Simple finite element formulation for computing stress singularities at bimaterial interfaces

Abstract

By using the weak form of the governing equations for sectorial bimaterial domains and assuming that the displacement field is proportional to the (λ+1)th power of the distance from the singular stress point, a second-order characteristic matrix equation on λ is derived by a one-dimensional finite element formulation that only discretizes the domain circumferentially. Numerical examples covering a variety of interfacial singularities are presented to demonstrate the efficacy of the formulation. Accurate solutions are yielded by very few elements whereas convergence can be attained by either h- or p-refinement. The related procedures are programmed in a short MAPLE worksheet given in the appendix.