MULTI-DOMAIN BOUNDARY ELEMENT METHOD FOR AXISYMMETRIC PROBLEMS IN POTENTIAL THEORY AND LINEAR ISOTROPIC ELASTICITY

Boundary Elements and other Mesh Reduction Methods XLI Pub Date : 2018-09-11 DOI:10.2495/be410021

Vasyl Gnitko, Kyryl Degtyariov, A. Karaiev, E. Strelnikova

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引用次数: 15

Abstract

The paper presents an approach based on reduced boundary element methods to resolve axisymmetric problems in potential and linear isotropic elasticity theories. The singular integral equations for these problems are received using fundamental solutions. Initially three-dimensional problems expressed in Cartesian coordinates are transformed to cylindrical ones and integrated with respect to the circumference coordinate. So the three-dimensional axisymmetric problems are reduced to systems of singular integral equations requiring the evaluation of linear integrals only. The fundamental solutions and their derivatives are expressed in terms of complete elliptic integrals. The effective algorithm for treatment of the singular integrals is proposed. The multi-domain boundary element method is applied for the numerical simulation. As examples, the following problems are considered: fluid induced vibrations of a compound cylindrical-spherical elastic shell partially filled with an ideal incompressible liquid, and axisymmetric elasticity problems for an isotropic body with rigid or elastic circular cylindrical inclusions.

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势理论和线各向同性弹性轴对称问题的多域边界元法

本文提出了一种基于边界元简化的方法来求解势弹性理论和线各向同性弹性理论中的轴对称问题。这些问题的奇异积分方程是用基本解得到的。最初，用笛卡尔坐标表示的三维问题被转化为圆柱形问题，并根据周长坐标进行积分。因此，三维轴对称问题可以简化为只需要求线性积分的奇异积分方程组。基本解及其导数用完全椭圆积分表示。提出了处理奇异积分的有效算法。采用多域边界元法进行数值模拟。作为例子，考虑了以下问题:部分填充理想不可压缩液体的复合圆柱球弹性壳的流体诱导振动问题，以及具有刚性或弹性圆柱内含物的各向同性体的轴对称弹性问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Boundary Elements and other Mesh Reduction Methods XLI

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