Causality condition relevant functions-orientated analytical treatment on in 3D TD-BEM

被引：9

作者：

Lei, Weidong ^{[1
]}

Qin, Xiaofei ^{[2
]}

Li, Hongjun ^{[3
]}

Fan, Youhua ^{[2
]}

机构：

[1] Harbin Inst Technol, Sch Civil & Environm Engn, Shenzhen 518055, Peoples R China

[2] Harbin Inst Technol, Sch Sci, Shenzhen 518055, Peoples R China

[3] Hebei Agr Univ, Urban & Rural Construct Inst, Baoding 071001, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2022年 / 427卷

关键词：

Time domain boundary element method; (TD-BEM); Three dimensional elastodynamics; Spatial singularity; Hadamard principle integral; BOUNDARY-ELEMENT METHOD; TRANSIENT ELASTODYNAMIC ANALYSIS; CONVOLUTION QUADRATURE; SINGULAR-INTEGRALS; TIME; FORMULATION; STRESS; EQUATION; VELOCITY; SPACE;

D O I：

10.1016/j.amc.2022.127113

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A direct analytical treatment on singularities in the 3D TD-BEM formulation is proposed, where the wavefront singularity and the dual singularity are analytically expressed. In the process of the solution of the spatial singularity, the integration domain is divided into the regular part and the singular part. The singularities in the singular part are analytically eliminated by the direct method of the concept of the finite part of an integral (Hadamard principal integral), while the singular integrals in the regular part are solved by the conve-nient Gaussian integration. Due to the increase of the dimension and the additional causal-ity relevant function, the 3D TD-BEM formulation is further more intricate than the 2D one. In order to reduce the complexity, in the process of the solution of the boundary in-tegral equation in the 3D TD-BEM formulation, a new coordinate transformation method is proposed to analytically transform the coefficient integrals on the spatial surface element into the 2D plane element. The 3D TD-BEM formulation based on the proposed analytical treatment on singularities is verified to be correct by three examples. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：16

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