Jordan-form special solutions corresponding to arbitrary anti-plane shear forces in polynomial forms imposed on bimaterial interfacial crack surfaces

Abstract

Bimaterial anti-plane interfacial crack problems with arbitrary distributed forces applied on crack surfaces are numerically investigated. The problems are in essence a kind of boundary value problems about Laplace's equations. Previous work of using Symplectic analytical singular element (SASE) with high-order accuracy and other singular finite elements for calculating mode III stress intensity becomes invalid when the distributed forces on each surface are different. In this paper, Jordan-form special solutions (JFSS) are proposed for the first time. We derive the JFSS for present problems and use them to improve displacement modes of SASE. The distributed forces are therefore converted into equivalent nodal forces of the nodes around SASE. The new SASE is found to be directly and conveniently used for cases where the two distributed forces are either equal (even both zero) or not equal. Numerical examples are provided to demonstrate the effectiveness and accuracy of the present method. The necessity and effectiveness of the JFSS is also validated. Moreover, the JFSS can be applied to some other physical problems represented by the Laplace's equation.