Showing papers on "Smoothed finite element method published in 2004"

Conforming polygonal finite elements

Abstract: SUMMARY In this paper, conforming finite elements on polygon meshes are developed. Polygonal finite elements provide greater flexibility in mesh generation and are better-suited for applications in solid mechanics which involve a significant change in the topology of the material domain. In this study, recent advances in meshfree approximations, computational geometry, and computer graphics are used to construct different trial and test approximations on polygonal elements. A particular and notable contribution is the use of meshfree (natural-neighbour, nn) basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons. This numerical formulation enables the construction of conforming approximation on n-gons (n 3), and hence extends the potential applications of finite elements to convex polygons of arbitrary order. Numerical experiments on second-order elliptic boundary-value problems are presented to demonstrate the accuracy and convergence of the proposed method. Copyright 2004 John Wiley & Sons, Ltd.

Classification and Overview of Meshfree Methods

Abstract: This paper gives an overview over Meshfree Methods Starting point is an extended and modified classification of Meshfree Methods due to three aspects: The construction of a partition of unity, the choice of an approximation either with or without using an extrinsic basis and the choice of test functions, resulting into a collocation, Bubnov-Galerkin or Petrov-Galerkin Meshfree Method Most of the relevant Meshfree Methods are described taking into account their different origins and viewpoints as well as their advantages and disadvantages Typical problems arising in meshfree methods like integration, treatment of essential boundary conditions, coupling with mesh-based methods etc~are discussed Some valuing comments about the most important aspects can be found at the end of each section This text was revised in 2004

Generalized finite element methods — main ideas, results and perspective

Abstract: This paper is an overview of the main ideas of the Generalized Finite Element Method (GFEM). We present the basic results, experiences with, and potentials of this method. GFEM is a generalization of the classical Finite Element Method — in its h, p, and h-p versions — as well as of the various forms of meshless methods used in engineering.

MooNMD – a program package based on mapped finite element methods

Abstract: The basis of mapped finite element methods are reference elements where the components of a local finite element are defined. The local finite element on an arbitrary mesh cell will be given by a map from the reference mesh cell. This paper describes some concepts of the implementation of mapped finite element methods. From the definition of mapped finite elements, only local degrees of freedom are available. These local degrees of freedom have to be assigned to the global degrees of freedom which define the finite element space. We will present an algorithm which computes this assignment. The second part of the paper shows examples of algorithms which are implemented with the help of mapped finite elements. In particular, we explain how the evaluation of integrals and the transfer between arbitrary finite element spaces can be implemented easily and computed efficiently.

Finite element methods for the non‐linear mechanics of crystalline sheets and nanotubes

Abstract: The formulation and finite element implementation of a finite deformation continuum theory for the mechanics of crystalline sheets is described. This theory generalizes standard crystal elasticity to curved monolayer lattices by means of the exponential Cauchy-Born rule. The constitutive model for a two-dimensional continuum deforming in three dimensions (a surface) is written explicitly in terms of the underlying atomistic model. The resulting hyper-elastic potential depends on the stretch and the curvature of the surface, as well as on internal elastic variables describing the rearrangements of the crystal within the unit cell. Coarse grained calculations of carbon nanotubes (CNTs) are performed by discretizing this continuum mechanics theory by finite elements. A smooth discrete representation of the surface is required, and subdivision finite elements, proposed for thin-shell analysis, are used. A detailed set of numerical experiments, in which the continuum/finite element solutions are compared to the corresponding full atomistic calculations of CNTs, involving very large deformations and geometric instabilities, demonstrates the accuracy of the proposed approach. Simulations for large multi-million systems illustrate the computational savings which can be achieved.

Possibilities of finite calculus in computational mechanics

Abstract: The expression “finite calculus” refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a domain of finite size. The governing equations resulting from this approach are different from those of infinitessimal calculus theory and they incorporate new terms depending on the dimensions of the balance domain. The new modified equations allow to derive naturally stabilized numerical schemes using finite element, finite difference, finite volume or meshless methods. The paper briefly discusses the possibilities of the modified governing equations derived via the finite calculus technique for the numerical solution of convection-diffusion problems, incompressible flow and incompressible solid mechanic problems and strain localization problems.

Fundamentals of a Vector Form Intrinsic Finite Element: Part II. Plane Solid Elements

Abstract: In the second article of the series, the vector form intrinsic finite element is extended to formulate plane solid elements, a three-node triangular element and a four-node isoparametric element. Also, conceptual differences of the intrinsic element and traditional element based on variational formulation are discussed.

Finite element simulation

Abstract: A method for automatic evaluation of a finite element simulation for an industrial system such as a motor vehicle body includes predefining an electronic design model of the industrial system and generating finite elements for the model. The stresses occurring in the finite elements are determined using a finite element simulation. Each finite element, which is a two-dimensional element and not a rigid object element and whose stress exceeds a predefined stress limiting value, is determined. For each determined two-dimensional element which is not a triangle, an element limiting value is determined on the basis of the stress limiting value. Each determined two-dimensional element is classified as critical if its computed stress exceeds the established element limiting value. The method enables identification of areas of the industrial system having a high stress and reduces the effect of inaccuracies that occur on the evaluation of the finite element simulation due to the approximation of the vehicle body by finite elements.

Finite Element Mapping for Spring Network Representations of the Mechanics of Solids

Abstract: We present a general finite element mapping procedure for defining spring network representations of solid mechanics. The procedure is rigorous and equally suitable for setting regular and unstructured spring network models of generally anisotropic solids. We use the procedure to define close-packed triangular and simple cubic lattice spring models of isotropic 2D and 3D elastic media, respectively. We extend the study to heterogeneous solids and show that the mapped spring network approach constitutes an appealing route for incorporating subelement level constitutive equations.

