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Analytical expressions for evaluation of radial integrals in stress computation of functionally graded material problems using RIBEM

机译：使用RIBEM评估功能梯度材料问题的应力计算中的径向积分的解析表达式

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摘要

This paper presents a set of new analytical expressions for evaluating radial integrals appearing in the stress computation of variable coefficient elastic problems using the radial integration boundary element method (RIBEM). The strong singularity involved in the stress integral equation is explicitly removed in the derivation of the analytical expressions. The fourth-order spline RBF is employed to approximate unknowns appearing in domain integrals from variation of the shear modulus. Using these analytical expressions, considerable computational efficiency can be improved by overcoming the time-consuming deficiency of using the radial integration method (RIM) to convert domain integrals to the boundary which results in a pure boundary discretization algorithm in solving variable coefficient problems. Numerical examples are given to demonstrate the efficiency of the presented formulations.
机译：本文提出了一组新的解析表达式，用于评估使用径向积分边界元法（RIBEM）进行的变系数弹性问题应力计算中出现的径向积分。在解析表达式的推导中明确消除了应力积分方程中涉及的强奇点。四阶样条RBF用于根据剪切模量的变化来估计出现在域积分中的未知数。使用这些解析表达式，可以克服使用径向积分方法（RIM）将域积分转换为边界所造成的耗时的缺陷，从而提高计算效率，从而产生纯边界离散化算法来解决变系数问题。数值例子说明了所提出配方的有效性。

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