Scholarlink

<p>The accuracy of evaluating nearly singular integrals is crucial to determining the accuracy and stability of BEM in solving elastic problems. A novel semi-analytic method is developed for calculating nearly singular integrals with various kernel functions. Different from the traditional semi-analytical method, the Taylor expansion for shape functions, Jacobian, and so on in our method is based on the nearest point from a source point to an integral element rather than the projection point from the source point to the integral element. Therefore, it can more accurately approximate the distance from the source point to Gaussian integration points. Based on these Taylor expansions, approximate expressions for the integrand functions of two-dimensional elastic problems are derived. The effectiveness of this method is demonstrated by evaluating the accuracy of physical quantities at various points within different geometric models and comparing the results with those of the traditional semi-analytic method and the distance transformation method.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A New Semi-Analytic Algorithm of Nearly Singular Integrals with Various Kernels in BEM for Analyzing 2D Elasticity Problems

  • 期刊论文

  • 发表日期：

    2026年7月13日

查看全文
  • Weicheng Lin,
  • Chuanming Ju,
  • Xin Wang,
  • Jiehao Chen,
  • Shuangyu Yu

摘要

The accuracy of evaluating nearly singular integrals is crucial to determining the accuracy and stability of BEM in solving elastic problems. A novel semi-analytic method is developed for calculating nearly singular integrals with various kernel functions. Different from the traditional semi-analytical method, the Taylor expansion for shape functions, Jacobian, and so on in our method is based on the nearest point from a source point to an integral element rather than the projection point from the source point to the integral element. Therefore, it can more accurately approximate the distance from the source point to Gaussian integration points. Based on these Taylor expansions, approximate expressions for the integrand functions of two-dimensional elastic problems are derived. The effectiveness of this method is demonstrated by evaluating the accuracy of physical quantities at various points within different geometric models and comparing the results with those of the traditional semi-analytic method and the distance transformation method.