular, we recall a priori error estimates in the energy norm and the L2-norm including their proofs for higher order standard finite element methods of Poisson's equation in Section 2 and for the standard and the streamline diffusion finite element method of the linear advection equation in Section 3. ...
The finite element method its basis and fundamentals
Zienkiewicz, Olek C; Zhu, JZ
2013-01-01
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob
Analysis of Finite Elements and Finite Differences for Shallow Water Equations: A Review
Neta, Beny
1992-01-01
Mathematics and Computers in Simulation, 34, (1992), 141–161. In this review article we discuss analyses of finite-element and finite-difference approximations of the shallow water equations. An extensive bibliography is given.
Continuous Finite Element Methods of Molecular Dynamics Simulations
Qiong Tang
2015-01-01
Full Text Available Molecular dynamics simulations are necessary to perform very long integration times. In this paper, we discuss continuous finite element methods for molecular dynamics simulation problems. Our numerical results about AB diatomic molecular system and A2B triatomic molecules show that linear finite element and quadratic finite element methods can better preserve the motion characteristics of molecular dynamics, that is, properties of energy conservation and long-term stability. So finite element method is also a reliable method to simulate long-time classical trajectory of molecular systems.
Ablative Thermal Response Analysis Using the Finite Element Method
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.
Introduction to finite and spectral element methods using Matlab
Pozrikidis, Constantine
2005-01-01
Why another book on the finite element method? There are currently more than 200 books in print with ""Finite Element Method"" in their titles. Many are devoted to special topics or emphasize error analysis and numerical accuracy. Others stick to the fundamentals and do little to describe the development and implementation of algorithms for solving real-world problems.Introduction to Finite and Spectral Element Methods Using MATLAB provides a means of quickly understanding both the theoretical foundation and practical implementation of the finite element method and its companion spectral eleme
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
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.
A coupling procedure for modeling acoustic problems using finite elements and boundary elements
Coyette, J.; Vanderborck, G.; Steichen, W.
1994-01-01
Finite element (FEM) and boundary element (BEM) methods have been used for a long time for the numerical simulation of acoustic problems. The development presented in this paper deals with a general procedure for coupling acoustic finite elements with acoustic boundary elements in order to solve efficiently acoustic problems involving non homogeneous fluids. Emphasis is made on problems where finite elements are used for a confined (bounded) fluid while boundary elements are selected for an e...
Application of the Finite-Element Z-Matrix Method to e-H2 Collisions
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.
Control volume finite element method for radiation
In this paper a new methodology is presented by the authors for the numerical treatment of radiative heat transfer in emitting, absorbing and scattering media. This methodology is based on the utilisation of Control Volume Finite Element Method (CVFEM) and the use, for the first time, of matrix formulation of the discretized Radiative Transfer Equation (RTE). The advantages of the proposed methodology is to avoid problems that confronted when previous techniques are used to predict radiative heat transfer, essentially, in complex geometries and when there is scattering and/or non-black boundaries surfaces. Besides, the new formulation of the discretized RTE presented in this paper makes it possible to solve the algebraic system by direct or iterative numerical methods. The theoretical background of CVFEM and matrix formulation is presented in the text. The proposed technique is applied to different test problems, and the results compared favourably against other published works. Moreover this paper discusses in detail the effects of some radiative parameters, such as optical thickness and walls emissivities on the spatial evolution of the radiant heat flux. The numerical simulation of radiative heat transfer for different cases using the algorithm proposed in this work has shown that the developed computer procedure needs an accurate CPU time and is exempt of any numerical oscillations
Studying a dental pathology by finite elements
Fernando Mejía Umaña
2010-04-01
Full Text Available Abfractives lesions or abfractions are non-cavity lesions of dental structures in which a biomechanical factor has been identified as being the most probable cause for it occurring. Even throught such lesion can be presented in any tooth, it occurs more frequently in people aged over 35. This article presents some results obtained by the Universidad Nacional de Colombia's multidisciplinary research group for studying "dental material's structure and propierties". The introduction describes such lesion's characteristics and possible causes. The results of various modelling exercises using finite elements (in two and three dimensions are presented regarding a first premolar tooth subjected to normal mastication load and also to abnormal loads produced by occlusion problems. The most important findings (accompanied by clinical observations were that: areas of high concentration of forces were identified where lesions were frequently presented, associated with loads whose line of action did not pass through the central part of the section of tooth at cervical level; a direct relationship between facets of wear being orientated with the direction of forces produced by a high concentration of force; and the presence of high compression forces in the cervical region.
Nonlinear finite element analysis of concrete structures
This report deals with nonlinear finite element analysis of concrete structures loaded in the short-term up until failure. A profound discussion of constitutive modelling on concrete is performed; a model, applicable for general stress states, is described and its predictions are compared with experimental data. This model is implemented in the AXIPLANE-program applicable for axisymmetrick and plane structures. The theoretical basis for this program is given. Using the AXIPLANE-program various concrete structures are analysed up until failure and compared with experimental evidence. These analyses include panels pressure vessel, beams failing in shear and finally a specific pull-out test, the Lok-Test, is considered. In these analyses, the influence of different failure criteria, aggregate interlock, dowel action, secondary cracking, magnitude of compressive strenght, magnitude of tensile strenght and of different post-failure behaviours of the concrete are evaluated. Moreover, it is shown that a suitable analysis of the theoretical data results in a clear insight into the physical behaviour of the considered structures. Finally, it is demonstrated that the AXISPLANE-program for widely different structures exhibiting very delicate structural aspects gives predictions that are in close agreement with experimental evidence. (author)
TACO: a finite element heat transfer code
TACO is a two-dimensional implicit finite element code for heat transfer analysis. It can perform both linear and nonlinear analyses and can be used to solve either transient or steady state problems. Either plane or axisymmetric geometries can be analyzed. TACO has the capability to handle time or temperature dependent material properties and materials may be either isotropic or orthotropic. A variety of time and temperature dependent loadings and boundary conditions are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additionally, TACO has some specialized features such as internal surface conditions (e.g., contact resistance), bulk nodes, enclosure radiation with view factor calculations, and chemical reactive kinetics. A user subprogram feature allows for any type of functional representation of any independent variable. A bandwidth and profile minimization option is also available in the code. Graphical representation of data generated by TACO is provided by a companion post-processor named POSTACO. The theory on which TACO is based is outlined, the capabilities of the code are explained, the input data required to perform an analysis with TACO are described. Some simple examples are provided to illustrate the use of the code
Finite Element Simulation for Springback Prediction Compensation
Agus Dwi Anggono
2011-01-01
Full Text Available An accurate modelling of the sheet metal deformations including the springback prediction is one of the key factors in the efficient utilisation of Finite Element Method (FEM process simulation in industrial application. Assuming that springback can be predicted accurately, there still remains the problem of how to use such results to appear at a suitable die design to produce a target part shape. It is this second step of springback compensation that is addressed in the current work. This paper presents an evaluation of a standard benchmark model defined as Benchmark II of Numisheet 2008, S-channel model with various drawbeads and blank holder force (BHF. The tool geometry modified based on springback calculation for a part to compensate springback. The result shows that the combination of the smooth bead with BHF of 650 kN resulted in the minimum springback and the tool compensation was successfully to accommodate the springback errors.
FINITE ELEMENT ANALYSIS OF WOOD ADHESIVE JOINTS
Thomas GEREKE
2016-03-01
Full Text Available Engineered wood products such as glulam or cross-laminated timber are widely established in the construction industry. Their structural behaviour and reliability clearly bases on the adhesive bonding. In order to understand and improve the performance of glued wood members a finite element modelling of standard single lap shear samples was carried out. A three-dimensional model of a longitudinal tensile-shear specimen with quasi-centric load application was developed. The main influences of wood and adhesive parameters on structural performance were identified. Therefore, variations of the elasticity, the annual ring angle, fibre angle, and the interface zone and their effect on the occurring stresses in the adhesive bond line were investigated numerically. The adhesive bond line is most significantly sensitive to the Young´s modulus of the adhesive itself. A variation of the fibre angle of the glued members in the standard test is an essential criterion and to be considered when preparing lap shear specimens. A model with representation of early- and latewood gives a more detailed insight into wooden adhesive joints.
Phase-space finite elements in a least-squares solution of the transport equation
The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshing tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)
MORTAR FINITE VOLUME METHOD WITH ADINI ELEMENT FOR BIHARMONIC PROBLEM
Chun-jia Bi; Li-kang Li
2004-01-01
In this paper, we construct and analyse a mortar finite volume method for the dis-cretization for the biharmonic problem in R2. This method is based on the mortar-type Adini nonconforming finite element spaces. The optimal order H2-seminorm error estimate between the exact solution and the mortar Adini finite volume solution of the biharmonic equation is established.
Finite Element Analysis (FEA) in Design and Production.
Waggoner, Todd C.; And Others
1995-01-01
Finite element analysis (FEA) enables industrial designers to analyze complex components by dividing them into smaller elements, then assessing stress and strain characteristics. Traditionally mainframe based, FEA is being increasingly used in microcomputers. (SK)
Multiplicative orders of elements in Conway towers of finite fields
Popovych, Roman
2015-01-01
We give a lower bound on multiplicative orders of some elements in defined by Conway towers of finite fields of characteristic two and also formulate a condition under that these elements are primitive
An efficient finite element solution for gear dynamics
A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.
Introduction to the finite element method in electromagnetics
Polycarpou, Anastasis
2006-01-01
This series lecture is an introduction to the finite element method with applications in electromagnetics. The finite element method is a numerical method that is used to solve boundary-value problems characterized by a partial differential equation and a set of boundary conditions. The geometrical domain of a boundary-value problem is discretized using sub-domain elements, called the finite elements, and the differential equation is applied to a single element after it is brought to a "weak" integro-differential form. A set of shape functions is used to represent the primary unknown variable
Finite element modelling of X-band RF flanges
Kortelainen, Laurie; Riddone, Germana
A finite element model of different versions of RF flange used in Compact Linear Collider modules was created in ANSYS Workbench software. A 2D idealisation of the assembly was modelled using both plane stress and plane strain elements. Three of the versions were also modelled using 3D elements. A detailed description of finite element models and theoretical background accompanying the models are presented in this thesis.
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
Bishnu P. Lamichhane
2014-01-01
We present a simple finite element method for the discretization of Reissner--Mindlin plate equations. The finite element method is based on using the nonconforming Crouzeix-Raviart finite element space for the transverse displacement, and the standard linear finite element space for the rotation of the transverse normal vector. We also present two examples for the discrete Lagrange multiplier space for the proposed formulation.
Finite element analysis for general elastic multi-structures
HUANG; Jianguo; SHI; Zhongci; XU; Yifeng
2006-01-01
A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.
Finite Element Analysis of Pipe T-Joint
P.M.Gedkar
2012-01-01
Full Text Available This paper reports stress analysis of two pressurized cylindrical intersection using finite element method. The different combinations of dimensions of run pipe and the branch pipe are used to investigate thestresses in pipe at the intersection. In this study the stress analysis is accomplished by finite element package ANSYS.
An introduction to the UNCLE finite element scheme
UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)
Finite element models applied in active structural acoustic control
Oude Nijhuis, Marco H.H.; Boer, de André; Rao, Vittal S.
2002-01-01
This paper discusses the modeling of systems for active structural acoustic control. The finite element method is applied to model structures including the dynamics of piezoelectric sensors and actuators. A model reduction technique is presented to make the finite element model suitable for controll
Implementation of a mixed finite element in a particle method
We present here a coupled particle-finite element method for the Vlasov-Maxwell equations. For the dicretization in space of the wave propagation equations, a Nedelec mixed finite element is chosen. A leapfrog scheme is used for time discretization. The Vlasov phase space is discretized into macroparticles assumed to be Dirac distributions
Finite element meshing of ANSYS (trademark) solid models
Kelley, F. S.
1987-01-01
A large scale, general purpose finite element computer program, ANSYS, developed and marketed by Swanson Analysis Systems, Inc. is discussed. ANSYS was perhaps the first commercially available program to offer truly interactive finite element model generation. ANSYS's purpose is for solid modeling. This application is briefly discussed and illustrated.
Finite Element Modelling of Seismic Liquefaction in Soils
Galavi, V.; Petalas, A.; Brinkgreve, R.B.J.
2013-01-01
Numerical aspects of seismic liquefaction in soils as implemented in the finite element code, PLAXIS, is described in this paper. After description of finite element equations of dynamic problems, three practical dynamic boundary conditions, namely viscous boundary tractions, tied degrees of freedom
About the Finite Element Method Applied to Thick Plates
Mihaela Ibănescu
2006-01-01
Full Text Available The present paper approaches of plates subjected to transverse loads, when the shear force and the actual boundary conditions are considered, by using the Finite Element Method. The isoparametric finite elements create real facilities in formulating the problems and great possibilities in creating adequate computer programs.
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Natalia Bakhova
2011-03-01
Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.
Discontinuous finite element formulations for neutron transport in spherical geometry
Highlights: • We developed linear and quadratic discontinuous finite element methods in sphere. • We found that quadratic discontinuous finite element method is the best method. • Quadratic method has the desired convergence properties. • Smallest L2 error norms are obtained in scalar fluxes if quadratic method is used. - Abstract: We have developed the linear and quadratic Galerkin discontinuous finite element methods for the solution of both time-independent and time-dependent spherical geometry neutron transport problems. Discrete ordinates method is used for the angular discretization while the implicit method is utilized for temporal discretization in time-dependent problems. In order to assess the relative performance of the newly developed linear and quadratic discontinuous finite element spatial differencing methods relative to the previously developed linear discontinuous finite element and diamond difference discretizations, a computer code is developed and numerical solutions of the neutron transport equation for some benchmark problems are obtained. These numerical applications reveal that the newly developed quadratic discontinuous finite element method produces the most accurate results while the newly developed linear discontinuous finite element method follows as the second best discontinuous finite element method
Experiment and finite element analysis of micromilling force
SUN Ya-zhou; MENG Qing-xin
2008-01-01
For predicting the milling force in process of micromilling aluminum alloy,the law for micromilling force changing under different milling parameters was studied.The elastic-plastic finite elelent model of micromilling was found using general commercial software.During modeling,the Johnson-Cook's coupled thermalmechanical model Was used as workpiece material model,the Johnson-Cook's shear failure principle Was adopted as workpiece failure principle,and the coupled thermal-mechanical hexahedron strain hybrid modules and self-adaptive grid technology based on the updated Lagrange formulation were used to mesh the workpiece's elements,while the friction between tool and workpiece obeys the modified Coulomb's law that combines with the sliding friction and the adhesive friction.By means of finite element analysis,the law for micromilling force changing under different milling parameters Was obtained,and the results were analyzed and compared.Finally micromilling experiments were carried out to validate the results of simulation.
OBJECT-ORIENTED FINITE ELEMENT ANALYSIS AND PROGRAMMING IN VC + +
马永其; 冯伟
2002-01-01
The design of finite element analysis program using object-oriented programming(OOP) techniques is presented. The objects, classes and the subclasses used in theprogramming are explained. The system of classes library of finite element analysis programand Windows-type Graphical User Interfaces by VC + + and its MFC are developed. Thereliability, reusability and extensibility of program are enhanced. It is a reference todevelop the large-scale, versatile and powerful systems of object-oriented finite elementsoftware.
ALTERNATING DIRECTION FINITE ELEMENT METHOD FOR SOME REACTION DIFFUSION MODELS
江成顺; 刘蕴贤; 沈永明
2004-01-01
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
Maple in discretizing equations by the Finite Volume Element method
Canright, David R.
1996-01-01
The Finite Volume Element (FVE) method combines the exact conservation of finite volumes with the continuous representation of finite elements One drawback of this approach is that to evaluate the coe cients in the equations "the stencils" many simple integrals involving unknowns must be evaluated. This problem is compounded when working with systems of di erential equations involving several different operators and or variable coeefficients This talk will examine one such project fo...
Nondestructive Evaluation Correlated with Finite Element Analysis
Abdul-Azid, Ali; Baaklini, George Y.
1999-01-01
Advanced materials are being developed for use in high-temperature gas turbine applications. For these new materials to be fully utilized, their deformation properties, their nondestructive evaluation (NDE) quality and material durability, and their creep and fatigue fracture characteristics need to be determined by suitable experiments. The experimental findings must be analyzed, characterized, modeled and translated into constitutive equations for stress analysis and life prediction. Only when these ingredients - together with the appropriate computational tools - are available, can durability analysis be performed in the design stage, long before the component is built. One of the many structural components being evaluated by the NDE group at the NASA Lewis Research Center is the flywheel system. It is being considered as an energy storage device for advanced space vehicles. Such devices offer advantages over electrochemical batteries in situations demanding high power delivery and high energy storage per unit weight. In addition, flywheels have potentially higher efficiency and longer lifetimes with proper motor-generator and rotor design. Flywheels made of fiber-reinforced polymer composite material show great promise for energy applications because of the high energy and power densities that they can achieve along with a burst failure mode that is relatively benign in comparison to those of flywheels made of metallic materials Therefore, to help improve durability and reduce structural uncertainties, we are developing a comprehensive analytical approach to predict the reliability and life of these components under these harsh loading conditions. The combination of NDE and two- and three-dimensional finite element analyses (e.g., stress analyses and fracture mechanics) is expected to set a standardized procedure to accurately assess the applicability of using various composite materials to design a suitable rotor/flywheel assembly.
Design of eddy current coil using finite element model
Eddy current signal evaluation is based on the relationship between signal shape and defect characteristics. As a numerical approach finite element model can be useful to eddy current phenomena. Using a finite element program for axi-symmetric and two-dimensional geometry, the effect of coil distance and width to the eddy current signal shapes were investigated. Various coils were fabricated and actual eddy current signals were compared with the finite element model calculations. As either coil distance or coil width increases, the signal shape changes from differential-like to absolute-like. The signals from the finite element analysis were well matched to the experimental results. The finite element analysis can be a useful tool for optimization of design parameters for eddy current coil, such as coil dimension, operating frequency, materials properties, and defect type, etc.
Finite Element Analysis of Fluid-Conveying Timoshenko Pipes
Chih-Liang Chu
1995-01-01
Full Text Available A general finite element formulation using cubic Hermitian interpolation for dynamic analysis of pipes conveying fluid is presented. Both the effects of shearing deformations and rotary inertia are considered. The development retains the use of the classical four degrees-of-freedom for a two-node element. The effect of moving fluid is treated as external distributed forces on the support pipe and the fluid finite element matrices are derived from the virtual work done due to the fluid inertia forces. Finite element matrices for both the support pipe and moving fluid are derived and given explicitly. A numerical example is given to demonstrate the validity of the model.