Arc-length technique for nonlinear finite element analysis

Abstract: Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.

Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics

Abstract: to Mechanics of Continua.- Dynamics of Inviscid Fluids.- Viscous Incompressible Fluid Dynamics.- to Numberical Solutions for Ordinary and Partial Differential Equations.- Finite-Difference Methods.- Finite Element and Boundary Element Methods.- The Finite Volume Method and the Generalized Difference Method.- Spectral Methods.

Finite element response sensitivity analysis using force-based frame models

Abstract: This paper presents a method to compute consistent response sensitivities of force-based finite element models of structural frame systems to both material constitutive and discrete loading parameters. It has been shown that force-based frame elements are superior to classical displacement-based elements in the sense that they enable, at no significant additional costs, a drastic reduction in the number of elements required for a given level of accuracy in the computed response of the finite element model. This advantage of force-based elements is of even more interest in structural reliability analysis, which requires accurate and efficient computation of structural response and structural response sensitivities. This paper focuses on material non-linearities in the context of both static and dynamic response analysis. The formulation presented herein assumes the use of a general-purpose non-linear finite element analysis program based on the direct stiffness method. It is based on the general so-called direct differentiation method (DDM) for computing response sensitivities. The complete analytical formulation is presented at the element level and details are provided about its implementation in a general-purpose finite element analysis program. The new formulation and its implementation are validated through some application examples, in which analytical response sensitivities are compared with their counterparts obtained using forward finite difference (FFD) analysis. The force-based finite element methodology augmented with the developed procedure for analytical response sensitivity computation offers a powerful general tool for structural response sensitivity analysis.

Finite element formulation for modelling large deformations in elasto-viscoplastic polycrystals

Abstract: Anisotropic, elasto-viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three-field form of the Hu-Washizu variational principle to create a stable finiteelement method in the context of nearly incompressible behaviour. The meso-scale is characterized by a representative volume element, which contains grains governed by single crystal behaviour. A new, fully implicit, two-level, backward Euler integration scheme together with an efficient finite element formulation, including consistent linearization, is presented. The proposed finite element model is capable of predicting non-homogeneous meso-fields, which, for example, may impact subsequent recrystallization. Finally, simple deformations involving an aluminium alloy are considered in order to demonstrate the algorithm.

The birth of the finite element method and of computational mechanics

Abstract: This brief paper attempts to indicate the motivation which led to the development of the finite element method by engineers and shows how later this became integrated with various current mathematical procedures. In the opinion of the writer, the broad definition of finite elements today includes all the known procedures of approximation for solving partial differential equations and allows the users to include a variety of methods which are mathematically acceptable. Copyright 2004 © John Wiley & Sons, Ltd.

Node‐by‐node parallel finite elements: a virtually meshless method

Abstract: FEM-based meshfree method named the free mesh method (FMM) or the node-by-node finite element method (NBN-FEM), and a short review of recent meshless and meshfree methods are presented Attempts to apply particle-like finite element analysis to problems that are difficult to handle using global mesh generation, especially on massively parallel processors, are presented Local finite elements are generated around each node, with local mesh data structures and a system of equations based on these nodes Accordingly, the FMM or NBN-FEM can overcome difficulties arising from the distortion of elements by simply adding or deleting nodes, similar to particle methods This property is particularly advantageous for use in parallel computing environments While parallelization of mesh generation is generally difficult, only the distribution of nodes needs to be considered to perform parallel remeshing computing This node-based finite element computation is realized by a robust local mesh generation technique based on the gift-wrapping method The method is implemented on parallel computers, including a PC cluster and a Hitachi SR8000 supercomputer Numerical examples show that the method achieves high parallel performance, both in pre-processing and main-processing Copyright © 2004 John Wiley & Sons, Ltd

An Introduction to Linear and Nonlinear Finite Element Analysis

Abstract: Preface Notation Introduction One-Dimensional Shape Functions One-Dimensional Second-Order Equations One-Dimensional Fourth-Order Equations Two-Dimensional Elements Two-Dimensional Problems More Two-Dimensional Problems Axisymmetric Heat Transfer Transient Problems Single Nonlinear One-Dimensional Equations Plane Elasticity Stokes Equations and Penalty Method Vibration Analysis Computer Codes: Mathematica Codes, Ansys Codes, MatLab Codes, Fortran Codes Appendix A: Integration Formulas Appendix B: Special Cases Appendix C: Temporal Approximations Appendix D: Isoparametric Elements Appendix E: Green's Identities Appendix F: Gaussian Quadrature Appendix G: Gradient-Based Methods Bibliography Index

A finite element approach to the immersed boundary method

Abstract: We consider a modification of the immersed boundary method which makes use of a finite element spatial discretization. We describe the method for a two-dimensional model problem and justify its variational formulation. We provide a preliminary analysis of the continuous problem in a one-dimensional setting using a fixed point theorem and a compactness argument. Finally, we report on some numerical tests which demonstrate the stability and robustness of the algorithm.

Finite-element simulation of micro-electromechanical systems (MEMS) by strongly coupled electromechanical transducers

Abstract: The paper introduces a new methodology for the strongly coupled electrostatic-structural finite-element (FE) simulation of micro-electromechanical systems (MEMS) using a novel distributed electromechanical transducer that is compatible with regular solid and lumped FE. Its application range is as general as the sequentially coupled procedures, but converges more robustly with about an order of magnitude smaller number of iteration. The new transducers apply automatic internal mesh morphing. The morphing allows the mesh density to be different across the domain permitting accurate modeling of fringing effects.