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# Weakly Singular Symmetric Galerkin Boundary Element Method for Fracture Analysis of Three-Dimensional Structures Considering Rotational Inertia and Gravitational Forces

Shuangxin He1, Chaoyang Wang1, Xuan Zhou1,*, Leiting Dong1,*, Satya N. Atluri2

1 School of Aeronautic Science and Engineering, Beihang University, Beijing, China
2 Department of Mechanical Engineering, Texas Tech University, Lubbock, USA

* Corresponding Authors: Xuan Zhou. Email: ; Leiting Dong. Email:

Computer Modeling in Engineering & Sciences 2022, 131(3), 1857-1882. https://doi.org/10.32604/cmes.2022.019160

## Abstract

The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures, because only boundary and crack-surface elements are needed. However, for engineering structures subjected to body forces such as rotational inertia and gravitational loads, additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain. In this study, weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed. By using divergence theorem or alternatively the radial integration method, the domain integral terms caused by body forces are transformed into boundary integrals. And due to the weak singularity of the formulated boundary integral equations, a simple Gauss-Legendre quadrature with a few integral points is suffcient for numerically evaluating the SGBEM equations. Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.

## Keywords

APA Style
He, S., Wang, C., Zhou, X., Dong, L., Atluri, S.N. (2022). Weakly singular symmetric galerkin boundary element method for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces. Computer Modeling in Engineering & Sciences, 131(3), 1857-1882. https://doi.org/10.32604/cmes.2022.019160
Vancouver Style
He S, Wang C, Zhou X, Dong L, Atluri SN. Weakly singular symmetric galerkin boundary element method for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces. Comput Model Eng Sci. 2022;131(3):1857-1882 https://doi.org/10.32604/cmes.2022.019160
IEEE Style
S. He, C. Wang, X. Zhou, L. Dong, and S.N. Atluri "Weakly Singular Symmetric Galerkin Boundary Element Method for Fracture Analysis of Three-Dimensional Structures Considering Rotational Inertia and Gravitational Forces," Comput. Model. Eng. Sci., vol. 131, no. 3, pp. 1857-1882. 2022. https://doi.org/10.32604/cmes.2022.019160

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