Finite element analysis of composites using chebyshev polynomials

A finite quasi-prismatic (FQP) element is modified to analyze anisotropic materials. The finite quasi-prismatic element is a three-dimensional finite element which uses conventional interpolating functions in two directions and functions based on Chebyshev polynomials in the third direction. This element is used to solve different anisotropic problems and the results are compared with that of conventional finite elements and analytical solutions.     

面向对象有限元并行计算框架PANDA求解器的服务构件化设计与集成

针对很多结构有限元程序需要使用数值方法进行系统方程组求解的共性特点,提出对数值求解部分进行构件化设计,形成求解器服务,用于面向对象有限元并行计算框架PANDA为不同应用类型的有限元程序开发提供数值算法.将美国Livermore国家实验室开发的数值求解器库HYPRE作为数值求解构件集成到PANDA框架中,利用其提供的数值...     

Poisson方程特征值的四种有限元解及比较

本文应用双线性元、旋转双线性元、拓广旋转双线性元、Wilson元计算Poisson方程的近似特征值.计算结果验证了[4]中特征值问题的有限元渐进误差展开理论的正确性.最后,我们分析了旋转双线性元的近似解的特殊情况,并预测了Wilson元给出特征值的下界.     

涡流检测系统仿真分析的自适应算法

该文针对电磁场有限元计算的特点,深入研究了涡流检测系统中电磁场有限元后验误差估计的误差模选择问题,并在分析Zienkiewicz-Zhu方法在电磁场有限元后验误差估计应用中存在局限性的基础上,提出了一种适合于涡流检测系统中电有限元分析的后验误差估计新方法。在此基础上,结合James R.Stewart和Thomas J.R.Hughes所提出的简单实用的有限元算法,提出了一种适合于涡流检测系统中电磁场有限元分析的hp 自适应新算法。     

An assessment of discretizations for convection-dominated convection–diffusion equations

The performance of several numerical schemes for discretizing convection-dominated convection–diffusion equations will be investigated with respect to accuracy and efficiency. Accuracy is considered in measures which are of interest in applications. The study includes an exponentially fitted finite volume scheme, the Streamline-Upwind Petrov–Galerkin (SUPG) finite element method, a spurious oscillations at layers diminishing (SOLD) finite element method, a finite element method with continuous interior penalty (CIP) stabilization, a discontinuous Galerkin (DG) finite element method, and a total variation diminishing finite element method (FEMTVD). A detailed assessment of the schemes based on the Hemker example will be presented.     

The simulation of sheet metal forming processes via integrating solid-shell element with explicit finite element method

Solid-shell elements can be seen as a class of typical double-surfaced shell elements with no rational degrees of freedom, which are more suitable for analyzing double-sided contact problems than conventional shell elements. In this study, a solid-shell finite element model is implemented into the explicit finite element software ABAQUS/Explicit as a user-defined element, through which the sheet metal forming processes are simulated. The main feature of this finite element model is that the solid-shell element formulation is embedded into an explicit finite element procedure, compared to the previous studies on the solid-shell elements under the implicit finite element framework. To obtain a straightforward element, a complete integration scheme is adopted. No loss of generality, a twelve-parameter enhance assumed strain method is employed to improve the element’s behavior. Two benchmarks from the NUMISHEET conference and a U-channel roll-forming process are simulated with this explicit solid-shell finite element model. The calculated results are comparable with experimental and numerical results presented in the literatures.     

LOD技术在地下水有限元后处理中的应用

地下水有限元后处理阶段的数据量较大,这对模型重现、网络快速传输和计算结果的实时可视化造成困难。为此,分析地下水有限元后处理中面临的主要问题和LOD技术,指出顶点元素删除法是一种适应地下水有限元后处理的有效数据模型简化方法,设计顶点删除和恢复过程中的主要数据结构,并应用DT方法对“空洞”进行局部三角剖分。实例证明该方法在地下水有限元后处理中应用的有效性。     

On various formulations of large amplitude free vibrations of beams

Various finite element formulations of large amplitude free vibrations of beams with immovably supported ends are discussed in this paper. Analytical formulation based on the Rayleigh-Ritz method is also presented. Numerical results of the analytical approach are seen to be in good agreement with some of these finite element formulations. Mixed finite element formulations based on two methods are derived to study the large amplitude free vibrations of beams. The mixed finite element methods also show good agreement with the analytical and the above finite element formulations. Various points of view raised from time to time on the applicability of these formulations can now be clarified through these formulations and the numerical results. The weakness of the so-called improved Ritz-type finite element model in predicting the nonlinear frequency ratio is highlighted through various results of the above formulations. As a typical example, a hinged-hinged beam on immovable ends is considered for all the above formulations and the nonlinear frequencies show a good agreement amongst themselves at all amplitude levels.     

Effect of thermal deformations of an optical pick-up base on the optical properties of DVD optical system

An analytical method is presented to analyze the effect of thermal deformations of an optical pick-up base on the optical properties of DVD optical system. To measure the amount of thermal deformations of an optical pick-up base, finite element analysis and holographic interferometry were used. First, thermal deformations of an aluminum pick-up base was analyzed in thermal environments using finite element analysis; finite element analysis was carried out without the initial surface stress condition. The measurement of thermal deformations by holographic interferometry was carried out to verify finite element analysis results. However, since the finite element analysis results were deviated from those by experiment, the effect of the initial surface stress condition was considered; finite element analysis was carried out with the initial surface residual stress condition, which was obtained from X-ray diffraction measurement. The finite element analysis results with the initial surface stress condition agreed well with the experimental results by holographic interferometry. Finally, to analyze the effect of thermal deformations of the pick-up base on the optical properties of DVD optical system, the deformation of optical path was analyzed. However, the drastic changes of beam spot, beam intensity profile, modulation transfer function curve and wavefront aberration were not observed.     

