Analytical treatment on singularities for 2-D elastoplastic dynamics by time domain boundary element method using Hadamard principle integral

Abstract

A fully analytical method by adopting the concept of the finite part of an integral, Hadamard principle integral, is proposed to treat the singularities in both time and space in the plastic strain-related coefficients matrices Q and F in the TD-BEM formulation for elastoplastic analysis. Comparing with the treatment on singularity by using the method of rigid body displacement, the novel analytical treatment on the singularity is from the viewpoint of dynamics, without any numerical component of the elastostatic concept, meaning that the treatment is theoretically suitable for elastoplastic analysis. Meanwhile, comparing with the treatment on singularity by the initial stress expansion technique and the method of the constant strain fields, the novel analytical treatment on the singularity retains all of the inherent advantages of the TD-BEM formulation for elastoplastic analysis, restricting the discretization on boundary and in the potential plastic region and allowing models with infinite or semi-infinite geometry extension without artificial boundaries. Finally, the novel analytical treatment on the singularity is strictly mathematically tenable, without any computational error. The proposed treatment on singularity for dynamic elastoplastic analysis in TD-BEM formulation is verified by three examples.