二维非连续边界元分析积分计算的精确表达式

以二维弹性力学问题为研究对象,采用线性非连续元离散边界积分方程,给出了系数矩阵计算的精确表达式,对二维弹性力学问题进行了数值计算,对非连续边界元配位点对计算结果精度的影响进行了讨论,结果表明准奇异积分计算是配位点影响计算结构精度的主要因素。

Closed-formed Expressions for Accurate Evaluation of Integrals Associated with Two-dimensional Boundary Integral Equation for Two-dimensional Elastostatics

In this paper,linear discontinuous boundary element is employed to discretize boundary integral equation of two-dimensional elastostatics.The closed-formed expressions are derived for accurate evaluation of both singular and nonsingular integrals associated with boundary element analysis, and are employed for the numerical implementation of both two-dimensional potential and elastostatics problems.By comparison with the conventional procedure for numerical integration scheme,i.e.Gauss quadrature rules,the optimum collocation points for discontinuous boundary element analysis is evaluated.The numerical implementation shows that the optimum collocation factor of discontinuous boundary elements is greatly influenced by the accuracy of the integral computation,especially the nearly singular integrals,which cannot be accurately computed by conventional Gauss quadrature rules.