任意四边形平面问题的样条有限元法

用三次B样条有限元通过坐标变换和变分法求解任意四边形区域上的平面问题,利用分区势能原理推广到由四边形组成的任意平面区域,推导出了具体的计算公式,为平面问题求解提供了一种高效的计算方法。与普通有限单元相比,该方法计算量小,而且计算结果具有对网格畸变不敏感,精度高等显著特点。     

形状自由的高性能有限元方法研究的一些进展

作为工程和科学计算的主要工具,有限元方法已经得到了广泛的应用,但是仍然受到网格畸变敏感等固有难题的困扰,并且一直没有能够彻底根治。该文系统介绍了新型有限元方法--形状自由的高性能有限元方法研究的最新进展,包括平面问题和二维断裂问题的杂交应力函数有限元方法,中厚板问题的杂交位移函数有限元法,平面和三维问题的新型非对称有限元方法。这些方法在已有的杂交应力元法和非对称有限元法基础上,综合利用了解析试函数法、新型自然坐标方法、广义协调方法等先进技术,获得重要进展:所发展的单元模型精度高且稳定,在网格极端畸变的情况下仍可保持原有精度,具有形状自由的优异特性;同时破解了MacNeal局限定理,解决了中厚板边缘效应计算等难题。论文的最后对上述方法的特点以及后续的研究工作进行了讨论。     

基于功率流有限元方法的异形薄板能量密度求解

在机械工程中,对结构在不同频率激励下的振动响应进行分析预测具有重要的意义。功率流有限元法以其适用频率范围较广,可得到结构响应的细节信息等优点成为振动分析领域的研究热点。利用功率流有限元方法对薄板的弯曲波能量密度进行了求解,使用加权残差法导出了薄板单元节点的能量密度残差,利用线性四边形网格对薄板进行网格划分并在此基础上建立了单元的有限元方程,进一步地通过对单元有限元方程的组装和求解得到了薄板上各个节点处的能量密度响应,引入线性三角形网格以处理复杂形状薄板能量密度的求解,对使用功率流有限元方法求解任意形状薄板上的能量密度分布问题具有一定意义。     

高性能有限元方法简介

本文认为所谓高性能有限元方法是一种特殊的低价位移算法 ,在理论和计算方面 ,它有以下优势 :1 )近似满足原数学 ,物理模型的全部特性 ;2 )它可以有效地满足工程中数值模拟的需要 ,具有粗网格高精度 ,对网格畸变敏感度低 ,不发生 Locking不收敛现象。基于以上两点看法 ,介绍了计算力学中两种不发生收敛闭锁现象的高性能有限元方法     

几类典型网格下三维弹性问题的代数多层网格法

有限元方法是数值求解三维弹性问题的一类重要的离散化方法.在有限元分析中,网格的几何形状及网格质量会对有限元离散代数系统的求解产生很大影响.该文系统研究了几类典型网格对几种常用AMG法计算效率的影响,并进行了详细的性能测试与比较.利用容易获知的部分几何与分析信息(如方程类型,节点自由度信息),再结合经典AMG法中的网格粗...     

发展基于CB壳单元的扩展有限元模拟三维任意扩展裂纹

该文提出了一种新的基于连续体壳单元的扩展有限元格式,以用于对曲面上任意形状裂纹的扩展问题进行模拟。扩充形函数的构造和应力强度因子的计算都是基于三维实体单元进行,因此可以模拟复杂的三维断裂情况,壳体厚度的变化也可以得到考虑。三维应力强度因子的计算公式被引入到这种方法中。为模拟裂纹扩展,三维最大能量释放率准则被用作裂纹扩展准则。计算结果显示了曲面上的裂纹扩展路径可以与网格无关,并且由于在裂纹尖端的单元设置了具有奇异性的形函数,裂尖应力场被精确捕捉,从而证明了这种方法的优越性。     

任意形状埋置基础滑移振动复合集总参数模型

根据基础振动弹性半空间理论的最新发展成果推导出一个计算埋置基础滑移振动的复合集总参数模型。采用该模型对复杂形状的埋置块体基础在水平谐和扰力作用下的动力响应进行计算,并将振幅计算结果与采用弹性半空间理论所得到的埋置基础滑移振动刚度和阻尼系数公式(由大量试验、数值计算所证实)的振幅计算结果进行比较,结果表明:两者结果吻合,振幅误差为22.9%。利用该模型可以容易地计算在水平扰力作用下任意频率、任意泊松比和任意形状(不包括环型)的均质半空间上块体埋置基础的动力响应。     

