New approach in Stochastic Finite Element Method

In the paper, the new methodology for Stochastic Finite Element Method (SFEM) as the means to analyze structure in the probabilistic framework is presented. The concept of random influence vector is introduced and used to develop the universal formulas in the framework of SFEM that can work effectively for a wide variety of random loads. Furthermore, the derived formulas enable to separate the structural uncertain properties from random parameters of load resulting in the hybrid formulation of SFEM and to analyze the structure in probabilistic framework subject to any stochastic space load. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Full-Discrete Finite Element Method for Stochastic Hyperbolic Equation

This paper is concerned with the finite element method for the stochastic wave equation and the stochastic elastic equation driven by space-time white noise. For simplicity, we rewrite the two types of stochastic hyperbolic equations into a unified form. We convert the stochastic hyperbolic equation into a regularized equation by discretizing the white noise and then consider the full-discrete finite element method for the regularized equation. We derive the modeling error by using "Green's method" and the finite element approximation error by using the error estimates of the deterministic equation. Some numerical examples are presented to verify the theoretical results.     

Non-linear Stochastic Finite Element

This paper investigates the uncertainty of physically non-linear problems by modeling the elastic random material parameters as stochastic fields. For its stochastic discretization a polynomial chaos (PC) is used to expand the coefficients into deterministic and stochastic parts. Then, from experimental data for an adhesive material the distribution of the random variables, i.e. Young's modulus E(θ), the static yield point Y₀ and the nonlinear hardening parameters q and b, are known. In the numerical example the distribution of the stresses obtained by the PC based SFEM and Monte Carlo simulation is compared. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一种用于平面弹性材料分析的有限元法

本文在有限元位移法的基础上,提出一种用于平面弹性材料机械性能分析的有限元法.利用这种方法及其微机程序,可以确定任一未知的平面弹性材料的机械性能,算出其全部弹性系数.     

Numerical Analysis of the Behaviour of Tooth Intrarradial Posts by the Finite Element Method

The aim of this work is to study the behaviour of a carbon/epoxi post housed in a canine tooth after endodontic treatment in order to support the typical loads present during mastication. The three-D basic design of the dental piece consisting of tooth + post was carried out with a three-dimensional parametric design program. We study the stresses and displacements of the different elements of the dental piece under normal load conditions, and present the results and conclusions.     

水波的界带有限元

研究了水波计算的位移法.采用物质坐标,以位移为基本未知量,考虑小变形条件,引入流函数满足不可压缩条件.于是,分析力学的变分原理可以运用了,界带有限元、正则变换、保辛积分等有效手段可使数值求解方便得多.     

Large Scale Simulation with Scaled Boundary Finite Element Method

Nowadays scientific and engineering applications often require wave propagation in infinite or unbounded domains. In order to model such applications we separate our model into near-field and far-field. The near-field is represented by the well-known finite element method (FEM), whereas the far-field is mapped by a scaled boundary finite element (SBFE) approach. This latter approach allows wave propagation in infinite domains and suppresses the reflection of waves at the boundary, thus being a suitable method to model wave propagation to infinity. It is non-local in time and space. From a computational point of view, those characteristics are a drawback because they lead to storage consuming calculations with high computational time-effort. The non-locality in space causes fully populated unit-impulse acceleration influence matrices for each time step, leading to immense storage consumption for problems with a large number of degrees of freedom. Additionally, a different influence matrix has to be assembled for each time step which yields unacceptable storage requirements for long simulation times. For long slender domains, where many nodes are rather far from each other and where the influence of the degrees of freedom of those distant nodes is neglectable, substructuring represents an efficient method to reduce storage requirements and computational effort. The presented simulation with substructuring still yields satisfactory results. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient Finite Element Analysis of Inelastic Structures with Iterative Solvers

This article treats the efficient solution of linear systems of equations which arise during the iterative process within the finite element analysis of inelastic structures. For the finite element analysis high order time integration methods and diagonally implicit Runge–Kutta methods (DIRK), in combination with an inexact Multilevel–Newton algorithm (MLNA) are applied. Up to 80% of the total computation time is spent by the solver for the linear systems, which suggests investigating this process. Two simple strategies to speed up the solution of the linear systems are described. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lamb wave propagation using Wave Finite Element Method

Some of the available techniques for Lamb wave propagation simulation are the Finite Element Method (FEM), the Boundary Element Method and the Finite Difference Method. The FEM is the best method when complex damage, geometry or boundary is involved. However, high Lamb wave frequency requires very small element size thus high computational cost in FEM analysis. By using the existence of periodicity in plates, an attempt to reduce this computational cost is done using Wave FEM. The applicability of this method to model Lamb wave propagation in plate is first assessed in this paper for the 1-D wave propagation and compared with FEM explicit method. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于Monte-Carlo随机有限元方法的随机边界条件下自然对流换热不确定性研究

为分析边界条件不确定性对方腔内自然对流换热的影响,发展了一种求解随机边界条件下自然对流换热不确定性传播的Monte-Carlo随机有限元方法.通过对输入参数场随机边界条件进行Karhunen-Loeve展开及基于Latin(拉丁)抽样法生成边界条件随机样本,数值计算了不同边界条件随机样本下方腔内自然对流换热流场与温度场,并用采样统计方法计算了随机输出场的平均值与标准偏差.根据计算框架编写了求解随机边界条件下方腔内自然对流换热不确定性的MATLAB随机有限元程序,分析了随机边界条件相关长度与方差对自然对流不确定性的影响.结果表明:平均温度场及流场与确定性温度场及流场分布基本相同;随机边界条件下Nu数概率分布基本呈现正态分布,平均Nu数随着相关长度和方差增加而增大;方差对自然对流换热的影响强于相关长度的影响.     

