Open Access

ARTICLE

# Spline Fictitious Boundary Element Alternating Method for Edge Crack Problems with Mixed Boundary Conditions

Z. Xu1, M. Chen1, X. M. Fan1,2,*

School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China.
State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou, China.

Computer Modeling in Engineering & Sciences 2018, 116(3), 407-431. https://doi.org/10.31614/cmes.2018.01816

## Abstract

The alternating method based on the fundamental solutions of the infinite domain containing a crack, namely Muskhelishvili’s solutions, divides the complex structure with a crack into a simple model without crack which can be solved by traditional numerical methods and an infinite domain with a crack which can be solved by Muskhelishvili’s solutions. However, this alternating method cannot be directly applied to the edge crack problems since partial crack surface of Muskhelishvili’s solutions is located outside the computational domain. In this paper, an improved alternating method, the spline fictitious boundary element alternating method (SFBEAM), based on infinite domain with the combination of spline fictitious boundary element method (SFBEM) and Muskhelishvili’s solutions is proposed to solve the edge crack problems. Since the SFBEM and Muskhelishvili’s solutions are obtained in the framework of infinite domain, no special treatment is needed for solving the problem of edge cracks. Different mixed boundary conditions edge crack problems with varies of computational parameters are given to certify the high precision, efficiency and applicability of the proposed method compared with other alternating methods and extend finite element method.

## Keywords

APA Style
Xu, Z., Chen, M., Fan, X.M. (2018). Spline fictitious boundary element alternating method for edge crack problems with mixed boundary conditions. Computer Modeling in Engineering & Sciences, 116(3), 407-431. https://doi.org/10.31614/cmes.2018.01816
Vancouver Style
Xu Z, Chen M, Fan XM. Spline fictitious boundary element alternating method for edge crack problems with mixed boundary conditions. Comput Model Eng Sci. 2018;116(3):407-431 https://doi.org/10.31614/cmes.2018.01816
IEEE Style
Z. Xu, M. Chen, and X.M. Fan "Spline Fictitious Boundary Element Alternating Method for Edge Crack Problems with Mixed Boundary Conditions," Comput. Model. Eng. Sci., vol. 116, no. 3, pp. 407-431. 2018. https://doi.org/10.31614/cmes.2018.01816

View