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

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.