Finite elements volumes methods: applications to the Navier-Stokes equations and convergence results
In the first chapter are described the equations modeling incompressible fluid flow and a quick presentation of finite volumes method. The second chapter is an introduction to the finite elements volumes method. The box model is described and a method adapted to Navier-Stokes problems is proposed. The third chapter shows a fault analysis of the finite elements volumes method for the Laplacian problem and some examples in one, two, three dimensional calculations. The fourth chapter is an extension of the error analysis of the method for the Navier-Stokes problem
Mattiussi, Claudio
1997-01-01
In this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods, illuminating the similarity between the discretization strategies adopted by the two methods, in the light of a geometric interpretation proposed for the role played by the weighting functions in finite elements. We discuss the intrinsic discrete nature of some of the factors appearing in the field equations, underlining the exception represented by the constitutive term, th...
Finite element-wavelet hybrid algorithm for atmospheric tomography.
Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny
2014-03-01
Reconstruction of the refractive index fluctuations in the atmosphere, or atmospheric tomography, is an underlying problem of many next generation adaptive optics (AO) systems, such as the multiconjugate adaptive optics or multiobject adaptive optics (MOAO). The dimension of the problem for the extremely large telescopes, such as the European Extremely Large Telescope (E-ELT), suggests the use of iterative schemes as an alternative to the matrix-vector multiply (MVM) methods. Recently, an algorithm based on the wavelet representation of the turbulence has been introduced in [Inverse Probl.29, 085003 (2013)] by the authors to solve the atmospheric tomography using the conjugate gradient iteration. The authors also developed an efficient frequency-dependent preconditioner for the wavelet method in a later work. In this paper we study the computational aspects of the wavelet algorithm. We introduce three new techniques, the dual domain discretization strategy, a scale-dependent preconditioner, and a ground layer multiscale method, to derive a method that is globally O(n), parallelizable, and compact with respect to memory. We present the computational cost estimates and compare the theoretical numerical performance of the resulting finite element-wavelet hybrid algorithm with the MVM. The quality of the method is evaluated in terms of an MOAO simulation for the E-ELT on the European Southern Observatory (ESO) end-to-end simulation system OCTOPUS. The method is compared to the ESO version of the Fractal Iterative Method [Proc. SPIE7736, 77360X (2010)] in terms of quality. PMID:24690653
Determination of an Initial Mesh Density for Finite Element Computations via Data Mining
Kanapady, R; Bathina, S K; Tamma, K K; Kamath, C; Kumar, V
2001-07-23
Numerical analysis software packages which employ a coarse first mesh or an inadequate initial mesh need to undergo a cumbersome and time consuming mesh refinement studies to obtain solutions with acceptable accuracy. Hence, it is critical for numerical methods such as finite element analysis to be able to determine a good initial mesh density for the subsequent finite element computations or as an input to a subsequent adaptive mesh generator. This paper explores the use of data mining techniques for obtaining an initial approximate finite element density that avoids significant trial and error to start finite element computations. As an illustration of proof of concept, a square plate which is simply supported at its edges and is subjected to a concentrated load is employed for the test case. Although simplistic, the present study provides insight into addressing the above considerations.
High order discontinuous finite-volume/finite-element method for CFD applications
Ramezani A; Stipcich G.
2014-01-01
The proposed method naturally merges the desirable conservative properties and intuitive physical formulation of the widely used finite-volume (FV) technique, with the capability of local arbitrary high-order accuracy and high-resolution which is distinctive in the discontinuous finite-element (FE) framework. This relatively novel scheme, the discontinuous hybrid control-volume/finite-element method (DCVFEM), has been already applied to the solution of advection-diffusion problems and shallow...
Discontinuous high-order finite-volume/finite-element method for inviscid compressible flows
Ramezani A; Stipcich G.; Remaki L.
2015-01-01
The discontinuous, hybrid control-volume/finite-element method merges the desirable conservative properties and intuitive physical formulation of the finite-volume technique, with the capability of local arbitrary high-order accuracy distinctive of the discontinuous finite-element method. This relatively novel scheme has been previously applied to the solution of advection-diffusion problems and the shallow-water equations, and is in the present work extended to the Euler equations. The deriv...
Adaptive finite difference for seismic wavefield modelling in acoustic media.
Yao, Gang; Wu, Di; Debens, Henry Alexander
2016-01-01
Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang's optimised finite difference scheme. PMID:27491333
Quadrilateral isoparametric finite elements for plane elastic Cosserat bodies
Hongwu Zhang; Hui Wang; Guozhen Liu; Keren Wang
2005-01-01
4-node, 8-node and 8(4)-node quadrilateral plane isoparametric elements are used for the solution of bound ary value problems in linear isotropic Cosserat elasticity. The patch test is applied to validate the finite elements. Engineering problems of stress concentration around a circular hole in plane strain condition and mechanical behaviors of heterogeneous materials with rigid inclusions and pores are computed to test the accuracy and capability of these three types of finite elements.
Contribution to stress sensitivity analysis of the shell finite elements
Hol'ková Z.
2008-11-01
Full Text Available The sensitivity analysis and the finite elements method represent an important tool for the influence analysis of the structural parameters. This analysis plays a significant role in the decision process of the formulation of the structural optimizing or probability analysis. The goal of the paper is to present theoretic and numerical aspects of the shell element stress sensitivity analysis with the respect to the thickness and its implementation into finite element code MATFEM inbuilt to Matlab.
Reactor kinetic formulation using the finite element method
This research has the objective of solving the spatial Kinetic equations for two energy groups using the finite element method. In the methodology, was applied the direct method, such that matrix equations coefficients from spatial discretization was generated by finite element method. The formulation of the time-dependent problem was obtained by analytical integration of precursor concentration equation and using the Euler implicit scheme in the dynamic diffusion problem. A 2D example of a reactor static diffusion problem was solved using a linear triangular finite element. This solution was compared with the numerical benchmark solution, found in the literature, and the numerical results calculated by the finite difference methods. This comparison shows the capacity of the finite element method to obtain a precise solution. (author)
A second generation finite element computer program for stress analysis
A second generation finite element computer program for stress analysis is under development. Incorporated in the computer program are finite elements which satisfy the completeness and continuity requirements for arbitrary order polynomial approximating functions. The distinguishing feature of the new algorithm is that it permits the user to exercise control over both the number of finite elements and the order of approximation over each element. Consequently, it is not necessary to define more finite elements than needed to specify the geometry of a structure. The order of polynomial approximating functions may be chosen either directly or indirectly; by specifying the required level of precision in terms of the quantities of interest. An automated iterative process then seeks the degree of approximation which corresponds to the specified level of precision. An important advantage of the new algorithm is that it substantially increases the computational power of the finite element method. Comparisons with state-of-the-art computer programs indicated significant reductions in the number of finite elements needed and the number of variables employed. The reduction in the number of finite elements was by at least an order of magnitude in all cases. The new finite element stress analysis capability is, of course, applicable to all problems which can be solved by current finite element methods. The potential benefits are the greatest in applications where, due to the presence of steep stress gradients, mechanical fatigue controls design and in dynamic and non-linear analyses where the number of variables must be kept to a minimum in order to make numerical analysis feasible
Teaching Finite Element Method of Structural Line Elements Assisted by Open Source FreeMat
Waluyo Adi Siswanto; Agung Setyo Darmawan
2012-01-01
One of the important objectives in teaching finite element method at introductory level is to bring students into the comprehension of finite element procedures. This study presents a strategy of teaching structural line elements involving an open source computer-aided learning tool FreeMat integrated with another open source CALFEM finite element toolbox. FreeMat, which is a programming based learning tool, is used together with other higher level learning tools; Open/Libre Office Spreadshee...
Development of polygon elements based on the scaled boundary finite element method
We aim to extend the scaled boundary finite element method to construct conforming polygon elements. The development of the polygonal finite element is highly anticipated in computational mechanics as greater flexibility and accuracy can be achieved using these elements. The scaled boundary polygonal finite element will enable new developments in mesh generation, better accuracy from a higher order approximation and better transition elements in finite element meshes. Polygon elements of arbitrary number of edges and order have been developed successfully. The edges of an element are discretised with line elements. The displacement solution of the scaled boundary finite element method is used in the development of shape functions. They are shown to be smooth and continuous within the element, and satisfy compatibility and completeness requirements. Furthermore, eigenvalue decomposition has been used to depict element modes and outcomes indicate the ability of the scaled boundary polygonal element to express rigid body and constant strain modes. Numerical tests are presented; the patch test is passed and constant strain modes verified. Accuracy and convergence of the method are also presented and the performance of the scaled boundary polygonal finite element is verified on Cook's swept panel problem. Results show that the scaled boundary polygonal finite element method outperforms a traditional mesh and accuracy and convergence are achieved from fewer nodes. The proposed method is also shown to be truly flexible, and applies to arbitrary n-gons formed of irregular and non-convex polygons.
Effective Stiffness: Generalizing Effective Resistance Sampling to Finite Element Matrices
Avron, Haim
2011-01-01
We define the notion of effective stiffness and show that it can used to build sparsifiers, algorithms that sparsify linear systems arising from finite-element discretizations of PDEs. In particular, we show that sampling $O(n\\log n)$ elements according to probabilities derived from effective stiffnesses yields an high quality preconditioner that can be used to solve the linear system in a small number of iterations. Effective stiffness generalizes the notion of effective resistance, a key ingredient of recent progress in developing nearly linear symmetric diagonally dominant (SDD) linear solvers. Solving finite elements problems is of considerably more interest than the solution of SDD linear systems, since the finite element method is frequently used to numerically solve PDEs arising in scientific and engineering applications. Unlike SDD systems, which are relatively easy to precondition, there has been limited success in designing fast solvers for finite element systems, and previous algorithms usually tar...
Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms
Kurdila, Andrew J.; Sharpley, Robert C.
1999-01-01
This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.
Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators
Taleghani, Barmac K.; Campbell, Joel F.
1999-01-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
P-Finite-Element Program For Analysis Of Plates
Smith, James P.
1995-01-01
BUCKY is p-finite-element computer program for highly accurate analysis of structures. Used to analyze buckling, bending, and in-plane stress-and-strain behaviors of plates. Provides elastic-plastic solutions for isotropic plates in states of plane stress, and axisymmetric solution sequence used to treat three-dimensional problems. Computes response of plate to variety of loading and boundary conditions by use of higher-order displacement function in p-finite-element method. Enables user to obtain results more accurate than obtained by use of traditional h-finite elements. Written in FORTRAN 77.
Response Surface Stochastic Finite Element Method of Composite Structure
Cai Deyong
2016-01-01
Full Text Available Response Surface Method (RSM has been applied to structural reliability problems successfully in many areas. Finite Element Method (FEM is one of the most widely used computational methods, which permit the analysis and design of large-scale engineering systems. In order to obtain a reliability analysis method of composite structure with satisfactory accuracy and computational efficiency, RSM and FEM were combined by secondary development of ABAQUS. Response Surface Stochastic Finite Element Method (RSSFEM which can solve the reliability problems of composite structure was developed. The numerical accuracy and the computational efficiency of the developed method were demonstrated by comparison with Monte-Carlo Stochastic Finite Element Method (MCSFEM.
Nonlinear finite element modeling of THUNDER piezoelectric actuators
Taleghani, Barmac K.; Campbell, Joel F.
1999-06-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (Thin Layer Unimorph Ferroelectric Driver) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
Five-point Element Scheme of Finite Analytic Method for Unsteady Groundwater Flow
Xiang Bo; Mi Xiao; Ji Changming; Luo Qingsong
2007-01-01
In order to improve the finite analytic method's adaptability for irregular unit, by using coordinates rotation technique this paper establishes a five-point element scheme of finite analytic method. It not only solves unsteady groundwater flow equation but also gives the boundary condition. This method can be used to calculate the three typical questions of groundwater. By compared with predecessor's computed result, the result of this method is more satisfactory.
Multigroup finite element-boundary element method for neutron diffusion
Full text: The finite element method (FEM) is an efficient method used for the solution of partial differential equations (PDE's) of engineering physics due to its symmetric, sparse and positive-definite coefficient matrix. FEM has been successfully applied for the solution of multigroup neutron transport and diffusion equations since 1970's. The boundary element method (BEM), on the other hand, is a newer method and is unique among the numerical methods used for the solution of PDE's with its property of confining the unknowns only to the boundaries of homogeneous regions, thus, greatly reducing matrix dimensions. The first application of BEM to the neutron diffusion equation (NDE) dates back to 1985 and many researchers are currently working in this area. Although BEM is known to have the desirable property of being an internal-mesh free method, this advantage is lost in some of its application to the NDE due to the existence of fission source volume integrals in fissionable regions unless domain-decomposition methods are used. To exploit the favorable properties of both FEM and BEM, a hybrid FE/BE method has been recently proposed for reflected systems treated by one or two-group diffusion theories in a recent paper co-authored by the first author. In this work, the hybrid FE/BE method for reflected systems is generalized to multigroup diffusion theory. The core is treated by FEM to preserve the high accuracy of FEM in such neutron-producing regions. Using a boundary integral equation formerly proposed by the second author, BEM, is utilized for the discretization of the reflector, thus, eliminating the internal mesh completely for this nonfissionable region. The multigroup FE/BE method has been implemented in our recently developed FORTRAN program. The program is validated by comparison of the calculated effective multiplication factor and the group fluxes with their analytical counterparts for a two-group reflected system. Comparison of these results and
Modelling optimization involving different types of elements in finite element analysis
Finite elements are used to express the mechanical behaviour of a structure in finite element analysis. Therefore, the selection of the elements determines the quality of the analysis. The aim of this paper is to compare and contrast 1D element, 2D element, and 3D element used in finite element analysis. A simple case study was carried out on a standard W460x74 I-beam. The I-beam was modelled and analyzed statically with 1D elements, 2D elements and 3D elements. The results for the three separate finite element models were compared in terms of stresses, deformation and displacement of the I-beam. All three finite element models yield satisfactory results with acceptable errors. The advantages and limitations of these elements are discussed. 1D elements offer simplicity although lacking in their ability to model complicated geometry. 2D elements and 3D elements provide more detail yet sophisticated results which require more time and computer memory in the modelling process. It is also found that the choice of element in finite element analysis is influence by a few factors such as the geometry of the structure, desired analysis results, and the capability of the computer
In the lagrangian calculations of some nuclear reactor problems such as a bubble expansion in the core of a fast breeder reactor, the crash of an airplane on the external containment or the perforation of a concrete slab by a rigid missile, the mesh may become highly distorted. A remesh is then necessary to continue the calculation with precision and economy. Similarly, an eulerian calculation of a fluid volume bounded by lagrangian shells can be facilitated by a remesh scheme with continuously adapts the boundary of the eulerian domain to the lagrangian shell. This paper reviews available remesh algorithms for finite element and finite difference calculations of solid and fluid continuum mechanics problems, and presents an improved Finite Element Remesh Method which is independent of the quantities at the nodal points (NP) and the integration points (IP) and permits a restart with a new mesh. (orig.)
Higher-Order Finite Elements for Computing Thermal Radiation
Gould, Dana C.
2004-01-01
Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higher-order finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times. One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications. In the basic form of the RSE method, each finite element selected for use in computing radiative heat transfer is considered to be a parent element and is divided into sub-elements for the purpose of solving the surface-to-surface radiation-exchange problem. The sub-elements are then treated as classical finite elements; that is, they are assumed to be isothermal, and their view factors and absorbed heat fluxes are calculated accordingly. The heat fluxes absorbed by the sub-elements are then transferred back to the parent element to obtain a radiative heat flux that varies spatially across the parent element. Variants of the RSE method involve the use of polynomials to interpolate and/or extrapolate to approximate spatial variations of physical quantities. The other variant of the finite-element method is termed the integration method (IM). Unlike in the RSE methods, the parent finite elements are not subdivided into smaller elements, and neither isothermality nor other
High convergence order finite elements with lumped mass matrix
Jensen, Morten skårup
1996-01-01
A method for deriving hexahedral finite elements with lumped mass matrices for three-dimensional problems is presented. These elements meet the theoretical conditions for high order convergence, and two numerical examples based on the three-dimensional scalar wave equation show that this is also...... the case in practice and that their accuracy is comparable to elements with consistent mass matrices....
The ANSYS finite element modelling package has been used to construct a three-dimensional, thermomechanical model of a CANDU fuel pin. The model includes individual UO2 pellets with end dishes and chamfers, and a Zircaloy-4 fuel cladding with end caps. Twenty node brick elements are used with both mechanical and thermal degrees of freedom, allowing for a full coupling between the thermal and mechanical solutions under both steady state and transient conditions. Each fuel pellet is modelled as a separate entity that interacts both thermally and mechanically with the cladding and other pellets via contact elements. The heat transfer between the pellets and cladding is dependent on both the interface pressure and temperature, and all material properties of both the pellets and the sheath are temperature dependant. Spatially and temporally varying boundary conditions for heat generation and convective cooling can be readily applied to the model. The model naturally exhibits phenomena such as pellet hour glassing and ridging of the cladding at the Pellet to pellet interfaces, allowing for the prediction of localized sheath stresses. The model also allows for the prediction of fuel pin bowing due to asymmetric thermal loads and fuel pin sagging due to overheating of the cladding, which may occur under accident conditions. (author)
Generalized finite element and finite differences methods for the Helmholtz problem
We briefly review the Quasi Optimal Finite Difference (QOFD) and Petrov-Galerkin finite element (QOPG) methods for the Helmholtz problem recently introduced in references [1] and [2], respectively, and extend these formulations to heterogeneous media and singular sources. Results of numerical experiments are presented illustrating the blended use of these methods on general meshes to take advantage of the lower cost and simplicity of the finite difference approach combined with the natural ability of the finite element method to deal with source terms, boundary and interface conditions.
无
2006-01-01
In this paper, we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems.It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H1- and L2-norms.