任意形状基础滑移振动复合集总参数模型

根据基础振动弹性半空间理论的最新发展成果推导出一个计算明置基础滑移振动的复合集总参数模型。采用该模型对复杂形状的明置块体基础在水平谐和扰力作用下的动力响应进行计算,并将振幅计算结果与采用弹性半空间理论所得到的滑移振动刚度和阻尼系数公式(由大量试验、数值计算所证实)的振幅计算结果进行比较,结果表明:两者结果非常吻合,基础沿x和y方向滑移时,振幅误差分别为9.2%和0.8%。利用该模型可以容易地计算在水平扰力作用下任意频率、任意泊松比和任意形状(不包括环型)的均质半空间上块体基础的动力响应。     

无网格彼得洛夫伽辽金法在大变形问题中的应用

将无网格局部彼得洛夫伽辽金(MLPG)法推广应用于大变形问题。导出了非线性局部子域对称弱形式,通过对该弱形式进行线性化得到了用于非线性计算的MLPG格式,并对MLPG的计算速度进行了优化,使MLPG成为一种复杂度为O(N)的算法。几何非线性和几何与材料双重非线性的数值算例表明,相对有限元方法,MLPG在处理此类大变形问题时收敛性好,精度高,并能减小有限元分析中易遇到的网格畸变带来的困难。     

复杂截面型材力控制拉弯成形数值模拟分析

复杂截面挤压型材的高精度拉弯成形是制造框架式车身的关键技术.本文基于动态显式有限元软件PAM-STAMP,针对一种典型的框架武车身用复杂截面挤压型材,对其力控制方式的直进台面式拉弯成形进行了数值模拟研究,对比分析了两种截面形状的型材截面畸变和回弹随补拉力增大的变形规律,并得到了摩擦系数对成形精度的影响.数值模拟结果表明,增加型材截面的变形刚度,可以显著地减小截面畸变和回弹;增加补拉力,增大了截面畸变但减小了回弹;增大摩擦系数,截面畸变量减小而回弹增加.     

Non‐reflecting boundary conditions for atomistic,continuum and coupled atomistic/continuum simulations

We present a method to numerically calculate a non‐reflecting boundary condition which is applicable to atomistic, continuum and coupled multiscale atomistic/continuum simulations. The method is based on the assumption that the forces near the domain boundary can be well represented as a linear function of the displacements, and utilizes standard Laplace and Fourier transform techniques to eliminate the unnecessary degrees of freedom. The eliminated degrees of freedom are accounted for in a time‐history kernel that can be calculated for arbitrary crystal lattices and interatomic potentials, or regular finite element meshes using an automated numerical procedure. The new theoretical developments presented in this work allow the application of the method to non‐nearest neighbour atomic interactions; it is also demonstrated that the identical procedure can be used for finite element and mesh‐free simulations. We illustrate the effectiveness of the method on a one‐dimensional model problem, and calculate the time‐history kernel for FCC gold using the embedded atom method (EAM). Copyright © 2005 John Wiley & Sons, Ltd.     

A displacement‐based finite element formulation for general polyhedra using harmonic shape functions

A displacement‐based continuous‐Galerkin finite element formulation for general polyhedra is presented for applications in nonlinear solid mechanics. The polyhedra can have an arbitrary number of vertices or faces. The faces of the polyhedra can have an arbitrary number of edges and can be nonplanar. The polyhedra can be nonconvex with only the mild restriction of star convexity with respect to the vertex‐averaged centroid. Conforming shape functions are constructed using harmonic functions defined on the undeformed configuration, thus requiring the use of a total‐Lagrangian finite element formulation in large deformation applications. For nonlinear applications with computationally intensive constitutive models, it is important to minimize the number of element quadrature points. For this reason, an integration scheme is adopted in which the number of quadrature points is equal to the number of vertices. As a first step toward verifying the element behavior in the general nonlinear setting, several linear verification examples are presented using both random Voronoi meshes and distorted hexahedral meshes. For the hexahedral meshes, results for the polyhedral formulation are compared to those of the standard trilinear hexahedral formulation. The element behavior in the nearly incompressible regime is also examined. Copyright © 2013 John Wiley & Sons, Ltd.     