角质层渗透性质的有限元数值模拟计算

角质层是皮肤屏障作用的最主要部分，它决定了外界物质对皮肤的渗透情况．在假设角质层细胞为一种三维的十四面体（物理学经典的tetrakaidecahedron体）的情况下，利用有限元法对角质层渗透性质进行了数值模拟研究．为此，首先完成了对角质层空间结构的网格拆分，拆分过程分两步进行：1．对角蛋白细胞的网格拆分；2．对角蛋白细胞周围的网状脂质体的网格拆分．在数值模拟过程中，则用有限元法得到方程离散的格式，用多重网格算法降低高频误差，提高计算精度．最后，给出了数值模拟结果的可视化效果图．     

Generalizations of the Finite Element Method

This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical method. To this end, we consider meshbased and meshfree generalizations of the finite element method and the use of smooth, discontinuous, singular and numerical enrichment functions.     

Semilinear Finite Element Method

In the Ritz-Galerkin method the linear subspace of the trial solution is extended to a closed subset. Some results, such as orthogonalization and minimum property of the error function, are obtained. A second order scheme is developed for solving a linear singular perturbation elliptic problem and error estimates are given for a uniform mesh size. Numerical results for linear and semilinear singular perturbation problems are included.     

精确有限元法

本文提出构造有限单元的新方法——精确有限元法.它可以求解在任意边界条件下任意变系数正定或非正定偏微分方程。文中给出它的收敛性证明和计算偏微分方程的一般格式。用精确元法所得到的单元是一个非协调元,单元之间的相容条件容易处理.与相同自由度普通有限元相比,由精确元法所得到的解的高阶导数具有较高的收敛精度.文末给出数值算例,所得到的结果均收敛于精确解,并有较好的数值精度.     

An Efficient Scheme for Stochastic Finite Element Solutions

The Polynomial Chaos expansion in Stochastic Finite Element Methods increases the size of the resulting linear systems dramatically. In iterative scheme which takes the underlying statistics into account is suggested for the efficient numerical solution. Additionally, an approach for the solution of von Mises stresses from the Polynomial Chaos representation of the displacement field is outlined. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond⁃Based Peridynamics北大核心CSCD

近场动力学是一种积分型非局部的连续介质力学理论,已广泛应用于固体材料和结构的非连续变形与破坏分析中,其数值求解方法主要采用无网格粒子类的显式动力学方法.近年来,弱形式近场动力学方程的非连续Galerkin有限元法得到发展,该方法不仅可以描述考察体的非局部作用效应和非连续变形特性,还可以充分利用有限单元法高效求解的特点,并继承了有限元法能直接施加局部边界条件的优点,可有效避免近场动力学的表面效应问题.该文阐述了键型近场动力学的非连续Galerkin有限元法的基本原理,导出了计算列式,给出了具体算法流程和细节,计算模拟了脆性玻璃板动态开裂分叉问题,并对爆炸冲击荷载作用下混凝土板的毁伤过程进行了计算分析.研究结果表明,该方法能够再现爆炸冲击荷载作用下结构的复杂破裂模式和毁伤破坏过程,且具有较高的计算效率,是模拟结构爆炸冲击毁伤效应的一种有效方法.     

A Three-Field Finite Element Method for Elliptic Partial Differential Equations Driven by Stochastic Loads

Abstract

This paper is concerned with the application of nonconforming finite element methods to stochastic partial differential equations. We present a mixed formulation of a three-field finite element method applied to an elliptic model problem involving stochastic loads. We then derive the exact form for the expected value and variance of the solution. Additionally, the rate of convergence for the stochastic error is presented. Finally, we demonstrate through numerical experiments that the method is robust and reliable.     

A Finite Element Method for Spatially Resolved Simulation of Packed Bed Chromatography

Packed bed chromatography is among the most important unit operations in bio-chemical process engineering for purifying target molecules from contaminants. A liquid solution of different species is pumped through the chromatography column, which is filled with porous particles (beads). Solute molecules can adsorb to the inner surfaces of these beads with different affinities which leads to different retention times in the column and consequently facilitates the desired separation. We present a stabilized space-time finite element scheme to solve for fluid flow and mass transfer in miniaturized chromatography columns, which are used in the design and optimization of industrial-scale applications. Our method can accurately handle realistic size systems with more than 10⁸ degrees of freedom on massively parallel computing facilities. It can also be applied for simulating sections of larger chromatographic beds in lab- and process-scale columns. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)