Complex finite element sensitivity method for creep analysis
The complex finite element method (ZFEM) has been extended to perform sensitivity analysis for mechanical and structural systems undergoing creep deformation. ZFEM uses a complex finite element formulation to provide shape, material, and loading derivatives of the system response, providing an insight into the essential factors which control the behavior of the system as a function of time. A complex variable-based quadrilateral user element (UEL) subroutine implementing the power law creep constitutive formulation was incorporated within the Abaqus commercial finite element software. The results of the complex finite element computations were verified by comparing them to the reference solution for the steady-state creep problem of a thick-walled cylinder in the power law creep range. A practical application of the ZFEM implementation to creep deformation analysis is the calculation of the skeletal point of a notched bar test from a single ZFEM run. In contrast, the standard finite element procedure requires multiple runs. The value of the skeletal point is that it identifies the location where the stress state is accurate, regardless of the certainty of the creep material properties. - Highlights: • A novel finite element sensitivity method (ZFEM) for creep was introduced. • ZFEM has the capability to calculate accurate partial derivatives. • ZFEM can be used for identification of the skeletal point of creep structures. • ZFEM can be easily implemented in a commercial software, e.g. Abaqus. • ZFEM results were shown to be in excellent agreement with analytical solutions
Finite-element method for above-core structures
Three-dimensional finite-element models for the treatment of the nonlinear, transient response of a fast breeder reactor's above-core structures are described. For purposes of treating arbitrarily large rotations, node orientations are described by unit vectors and the deformable elements are treated by a corotational formulation in which the coordinate system is embedded in the elements. Deformable elements may be connected either to nodes directly or through rigid bodies. The time integration is carried out by the Newmark β method. These features have been incorporated to form the finite-element program SAFE/RAS (Safety Analysis by Finite Elements/Reactor Analysis and Safety Division). Computations are presented for semianalytical comparisons, simple scoping studies, and Stanford Research Institute (SRI) test comparisons
Completely normal elements in finite abelian extensions
Koo, Ja Kung
2011-01-01
We give a completely normal element in the maximal real subfield of a cyclotomic field over the field of rational numbers, which is different from that of Okada. This result is a consequence of the criterion for a normal element developed in [Normal bases of ray class fields over imaginary quadratic fields, Math. Zeit.]. Furthermore, we find a completely normal element in certain extension of modular function fields in terms of a quotient of the modular discriminant function.
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.
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. © 2013 Elsevier Inc.
Accurate Parallel Algorithm for Adini Nonconforming Finite Element
罗平; 周爱辉
2003-01-01
Multi-parameter asymptotic expansions are interesting since they justify the use of multi-parameter extrapolation which can be implemented in parallel and are well studied in many papers for the conforming finite element methods. For the nonconforming finite element methods, however, the work of the multi-parameter asymptotic expansions and extrapolation have seldom been found in the literature. This paper considers the solution of the biharmonic equation using Adini nonconforming finite elements and reports new results for the multi-parameter asymptotic expansions and extrapolation. The Adini nonconforming finite element solution of the biharmonic equation is shown to have a multi-parameter asymptotic error expansion and extrapolation. This expansion and a multi-parameter extrapolation technique were used to develop an accurate approximation parallel algorithm for the biharmonic equation. Finally, numerical results have verified the extrapolation theory.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Vehicle Interior Noise Prediction Using Energy Finite Element Analysis Project
National Aeronautics and Space Administration — It is proposed to develop and implement a computational technique based on Energy Finite Element Analysis (EFEA) for interior noise prediction of advanced aerospace...
COHESIVE ZONE FINITE ELEMENT-BASED MODELING OF HYDRAULIC FRACTURES
Zuorong Chen; A.P. Bunger; Xi Zhang; Robert G. Jeffrey
2009-01-01
Hydraulic fracturing is a powerful technology used to stimulate fluid production from reservoirs. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to the efficient application of this technology, but is also a great challenge because of the strong nonlinear coupling between the viscous flow of fluid and fracture propagation. By taking advantage of a cohesive zone method to simulate the fracture process, a finite element model based on the existing pore pressure cohesive finite elements has been established to investigate the propagation of a penny-shaped hydraulic fracture in an infinite elastic medium. The effect of cohesive material parameters and fluid viscosity on the hydraulic fracture behaviour has been investigated. Excellent agreement between the finite element results and analytical solutions for the limiting case where the fracture process is dominated by rock fracture toughness demonstrates the ability of the cohesive zone finite element model in simulating the hydraulic fracture growth for this case.
Finite Element Models for Electron Beam Freeform Fabrication Process Project
National Aeronautics and Space Administration — This Small Business Innovation Research Phase II proposal offers to develop a comprehensive computer simulation methodology based on the finite element method for...
Finite element analyses for RF photoinjector gun cavities
This paper details electromagnetical, thermal and structural 3D Finite Element Analyses (FEA) for normal conducting RF photoinjector gun cavities. The simulation methods are described extensively. Achieved results are presented. (orig.)
Finite Element Meshes Auto-Generation for the Welted Bifurcation
YUANMei; LIYa-ping
2004-01-01
In this paper, firstly, a mathematical model for a specific kind of welted bifurcation is established, the parametric equation for the intersecting curve is resulted in. Secondly, a method for partitioning finite element meshes of the welted bifurcation is put forward, its main idea is that developing the main pipe surface and the branch pipe surface respectively, dividing meshes on each developing plane and obtaining meshes points, then transforming their plane coordinates into space coordinates. Finally, an applied program for finite element meshes auto-generation is simply introduced, which adopt ObjectARX technique and its running result can be shown in AutoCAD. The meshes generated in AutoCAD can be exported conveniently to most of finite element analysis soft wares, and the finite element computing result can satisfy the engineering precision requirement.
Finite Element Crash Simulations and Impact-Induced Injuries
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element simulations of crashes, impact-induced injuries and their protection that were published in 1980–1998. 390 citations are listed.
Finite element modeling for materials engineers using Matlab
Oluwole, Oluleke
2011-01-01
Discusses the finite element method with a particular focus on the requirements of materials engineers Uses the MATLAB® pdetool to develop a code-free way of modelling Contains exercises to help develop the reader's understanding
Finite Element Models for Electron Beam Freeform Fabrication Process Project
National Aeronautics and Space Administration — This Small Business Innovation Research proposal offers to develop the most accurate, comprehensive and efficient finite element models to date for simulation of...
Structural analysis with the finite element method linear statics
Oñate, Eugenio
2013-01-01
STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD Linear Statics Volume 1 : The Basis and Solids Eugenio Oñate The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years. Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elas...
Validation of high displacement piezoelectric actuator finite element models
Taleghani, Barmac K.
2000-08-01
The paper presents the results obtained by using NASTRAN and ANSYS finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness and important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN and ANSYS used different methods for modeling piezoelectric effects. In NASTRAN, a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.
Randomized Oversampling for Generalized Multiscale Finite Element Methods
Calo, Victor M.
2016-03-23
In this paper, we develop efficient multiscale methods for flows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approximates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the randomized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed.
Higher-Order Finite Elements for Hybrid Meshes Using New Nodal Pyramidal Elements
Bergot, Morgane; Cohen, Gary; Duruflé, Marc
2010-01-01
We provide a comprehensive study of arbitrarily high-order finite elements defined on pyramids. We propose a new family of high-order nodal pyramidal finite element which can be used in hybrid meshes which include hexahedra, tetrahedra, wedges and pyramids. Finite elements matrices can be evaluated through approximate integration, and we show that the order of convergence of the method is conserved. Numerical results demonstrate the efficiency of hybrid meshes compared to pure tetrahedral mes...
Efficient optimization of hollow-core photonic crystal fiber design using the finite-element method
Holzlöhner, Ronald; Burger, Sven; Roberts, John; Pomplun, Jan
2006-01-01
We employ a finite-element (FE) solver with adaptive grid refinement to model hollow-core photonic crystal fibers (HC-PCFs) whose core is formed from 19 omitted cladding unit cells. We optimize the complete fiber geometry for minimal field intensity at material/air interfaces, which indicates low...
Fluid flow in cavity solved by finite element method
Burda, P.; Novotný, J.; Šístek, J. (Jakub)
2010-01-01
The problem of singularities caused by boundary conditions is studied in the flow of lid driven cavity. The asymptotic behaviour near the singularity points is used together with the apriori error estimates of the finite element solution, in order to design the finite element mesh adjusted to singularity. A posteriori error estimates are used as the principal tool for error analysis. Thus we obtain very precise solution in the vicinity of the singularity. Numerical results are presented.
OCTG Premium Threaded Connection 3D Parametric Finite Element Model
Ahsan, Nabeel
2016-01-01
Full 360 degree 3D finite element models are the most complete representation of Oil Country Tubular Goods (OCTG) premium threaded connections. Full 3D models can represent helical threads and boundary conditions required to simulate make-up and service loading. A methodology is developed to create a 360 degree full 3D parametric finite element model with helical threads as an effective design and analysis tool. The approach is demonstrated with the creation of a metal-to-metal seal integral ...
Finite element simulation of magnesium alloys laser beam welding
BELHADJ, Asma; BESSROUR, Jamel; MASSE, Jean-Eric; BOUHAFS, Mahmoud; Barrallier, Laurent
2010-01-01
In this paper, a three-dimensional finite element model is developed to simulate thermal history magnesium-based alloys during laser beam welding. Space-time temperature distributions in weldments are predicted from the beginning of welding to the final cooling. The finite element calculations were performed using Cast3M code with which the heat equation is solved considering a non-linear transient behaviour. The applied loading is a moving heat source that depends on process parameters such ...
Finite element models applied in active structural acoustic control
Oude Nijhuis, Marco H.H.; de Boer; Rao, Vittal S.
2002-01-01
This paper discusses the modeling of systems for active structural acoustic control. The finite element method is applied to model structures including the dynamics of piezoelectric sensors and actuators. A model reduction technique is presented to make the finite element model suitable for controller design. The reduced structural model is combined with an acoustic model which uses the radiation mode concept. For a test case consisting of a rectangular plate with one piezo patch the model re...
Determination of a synchronous generator characteristics via Finite Element Analysis
Kolondzovski Zlatko
2005-01-01
Full Text Available In the paper a determination of characteristics of a small salient pole synchronous generator (SG is presented. Machine characteristics are determined via Finite Element Analysis (FEA and for that purpose is used the software package FEMM Version 3.3. After performing their calculation and analysis, one can conclude that most of the characteristics presented in this paper can be obtained only by using the Finite Element Method (FEM.
Anisotropic rectangular nonconforming finite element analysis for Sobolev equations
SHI Dong-yang; WANG Hai-hong; GUO Cheng
2008-01-01
An anisotropic rectangular nonconforming finite element method for solving the Sobolev equations is discussed under semi-discrete and full discrete schemes.The corresponding optimal convergence error estimates and superclose property are derived,which are the same as the traditional conforming finite elements.Furthermore,the global superconvergence is obtained using a post-processing technique.The numerical results show the validity of the theoretical analysis.
A weak Galerkin finite element method for Burgers' equation
Chen, Yanli; Zhang, Tie
2016-01-01
We propose a weak Galerkin(WG) finite element method for solving the one-dimensional Burgers' equation. Based on a new weak variational form, both semi-discrete and fully-discrete WG finite element schemes are established and analyzed. We prove the existence of the discrete solution and derive the optimal order error estimates in the discrete $H^1$-norm and $L^2$-norm, respectively. Numerical experiments are presented to illustrate our theoretical analysis.
TWO-SCALE FINITE ELEMENT DISCRETIZATIONS FOR PARTIAL DIFFERENTIAL EQUATIONS
Fang Liu; Aihui Zhou
2006-01-01
Some two-scale finite element discretizations are introduced for a class of linear partial differential equations. Both boundary value and eigenvalue problems are studied. Basedon the two-scale error resolution techniques, several two-scale finite element algorithms are proposed and analyzed. It is shown that this type of two-scale algorithms not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.
Multibody Finite Element Method and Application in Hydraulic Structure Analysis
Chao Su; Yebin Zhao; Yusong Jiang
2015-01-01
Multibody finite element method is proposed for analysis of contact problems in hydraulic structure. This method is based on the block theory of discontinuous deformation analysis (DDA) method and combines advantages of finite element method (FEM) and the displacement compatibility equation in classical elastic mechanics. Each single block is analyzed using FEM in corresponding local coordinate system and all contacting blocks need to satisfy the displacement compatibility requirement between...
PMD: a modular code for finite element analysis
Pařík, Petr
Praha : Ústav termomechaniky AV ČR, v. v. i, 2015 - (Plešek, J.; Gabriel, D.; Kolman, R.; Masák, J.), s. 53-54 ISBN 978-80-87012-56-7. [Výpočty konstrukcí metodou konečných prvků 2015. Praha (CZ), 26.11.2015] Institutional support: RVO:61388998 Keywords : finite element analysis * finite element code * sparse direct solver Subject RIV: JR - Other Machinery
A FINITE ELEMENT MODEL FOR SEISMICITY INDUCED BY FAULT INTERACTION
ChenHuaran; LiYiqun; HeQiaoyun; ZhangJieqing; MaHongsheng; LiLi
2003-01-01
On ths basis of interaction between faults, a finite element model for Southwest China is constructed, and the stress adjustment due to the strong earthquake occurrence in this region was studied. The preliminary results show that many strong earthquakes occurred in the are a of increased stress in the model. Though the results are preliminary, the quasi-3D finite element model is meaningful for strong earthquake prediction.
A FINITE ELEMENT MODEL FOR SEISMICITY INDUCED BY FAULT INTERACTION
Chen Huaran; Li Yiqun; He Qiaoyun; Zhang Jieqing; Ma Hongsheng; Li Li
2003-01-01
On ths basis of interaction between faults, a finite element model for Southwest China is constructed, and the stress adjustment due to the strong earthquake occurrence in this region was studied. The preliminary results show that many strong earthquakes occurred in the area of increased stress in the model. Though the results are preliminary, the quasi-3D finite element model is meaningful for strong earthquake prediction.
Finite Element Residual Stress Analysis of Planetary Gear Tooth
Jungang Wang; Yong Wang; Zhipu Huo
2013-01-01
A method to simulate residual stress field of planetary gear is proposed. In this method, the finite element model of planetary gear is established and divided to tooth zone and profile zone, whose different temperature field is set. The gear’s residual stress simulation is realized by the thermal compression stress generated by the temperature difference. Based on the simulation, the finite element model of planetary gear train is established, the dynamic meshing process is simulated, and in...
Enhanced patch test of finite element methods
CHEN; Wanji
2006-01-01
Theoretically, the constant stress patch test is not rigorous. Also, either the patch test of non-zero constant shear for Mindlin plate problem or non-zero strain gradient curvature of the microstructures cannot be performed. To improve the theory of the patch test, in this paper, based on the variational principle with relaxed continuity requirement of nonconforming element for homogeneous differential equations, the author proposed the individual element condition for passing the patch test and the convergence condition of the element: besides passing the patch test, the element function should include the rigid body modes and constant strain modes and satisfy the weak continuity condition, and no extra zero energy modes occur. Moreover, the author further established a variational principle with relaxed continuity requirement of nonconforming element for inhomogeneous differential equations, the enhanced patch test condition and the individual element condition. To assure the convergence of the element that should pass the enhanced patch test, the element function should include the rigid body modes and non-zero strain modes which satisfied the equilibrium equations, and no spurious zero energy modes occur and should satisfy new weak continuity condition. The theory of the enhanced patch test proposed in this paper can be applied to both homogeneous and inhomogeneous differential equations. Based on this theory, the patch test of the non-zero constant shear stress for Mindlin plate and the C0-1 patch test of the non-zero constant curvature for the couple stress/strain gradient theory were established.
Azimuthally-dependent Finite Element Solution to the Cylindrical Resonator
Osegueda, R.; Pierluissi, J.; Gil, L.; Revilla, A.; Villalva, G.; Dick, G.; Wang, D. SantiagoR.
1994-01-01
The cylindrical cavity resonator loaded with an anisotropic dielectric is analyzed as a two-dimensional problem using a finite element approach that assumes sinusoidal dependence in azimuth. This methodology allows the first finite element treatment of the technically important case of a resonator containing a sapphire element with a cylindrically aligned c axis. Second order trial functions together with quadrilateral elements are adopted in the calculations. The method was validated through comparisons with the analytical solutions for the hollow metal cavity and a coaxial cavity, as well as through measurements on a shielded sapphire resonator.
A finite element primer for beginners the basics
Zohdi, Tarek I
2014-01-01
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model problem for one-dimensional?linear elastostatics,(3) Weak formulations in one dimension,(4) Minimum principles in one dimension,(5) Error estimation in one dimension,(5) Construction of Finite Element basis functions in one dimension,(6) Gaussian Quadrature,(7) Iterative solvers and element by element data structures,(8) A model problem for th
A finite element solution method for quadrics parallel computer
A distributed preconditioned conjugate gradient method for finite element analysis has been developed and implemented on a parallel SIMD Quadrics computer. The main characteristic of the method is that it does not require any actual assembling of all element equations in a global system. The physical domain of the problem is partitioned in cells of np finite elements and each cell element is assigned to a different node of an np-processors machine. Element stiffness matrices are stored in the data memory of the assigned processing node and the solution process is completely executed in parallel at element level. Inter-element and therefore inter-processor communications are required once per iteration to perform local sums of vector quantities between neighbouring elements. A prototype implementation has been tested on an 8-nodes Quadrics machine in a simple 2D benchmark problem
The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion
Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite-difference, finite-element, and hybrid finite-difference-finite-element methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. (Author)
A new component mode synthesis for dynamic mixed thin plate finite element models
Garambois, Pierre; Besset, Sébastien; Jézéquel, Louis
2015-01-01
International audience This paper presents a methodology for the reduction in dynamic mixed finite element models (DM-FEMs) based on the use of a sub-structuring primal methods adapted to such models. We implement a DM-FEM for Kirchhoff–Love thin plates using the Hellinger–Reissner variational mixed formulation adapted to dynamic, and give a quick insight of its convergence. This model uses both displacement and generalized stress fields within the plate, obtained as a primary result, but ...
Advances in the study of hybrid finite elements
无
2000-01-01
Some new concepts and research progress in hybrid finite elements advanced in recent years are in troduced. On the basis of incompatible energy consistency analysis, the optimal condition of hybrid elements is derived and the formulation for fulfilling this condition is given. A post-processing penalty equilibrium optimization technique of hybrid element is presented to create high quality hybrid model. For incompressible problems, a method of deviatoric hybrid element is proposed and unification of computation between compressible and incompressible media is achieved.
Adaptive Algorithms of Nonlinear Approximation with Finite Terms
Wen Bin WEI; Yue Sheng XU; Pei Xin YE
2007-01-01
This paper deals with realizable adaptive algorithms of the nonlinear approximation with finite terms based on wavelets. We present a concrete algorithm by which we may find the required index set Am for the greedy algorithm GPm(·,ψ). This makes the greedy algorithm realize the near best approximation in practice. Moreover, we study the efficiency of the finite-term approximation of another algorithm introduced by Birge and Massart.
