An approximate numerical method for solving Cauchy singular integral equations composed of multiple implicit parameter functions with unknown integral limits in contact mechanics

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:482

Article

Wen, Qi^1,2  Du, Qungui^1,2 

[1] South China Univ Technol, Sch Mech & Automot Engn, 381 WuShan Rd, Guangzhou 510641, Guangdong, Peoples R China

[2] Guangdong Prov Key Lab Automot Engn, 381 WuShan Rd, Guangzhou 510641, Guangdong, Peoples R China

关键词: Cauchy singular integral;    Unknown integral limits;    Implicit parameter function;    Approximate numerical method;   

DOI  :  10.1016/j.jmaa.2019.123530

来源: Elsevier

【 摘 要 】

Cauchy singular integral equations are widely used in physics and mathematics, especially in solid contact mechanics. The solution of Cauchy singular integral equations composed of explicit functions has already been achieved in existing research. However, when dealing with the contact problem between two solid bodies with irregular surfaces described by implicit parametric functions, difficulties arise when trying to solve the Cauchy singular integral because it is composed of multiple implicit parameter functions. Moreover, the integral limits are unknown, and constrained by physical characteristics. To solve this kind of problem, an approximate calculation method with high accuracy will be provided in this paper. Specifically, based on the quadrature method and taking the constraint function of the boundary as the convergence criterion, both the integral limits satisfying the physical characteristics condition and the solution of the Cauchy singular integral equations composed of multiple parameter functions can be derived by an iterative method. Finally, five different examples are calculated using the new method, and the absolute errors between the approximate values provided by the new method and the true values are analysed. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free