An Schwartz-Neumann Alternating Method for the Elastic-Plastic Analysis of Elliptical Cracks in 3D Body

Abstract

Elliptical cracks are very important in the assessment of residual strength of structures, because an actual flaw in the structural component can be modelled as an ellipse or a part of an ellipse. After Vijayakumar and Atluri[1] derived a general solution procedure for an embedded elliptical crack subject to arbitrary crack surface load in an infinite solid, the Schwartz-Neumann Alternating Method[3] became a very efficient and accurate method in the analysis of elliptical cracks. The Finite Element Alternating Method(FEAM)[2] uses the FEM to solve the uncracked body subject to the external loading. It uses the analytical solution to solve the elliptical crack in the finite body, subject to the crack surface loading. Since the crack is not modelled explicitly, it is not necessary to refine the mesh at the crack front. Thus, the FEM model involved is much simpler than those modelling the crack explicitly. Consequently, FEAM is much more efficient than the traditional FEM in solving the fracture mechanics problems. Further more, it is much easier to generate a mesh without any refinement at the crack front. Recently, Nikishkov and Atluri[4] developed the alternating method for the elastic-plastic analysis of cracks. We present here the elastic-plastic analysis of elliptical cracks.