Adaptive finite-time control for hyperchaotic Lorenz–Stenflo systems
This paper investigates the issue of adaptive finite-time control for hyperchaotic Lorenz–Stenflo systems with parameter uncertainties. Based on finite-time Lyapunov theory, a class of non-smooth adaptive finite time controllers is given to guarantee the adaptive finite-time stability and make the states of the systems converge to the origins within a finite-time. Finally, illustrative examples are presented to verify the effectiveness of the proposed adaptive finite-time controller. (paper)
Finite element analysis of soil-sheet pile interaction
Nyby, D. W.
A finite element model which accurately and economically models soil-sheet pile structures was developed. The model was used to analyze cantilever and anchored sheet pile walls. The finite element model includes transition and interface elements. The transition element has the capability of conforming to the displaced shape of the sheet pile elements on one side (cubic element) and soil elements on the other sides (bilinear element). The interface element models the frictional resistance between the soil and the sheet pile. It behaves elastically below a threshold force level (Coulomb friction) and perfectly plastic above this value. The soil is modeled using nonlinear constitutive relations. These relations are used for both the transition elements and the bilinear elements. The economy of the finite element model was increased in two ways. Closed-form integration was used to reduce the computational effort and an equation solver was used which takes advantage of the banded, symmetric, and positive-definite characteristics of the global stiffness matrix.
A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2012-01-01
The finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex geo
陈蔚
2003-01-01
The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density.The electric potential equation is discretized by a mixed finite element method.The electron and hole density equations are treated by implicit-explicit multistep finite element methods.The schemes are very efficient.The optimal order error estimates both in time and space are derived.
A moving finite element model of the tokamak scrapeoff region
The scrapeoff region of a tokamak, associated with the poloidal divertor and collector plates, has been a subject of intense recent interest because it is responsible for handling a major portion of the heat load from the fusion reactions and must survive great stresses. Detailed fluid modeling has been done to optimize the design of this region, with the expectation that it is a crucial component of a practical tokamak reactor. Severe numerical problems are caused by extreme anisotropy of the plasma transport, the presence of a magnetic x-point inside the computational domain, thin boundary layers at the collector plates, and multiple time scales associated with Alfven and sound waves. The authors present a new approach based on the use of Moving Finite Elements and Graph Massage. They use an unstructured grid of triangles, providing great flexibility in fitting the complex domain in the original cylindrical coordinates. The grid automatically and dynamically adapts to the evolving solution with no reliance on the coordinate system, naturally approximating a flux coordinate system where the poloidal field is strong while relaxing to a more isotropic distribution in the neighborhood of the x-point. The elimination of the flux coordinate transformation simplifies the fluid equations, avoids the singularity at the x-point and the problem of non-orthogonal collector plates, and allows for the treatment of time-dependent magnetic fields. The adaptivity of the grid automatically refines the resolution near the plates with no human intervention. A fully implicit time step allows for efficient treatment of the multiple time scales. The Graph Massage algorithm, whose primary role is in enhancing grid adaptivity for the evolving solution, plays a role as well in the non-trivial task of initially gridding up the computational domain. Results are illustrated with 3D color movies showing the evolution of the grid and the solution
Finite element thermal analysis of convectively-cooled aircraft structures
Wieting, A. R.; Thornton, E. A.
1981-01-01
The design complexity and size of convectively-cooled engine and airframe structures for hypersonic transports necessitate the use of large general purpose computer programs for both thermal and structural analyses. Generally thermal analyses are based on the lumped-parameter finite difference technique, and structural analyses are based on the finite element technique. Differences in these techniques make it difficult to achieve an efficient interface. It appears, therefore, desirable to conduct an integrated analysis based on a common technique. A summary is provided of efforts by NASA concerned with the development of an integrated thermal structural analysis capability using the finite element method. Particular attention is given to the development of conduction/forced-convection finite element methodology and applications which illustrate the capabilities of the developed concepts.
Numerical experiment on finite element method for matching data
Numerical experiments are presented on the finite element method by Pletzer-Dewar for matching data of an ordinary differential equation with regular singular points by using model equation. Matching data play an important role in nonideal MHD stability analysis of a magnetically confined plasma. In the Pletzer-Dewar method, the Frobenius series for the 'big solution', the fundamental solution which is not square-integrable at the regular singular point, is prescribed. The experiments include studies of the convergence rate of the matching data obtained by the finite element method and of the effect on the results of computation by truncating the Frobenius series at finite terms. It is shown from the present study that the finite element method is an effective method for obtaining the matching data with high accuracy. (author)
Ein mechanisches Finite-Elemente-Modell des menschlichen Kopfes
Hartmann, U.
1999-01-01
In dieser Arbeit wird ein dreidimensionales Modell des menschlichen Kopfes beschrieben, das es erlaubt, mit der Methode der Finiten Elemente mechanische Einfluesse auf den Kopf zu modellieren. Eine exakte Geometriebeschreibung eines individuellen Modells wird aus einem Kernspintomogramm des Kopfes gewonnen. Ausgehend von diesen medizinischen Bilddaten wird die diskrete Darstellung des Kopfes als Verbund finiter Elemente mit einem Gittergenerator gewonnen. Dieser schnelle und stabile Algorithm...
A COMBINED HYBRID FINITE ELEMENT METHOD FOR PLATE BENDING PROBLEMS
Tian-xiao Zhou; Xiao-ping Xie
2003-01-01
In this paper, a combined hybrid method is applied to finite element discretization ofplate bending problems. It is shown that the resultant schemes are stabilized, i.e., theconvergence of the schemes is independent of inf-sup conditions and any other patch test.Based on this, two new series of plate elements are proposed.
Finite Element Vibration Analysis of Beams, Plates and Shells
Jaroslav Mackerle
1999-01-01
This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element vibration analysis of beams, plates and shells that were published in 1994–1998. It contains 361 citations. Also included, as separated subsections, are vibration analysis of composite materials and vibration analysis of structural elements with cracks/contacts.
Design of Finite Element Tools for Coupled Surface and Volume Meshes
Daniel K(o)ster; Oliver Kriessl; Kunibert G. Siebert
2008-01-01
Many problems with underlying variational structure involve a coupling of volume with surface effects. A straight-forward approach in a finite element discretization is to make use of the surface triangulation that is naturally induced by the volume triangulation. In an adaptive method one wants to facilitate "matching" local mesh modifications, i.e., local refinement and/or coarsening, of volume and surface mesh with standard tools such that the surface grid is always induced by the volume grid. We describe the concepts behind this approach for bisectional refinement and describe new tools incorporated in the finite element toolbox ALBERTA. We also present several important applications of the mesh coupling.
Preconditioned CG-solvers and finite element grids
Bauer, R.; Selberherr, S. [Technical Univ. of Vienna (Austria)
1994-12-31
To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.
A direct implementation for influence lines in finite element software
Jepsen, Michael S.; Damkilde, Lars
2014-01-01
The use of influence lines is a recognized method for determining the critical design load conditions and this paper shows a direct method for applying influence lines in any structural finite element software. The main idea is to equate displacement or angular discontinuities with nodal forces...... approach equated to consistent nodal forces, which makes it very suitable for implementation in finite element schemes and applicable for all element types, such as shell, plates, beams etc. This paper derives the consistent nodal forces for angular, lateral and axial displacement discontinuities for a...
Finite element analysis of two disk rotor system
Dixit, Harsh Kumar
2016-05-01
A finite element model of simple horizontal rotor system is developed for evaluating its dynamic behaviour. The model is based on Timoshenko beam element and accounts for the effect of gyroscopic couple and other rotational forces. Present rotor system consists of single shaft which is supported by bearings at both ends and two disks are mounted at different locations. The natural frequencies, mode shapes and orbits of rotating system for a specific range of rotation speed are obtained by developing a MATLAB code for solving the finite element equations of rotary system. Consequently, Campbell diagram is plotted for finding a relationship between natural whirl frequencies and rotation of the rotor.
Time domain finite element analysis of multimode microwave applicators
Dibben, D.C.; Metaxas, R. [Cambridge Univ. (United Kingdom)
1996-05-01
Analysis of multimode applicators in the frequency domain via the finite element technique produces a set of very ill-conditioned equations. This paper outlines a time domain finite element method (TDFE) for analyzing three dimensional microwave applicators where this ill-conditioning is avoided. Edge elements are used in order to handle sharp metal edges and to avoid spurious solutions. Analysis in the time domain allows field distributions at a range of different frequencies to be obtained with a single calculation. Lumping is investigated as a means of reducing the time taken for the calculation. The reflection coefficient is also obtained.
Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)
Finite Element Vibration Analysis of Laminated Composite Folded Plate Structures
A. Guha Niyogi
1999-01-01
Full Text Available A nine-noded Lagrangian plate bending finite element that incorporates first-order transverse shear deformation and rotary inertia is used to predict the free and forced vibration response of laminated composite folded plate structures. A 6 × 6 transformation matrix is derived to transform the system element matrices before assembly. The usual five degrees-of-freedom per node is appended with an additional drilling degree of freedom in order to fit the transformation. The present finite element results show good agreement with the available semi-analytical solutions and finite element results. Parametric studies are conducted for free and forced vibration analysis for laminated folded plates, with reference to crank angle, fibre angle and stacking sequence. The natural frequencies and mode shapes, and forced vibration responses furnished here may serve as a benchmark for future investigations.
Locally upwinded discontinuous finite element discretizations for the transport equation
Numerical solutions of transport processes are plagued by difficulties in representing the first-order advecting terms. Standard (continuous) finite element discretizations are known to have difficulty in accurately modeling problems in which the solution varies abruptly or shows nearly discontinuous behavior at material interfaces or wave fronts. In this paper, the authors describe a class of discontinuous finite element (DFE) discretizations that are capable of producing accurate and physically meaningful (nonnegative) solutions to the space-time linear Boltzmann transport equation. The novelty of the approach is the presence of an upwinding term within an element that may enforce the positivity of the solutions. This works by reducing the order of the finite element approximation where appropriate, thus suppressing numerical oscillations. The method also enforces elementwise particle conservation and is easily generalized to multidimensions
Finite Size Scaling for Quantum Criticality Using the Finite Element Method
Antillon, Edwin; Kais, Sabre
2011-01-01
Finite size scaling for the Schrodinger equation, is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach was shown (S. Kais and P. Serra, Adv. Chem. Phys. 125, 1 (2003)) to give very accurate results for critical parameters by using a systematic expansion in a finite basis set. Recently, the finite element method, on the other hand, was shown to be a powerful numerical method for ab initio electronic structure calculations (R. Alizadegan, K.J. Hsia and T. J. Martinez, J. Chem. Phys. 132, 034101 (2010)) with a variable real-space resolution. The implementation produces sparse matrices since it is implemented in terms of local basis functions, making it ideal for parallel implementation. Here, we demonstrate how to obtain quantum critical parameters by combining finite element method (FEM) with finite size scaling (FSS). The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and externa...
Nascimento, Francisco Rogerio Teixeira do
2013-07-01
The main objective of this work is to simulate electromagnetic fields using the Finite Element Method. Even in the easiest case of electrostatic and magnetostatic numerical simulation some problems appear when the nodal finite element is used. It is difficult to model vector fields with scalar functions mainly in non-homogeneous materials. With the aim to solve these problems two types of techniques are tried: the adaptive remeshing using nodal elements and the edge finite element that ensure the continuity of tangential components. Some numerical analysis of simple electromagnetic problems with homogeneous and non-homogeneous materials are performed using first, the adaptive remeshing based in various error indicators and second, the numerical solution of waveguides using edge finite element. (author)
FINITE ELEMENT METHODS FOR THE NAVIER-STOKES EQUATIONS BY H(div) ELEMENTS
Junping Wang; Xiaoshen Wang; Xiu Ye
2008-01-01
We derived and analyzed a new numerical scheme for the Navier-Stokes equations by using H(div) conforming finite elements. A great deal of effort was given to an establishment of some Sobolev-type inequalities for piecewise smooth functions. In particular, the newly derived Sobolev inequalities were employed to provide a mathematical theory for the H(div) finite element scheme. For example, it was proved that the new finite element scheme has solutions which admit a certain boundedness in terms of the input data. A solution uniqueness was also possible when the input data satisfies a certain smallness condition. Optimal-order error estimates for the corresponding finite element solutions were established in various Sobolev norms. The finite element solutions from the new scheme feature a full satisfaction of the continuity equation which is highly demanded in scientific computing.
Shurina, E.; Solonenko, O.; Voitovich, T.
2002-01-01
Finite volume-finite element techniques on unstructured grids with the application to the numerical solution of the incompressible Navier-Stokes equations are considered. The paper addresses two issues that affect the accuracy of the finite volume-finite element approximations: exact integration of interpolation polynomials and development of high-order-accurate upwind schemes.
Non-conforming finite element methods for transmission eigenvalue problem
Yang, Yidu; Han, Jiayu; Bi, Hai
2016-01-01
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 ...
Finite element modeling of engineered thin film/coating systems
Finite element modeling is becoming an increasingly important tool used in the design methodology and in the analysis of engineered functional thin film/coating systems. In contrast with many analytical modeling methods, modem finite element analysis can readily model non-linear static and transient thermo-mechanical behavior of engineered coating systems. Non-linear finite element analysis can be applied to multi-layered coating systems to predict the stresses and deformations generated during the processing of the coating system and under operating conditions. For example thermo-mechanical finite element analysis can be used to determine the composition and layer geometry of a coating system such that the stresses generated under operating conditions are minimized. In this paper we demonstrate the use of non-linear finite element analysis in the following situations: a) the prediction of contact stresses and film surface crack propagation within the coating system developed during the normal indentation of a hard wear-resistant coating on a soft substrate, and b) the determination of stresses generated in a multi-layered non-wetting, wear-resistant and oxidation resistant glass molding coating system during repeated thermal shot cycling. (author)
Unstructured finite element simulations of compressible phase change phenomena
Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad; Scientific Computation Research Center (Scorec) Team
2015-11-01
Modeling interactions between compressible gas flow and multiple combusting solid objects, which may undergo large deformations, is a problem with several challenging aspects that include, compressible turbulent flows, shocks, strong interfacial fluxes, discontinuous fields and large topological changes. We have developed and implemented a mathematically consistent, computational framework for simulating such problems. Within our framework the fluid is modeled by solving the compressible Navier Stokes equations with a stabilized finite element method. Turbulence is modeled using large eddy simulation, while shocks are captured using discontinuity capturing methods. The solid is modeled as a hyperelastic material, and its deformation is determined by writing the constitutive relation in a rate form. Appropriate jump conditions are derived from conservations laws applied to an evolving interface, and are implemented using discontinuous functions at the interface. The mesh is updated using the Arbitrary Lagrangian Eulerian (ALE) approach, and is refined and adapted during the simulation. In this talk we will present this framework and will demonstrate its capabilities by solving canonical phase change problems. We acknowledge the support from Army Research Office (ARO) under ARO Grant # W911NF-14-1-0301.
Prediction of Three-Dimensional Milling Forces Based on Finite Element
Lida Zhu
2014-01-01
Full Text Available The model of milling force is mainly proposed to predict and analyze the cutting process based on finite element method in this paper. Firstly, milling finite element model is given based on orthogonal cutting principle, and then the influence laws of cutting parameters on chip formation are analyzed by using different simulation parameters. In addition, the three-dimensional milling forces are obtained from finite element models. Finally, the values of milling force by the milling experiment are also compared and analyzed with the simulation values to verify the feasibility and reasonability. It can be shown that milling forces match well between simulation and experiment results, which can provide many good basic data and analysis methods to optimize the machining parameters, reduce tool wear, and improve the workpiece surface roughness and adapt to the programming strategy of high speed machining.
The Discontinuous Galerkin Finite Element Method for electromagnetics and elastodynamics
Vandewoestyne, Bart; Bou Matar, Olivier; De Gersem, Herbert; Van Den Abeele, Koen
2011-01-01
The propagation of electromagnetic waves can be studied by solving Maxwell’s equations. Similarly, a combination of Newton’s second law and Hooke’s law, leads to a system of partial differential equations (PDEs) that describe the propagation of elastodynamic waves. Both systems of PDEs can be solved by a broad range of numerical techniques. Well-known and applicable to both electromagnetics and elastodynamics are the Finite Volume Method (FVM) and the Finite Element Method (FEM). Other me...
Finite Element Method for Capturing Ultra-relativistic Shocks
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.
Isogeometric analysis based on scaled boundary finite element method
This paper presents a new approach which possesses the semi-analytical feature of scaled boundary finite element method and the exact geometry feature of isogeometric analysis. NURBS basis functions are employed to construct an exact boundary geometry. The domain boundary is discretized by NURBS curves for the 2D case, and NURBS surfaces for the 3D case. Especially the closed-form NURBS curves or surfaces are needed if there are no side-faces. The strategy of using finite elements on domain boundary with NURBS shape functions for approximation of both boundary geometry and displacements arises from the sense of isoparametric concept. With h-,p-,k- refinement strategy implemented, the geometry is refined with maintaining exact geometry at all levels, so the geometry is the same exact represented as the initial geometry imported from CAD system without the necessity of subsequent communication with a CAD system. Additionally, numerical example exhibits that flexible continuity within the NURBS patch rather than traditional shape functions improves continuity and accuracy of derivative stress and strain field across not only boundary elements but also domain elements, as the results of the combination of the intrinsic analytical property along radial direction and the higher continuity property of NURBS basis, i.e. it's more powerful in accuracy of solution and less DOF-consuming than either traditional finite element method or scaled boundary finite element method.
GUZELBEY Ibrahim H.; KANBER Bahattin; AKPOLAT Abdullah
2004-01-01
In this study, the stress based finite element method is coupled with the boundary element method in two different ways. In the first one, the ordinary distribution matrix is used for coupling. In the second one, the stress traction equilibrium is used at the interface line of both regions as a new coupling process. This new coupling procedure is presented without a distribution matrix. Several case studies are solved for the validation of the developed coupling procedure. The results of case studies are compared with the distribution matrix coupling, displacement based finite element method, assumed stress finite element method, boundary element method, ANSYS and analytical results whenever possible. It is shown that the coupling of the stress traction equilibrium with assumed stress finite elements gives as accurate results as those by the distribution matrix coupling.
Electrical and Joule heating relationship investigation using Finite Element Method
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.
