A Subdivision Transformation Method for Weakly Singular Boundary Integrals in Thin-structural Problem

IF 0.6 4区 工程技术 Q4 MECHANICS
Mechanika Pub Date : 2023-06-17 DOI:10.5755/j02.mech.31683
Junjian Hou, L. Zeng, Y. Zhong, Dengfeng Zhao, Mingyuan Zhao
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引用次数: 0

Abstract

Accurate and effective calculation of weakly singular integral in the boundary integral equation of the thin-structural problem is the key to the numerical implementation of the boundary element method. In this paper, a subdivision transformation method evaluated for weakly singular integrals is proposed, and the method is implemented as follows: based on the position of the source points, the shape information of the elements and the nearest distance from the source point to the integral element, a subdivision technology is constructed at first. With this subdivision technology, the integral element can be divided into several integral blocks with good shapes. And then, a simpler coordinate transformation method is constructed to remove the weak singularities of the integral blocks obtained by the subdivision technology. Compared with the conventional polar coordinate transformation method, the present transformation method does not need to calculate their integral interval, which is more simple and effective to implement. Finally, the paper gives three numerical examples to verify the accuracy and validity of the present method.
薄结构问题中弱奇异边界积分的细分变换方法
精确有效地计算薄结构问题边界积分方程中的弱奇异积分是边界元法数值实现的关键。本文提出了一种评估弱奇异积分的细分变换方法,该方法的实现如下:基于源点的位置、单元的形状信息以及源点到积分单元的最近距离,首先构造了一种细分技术。利用这种细分技术,可以将积分单元划分为几个形状良好的积分块。然后,构造了一种更简单的坐标变换方法来去除通过细分技术获得的积分块的弱奇异性。与传统的极坐标变换方法相比,该变换方法不需要计算它们的积分区间,实现起来更简单有效。最后,通过三个算例验证了该方法的准确性和有效性。
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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来源期刊
Mechanika
Mechanika 物理-力学
CiteScore
1.30
自引率
0.00%
发文量
50
审稿时长
3 months
期刊介绍: The journal is publishing scientific papers dealing with the following problems: Mechanics of Solid Bodies; Mechanics of Fluids and Gases; Dynamics of Mechanical Systems; Design and Optimization of Mechanical Systems; Mechanical Technologies.
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