Numerical methods for solving singular integral equations obtained by fracture mechanical analysis of cracked wedge

作     者：M.GHADIRI H.GHASEMI 

作者机构：Faculty of Engineering and TechnologyDepartment of Mechanical EngineeringImam Khomeini International University 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2014年第35卷第3期

页      面：311-324页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

主　　题：fracture mechanics numerical analytical singular integral equation Gauss-Legendre 

摘      要：The numerical solutions to the singular integral equations obtained by the fracture mechanical analyses of a cracked wedge under three different conditions are considered. The three considered conditions are:(i) a radial crack on a wedge with a nonfinite radius under the traction-traction boundary condition,(ii) a radial crack on a wedge with a finite radius under the traction-traction boundary condition, and(iii) a radial crack on a finite radius wedge under the traction-displacement boundary condition. According to the boundary conditions, the extracted singular integral equations have different forms. Numerical methods are used to solve the obtained coupled singular integral equations, where the Gauss-Legendre and the Gauss-Chebyshev polynomials are used to approximate the responses of the singular integral equations. The results are presented in figures and compared with those obtained by the analytical response. The results show that the obtained Gauss-Chebyshev polynomial response is closer to the analytical response.