Finite element modeling for volume phantom in Electrical Impedance Tomography
I. O. Rybina
2011-10-01
Full Text Available Using surface phantom, "shadows" of currents, which flow below and under surface tomographic lays, include on this lay, that is cause of adding errors in reconstruction image. For processing modeling in studied object volume isotropic finite elements should be used. Cube is chosen for finite element modeling in this work. Cube is modeled as sum of six rectangular (in the base pyramids, each pyramid consists of four triangular pyramids (with rectangular triangle in the base and hypotenuse, which is equal to cube rib to provide its uniformity and electrical definition. In the case of modeling on frequencies higher than 100 kHz biological tissue resistivities are complex. In this case weight coefficient k will be complex in received cube electrical model (inverse conductivity matrix of the cube finite element.
Choice of input fields in stochastic finite elements
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1996-01-01
flexibility field, as the input to the stochastic finite element model. To answer this question the focus should be on the error of the output of the mechanical model rather than on the input field itself when discretizing the field through replacing it by a field defined in terms of a finite number of random...... stiffness and compliance, Stochastic finite elements, Discretization of random fields, Winterstein approximations.......The problem of the arbitrary choice of variables for random field modelling in structural mechanics or in soil mechanics is treated. For example, it is relevant to ask the question of whether it is best to choose a stiffness field along a beam element or to choose its reciprocal field, the...
Flow Applications of the Least Squares Finite Element Method
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 for eigenvalue problems in electromagnetics
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.
Choice of input fields in stochastic finite elements
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
flexibility field, as the input to the stochastic finite element model. To answer this question the focus should be on the error of the output of the mechanical model rather than on the input field itself when discretizing the field through replacing it by a field defined in terms of a finite number of random...... stiffness and compliance, Stochastic finite elements, Discretization of random fields, Winterstein approximations.......The problem of the arbitrary choice of variables for random field modelling in structural mechanics or in soil mechanics is treated. For example, it is relevant to ask the question of whether it is best to choose a stiffness field along a beam element or to choose its reciprocal field, the...
Finite element analysis of magnetization reversal in granular thin films
Spargo, A W
2002-01-01
This thesis develops a Galerkin finite element model of magnetisation dynamics in granular thin films. The governing equations of motion are the Gilbert equations with an effective magnetic field taking contributions from exchange interactions, magnetocrystalline anisotropy, applied magnetic field as well as the magnetostatic field given by Maxwells equations. The magnetostatic field is formulated as a scalar potential described by Poissons equation which is solved using a second order finite element method. The Gilbert equations are discretized in time using an implicit midpoint method which naturally conserves the magnitude of the magnetisation vector. An infinite thin film is approximated using periodic boundary conditions with material microstructure represented using the Voronoi tessellation. The effects of thermal fluctuations are modelled by the stochastic Langevin-Gilbert equations, again solved by a Galerkin finite element method. The implicit midpoint time-stepping scheme ensures that solutions conv...
An Object Oriented, Finite Element Framework for Linear Wave Equations
Koning, J M
2004-08-12
This dissertation documents an object oriented framework which can be used to solve any linear wave equation. The linear wave equations are expressed in the differential forms language. This differential forms expression allows a strict discrete interpretation of the system. The framework is implemented using the Galerkin Finite Element Method to define the discrete differential forms and operators. Finite element basis functions including standard scalar Nodal and vector Nedelec basis functions are used to implement the discrete differential forms resulting in a mixed finite element system. Discretizations of scalar and vector wave equations in the time and frequency domains will be demonstrated in both differential forms and vector calculi. This framework conserves energy, maintains physical continuity, is valid on unstructured grids, conditionally stable and second order accurate. Examples including linear electrodynamics, acoustics, elasticity and magnetohydrodynamics are demonstrated.
Engineering computation of structures the finite element method
Neto, Maria Augusta; Roseiro, Luis; Cirne, José; Leal, Rogério
2015-01-01
This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It us...
Finite Element Method for Analysis of Material Properties
Rauhe, Jens Christian
The use of cellular and composite materials have in recent years become more and more common in all kinds of structural components and accurate knowledge of the effective properties is therefore essential. In this wok the effective properties are determined using the real material microstructure...... determined using theoretical models. Besides the determination of the effective properties, viscoelastic and damage analysis have been performed on a number of material microstructures....... obtain a proper description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged...
Finite Element Modeling of Pellet-Clat Mechanical Interaction
Pellet-clad interaction is one of the operational problems encountered in nuclear industry. Failure of fuel elements due to pellet-clad interactions in a significant release of radioactivity to coolant. This in turn may be cause more serious safety problems. Nuclear industry is seeking solution to avoid such problems. On the other hand mechanisms for the development of pellet-clad interactions are not well understood. In this study, mechanical part of pellet-clad interaction is analyzed with a simple model based on finite element analysis. General Electric BWR/6 fuel element is used to provide model parameters. Coupled thermal and mechanical analyses of fuel element are performed using a general purpose finite element software ANSYS. In the model, pellet-clad interactions are created by considering certain contact points with various sizes. local parameters such as temperature, strain, and stress are calculated. Results are used to make an essessment of operational conditions
FINITE ELEMENT EVALUATION AND OPTIMIZATION OF GEOMETRY WITH DOE
Janko D. Jovanovic
2011-03-01
Full Text Available Since 1960, Taguchi methods have been used for improving the quality of Japanese products with great success. Basic assumption of Taguchi's design for six sigma or robust design is that quality must be designed into a product from the start at both the product and process design stage in order to improve product reliability and manufacturability. This paper deals with case study of product design based on Taguchi's approach that involves parametric optimization of piston rod geometry aiming mass reduction with stress restriction. Finite element analysis software ANSYS Workbench was used to get access to CAD parameters of piston rod within a process of parametric finite element evaluation and optimization.
Large eddy simulation with unstructured grids and finite elements
A large Eddy simulation was conducted with a general purpose Finite Element code (N3S). The flow around a square cylinder, a typical case for Bluff Body Aerodynamics and with well documented experiments (Lyn and Durao), was used as a test case. The simple mixing length model of Smagorinsky was applied together with wall functions and yielded reasonable agreement with experiment for mean, and pseudo periodic velocities. Filtering difficulties associated with LES in finite elements and possible improvements are considered. (authors). 10 refs., 7 figs
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Two-dimensional finite-element temperature variance analysis
Heuser, J. S.
1972-01-01
The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.
Finite element methods for nonlinear elastostatic problems in rubber elasticity
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 elements modeling of delaminations in composite laminates
Gaiotti, m.; Rizzo, C.M.; Branner, Kim;
2011-01-01
The application of composite materials in many structures poses to engineers the problem to create reliable and relatively simple methods, able to estimate the strength of multilayer composite structures. Multilayer composites, like other laminated materials, suffer from layer separation, i.e., d...... finite elements using different techniques. Results obtained with different finite element models are compared and discussed....... buckling strength of composite laminates containing delaminations. Namely, non-linear buckling and post-buckling analyses are carried out to predict the critical buckling load of elementary composite laminates affected by rectangular delaminations of different sizes and locations, which are modelled by...
Experimentally validated finite element model of electrocaloric multilayer ceramic structures
A novel finite element model to simulate the electrocaloric response of a multilayer ceramic capacitor (MLCC) under real environment and operational conditions has been developed. The two-dimensional transient conductive heat transfer model presented includes the electrocaloric effect as a source term, as well as accounting for radiative and convective effects. The model has been validated with experimental data obtained from the direct imaging of MLCC transient temperature variation under application of an electric field. The good agreement between simulated and experimental data, suggests that the novel experimental direct measurement methodology and the finite element model could be used to support the design of optimised electrocaloric units and operating conditions.
Compatible finite element spaces for geophysical fluid dynamics
Natale, Andrea
2016-01-01
Compatible finite elements provide a framework for preserving important structures in equations of geophysical fluid dynamics, and are becoming important in their use for building atmosphere and ocean models. We survey the application of compatible finite element spaces to geophysical fluid dynamics, including the application to the nonlinear rotating shallow water equations, and the three-dimensional compressible Euler equations. We summarise analytic results about dispersion relations and conservation properties, and present new results on approximation properties in three dimensions on the sphere, and on hydrostatic balance properties.
Matlab and C programming for Trefftz finite element methods
Qin, Qing-Hua
2008-01-01
Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in the literature, MATLAB® and C Programming for Trefftz Finite Element Methods provides the detailed MATLAB® and C programming processes in applications of the Trefftz FEM to potential and elastic problems. The book begins with an introduction to th
Robust Hybrid Finite Element Methods for Antennas and Microwave Circuits
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.
Finite Element Modelling and Analysis of Conventional Pultrusion Processes
Akishin, P.; Barkanov, E.; Bondarchuk, A.
2015-11-01
Pultrusion is one of many composite manufacturing techniques and one of the most efficient methods for producing fiber reinforced polymer composite parts with a constant cross-section. Numerical simulation is helpful for understanding the manufacturing process and developing scientific means for the pultrusion tooling design. Numerical technique based on the finite element method has been developed for the simulation of pultrusion processes. It uses the general purpose finite element software ANSYS Mechanical. It is shown that the developed technique predicts the temperature and cure profiles, which are in good agreement with those published in the open literature.
Discontinuous Galerkin finite element methods for gradient plasticity.
Garikipati, Krishna. (University of Michigan, Ann Arbor, MI); 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.
Preconditioning for Mixed Finite Element Formulations of Elliptic Problems
Wildey, Tim
2013-01-01
In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.
Local and Parallel Finite Element Algorithms for Eigenvalue Problems
Jinchao Xu; Aihui Zhou
2002-01-01
Some new local and parallel finite element algorithms are proposed and analyzed in this paper for eigenvalue problems. With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraic systems on fine grid by using some local and parallel procedure. A theoretical tool for analyzing these algorithms is some local error estimate that is also obtained in this paper for finite element approximations of eigenvectors on general shape-regular grids.
Stress analysis of heated concrete using finite elements
Described is a finite element analysis of concrete, which is subjected to rapid heating. Using thermal mass transport calculation, the moisture content, temperature and pore pressure distribution over space and time is obtained first. From these effects, stress at various points of the concrete are computed using the finite element method. Contribution to the stress formulation comes from three components, namely the thermal expansion, pore pressure, and the shrinkage of concrete due to moisture loss (from dehydration). The material properties of concrete are assumed to be homogeneous, elastic, and cracking is not taken into consideration. (orig.)
Finite element microscopic stress analysis of cracked composite systems
Ko, W. L.
1978-01-01
This paper considers the stress concentration problems of two types of cracked composite systems: (1) a composite system with a broken fiber (a penny-shaped crack problem), and (2) a composite system with a cracked matrix (an annular crack problem). The cracked composite systems are modeled with triangular and trapezoidal ring finite elements. Using NASTRAN (NASA Structural Analysis) finite element computer program, the stress and deformation fields in the cracked composite systems are calculated. The effect of fiber-matrix material combination on the stress concentrations and on the crack opening displacements is studied.
Diffusive mesh relaxation in ALE finite element numerical simulations
Dube, E.I.
1996-06-01
The theory for a diffusive mesh relaxation algorithm is developed for use in three-dimensional Arbitary Lagrange/Eulerian (ALE) finite element simulation techniques. This mesh relaxer is derived by a variational principle for an unstructured 3D grid using finite elements, and incorporates hourglass controls in the numerical implementation. The diffusive coefficients are based on the geometric properties of the existing mesh, and are chosen so as to allow for a smooth grid that retains the general shape of the original mesh. The diffusive mesh relaxation algorithm is then applied to an ALE code system, and results from several test cases are discussed.
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett
2012-02-03
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.
Behaviour of Lagrangian triangular mixed fluid finite elements
S Gopalakrishnan; G Devi
2000-02-01
The behaviour of mixed fluid finite elements, formulated based on the Lagrangian frame of reference, is investigated to understand the effects of locking due to incompressibility and irrotational constraints. For this purpose, both linear and quadratic mixed triangular fluid elements are formulated. It is found that there exists a close relationship between the penalty finite element approach that uses reduced/selective numerical integration to alleviate locking, and the mixed finite element approach. That is, performing reduced/selective integration in the penalty approach amounts to reducing the order of pressure interpolation in the mixed finite element approach for obtaining similar results. A number of numerical experiments are performed to determine the optimum degree of interpolation of both the mean pressure and the rotational pressure in order that the twin constraints are satisfied exactly. For this purpose, the benchmark solution of the rigid rectangular tank is used. It is found that, irrespective of the degree of mean and the rotational pressure interpolation, the linear triangle mesh, with or without central bubble function (incompatible mode), locks when both the constraints are enforced simultaneously. However, for quadratic triangle, linear interpolation of the mean pressure and constant rotational pressure ensures exact satisfaction of the constraints and the mesh does not lock. Based on the results obtained from the numerical experiments, a number of important conclusions are arrived at.
LEE, Ki-tak; HA, Taeyoung; SHEEN, Dongwoo
2007-01-01
In this paper we analyze numerical dispersion relation of some conforming and nonconforming quadrilateral finite elements. The elements employed in this analysis are the standard $Q_1$ conforming finite element, the DSSY nonconforming element [5] and the $P_1$-nonconforming quadrilateral finite element [14]. Several aspects of comparative analyses of the above three elements for two or three dimensional problems are shown.
Numerical techniques in linear duct acoustics. [finite difference and finite element analyses
Baumeister, K. J.
1980-01-01
Both finite difference and finite element analyses of small amplitude (linear) sound propagation in straight and variable area ducts with flow, as might be found in a typical turboject engine duct, muffler, or industrial ventilation system, are reviewed. Both steady state and transient theories are discussed. Emphasis is placed on the advantages and limitations associated with the various numerical techniques. Examples of practical problems are given for which the numerical techniques have been applied.
An Hybrid Finite Volume-Finite Element Method for Variable Density Incompressible Flows
Calgaro, Caterina; Creusé, Emmanuel; Goudon, Thierry
2008-01-01
This paper is devoted to the numerical simulation of variable density incompressible flows, modeled by the Navier-Stokes system. We introduce an hybrid scheme which combines a Finite Volume approach for treating the mass conservation equation and a Finite Element method to deal with the momentum equation and the divergence free constraint. The breakthrough relies on the definition of a suitable footbridge between the two methods, through the design of compatibility condition. In turn, the met...
Valuing Asian options using the finite element method and duality techniques
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.
Wave propagation through Timoshenko beams: spectral finite element model
Present study deals with the wave propagation through structures. Timoshenko beams, being the most important structural elements, are studied here. The paper presents solution of elastic waves propagating through varying thickness Timoshenko beam under point load using Spectral Finite Element Methodology. Beam theory applied here includes effects of shear deformation and rotary inertia. The temporal and spatially dependent equations of motion are transferred to frequency domain by employing Fast Fourier Transformation (FFT). This results in the conversion of transient problem into pseudo-static problem. The ordinary differential equations (ODEs) thus obtained are then solved by the well-established Finite Element methodology against each frequency within the band-limited signal. The frequency dependant response of beam is then back-transformed into time domain by Inverse Fast Fourier Transformation (IFFT). Different types of boundary conditions including throw-off element are applied. Results are validated with the analytical solutions of Euler beams. Different propagating modes are also investigated. (author)
Finite Element Analysis of Connecting Rod of IC Engine
Samal Prasanta Kumar; Murali B; Abhilash; Pasha Tajmul
2015-01-01
A connecting rod of IC engine is subjected to complex dynamic loading conditions. Therefore it is a critical machine element which attracts researchers’ attention. This paper aims at development of simple 3D model, finite element analyses and the optimization by intuition of the connecting rod for robust design. In this study the detailed load analysis under in-service loading conditions was performed for a typical connecting rod. The CAD model was prepared taking the detailed dimensions from...
Finite Element Analysis of a Contactless Power Transformer with Metamaterial
Lan Jian Yu
2013-01-01
Wireless power transfer technologies enable power transfer to loads through air. The contactless power transformer is a key element of it. In this work, a new transformer with metamaterial is proposed, through which the power transfer distance increases. The electromagnetic properties about metamaterial are discussed at first. Then, the finite element analyses of this transformer are presented as well. The magnetic field distributions and the computational results show that this type of trans...
Interlaminar Stress Recovery for Three-Dimensional Finite Elements
Fagiano, C.; Abdalla, M.M.; Kassapoglou, C.; Gürdal, Z.
2010-01-01
Abstract An accurate evaluation of interlaminar stresses in multilayer composite laminates is crucial for the correct prediction of the onset of delamination. In general, three dimensional finite element models are required for acceptable accuracy, especially near free edges and stress concentrations. Interlaminar stresses are continuous both across and along layer interfaces. Nonetheless, the continuity of interlaminar stresses is difficult to enforce in C0 interpolated elements. ...
A nonlinear truss finite element with varying stiffness
Ďuriš R.; Murín J.
2007-01-01
This contribution deals with a new truss element with varying stiffness intended to geometric and physically nonlinear analysis of composite structures. We present a two-node straight composite truss finite element derived by new nonincremental full geometric nonlinear approach. Stiffness matrix of this composite truss contains transfer constants, which accurately describe the polynomial longitudinal variation of cross-section area and material properties. These variations could be caused by ...
Finite elements for the thermomechanical calculation of massive structures
The paper examines the fine element analysis of thermal stress and deformation problems in massive structures. To this end compatible idealizations are utilized for heat conduction and static analysis in order to minimize the data transfer. For transient behaviour due to unsteady heat flow and/or inelastics material processes the two computational parts are interwoven in form of an integrated software package for finite element analysis of thermomechanical problems in space and time. (orig.)
Finite Element Modeling of the Buckling Response of Sandwich Panels
Rose, Cheryl A.; Moore, David F.; Knight, Norman F., Jr.; Rankin, Charles C.
2002-01-01
A comparative study of different modeling approaches for predicting sandwich panel buckling response is described. The study considers sandwich panels with anisotropic face sheets and a very thick core. Results from conventional analytical solutions for sandwich panel overall buckling and face-sheet-wrinkling type modes are compared with solutions obtained using different finite element modeling approaches. Finite element solutions are obtained using layered shell element models, with and without transverse shear flexibility, layered shell/solid element models, with shell elements for the face sheets and solid elements for the core, and sandwich models using a recently developed specialty sandwich element. Convergence characteristics of the shell/solid and sandwich element modeling approaches with respect to in-plane and through-the-thickness discretization, are demonstrated. Results of the study indicate that the specialty sandwich element provides an accurate and effective modeling approach for predicting both overall and localized sandwich panel buckling response. Furthermore, results indicate that anisotropy of the face sheets, along with the ratio of principle elastic moduli, affect the buckling response and these effects may not be represented accurately by analytical solutions. Modeling recommendations are also provided.
