边界元法中的改进等参变换

首先考察三维边界元法中八结点等参单元边中结点的敏感性,指出对于常规等参变换计算,边中结点同有限元计算情形一样,仍必须遵守位于相邻角点间距离的三分之一内的建议,且限制应更严格,才能保证计算的有效性.其次,将改进等参变换引入到边界元法,并解决了相应的奇异积分处理等问题,提出了一个比常规等参变换时更加一般的坐标变换关系式.最后,对于立方块受单向拉伸和纯弯曲两种情况作了计算,结果表明,在边界元法中,改进等参变换的引入,使得计算具有更大的适应性.     

分析表面裂纹的一种新方法

本文作者综合了线弹簧模型及边界元法的优点,开发了一种新的线弹簧边界元法.该方法把表面裂纹这一三维问题简化为拟一维问题,可用于分析受到多种载荷作用的含表面裂纹的板.本文对该方法进行了理论分析和数值验证,报告了计算结果.结果表明,该方法经济有效.利用该方法仅使用个人计算机就可以分析表面裂纹问题.     

外边值问题的边界元法与有限元法组合及奇性处理

本文讨论了以一条直线为边界的Helmholts方程外边值问题的边界元法与有限元法的组合过程,推导变分公式,并分别用奇性函数扩大有限元空间和用奇性单元处理尖点附近解的奇性,同边界元法的结果相比较,边界元法与有限元法的组合优越于边界元法。     

连铸中的自由边界问题的边界元解法

本文应用边界元法求解钢铁生产中连铸工艺出现的自由边界问题。首先,对较一般的连铸过程的数学模型进行简化并给出相应的边界积分方程,以及叙述了用边界元法求解该问题的步骤。然后,我们给出了一个计算实例,并对该方法的收敛快慢、对初值的敏感性和对区域形状的适应性等问题进行了探讨。最后,针对一种简化的模型,将数值解与解析解进行比较,两者吻合较好。     

多裂纹问题计算分析的本征COD边界积分方程方法

针对多裂纹问题，若采用常规的数值求解技术，计算效率较低.为实现多裂纹问题的大规模数值模拟，建立了本征裂纹张开位移（crack opening displacement, COD）边界积分方程及其迭代算法，并引入Eshelby矩阵的定义，将多裂纹分为近场裂纹和远场裂纹来处理裂纹间的相互影响.以采用常单元作为离散单元的快速多极边界元法为参照，对提出的计算模型和迭代算法进行了数值验证.结果表明，本征COD边界积分方程方法在处理多裂纹问题时取得较大的改进，其计算效率显著高于传统的边界元法和快速多极边界元法.     

利用边界元法求解一类重调和方程

边界元法(BEM)和多重互易法(MRM)相结合求解一类重调和方程.通过重调和基本解序列给出的MRM-方法和BEM, 推导出该类问题的MRM-边界变分方程, 用边界元法求解该变分方程, 从而得到重调和方程的近似解, 并给出了解的存在唯一性证明.通过数值算例说明了MRM-方法具有收敛速度快、计算精度高, 易编程等优点, 为使用边界元法数值求解重调和方程提供了方法和理论依据.适合于工程中的实际运算.     

边界元的分区解法

边界元法是一种比‘区域’型解法(如有限单元法,有限差分法)有着更多优点的方法。由于它能使所考虑的问题在维数上降阶,只需要对结构的边界进行离散,离散误差仅来自边界[1],因而具有输入量小,精度高等优点,在工程界受到广泛的重视.随着边界元网格的增加,其非对称满值的系数矩阵呈自由度平方级的增大,系数矩阵的总量可高达几千上万个。如此巨大的数组空间,一次送入计算机内存进行整体计算显然是办不到的,本文所提出的分区解法,使用了静力凝聚的概念,将一个整体的定解问题转化为若干个彼此有联系的分区定解问题,这样不仅解决了容量问题,而且提高了计算效率。     

一种对称非奇异核边界元法

本文依据泛函分析的基本理论,提出利用完备直交的本征函数系构造对称非奇异的基本解,给出了又一种非奇异边界元法.     

平面Laplace方程的边界元方法

本文对平面Laplace方程给出一种边界元算法,讨论了它的计算并给出了数值算例,最后证明了边界元解的收敛性及超收敛性。由误差估计式还看出,近似解及其微商在最大模意义下具有同阶精度,这是边界元法相对于有限元法的另一优点。     

基于三维弹性问题的多极边界元法核函数分解

多极边界元法已经成功地应用于大规模工程计算中.得到并且证明了基于三维弹性问题的多极边界元法核函数分解的定理(定理1),完善了多击边界元法的数学理论.     

