An analytical method for solving Cauchy singular integral equations of the second kind with applications to fracture and contact analyses
Due to the presence of complex singularity, solutions to the singular integration equation (SIE) of the second kind are still under development.As a matter of fact, numerical methods for SIE of the first kind are hardly applicable to SIE of the second kind.With the assistance of maple programming, this paper presents a novel approach to formulate an analytical solution to a typical SIE of the second kind.By splitting the Cauchy kernel, and taking advantage of the orthogonality of Jacobi polynomials, we derive an analytical solution corresponding to the monomial loading case.Furthermore, the solution to a general loading case may be obtained via series expansion.The present method appears efficient and convenient, providing an effective tool for treating tangentially loaded contact analyses and interface crack problems.
SIE of the second kindCauchy principal value integrationcomplex singularityinterface crack
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NSTL
万方数据
维普