Choice of input fields in stochastic finite elements
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1999-01-01
flexibility field, as the input to the stochastic finite element model. To answer this question the focus should be on the error of the output of the mechanical model rather than on the input field itself when discretizing the held through replacing it by a field defined in terms of a finite number of random......The problem of the arbitrary choice of variables for random field modelling in structural mechanics or in soil mechanics is treated. For example, it is relevant to ask the question of whether it is best to choose a stiffness field along a beam element or to choose its reciprocal field, the...... variables. Several reported discretization methods define these random variables as integrals of the product of the held and some suitable weight functions. In particular, the weight functions can be Dirac delta functions whereby the random variables become the field values at a finite set of given points...
Finite element simulation of stress intensity factors in elastic-plastic crack growth
ALSHOAIBI Abdulnaser M.; ARIFFIN Ahmad Kamal
2006-01-01
A finite element program developed elastic-plastic crack propagation simulation using Fortran language. At each propagation step, the adaptive mesh is automatically refined based on a posteriori h-type refinement using norm stress error estimator. A rosette of quarter-point elements is then constructed around the crack tip to facilitate the prediction of crack growth based on the maximum normal stress criterion and to calculate stress intensity factors under plane stress and plane strain conditions.Crack was modelled to propagate through the inter-element in the mesh. Some examples are presented to show the results of the implementation.
Implicit extrapolation methods for multilevel finite element computations
Jung, M.; Ruede, U. [Technische Universitaet Chemnitz-Zwickau (Germany)
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.
Piezoelectric Accelerometers Modification Based on the Finite Element Method
Liu, Bin; Kriegbaum, B.
2000-01-01
The paper describes the modification of piezoelectric accelerometers using a Finite Element (FE) method. Brüel & Kjær Accelerometer Type 8325 is chosen as an example to illustrate the advanced accelerometer development procedure. The deviation between the measurement and FE simulation results...
A Dual Orthogonality Procedure for Nonlinear Finite Element Equations
Krenk, S.; Hededal, O.
In the orthogonal residual procedure for solution of nonlinear finite element equations the load is adjusted in each equilibrium iteration to satisfy an orthogonality condition to the current displacement increment. It is here shown that the quasi-newton formulation of the orthogonal residual...
Finite element modeling of plasmon based single-photon sources
Chen, Yuntian; Gregersen, Niels; Nielsen, Torben Roland;
2011-01-01
A finite element method (FEM) approach of calculating a single emitter coupled to plasmonic waveguides has been developed. The method consists of a 2D model and a 3D model: (I) In the 2D model, we have calculated the spontaneous emission decay rate of a single emitter into guided plasmonic modes by...
Parallel solution to contact problems by finite element method
Dobiáš, Jiří
Edinburgh : EPCC, 2002, s. 1-20. [EPCC seminar. Edinburgh (GB), 20.06.2002] R&D Projects: GA ČR GA101/02/0072 Institutional research plan: CEZ:AV0Z2076919 Keywords : high performance computing * contact * finite element method Subject RIV: BD - Theory of Information
TWODEPEP, a small general purpose finite element program
A small but quite versatile finite element program is described which solves elliptic, parabolic and eigenvalue partial differential equations in general two dimensional regions. The program includes a preprocessor and a graphical output package, and has the ability to automatically refine and grade the triangular mesh. (orig.)
Experiences in interfacing NASTRAN with another finite element program
Schwerzler, D. D.; Leverenz, R. K.
1972-01-01
The coupling of NASTRAN to another finite element program developed for the static analysis of automotive structures is discussed. The two programs were coupled together to use the substructuring capability of the in-house program and the normal mode analysis capability of NASTRAN. Modifications were made to the NASTRAN program in order to make the coupling feasible.
Convergent finite element methods for compressible barotropic Stokes systems
Kenneth H. Karlsen; Karper, Trygve K.
2008-01-01
We propose finite element methods for compressible barotropic Stokes systems. We state convergence results for these methods and outline their proofs. The principal tools of the proofs are higher integrability estimates for the discrete density, equations for the discrete effective viscous flux, and renormalized formulations of the numerical method for the density equation.
Discontinuous Galerkin Immersed Finite Element Methods for Parabolic Interface Problems
Yang, Qing; Zhang, Xu
2015-01-01
In this article, interior penalty discontinuous Galerkin methods using immersed finite element functions are employed to solve parabolic interface problems. Typical semi-discrete and fully discrete schemes are presented and analyzed. Optimal convergence for both semi-discrete and fully discrete schemes are proved. Some numerical experiments are provided to validate our theoretical results.
Finite element modelling of fibre-reinforced brittle materials
Kullaa, J.
1997-01-01
The tensile constitutive behaviour of fibre-reinforced brittle materials can be extended to two or three dimensions by using the finite element method with crack models. The three approaches in this study include the smeared and discrete crack concepts and a multi-surface plasticity model. The tensi
Stochastic Finite Elements in Reliability-Based Structural Optimization
Sørensen, John Dalsgaard; Engelund, S.
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to...
Stochastic Finite Elements in Reliability-Based Structural Optimization
Sørensen, John Dalsgaard; Engelund, S.
1995-01-01
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to...
Partially Penalized Immersed Finite Element Methods for Parabolic Interface Problems
Lin, Tao; Yang, Qing; Zhang, Xu
2015-01-01
We present partially penalized immersed finite element methods for solving parabolic interface problems on Cartesian meshes. Typical semi-discrete and fully discrete schemes are discussed. Error estimates in an energy norm are derived. Numerical examples are provided to support theoretical analysis.
Finite Element Vibration and Dynamic Response Analysis of Engineering Structures
Jaroslav Mackerle
2000-01-01
Full Text Available This bibliography lists references to papers, conference proceedings, and theses/dissertations dealing with finite element vibration and dynamic response analysis of engineering structures that were published from 1994 to 1998. It contains 539 citations. The following types of structures are included: basic structural systems; ground structures; ocean and coastal structures; mobile structures; and containment structures.
2-D Finite Element Analysis of Massive RC Structures
Saabye Ottosen, Niels
1982-01-01
Nonlinear analysis of concrete structures using finite elements is discussed. The applications include a thick-walled top-closure for a pressure vessel as well as the delicate problems of beams failing in shear. The top-closure analysis evaluates the effect of two different failure criteria and...
A finite element kinematic analysis of planar granular solids flow
Watson, G.R.; Rotter, J.M. [University of Edinburgh, Edinburgh (United Kingdom). Dept. of Civil Engineering and Building Science
1996-08-01
A finite element analysis is presented to calculate the steady-state velocity fields in a cohesionless granular solid discharging from a planar flat-bottomed silo. The work treats a wide range of geometries, material properties and boundary conditions. The approach is kinematic and gravity-based, solving for the velocity field and assuming complete stress independence. 36 refs., 22 figs.
An Orthogonal Residual Procedure for Nonlinear Finite Element Equations
Krenk, S.
A general and robust solution procedure for nonlinear finite element equations with limit points is developed. At each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state. The...
Hands on applied finite element analysis application with ANSYS
Arslan, Mehmet Ali
2015-01-01
Hands on Applied Finite Element Analysis Application with Ansys is truly an extraordinary book that offers practical ways of tackling FEA problems in machine design and analysis. In this book, 35 good selection of example problems have been presented, offering students the opportunity to apply their knowledge to real engineering FEA problem solutions by guiding them with real life hands on experience.
Finite Groups with Three Conjugacy Class Sizes of some Elements
Qingjun Kong
2012-08-01
Let be a finite group. We prove as follows: Let be a -solvable group for a fixed prime . If the conjugacy class sizes of all elements of primary and biprimary orders of are $\\{1,p^a,n\\}$ with and two positive integers and (,)=1, then is -nilpotent or has abelian Sylow -subgroups.
2-D Finite Element Analysis of Massive RC Structures
Saabye Ottosen, Niels
1982-01-01
Nonlinear analysis of concrete structures using finite elements is discussed. The applications include a thick-walled top-closure for a pressure vessel as well as the delicate problems of beams failing in shear. The top-closure analysis evaluates the effect of two different failure criteria and m...
The future of the finite element method in geotechnics
Brinkgreve, R.B.J.
2012-01-01
In this presentation a vision is given on tlie fiiture of the finite element method (FEM) for geotechnical engineering and design. In the past 20 years the FEM has proven to be a powerful method for estimating deformation, stability and groundwater flow in geoteclmical stmctures. Much has been achie
Finite element modelling of human vocal folds self-oscillation
Švancara, Pavel; Horáček, Jaromír; Švec, Jan G.
Salt Lake City : National Center for Voice and Speech, University of Utah, 2014. s. 83. [International Conference on Voice Physiology and Biomechanics /9./. 10.04.2014-12.04.2014, Salt Lake City] Institutional support: RVO:61388998 Keywords : biomechanics of voice * fluid-structure-acoustic interaction * finite element method * videokymography Subject RIV: BI - Acoustics
Multilayered shell finite element with interlaminar continuous shear stresses
Brank, Boštjan; Carrera, Erasmo
2015-01-01
A finite element formulation for refined linear analysis of multilayered shell structures of moderate thickness is presented. An underlying shell model is a direct extension of the first-order shear-deformation theory of Reissner-Mindlin type. A refined theory with seven unknown kinematic fields is developed
Predicting target displacements using ultrasound elastography and finite element modeling
Buijs, J.O. den; Hansen, H.H.G.; Lopata, R.G.P.; Korte, C.L. de; Misra, S.
2011-01-01
Soft tissue displacements during minimally invasive surgical procedures may cause target motion and subsequent misplacement of the surgical tool. A technique is presented to predict target displacements using a combination of ultrasound elastography and finite element (FE) modeling. A cubic gelatin/
Finite Element Method application for modeling of PVD coatings properties
W. Sitek
2008-04-01
Full Text Available Purpose: The main subject of this paper is the computer simulation with the use of finite element method for determining the internal stresses in coatings Ti+TiN obtained in the magnetron PVD process on the sintered high-speed steel of the ASP 30 in different temperatures of 460, 500 and 540 °C.Design/methodology/approach: Computer simulation of stresses was carried out with the help of finite element method in ANSYS environment, and the experimental values of stresses were determined basing on the X-ray diffraction patterns.Findings: The presented model meets the initial criteria, which gives ground to the assumption about its usability for determining the stresses in coatings, employing the finite element method using the ANSYS program. The computer simulation results correlate with the experimental results.Research limitations/implications: To evaluate with more details the possibility of applying these coatings tools, further computer simulation should be concentrated on the determination of other properties of the coatings for example- microhardness.Originality/value: Presently the computer simulation is very popular and it is based on the finite element method, which allows to better understand the interdependence between parameters of process and choosing optimal solution. The possibility of application faster and faster calculation machines and coming into being many software make possible the creation of more precise models and more adequate ones to reality.
A FINITE VOLUME ELEMENT METHOD FOR THERMAL CONVECTION PROBLEMS
芮洪兴
2004-01-01
Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H1 norm error estimates are given.
A parallel finite element simulator for ion transport through three-dimensional ion channel systems.
Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo
2013-09-15
A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can
Finite element analysis of degraded concrete structures - Workshop proceedings
This workshop is related to the finite element analysis of degraded concrete structures. It is composed of three sessions. The first session (which title is: the use of finite element analysis in safety assessments) comprises six papers which titles are: Historical Development of Concrete Finite Element Modeling for Safety Evaluation of Accident-Challenged and Aging Concrete Structures; Experience with Finite Element Methods for Safety Assessments in Switzerland; Stress State Analysis of the Ignalina NPP Confinement System; Prestressed Containment: Behaviour when Concrete Cracking is Modelled; Application of FEA for Design and Support of NPP Containment in Russia; Verification Problems of Nuclear Installations Safety Software of Strength Analysis (NISS SA). The second session (title: concrete containment structures under accident loads) comprises seven papers which titles are: Two Application Examples of Concrete Containment Structures under Accident Load Conditions Using Finite Element Analysis; What Kind of Prediction for Leak rates for Nuclear Power Plant Containments in Accidental Conditions; Influence of Different Hypotheses Used in Numerical Models for Concrete At Elevated Temperatures on the Predicted Behaviour of NPP Core Catchers Under Severe Accident Conditions; Observations on the Constitutive Modeling of Concrete Under Multi-Axial States at Elevated Temperatures; Analyses of a Reinforced Concrete Containment with Liner Corrosion Damage; Program of Containment Concrete Control During Operation for the Temelin Nuclear Power Plant; Static Limit Load of a Deteriorated Hyperbolic Cooling Tower. The third session (concrete structures under extreme environmental load) comprised five papers which titles are: Shear Transfer Mechanism of RC Plates After Cracking; Seismic Back Calculation of an Auxiliary Building of the Nuclear Power Plant Muehleberg, Switzerland; Seismic Behaviour of Slightly Reinforced Shear Wall Structures; FE Analysis of Degraded Concrete
The finite element method: Is weighted volume integration essential?
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.
Exploring Critical Collapse in the Semilinear Wave Equation using Space-Time Finite Elements
Lim, Hyun; Kimn, Jung-Han
2014-01-01
A fully implicit numerical approach based on the space-time finite element method is implemented for the semilinear wave equation in 1(space) + 1(time) dimensions to explore critical collapse and search for self-similar solutions. Previous work studied this behavior by exploring the threshold of singularity formation using time marching finite difference techniques while this work introduces an adaptive time parallel numerical method to the problem. The semilinear wave equation with a $p = 7$ term is examined in spherical symmetry. The impact of mesh refinement and the time additive Schwarz preconditioner in conjunction with Krylov Subspace Methods are examined.
DECROOS Koenraad; OHMS Carsten; Petrov, Roumen; Seefeldt, Marc; Verhaeghe, Frederik; Kestens, Leo
2013-01-01
A new method has been designed to automatically adapt the geometry of the fusion zone of a weld according to the temperature calculations when the thermal welding heat source parameters are known. In the material definition in a Finite Element code for welding stress calculations, the fusion zone material has different properties than the base material since, among others, the temperature at which the material is stress free is the melting temperature instead of room temperature. In this work...
Residual-driven online generalized multiscale finite element methods
Chung, Eric T.
2015-09-08
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.
Investigations on Actuator Dynamics through Theoretical and Finite Element Approach
Somashekhar S. Hiremath
2010-01-01
Full Text Available This paper gives a new approach for modeling the fluid-structure interaction of servovalve component-actuator. The analyzed valve is a precision flow control valve-jet pipe electrohydraulic servovalve. The positioning of an actuator depends upon the flow rate from control ports, in turn depends on the spool position. Theoretical investigation is made for No-load condition and Load condition for an actuator. These are used in finite element modeling of an actuator. The fluid-structure-interaction (FSI is established between the piston and the fluid cavities at the piston end. The fluid cavities were modeled with special purpose hydrostatic fluid elements while the piston is modeled with brick elements. The finite element method is used to simulate the variation of cavity pressure, cavity volume, mass flow rate, and the actuator velocity. The finite element analysis is extended to study the system's linearized response to harmonic excitation using direct solution steady-state dynamics. It was observed from the analysis that the natural frequency of the actuator depends upon the position of the piston in the cylinder. This is a close match with theoretical and simulation results. The effect of bulk modulus is also presented in the paper.
Finite Element Modeling of the NASA Langley Aluminum Testbed Cylinder
Grosveld, Ferdinand W.; Pritchard, Joselyn I.; Buehrle, Ralph D.; Pappa, Richard S.
2002-01-01
The NASA Langley Aluminum Testbed Cylinder (ATC) was designed to serve as a universal structure for evaluating structural acoustic codes, modeling techniques and optimization methods used in the prediction of aircraft interior noise. Finite element models were developed for the components of the ATC based on the geometric, structural and material properties of the physical test structure. Numerically predicted modal frequencies for the longitudinal stringer, ring frame and dome component models, and six assembled ATC configurations were compared with experimental modal survey data. The finite element models were updated and refined, using physical parameters, to increase correlation with the measured modal data. Excellent agreement, within an average 1.5% to 2.9%, was obtained between the predicted and measured modal frequencies of the stringer, frame and dome components. The predictions for the modal frequencies of the assembled component Configurations I through V were within an average 2.9% and 9.1%. Finite element modal analyses were performed for comparison with 3 psi and 6 psi internal pressurization conditions in Configuration VI. The modal frequencies were predicted by applying differential stiffness to the elements with pressure loading and creating reduced matrices for beam elements with offsets inside external superelements. The average disagreement between the measured and predicted differences for the 0 psi and 6 psi internal pressure conditions was less than 0.5%. Comparably good agreement was obtained for the differences between the 0 psi and 3 psi measured and predicted internal pressure conditions.
Tet-to-Hex Conversion for Finite Element Analysis
McDill, J. M. J.; Carmona Garcia, A.
2004-06-01
It is well known that hexahedra; i.e., brick elements, provide superior performance to tetrahedra in certain types of finite element analysis, notably dynamic cases and in processes such as welding in which elasto-plastic boundaries and phase changes are present. The development of robust and complete free meshing schemes for hexahedra has been problematic. Typically, the user employs time consuming mapped meshing to create the necessary hexahedral meshes. On the other hand, complex geometries can be quickly free meshed, or populated, with tetrahedra, a main stay of commercial CAD/CAM packages. This does not require the time consuming operations of mapped meshing with hexahedra. Clearly, there is a need for a simple tetrahedra-to-hexahedra (TTH) conversion algorithm, which exploits the advantages of tetrahedral meshing. The development and testing of a TTH algorithm is presented. It uses a simple splitting method in which each hexahedron is divided into four hexahedra. A number of mesh optimization routines are implemented to improve the overall quality of the resulting finite element mesh. It is shown that the TTH algorithm is capable of handling a variety of geometries incorporating features typical in finite element analysis. While poorly formed elements cannot be entirely eliminated, the resulting meshes are useful. A number of initiatives in the continued development of the TTH are also presented.
Evaluation of Concrete Cylinder Tests Using Finite Elements
Saabye Ottosen, Niels
1984-01-01
Nonlinear axisymmetric finite element analyses are performed on the uniaxial compressive test of concrete cylinders. The models include thick steel loading plates, and cylinders with height‐to‐diameter ratios (h/d) ranging from 1‐3 are treated. A simple constitutive model of the concrete is...... uniaxial strength the use of geometrically matched loading plates seems to be advantageous. Finally, it is observed that for variations of the element size within limits otherwise required to obtain a realistic analysis, the results are insensitive to the element size....