A BOUNDARY ELEMENT METHOD FOR A NONLINEAR BOUNDARY VALUE PROBLEM IN STEADY-STATE HEAT TRANSFER IN DIMENSION THREE

In this paper, a new method of boundary reduction is proposed, which reduces thesteady-state heat transfer equation with radiation. Moreover, a boundary element method is pre-sented for its solution and the error estimates of the numerical approximations are given.     

A boundary element method for homogenization of periodic structures

Homogenized coefficients of periodic structures are calculated via an auxiliary partial differential equation in the periodic cell. Typically, a volume finite element discretization is employed for the numerical solution. In this paper, we reformulate the problem as a boundary integral equation using Steklov–Poincaré operators. The resulting boundary element method only discretizes the boundary of the periodic cell and the interface between the materials within the cell. We prove that the homogenized coefficients converge super-linearly with the mesh size, and we support the theory with examples in two and three dimensions.     

Boundary element method in Biot's linear consolidation

A boundary element method is formulated for the general theory of Biot's linear consolidation. Results for typical examples show good agreement with finite element solutions. As the cpu time in two dimensions is unsatisfactory an alternative method of calculating the stresses is suggested.     

解一类半线性外边值问题的自然边界元与有限元耦合法

In this paper, we combine a finite element approach with the natural boundary element method to stduy the weak solvability and Galerkin approximations of a class of semilinear exterior boundary value problems. Our analysis is mainly based on the variational formulation with constraints. We discuss the error estimate of the finite element solution and obtain the asymptotic rate of convergence O（h^n) Finally, we also give two numerical examples.     

边界层问题的小波—有限元解

本文将小波分析与有限元法结合起来，建立了一种小波－有限元计算格式，并用该算法计算了一个典型的边界层问题，探讨了寻找边界层位置的过程以及计算边界层区的内部解及外部解的步骤。计算结果表明，用该法寻找的边界层位置以及所求得的内部解与真实结果完全符合。     

On the coupled NBEM and FEM for a class of nonlinear exterior Dirichlet problem in R~(2*)

In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite element approach with the natural boundary element method to study the weak solvability and Galerkin approximation of a class of nonlinear exterior boundary value problems. The analysis is mainly based on the variational formulation with constraints. We prove the error estimate of the finite element solution and obtain     

Boundary element method and wave equation

In this paper the boundary integral expression for a one-dimensional wave equation with homogeneous boundary conditions is developed. This is done using the time dependent fundamental solution of the corresponding hyperbolic partial differential equation. The integral expression developed is a generalized function with the same form as the well-known D'Alembert formula. The derivatives of the solution and some useful invariants on the characteristics of the partial differential equation are also calculated.The boundary element method is applied to find the numerical solution. The results show excellent agreement with analytical solutions.A multi-step procedure for large time steps which can be used in the boundary element method is also described.In addition, the way in which boundary conditions are introduced during the time dependent process is explained in detail. In the Appendix the main properties of Dirac's delta function and the Heaviside unit step function are described.     

平面弹性裂纹分析的一种有效边界元方法

提出了一种简单而有效的平面弹性裂纹应力强度因子的边界元计算方法．该方法由Crouch与Starfield建立的常位移不连续单元和闫相桥最近提出的裂尖位移不连续单元构成A·D2在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界．算例(如单向拉伸无限大板中心裂纹、单向拉伸无限大板中圆孔与裂纹的作用)说明平面弹性裂纹应力强度因子的边界元计算方法是非常有效的．此外,还对双轴载荷作用下有限大板中方孔分支裂纹进行了分析．这一数值结果说明平面弹性裂纹应力强度因子的边界元计算方法对有限体中复杂裂纹的有效性,可以揭示双轴载荷及裂纹体几何对应力强度因子的影响．     

A BOUNDARY ELEMENT PROCEDURE FOR THE SIGNORINI PROBLEM IN THREE-DIMENSIONAL ELASTICITY

In this paper, a new numerical method for the Signorini problem in three-dimensional elasticity is presented. The problem is reduced to a boundary variational inequality based on a new representation of the derivative of the doublelayer potential. Furthermore, a boundary element procedure is described for the numerical approximation of its solution and an abstract error estimate is given.     

A new boundary element technique for solving plane problems of linear elasticity: improved theory and an application to fracture mechanics

An improved boundary element method for solving plane problems of linear elasticity theory is described. The method is based on the Muskhelishvili complex variable representation for the displacement and stress fields. The paper shows how to take account of symmetry about the x and/or y axes.The potential accuracy of the method is illustrated by its application to the calculation of stress intensity factors associated with cracks in both a square and a circular plate. The crack problem is solved using a Gauss-Chebyshev representation of a singular integral equation by a set of linear algebraic equations. The integral equation involves an analytic function which takes account of the presence of the external boundary. This function is determined directly using the boundary element method.Numerical results are believed to be more accurate than the existing published values which are quoted to four significant figures.