MooNMD – a program package based on mapped finite element methods

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. Communicated by: M.S. Espedal, A. Quarteroni, A. Sequeira     

MooNMD – a program package based on mapped finite element methods

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.     

Lower Bounds for Eigenvalues of Elliptic Operators: By Nonconforming Finite Element Methods

The paper is to introduce a new systematic method that can produce lower bounds for eigenvalues. The main idea is to use nonconforming finite element methods. The conclusion is that if local approximation properties of nonconforming finite element spaces are better than total errors (sums of global approximation errors and consistency errors) of nonconforming finite element methods, corresponding methods will produce lower bounds for eigenvalues. More precisely, under three conditions on continuity and approximation properties of nonconforming finite element spaces we analyze abstract error estimates of approximate eigenvalues and eigenfunctions. Subsequently, we propose one more condition and prove that it is sufficient to guarantee nonconforming finite element methods to produce lower bounds for eigenvalues of symmetric elliptic operators. We show that this condition hold for most low-order nonconforming finite elements in literature. In addition, this condition provides a guidance to modify known nonconforming elements in literature and to propose new nonconforming elements. In fact, we enrich locally the Crouzeix-Raviart element such that the new element satisfies the condition; we also propose a new nonconforming element for second order elliptic operators and prove that it will yield lower bounds for eigenvalues. Finally, we prove the saturation condition for most nonconforming elements.     

Automating the Finite Element Method

The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations. However, the generality of the framework provided by the finite element method is seldom reflected in implementations (realizations), which are often specialized and can handle only a small set of variational problems and finite elements (but are typically parametrized over the choice of mesh). This paper reviews ongoing research in the direction of a complete automation of the finite element method. In particular, this work discusses algorithms for the efficient and automatic computation of a system of discrete equations from a given variational problem, finite element and mesh. It is demonstrated that by automatically generating and compiling efficient low-level code, it is possible to parametrize a finite element code over variational problem and finite element in addition to the mesh.     

An Algebraic Multigrid Method for Higher-order Finite Element Discretizations

In this paper, we will design and analyze a class of new algebraic multigrid methods for algebraic systems arising from the discretization of second order elliptic boundary value problems by high-order finite element methods. For a given sparse stiffness matrix from a quadratic or cubic Lagrangian finite element discretization, an algebraic approach is carefully designed to recover the stiffness matrix associated with the linear finite element disretization on the same underlying (but nevertheless unknown to the user) finite element grid. With any given classical algebraic multigrid solver for linear finite element stiffness matrix, a corresponding algebraic multigrid method can then be designed for the quadratic or higher order finite element stiffness matrix by combining with a standard smoother for the original system. This method is designed under the assumption that the sparse matrix to be solved is associated with a specific higher order, quadratic for example, finite element discretization on a finite element grid but the geometric data for the underlying grid is unknown. The resulting new algebraic multigrid method is shown, by numerical experiments, to be much more efficient than the classical algebraic multigrid method which is directly applied to the high-order finite element matrix. Some theoretical analysis is also provided for the convergence of the new method.     

Study of elastic behaviour of plates containing cracks by finite element analysis

This work applies finite element analysis very simply to cracked plates. An infinite plate and a finite plate, both with a central crack, are considered to study their elastic behaviour and some fracture mechanics concepts, such as the geometry factor and the fracture toughness. These magnitudes are calculated by means of finite element methods and the results are in very good agreement with the established theory, which proves that the finite element approach is very appropriate. The fracture toughness fraction is defined and calculated for a finite plate to predict its failure.     

基于Solid Works Simulation的产品设计有限元分析

本研究旨在探讨有限元分析方法以及基于SolidWorks Simulation的有限元分析方法在产品设计过程中的实际应用。首先详细分析了基于SotidWorksSimulation的有限元分析方法的具体过程,然后通过实例详细探讨了SolidWorks Simulation的基本功能及其使用方法,包括SimulationXPress应力分析、Simulation结构有限元分析以及Simulation优化分析的应用方法。实例证明,基于Solid Works Simulation的有限元分析方法应用于实践中有助于提高产品设计的质量与效率。     

A survey of the extended finite element

This article presents an overview and recent progress of the extended finite element method X-FEM in the analysis of crack growth modeling. It summarizes the important milestones achieved by the finite element community in the arena of computational fracture mechanics. The methodology of X-FEM, different from that of the classical finite element method, presents a very particular interest since it does not force the discontinuities to be in conformity with the borders. It makes possible the accurate solution of engineering problems in complex domains, which may be practically impossible to solve using the classical finite element method.     

有限元法在两相流检测中的应用研究

电容层析成像技术（ECT）是两相流参数检测领域中的一门新技术,在工业生产中有着广阔的应用前景.通过建立有限元模型,编写有限元仿真程序,进行有限元的计算,对两相流典型流型的敏感场场域进行建模仿真,得到的电容值可以作为图像重构的样本数据.     

Non-Nested Multi-Level Solvers for Finite Element Discretisations of Mixed Problems

We consider a general framework for analysing the convergence of multi-grid solvers applied to finite element discretisations of mixed problems, both of conforming and nonconforming type. As a basic new feature, our approach allows to use different finite element discretisations on each level of the multi-grid hierarchy. Thus, in our multi-level approach, accurate higher order finite element discretisations can be combined with fast multi-level solvers based on lower order (nonconforming) finite element discretisations. This leads to the design of efficient multi-level solvers for higher order finite element discretisations. Received May 17, 2001; revised February 2, 2002 Published online April 25, 2002