A stabilized mixed finite element method for darcy flow
This paper presents a new stabilized mixed finite element method for Darcy flow. The new method finds its roots in the variational multiscale framework proposed by Hughes. The stabilized form is stable and convergent for arbitrary combinations of pressure and velocity interpolations. A global convergence proof is provided and convergence rates are derived. Based on the formulation, a family of triangular and quadrilateral elements is developed. Several numerical simulations are presented that corroborate the theoretical convergence rates. Simulations of various distorted mesh configurations as well as arbitrary combinations of triangular and quadrilateral elements are presented to show the superior performance of the method for various practical applications. Refs. 1 (author)
Stress analysis of coated particle fuel using finite element method
The fuel element of high temperature gas-cooled reactor is composed of coated particle fuel which is dispersed in graphite matrix. In normal operation, the stress due to irradiation and a variety of complex physical and chemical reactions will cause failure of the coated particle fuel. Therefore, the stress analysis of coated particle fuel is important for the safety of fuel element and reactor. The stress was analyzed by the finite element method based on the inner pressure failure mechanism considering asphericity of the particles. (authors)
A nonlinear truss finite element with varying stiffness
Ďuriš R.
2007-11-01
Full Text Available This contribution deals with a new truss element with varying stiffness intended to geometric and physically nonlinear analysis of composite structures. We present a two-node straight composite truss finite element derived by new nonincremental full geometric nonlinear approach. Stiffness matrix of this composite truss contains transfer constants, which accurately describe the polynomial longitudinal variation of cross-section area and material properties. These variations could be caused by nonhomogenous temperature field or by varying components volume fractions of the composite or/and functionally graded materials (FGM´s. Numerical examples were solved to verify the established relations. The accuracy of the new proposed finite truss element are compared and discused.
Finite element dynamic analysis on CDC STAR-100 computer
Noor, A. K.; Lambiotte, J. J., Jr.
1978-01-01
Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.
Streamline upwind finite element method for conjugate heat transfer problems
Niphon Wansophark; Atipong Malatip; Pramote Dechaumphai; Yunming Chen
2005-01-01
This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components,the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method.
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.
A tensor artificial viscosity using a finite element approach
Kolev, Tz. V.; Rieben, R. N.
2009-12-01
We derive a tensor artificial viscosity suitable for use in a 2D or 3D unstructured arbitrary Lagrangian-Eulerian (ALE) hydrodynamics code. This work is similar in nature to that of Campbell and Shashkov [1]; however, our approach is based on a finite element discretization that is fundamentally different from the mimetic finite difference framework. The finite element point of view leads to novel insights as well as improved numerical results. We begin with a generalized tensor version of the Von Neumann-Richtmyer artificial viscosity, then convert it to a variational formulation and apply a Galerkin discretization process using high order Gaussian quadrature to obtain a generalized nodal force term and corresponding zonal heating (or shock entropy) term. This technique is modular and is therefore suitable for coupling to a traditional staggered grid discretization of the momentum and energy conservation laws; however, we motivate the use of such finite element approaches for discretizing each term in the Euler equations. We review the key properties that any artificial viscosity must possess and use these to formulate specific constraints on the total artificial viscosity force term as well as the artificial viscosity coefficient. We also show, that under certain simplifying assumptions, the two-dimensional scheme from [1] can be viewed as an under-integrated version of our finite element method. This equivalence holds on general distorted quadrilateral grids. Finally, we present computational results on some standard shock hydro test problems, as well as some more challenging problems, indicating the advantages of the new approach with respect to symmetry preservation for shock wave propagation over general grids.
GPU-Accelerated Direct Volume Rendering of Finite Element Data Sets
Liu, Bingchen; Bock, Alexander; Ropinski, Timo; Nash, Martyn,; Nielsen, Poul; Wünsche, Burkhard
2012-01-01
Direct Volume Rendering of Finite Element models is challengingsince the visualisation process is performed in worldcoordinates, whereas data fields are usually defined overthe elements’ material coordinate system. In this paper wepresent a framework for Direct Volume Rendering of FiniteElement models. We present several novel implementationsvisualising Finite Element data directly without requiring resamplinginto world coordinates. We evaluate the methodsusing several biomedical Finite Eleme...
Finite element analysis of ultrasonic wave propagation and scattering
In an effort to improve the reliability of ultrasonic nondestructive testing methods, a finite element method was employed to calculate the scattered fields of ultrasound. The accurate analysis of ultrasonic propagation and scattering plays an important role in predicting the response of measurement system, and help the operators optimize test procedures when combined with other components of the testing system. A good system model also makes it possible to perform parametric studies, and in this way the probability of detection and reliability can be improved. In this study, a finite element modeling was developed for the analysis of scattered fields due to cracks, and then the accuracy of results was checked by solving several representative problems. The size of element and the integral time step, which are the critical components for the convergence of numerical results, were determined in ANSYS commercial finite element code. Several propagation and scattering problems in 2-D isotropic and anisotropic materials were solved and their results were compared with analytical results.
Finite element analysis of ultrasonic wave propagation and scattering
In an effort to improve the reliability of ultrasonic nondestructive testing methods, a finite element method was employed to calculate the scattered fields of ultrasound. The accurate analysis of ultrasonic propagation and scattering plays an important role in predicting the response of measurement system, and help tile operators optimize test procedures when combined with other components of the testing system. A good system model also makes it possible to perform parametric studies, and in this way the probability of detection and reliability can be improved. In this study, a finite element modeling was developed for the analysis of scattered fields due to cracks, and then the accuracy of results was checked by solving several representative problems. The size of element and the integral time step, which are the critical components for the convergence of numerical results, were determined in ANSYS commercial finite element code. Several propagation and scattering problems in 2-D isotropic and anisotropic materials were solved and their results were compared with analytical results.
A tool for finite element deflection analysis of wings
Carlen, Ingemar
2005-03-01
A first version (ver 0.1) of a new tool for finite element deflection analysis of wind turbine blades is presented. The software is called SOLDE (SOLid blaDE), and was developed as a Matlab shell around the free finite element codes CGX (GraphiX - pre-processor), and CCX (CrunchiX - solver). In the present report a brief description of SOLDE is given, followed by a basic users guide. The main features of SOLDE are: - Deflection analysis of wind turbine blades, including 3D effects and warping. - Accurate prediction of eigenmodes and eigenfrequencies. - Derivation of 2-node slender elements for use in various aeroelastic analyses. The main differences between SOLDE and other similar tools can be summarised as: - SOLDE was developed without a graphical user interface or a traditional text file input deck. Instead the input is organised as Matlab data structures that have to be formed by a user provided pre-processor. - SOLDE uses a solid representation of the geometry instead of a thin shell approximation. The benefit is that the bending-torsion couplings will automatically be correctly captured. However, a drawback with the current version is that the equivalent orthotropic shell idealisation violates the local bending characteristics, which makes the model useless for buckling analyses. - SOLDE includes the free finite element solver CCX, and thus no expensive commercial software (e.g. Ansys, or Nastran) is required to produce results.
Finite element evaluation of erosion/corrosion affected reducing elbow
Erosion/corrosion is a primary source for wall thinning or degradation of carbon steel piping systems in service. A number of piping failures in the power industry have been attributed to erosion/corrosion. Piping elbow is one of such susceptible components for erosion/corrosion because of increased flow turbulence due to its geometry. In this paper, the acceptability of a 12 in. x 8 in. reducing elbow in RHR service water pump discharge piping, which experienced significant degradation due to wall thinning in localized areas, was evaluated using finite element analysis methodology. Since the simplified methods showed very small margin and recommended replacement of the elbow, a detailed 3-D finite element model was built using shell elements and analyzed for internal pressure and moment loadings. The finite element analysis incorporated the U.T. measured wall thickness data at various spots that experienced wall thinning. The results showed that the elbow is acceptable as-is until the next fuel cycle. FEA, though cumbersome, and time consuming is a valuable analytical tool in making critical decisions with regard to component replacement of border line situation cases, eliminating some conservatism while not compromising the safety
Finite element analysis of structures through unified formulation
Carrera, Erasmo; Petrolo, Marco; Zappino, Enrico
2014-01-01
The finite element method (FEM) is a computational tool widely used to design and analyse complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another. Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of linear elasticity. The novelty of this book is that the finite elements (FEs) are formulated on the basis of a class of theories of structures known as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and 3D FEs on the basis of the same ''fundamental nucleus'' that comes from geometrical relations and Hooke''s law, and presents both 1D and 2D refined FEs that only have displacement variables as in 3D elements. It also covers 1D...
A finite element model for protein transport in vivo
Montas Hubert J
2007-06-01
Full Text Available Abstract Background Biological mass transport processes determine the behavior and function of cells, regulate interactions between synthetic agents and recipient targets, and are key elements in the design and use of biosensors. Accurately predicting the outcomes of such processes is crucial to both enhancing our understanding of how these systems function, enabling the design of effective strategies to control their function, and verifying that engineered solutions perform according to plan. Methods A Galerkin-based finite element model was developed and implemented to solve a system of two coupled partial differential equations governing biomolecule transport and reaction in live cells. The simulator was coupled, in the framework of an inverse modeling strategy, with an optimization algorithm and an experimental time series, obtained by the Fluorescence Recovery after Photobleaching (FRAP technique, to estimate biomolecule mass transport and reaction rate parameters. In the inverse algorithm, an adaptive method was implemented to calculate sensitivity matrix. A multi-criteria termination rule was developed to stop the inverse code at the solution. The applicability of the model was illustrated by simulating the mobility and binding of GFP-tagged glucocorticoid receptor in the nucleoplasm of mouse adenocarcinoma. Results The numerical simulator shows excellent agreement with the analytic solutions and experimental FRAP data. Detailed residual analysis indicates that residuals have zero mean and constant variance and are normally distributed and uncorrelated. Therefore, the necessary and sufficient criteria for least square parameter optimization, which was used in this study, were met. Conclusion The developed strategy is an efficient approach to extract as much physiochemical information from the FRAP protocol as possible. Well-posedness analysis of the inverse problem, however, indicates that the FRAP protocol provides insufficient
A parallel adaptive finite difference algorithm for petroleum reservoir simulation
Hoang, Hai Minh
2005-07-01
Adaptive finite differential for problems arising in simulation of flow in porous medium applications are considered. Such methods have been proven useful for overcoming limitations of computational resources and improving the resolution of the numerical solutions to a wide range of problems. By local refinement of the computational mesh where it is needed to improve the accuracy of solutions, yields better solution resolution representing more efficient use of computational resources than is possible with traditional fixed-grid approaches. In this thesis, we propose a parallel adaptive cell-centered finite difference (PAFD) method for black-oil reservoir simulation models. This is an extension of the adaptive mesh refinement (AMR) methodology first developed by Berger and Oliger (1984) for the hyperbolic problem. Our algorithm is fully adaptive in time and space through the use of subcycling, in which finer grids are advanced at smaller time steps than the coarser ones. When coarse and fine grids reach the same advanced time level, they are synchronized to ensure that the global solution is conservative and satisfy the divergence constraint across all levels of refinement. The material in this thesis is subdivided in to three overall parts. First we explain the methodology and intricacies of AFD scheme. Then we extend a finite differential cell-centered approximation discretization to a multilevel hierarchy of refined grids, and finally we are employing the algorithm on parallel computer. The results in this work show that the approach presented is robust, and stable, thus demonstrating the increased solution accuracy due to local refinement and reduced computing resource consumption. (Author)
FECAP - FINITE ELEMENT COMPOSITE ANALYSIS PROGRAM FOR A MICROCOMPUTER
Bowles, D. E.
1994-01-01
Advanced composite materials have gained use in the aerospace industry over the last 20 years because of their high specific strength and stiffness, and low coefficient of thermal expansion. Design of composite structures requires the analysis of composite material behavior. The Finite Element Composite Analysis Program, FECAP, is a special purpose finite element analysis program for analyzing composite material behavior with a microcomputer. Composite materials, in regard to this program, are defined as the combination of at least two distinct materials to form one nonhomogeneous anisotropic material. FECAP assumes a state of generalized plane strain exists in a material consisting of two or more orthotropic phases, subjected to mechanical and/or thermal loading. The finite element formulation used in FECAP is displacement based and requires the minimization of the total potential energy for each element with respect to the unknown variables. This procedure leads to a set of linear simultaneous equations relating the unknown nodal displacements to the applied loads. The equations for each element are assembled into a global system, the boundary conditions are applied, and the system is solved for the nodal displacements. The analysis may be performed using either 4-mode linear or 8-mode quadratic isoparametric elements. Output includes the nodal displacements, and the element stresses and strains. FECAP was written for a Hewlett Packard HP9000 Series 200 Microcomputer with the HP Basic operating system. It was written in HP BASIC 3.0 and requires approximately 0.5 Mbytes of RAM in addition to what is required for the operating system. A math coprocessor card is highly recommended. FECAP was developed in 1988.
Radiative transfer with finite elements. Pt. 1. Basic method and tests
Richling, S. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Astrophysik; Meinkoehn, E. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Astrophysik]|[Heidelberg Univ. (Germany). Inst. fuer Angewandte Mathematik; Kryzhevoi, N. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Astrophysik]|[Heidelberg Univ. (DE). Interdisziplinaeres Zentrum fuer Wissenschaftliches Rechnen (IWR); Kanschat, G. [Heidelberg Univ. (Germany). Inst. fuer Angewandte Mathematik]|[Heidelberg Univ. (DE). Interdisziplinaeres Zentrum fuer Wissenschaftliches Rechnen (IWR)
2001-10-01
A finite element method for solving the monochromatic radiation transfer equation including scattering in three dimensions is presented. The algorithm employs unstructured grids which are adaptively refined. Adaptivity as well as ordinate parallelization reduce memory requirements and execution time and make it possible to calculate the radiation field across several length scales for objects with strong opacity gradients. An a posteriori error estimate for one particular quantity is obtained by solving the dual problem. The application to a sample of test problems reveals the properties of the implementation. (orig.)
Diagonal multi-soliton matrix elements in finite volume
Pálmai, T
2012-01-01
We consider diagonal matrix elements of local operators between multi-soliton states in finite volume in the sine-Gordon model, and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Tak\\'acs which were only valid for diagonal scattering. In order to test the conjecture we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.
Deuring, Paul; Eymard,, Robert; Mildner, Marcus
2014-01-01
We consider a time-dependent and a steady linear convection-diffusion equation. These equations are approximately solved by a combined finite element -- finite volume method: the diffusion term is discretized by Crouzeix-Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is used as time discretization. This scheme is shown to be unconditionally L2-stable, uniformly with re...
Nonlinear Finite Element Analysis of FRP Strengthened Reinforced Concrete Beams
Sasmal, S.; Kalidoss, S.; Srinivas, V.
2012-12-01
This paper focuses on nonlinear analysis of parent and fiber reinforced polymer (FRP) strengthened reinforced concrete (RC) beam using general purpose finite element software, ANSYS. Further, it is aimed to investigate the suitability of different elements available in ANSYS library to represent FRP, epoxy and interface. 3-D structural RC solid element has been used to model concrete and truss element is employed for modeling the reinforcements. FRP has been modelled using 3-D membrane element and layered element with number of layers, epoxy is modelled using eight node brick element, and eight node layered solid shell is used to mathematically represent the concrete-FRP interface behavior. Initially, the validation of the numerical model for the efficacy of different elements (SOLID65 for concrete and LINK8 for reinforcement) and material models is carried out on the experimental beam reported in literature. The validated model, elements and material properties is used to evaluate the load-displacement and load-strain response behavior and crack patterns of the FRP strengthened RC beams. The numerical results indicated that significant improvement in the displacement in the strengthened RC beams with the advancement of cracks. The study shows that FRP with shell elements is recommended when single layer of FRP is used. When multi layered FRP is used, solid layered element can be a reasonably good choice whereas the epoxy matrix with linear solid element does not need further complicated model. Interfacial element makes the analysis minimally improved at the cost of complicated modeling issues and considerable computation time. Hence, for nonlinear analysis of usual strengthened structures, unless it is specifically required for, interface element may not be required and a full contact can be assumed at interface.
Tezduyar, T. E.; Liou, J.
1988-01-01
Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.
Finite element solution of a Schelkunoff vector potential for frequency domain, EM field simulation
Kordy, M. A.; Wannamaker, P. E.; Cherkaev, E.
2011-12-01
A novel method for the 3-D diffusive electromagnetic (EM) forward problem is developed and tested. A Lorentz-gauge, Schelkunoff complex vector potential is used to represent the EM field in the frequency domain and the nodal finite element method is used for numerical simulation. The potential allows for three degrees of freedom per node, instead of four if Coulomb-gauge vector and scalar potentials are used. Unlike the finite-difference method, which minimizes error at discrete points, the finite element method minimizes error over the entire domain cell volumes and may easily adapt to complex topography. Existence and uniqueness of this continuous Schelkunoff potential is proven, boundary conditions are found and a governing equation satisfied by the potential in weak form is obtained. This approach for using a Schelkunoff potential in the finite element method differs from other trials found in the literature. If the standard weak form of the Helmholtz equation is used, the obtained solution is continuous and has continuous normal derivative across boundaries of regions with different physical properties; however, continuous Schelkunoff potential components do not have continuous normal derivative, divergence of the potential divided by (complex) conductivity and magnetic permeability is continuous instead. The weak form of governing equation used here imposes proper boundary conditions on the solution. Moreover, as the solution is continuous, nodal shape functions are used instead of edge elements. Magnetotelluric (MT) simulation results using the new method are compared with those from other MT forward codes
Development and validation of a weight-bearing finite element model for total knee replacement.
Woiczinski, M; Steinbrück, A; Weber, P; Müller, P E; Jansson, V; Schröder, Ch
2016-08-01
Total knee arthroplasty (TKA) is a successful procedure for osteoarthritis. However, some patients (19%) do have pain after surgery. A finite element model was developed based on boundary conditions of a knee rig. A 3D-model of an anatomical full leg was generated from magnetic resonance image data and a total knee prosthesis was implanted without patella resurfacing. In the finite element model, a restarting procedure was programmed in order to hold the ground reaction force constant with an adapted quadriceps muscle force during a squat from 20° to 105° of flexion. Knee rig experimental data were used to validate the numerical model in the patellofemoral and femorotibial joint. Furthermore, sensitivity analyses of Young's modulus of the patella cartilage, posterior cruciate ligament (PCL) stiffness, and patella tendon origin were performed. Pearson's correlations for retropatellar contact area, pressure, patella flexion, and femorotibial ap-movement were near to 1. Lowest root mean square error for retropatellar pressure, patella flexion, and femorotibial ap-movement were found for the baseline model setup with Young's modulus of 5 MPa for patella cartilage, a downscaled PCL stiffness of 25% compared to the literature given value and an anatomical origin of the patella tendon. The results of the conducted finite element model are comparable with the experimental results. Therefore, the finite element model developed in this study can be used for further clinical investigations and will help to better understand the clinical aspects after TKA with an unresurfaced patella. PMID:26618541
A 3D Finite Element evaluation of the exophthalmia reduction
Luboz, V; Boutault, F; Swider, P; Payan, Y; Luboz, Vincent; Pedrono, Annaig; Boutault, Franck; Swider, Pascal; Payan, Yohan
2003-01-01
This paper presents a first evaluation of the feasibility of Finite Element modelling of the orbital decompression, in the context of exophthalmia. First simulations are carried out with data extracted from a patient TDM exam. Results seem to qualitatively validate the feasibility of the simulations, with a Finite Element analysis that converges and provides a backward movement of the ocular globe associated with displacements of the fat tissues through the sinuses. This FE model can help a surgeon for the planning of the exophthalmia reduction, and especially for the position and the size of the decompression hole. To get an estimation of the fat tissues volume affected by the surgery, an analytical model seems to provide quicker results for an equivalent efficiency.
