This paper presents the particular integral formulation for two (2D) and three (3D) dimensional transient dynamic elastoplastic analyses. The elastostatic equation is used for the complementary solution. The particular integrals for displacement, traction and stress rates are obtained by introducing the concept of a global shape function to approximate acceleration and initial stress rate terms of the inhomogeneous equation. The Houbolt time integration scheme is used for the time-marching process. The Newton-Raphson algorithm for plastic multiplier is used to solve the system equation. The developed program is integrated with the pre- and post-processor. Numerical results for four example problems are given to demonstrate the validity and accuracy of the present formulation. © 2007 Elsevier Ltd. All rights reserved.
Owatsiriwong, A., & Park, K. H. (2008). A BEM formulation for transient dynamic elastoplastic analysis via particular integrals. International Journal of Solids and Structures, 45(9), 2561–2582. https://doi.org/10.1016/j.ijsolstr.2007.12.009