Variable-node elements for non-matching meshes by means of MLS (moving least-square) scheme

A new class of finite elements is described for dealing with non-matching meshes, for which the existing finite elements are hardly efficient. The approach is to employ the moving least-square (MLS) scheme to devise a class of elements with an arbitrary number of nodal points on the parental domain. This approach generally leads to elements with the rational shape functions, which significantly extends the function space of the conventional finite element method. With a special choice of the nodal points and the base functions, the method results in useful elements with the polynomial shape functions for which the C¹ continuity breaks down across the boundaries between the subdomains comprising one element. The present scheme possesses an extremely high potential for applications which deal with various problems with discontinuities, such as material inhomogeneity, crack propagation, phase transition and contact mechanics. The effectiveness of the new elements for handling the discontinuities due to non-matching interfaces is demonstrated using appropriate examples. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of nets with hexagonal mesh using triangular elements

The calculation of net shapes is achieved using the finite element method. A triangular element is developed for the modelling of the net. The main hypotheses are that the strain in each triangular element is constant, that the hexagonal meshes have three directions of twine, and that the twines are elastic. The forces due to the tension in twines are described and calculated by a direct method. The results of the model based on such triangular elements are provided. The comparison with a model where each twine is described as an elastic bar, is quite good. Copyright © 2003 John Wiley & Sons, Ltd.     

Automatic mesh generation and adaptation by using contours

A general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing function. The contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions, where finite element meshes of different element sizes are generated using the available general-purpose mesh generators.^{1, 2} Examples of remeshing for various node spacing functions are given to illustrate that high-quality gradation meshes can be generated automatically without any user's intervention by this simple contour line method.     

An alternative pseudoperipheral node finder for resequencing schemes

Many resequencing algorithms for reducing the bandwidth, profile and wavefront of sparse symmetric matrices have been published. In finite element applications, the sparsity of a matrix is related to the nodal ordering of the finite element mesh. Some of the most successful algorithms, which are based on graph theory, require a pair of starting pseudoperipheral nodes. These nodes, located at nearly maximal distance apart, are determined using heuristic schemes. This paper presents an alternative pseadoperipheral node finder, which is based on the algorithm developed by Gibbs, Poole and Stockmeyer. This modified scheme is suitable for nodal reordering of finite meshes and provides more consistency in the effective selection of the starting nodes in problems where the selection becomes arbitrary due to the number of candidates for these starting nodes. This case arises, in particular, for square meshes. The modified scheme was implemented in Gibbs-Poole-Stockmeyer, Gibbs-King and Sloan algorithms. Test problems of these modified algorithms include: (1) Everstine's 30 benchmark problems; (2) sets of square, rectangular and annular (cylindrical) finite element meshes with quadrilateral and triangular elements; and (3) additional examples originating from mesh refinement schemes. The results demonstrate that the modifications to the original algorithms contribute to the improvement of the reliability of all the resequencing algorithms tested herein for the nodal reordering of finite element meshes.     

Automatic reduction of frontwidth for finite element analysis

An algorithm is presented for reducing the frontwidth of finite element meshes. The technique takes an arbitrary input scheme and reorders the elements so as to reduce the frontwidth. A number of examples are presented to demonstrate the reliability and effectiveness of the method.     

A new method for finite element transitional mesh generation

In the preparation of finite element meshes, inclusion of transitional blocks is important in order to construct optimal meshes. In this paper, a new method is proposed which is capable of generating quaddominated arbitrary transitional meshes. These meshes are well graded and do not require any mesh smoothening algorithm. The inverse isoparametric mapping combined with an elimination procedure is used to construct transition zones. This new algorithm is described in detail and its efficiency is illustrated with appropriate examples. Different methods available for inverse isoparametric mapping are discussed with their merits and limitations. Many of the existing techniques for inverse isoparametric mapping require the calculation of some special coefficients which may vary with the element type. These techniques lose their clarity and efficiency in the case of three dimensional and higher order two dimensional elements. In this paper, a generalized iterative procedure is proposed to carry out the inverse isoparametric mapping. The computations in this approach are already part of every finite element program based on the isoparametric formulation. Hence implementation of the new algorithm is very simple and straightforward.     

A non‐oscillatory method for spallation studies

This paper introduces a non‐oscillatory method, the finite element flux‐corrected transport (FE‐FCT) method for spallation studies. This method includes the implementation of a one‐dimensional FCT algorithm into a total Lagrangian finite element method. Consequently, the FE‐FCT method can efficiently eliminate fluctuations behind shock wave fronts without smearing them. In multidimensional simulations, the one‐dimensional FCT algorithm is used on each grid line of the structured meshes to correct the corresponding component of nodal velocities separately. The requirement of structured meshes is satisfied by using an implicit function so that arbitrary boundaries of the simulated object can be described. In this paper, the proposed FE‐FCT method is applied in spallation studies. One‐ and two‐dimensional examples show this non‐oscillatory method could be one of the candidates to accurately predict spallation and the spall thickness. Copyright © 2005 John Wiley & Sons, Ltd.