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
Copeland, Dylan
2010-10-05
The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.
FEMWASTE FEMWATER, Finite Elements Method Waste Transport Through Porous Media
1 - Description of program or function: FEMWASTE is a two-dimensional transient model for the transport of dissolved constituents through porous media. The transport mechanisms include: convection, hydro- dynamic dispersion, chemical sorption, and first-order decay. The waste transport model is compatible with the water flow model (FEMWATER)) for predicting convective Darcy velocities in porous media which may be partially saturated. 2 - Method of solution: Implementation of quadrilateral iso-parametric finite elements, bilinear spatial interpolation, asymmetric weighting functions, several time-marching techniques, and Gaussian elimination are employed in the numerical formulation of the transport equation. The application of the finite element method ensures that mass balance over the whole region is preserved. A mixture-dependent retardation factor is employed in the definition of solute sorption
Assembly of finite element methods on graphics processors
Cecka, Cris
2010-08-23
Recently, graphics processing units (GPUs) have had great success in accelerating many numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are created and analyzed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor using single-precision arithmetic achieves speedups of 30 or more in comparison to a well optimized double-precision single core implementation. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite element discretization. © 2010 John Wiley & Sons, Ltd.
Some benchmark shielding problems solved by the finite element method
Some of the test cases on bulk shields for the two-dimensional codes MARC, TRIMOM and FELICIT are described. These codes use spherical harmonic expansions for neutron directions and a finite element grid over space. MARC was developed primarily as a reactor physics code with a finite element option and it assumes isotropic scattering. TRIMOM is being developed as a general purpose shielding code for anisotropic scatterers. FELICIT is being developed as a module of TRIMOM for cylindrical systems. All three codes employ continuous trial functions at present. Exploratory work on the use of discontinuous trial functions is described. Discontinuous trial functions permit the splicing of methods which use different angular expansions, so that, for example, transport theory can be used where it is necessary and diffusion theory can be used elsewhere. (author)
A finite element model for residual stress in repair welds
Feng, Z. [Edison Welding Inst., Columbus, OH (United States); Wang, X.L.; Spooner, S.; Goodwin, G.M.; Maziasz, P.J.; Hubbard, C.R.; Zacharia, T. [Oak Ridge National Lab., TN (United States)
1996-03-28
This paper describes a three-dimensional finite element model for calculation of the residual stress distribution caused by repair welding. Special user subroutines were developed to simulate the continuous deposition of filler metal during welding. The model was then tested by simulating the residual stress/strain field of a FeAl weld overlay clad on a 2{1/4}Cr-1 Mo steel plate, for which neutron diffraction measurement data of the residual strain field were available. It is shown that the calculated residual stress distribution was consistent with that determined with neutron diffraction. High tensile residual stresses in both the longitudinal and transverse directions were observed around the weld toe at the end of the weld. The strong spatial dependency of the residual stresses in the region around the weld demonstrates that the common two-dimensional cross-section finite element models should not be used for repair welding analysis.
Finite element simulation of temperature dependent free surface flows
Engelman, M. S.; Sani, R. L.
1985-01-01
The method of Engelman and Sani (1984) for a finite-element simulation of incompressible surface flows with a free and/or moving fluid interface, such as encountered in crystal growth and coating and polymer technology, is extended to temperature-dependent flows, including the effect of temperature-dependent surface tension. The basic algorithm of Saito and Scriven (1981) and Ruschak (1980) has been generalized and implemented in a robust and versatile finite-element code that can be employed with relative ease for the simulation of free-surface problems in complex geometries. As a result, the costly dependence on the Newton-Raphson algorithm has been eliminated by replacing it with a quasi-Newton iterative method, which nearly retains the superior convergence properties of the Newton-Raphson method.
A mixed finite element method in compressible flow mechanics
This study concerns the numerical treatment of time-dependent tridimensional multifluid flow. No sleeping between the two phases as physical hypotheses leads to an ultra-compressible homogeneous fluid equations. The theoretical study, in the steady state case, comes from NAVIER-STOKES equations where viscosity support exists. The time dependent framework is the wave equation. The retained approximation method is the ''mixed'' finite element method, as regards speed and pressure functions. The improvement brought about are as follows: generalization to tri-dimensional case of finite-element vectorial field where divergence function exists, approximation convergence by this method and in the steady case, numerical stability study in linearised case of wave equations. In the last part, a solution algorithm is presented where integrals are calculated by Gauss numerical integration.
Finite element thermo-viscoplastic analysis of aerospace structures
Pandey, Ajay K.; Dechaumphai, Pramote; Thornton, Earl A.
1990-01-01
The time-dependent thermo-viscoplastic response of aerospace structures subjected to intense aerothermal loads is predicted using the finite-element method. The finite-element analysis uses the Bodner-Partom unified viscoplastic constitutive relations to determine rate-dependent nonlinear material behavior. The methodology is verified by comparison with experimental data and other numerical results for a uniaxially-loaded bar. The method is then used (1) to predict the structural response of a rectangular plate subjected to line heating along a centerline, and (2) to predict the thermal-structural response of a convectively-cooled engine cowl leading edge subjected to aerodynamic shock-shock interference heating. Compared to linear elastic analysis, the viscoplastic analysis results in lower peak stresses and regions of plastic deformations.
Finite-element thermo-viscoplastic analysis of aerospace structures
Pandey, Ajay; Dechaumphai, Pramote; Thornton, Earl A.
1990-01-01
The time-dependent thermo-viscoplastic response of aerospace structures subjected to intense aerothermal loads is predicted using the finite-element method. The finite-element analysis uses the Bodner-Partom unified viscoplastic constitutive relations to determine rate-dependent nonlinear material behavior. The methodology is verified by comparison with experimental data and other numerical results for a uniaxially-loaded bar. The method is then used (1) to predict the structural response of a rectangular plate subjected to line heating along a centerline, and (2) to predict the thermal-structural response of a convectively-cooled engine cowl leading edge subjected to aerodynamic shock-shock interference heating. Compared to linear elastic analysis, the viscoplastic analysis results in lower peak stresses and regions of plastic deformations.
Finite element model of reinforcement corrosion in concrete
Jin-xia XU
2009-06-01
Full Text Available A nonlinear finite element model (FEM of the corrosion of steel reinforcement in concrete has been successfully developed on the basis of mathematical analysis of the electrochemical process of steel corrosion in concrete. The influences of the area ratio and the Tafel constants of the anode and cathode on the potential and corrosion current density have been examined with the model. It has been found that the finite element calculation is more suitable for assessing the corrosion condition of steel reinforcement than ordinary electrochemical techniques due to the fact that FEM can obtain the distributions of potential and corrosion current density on the steel surface. In addition, the local corrosion of steel reinforcement in concrete is strengthened with the decrease of both the area ratio and the Tafel constants. These results provide valuable information to the researchers who investigate steel corrosion.
Finite Element Modeling of Micromachined MEMS Photon Devices
The technology of microelectronics that has evolved over the past half century is one of great power and sophistication and can now be extended to many applications (MEMS and MOEMS) other than electronics. An interesting application of MEMS quantum devices is the detection of electromagnetic radiation. The operation principle of MEMS quantum devices is based on the photoinduced stress in semiconductors, and the photon detection results from the measurement of the photoinduced bending. These devices can be described as micromechanical photon detectors. In this work, we have developed a technique for simulating electronic stresses using finite element analysis. We have used our technique to model the response of micromechanical photon devices to external stimuli and compared these results with experimental data. Material properties, geometry, and bimaterial design play an important role in the performance of micromechanical photon detectors. We have modeled these effects using finite element analysis and included the effects of bimaterial thickness coating, effective length of the device, width, and thickness
The finite element method and applications in engineering using ANSYS
Madenci, Erdogan
2015-01-01
This textbook offers theoretical and practical knowledge of the finite element method. The book equips readers with the skills required to analyze engineering problems using ANSYS®, a commercially available FEA program. Revised and updated, this new edition presents the most current ANSYS® commands and ANSYS® screen shots, as well as modeling steps for each example problem. This self-contained, introductory text minimizes the need for additional reference material by covering both the fundamental topics in finite element methods and advanced topics concerning modeling and analysis. It focuses on the use of ANSYS® through both the Graphics User Interface (GUI) and the ANSYS® Parametric Design Language (APDL). Extensive examples from a range of engineering disciplines are presented in a straightforward, step-by-step fashion. Key topics include: • An introduction to FEM • Fundamentals and analysis capabilities of ANSYS® • Fundamentals of discretization and approximation functions • Modeling techniq...
Advanced Finite Element Discretizations for High-Energy Ion Transport
The dominant continuous slowing-down energy loss process coupled with the small (but nonnegligible) straggling poses a significant challenge for deterministic numerical solution when incident beams are monoenergetic or have discontinuous energy spectra. Such spectra broaden very slowly with depth into the target material. Advanced space-energy discretization methods are consequently necessary to achieve numerical robustness. Finite element solutions to this problem were investigated using two general families of discontinuous trial functions, one linear and the other nonlinear. The two families were numerically tested, and results are shown for 1.7-GeV protons incident on a W target. Results from quadratic and exponential-quadratic discontinuous trial functions are in excellent agreement with Monte Carlo results. It is found that very high order finite element schemes are necessary for monoenergetic charged-particle beam transport
Nonlinear finite element analysis of steel-concrete composite beams
QIU Wen-liang; JIANG Meng
2005-01-01
Proposes a simplified finite element model for steel-concrete composite beams. The effects of slip can be taken into account by creating a special matrix of shear connector stiffness and using the iteration method.Meanwhile, the effect of material non-linearity of steel and concrete on rigidity and strength of composite beams is considered. With the age-adjusted effective modulus method, the analysis for the whole process of shrinkage and creep under long-term load can be performed. The ultimate load, deflection, stress and slip of continuous composite beams under short-term and long-term load are computed using the proposed finite element model.The numerical results are compared with the experimental results and existing values based on other numerical methods, and are found to be in good agreement.
Finite element dynamic analysis of finite beams on a bilinear foundation under a moving load
Castro Jorge, P.; Pinto da Costa, A.; Simões, F. M. F.
2015-06-01
The present paper is concerned with the behaviour of finite elastic beams, acted by a moving transverse concentrated load, interacting with elastic foundations of different stiffnesses in compression and in tension. Using finite element analyses, the displacement amplitudes and the critical velocities of the load on a UIC-60 rail are computed and their dependence with respect to the difference between the foundation's moduli in compression and in tension is evaluated. The limit case of a tensionless foundation is as well analyzed. The numerical algorithm relies on the internal force vectors and tangent stiffness matrices computed exactly with automatic symbolic manipulation.
On angle conditions in the finite element method
Brandts, J.; Hannukainen, A.; Korotov, S.; Křížek, Michal
2011-01-01
Roč. 56, - (2011), s. 81-95. ISSN 1575-9822 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : simplicial finite elements * minimum and maximum angle condition * ball conditions Subject RIV: BA - General Mathematics http://www.sema.org.es/ojs/index.php?journal=journal&page=article&op=viewArticle& path %5B%5D=612
Finite Element Simulation of Heat Transfer in Ferrofluid
Strek, Tomasz
2008-01-01
We have simulated two-dimensional heat transfer in ferrofluid channel flow under the influence of the magnetic field created by magnetic dipole using computational fluid dynamics code COMSOL based on finite element method. At the left end of rectangular channel there was assumed a parabolic laminar flow profile. The upper plate was kept at constant temperature Tu and the lower at Tl . The flow was relatively uninfluenced by the magnetic field until its strength was large enough for the Kelvin...
Multiphysics Finite Element Methods for a Poroelasticity Model
Feng, Xiaobing; Ge, Zhihao; Li, Yukun
2014-01-01
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To better describe the multiphysics process of deformation and diffusion for poro-elastic materials, we first present a reformulation of the original model by introducing two pseudo-pressures, one of them is shown to satisfy a diffusion equation, we then propo...
Biomechanical simulation of thorax deformation using finite element approach
Zhang, Guangzhi; Chen, Xian; Ohgi, Junji; Miura, Toshiro; Nakamoto, Akira; Matsumura, Chikanori; Sugiura, Seiryo; Hisada, Toshiaki
2016-01-01
Background The biomechanical simulation of the human respiratory system is expected to be a useful tool for the diagnosis and treatment of respiratory diseases. Because the deformation of the thorax significantly influences airflow in the lungs, we focused on simulating the thorax deformation by introducing contraction of the intercostal muscles and diaphragm, which are the main muscles responsible for the thorax deformation during breathing. Methods We constructed a finite element model of t...
Slope Stability Evaluations by Limit Equilibrium and Finite Element Methods
Aryal, Krishna Prasad
2006-01-01
This thesis deals with slope stability evolutions carried out by commonly used limit equilibrium (LE) and finite element (FE) methods. The study utilizes two LE based software (SLOPE/W and SLIDE) and one FE based software (PLAXIS). The principal difference between these two analyses approaches is that the LE methods are based on the static of equilibrium whereas FE methods utilise the stress‐strain relationship or constitutive law. To fulfil one of the aims of the study, the LE based method...
The Development of Piezoelectric Accelerometers Using Finite Element Analysis
Liu, Bin
1999-01-01
This paper describes the application of Finite Element (FE) approach for the development of piezoelectric accelerometers. An accelerometer is simulated using the FE approach as an example. Good agreement is achieved between simulated results and calibrated results. It is proved that the FE modeling...... can be effectively used to predict the specifications of the accelerometer, especially when modification of the accelerometer is required. The FE developing technology forms the bases of fast responsiveness and flexible customized design of piezoelectric accelerometers....
Finite element analysis of microelectrotension of cell membranes
Bae, Chilman; Butler, Peter J.
2007-01-01
Electric fields can be focused by micropipette-based electrodes to induce stresses on cell membranes leading to tension and poration. To date, however, these membrane stress distributions have not been quantified. In this study, we determine membrane tension, stress, and strain distributions in the vicinity of a microelectrode using finite element analysis of a multiscale electro-mechanical model of pipette, media, membrane, actin cortex, and cytoplasm. Electric field forces are coupled to me...
Finite element analysis of a modified short hip endoprosthesis
Augustin Semenescu; Florentina Ioniță Radu; Ileana M. Mateș; Petre Bădică; Nicolae D. Batalu
2016-01-01
A finite element simulation of the mechanical static features for a modified short hip endoprosthesis was performed. The corkscrew-like femoral stem was modified introducing more turns of the thread. By such an approach it is expected that for some cases the mechanical fixation of the prosthesis to the bone will be improved or the use of the cement for bonding is not necessary. Our scenario was estimated for titanium and stainless steel, and both materials show good safety fact...
Prediction of Water Movement in Soil by Finite Element Method
Morii, Toshihiro; 森井,俊広
1999-01-01
A computer program SUSFEM for simulating water movement in two-dimensional or axisymmetric unsaturated, partially saturated, or saturated soil is developed. Richards' potential equation supplemented by appropriate boundary and initial conditions is described and formulated on the basis of Galerkin-type finite element method in conj unction with a fully implicit iterative scheme. SUSFEM calculates sequential and spatial variations of pressure head in soil, h. The saturated water movement is pr...
Equal-order finite elements of hydrostatic flow problems
Kimmritz, Madlen
2013-01-01
Subject of this thesis is the issue of equal-order finite element discretization of hydrostatic flow problems. These flow problems typically arise in geophysical fluid dynamics on large scales and in flat domains. This small aspect ratio between the depth and the horizontal extents of the considered domain allows to efficiently reduce the complexity of the incompressible three dimensional Navier-Stokes equations, which form the basis of geophysical flows. In the resulting set of equations, th...
A minimal stabilisation procedure for mixed finite element methods.
Brezzi, Franco; Fortin, Michel
2000-01-01
Stabilisation methods are often used to circumvent the difficulties associated with the stability of mixed finite element methods. Stabilisation however also means an excessive amount of dissipation or the loss of nice conservation properties. It would thus be desirable to reduce these disadvantages to a minimum. We present a general framework, not restricted to mixed methods, that permits to introduce a minimal stabilising term and hence a minimal perturbation with respect...
The development of finite element software for creep damage analysis
Liu, Dezheng
2015-01-01
Creep deformation and failure in high temperature structures is a serious problem for industry and is becoming even more so under the current increasing pressures of power, economics and sustainability. Laboratory creep tests can be used in the description of creep damage behaviour; however, it’s usually expensive and time-consuming. Thus, the computer-based finite element (FE) technique is considered here for both time and economic efficiency. This project aims to develop an in-house FE soft...
Nonlinear Finite Element Analysis of Pull-Out Test
Saabye Ottesen, N
1981-01-01
A specific pull-out test used to determine in-situ concrete compressive strength is analyzed. This test consists of a steel disc that is extracted from the structure. The finite element analysis considers cracking as well as strain hardening and softening in the pre- and post-failure region, resp...... constitutes the load-carrying mechanism. The failure is caused by the crushing of the concrete in this region, and not by cracking....
Finite Element Analysis: A Maxillofacial Surgeon’s Perspective
Shyam Sundar, S.; Nandlal, B; Saikrishna, D.; Mallesh, G.
2011-01-01
The science of finite element analysis (FEA) is purely a mathematical way of solving complex problems in the universe. In medical field, this is an innovation in biomedical research and development, as it gives easier mathematical solution to biological problems. This article deals with the understanding of various basic material properties of bone like Young’s modulus, yield strength, Bulk modulus, shear modulus, Poisson’s ratio and density from a maxillofacial surgeon’s perspective. Basic c...