An efficient implementation of BEM for two- and three-dimensional multi-region elastoplastic analyses

Boundary element methods (BEM) have been implemented for solving multi-region elastoplastic problems with the maximum efficiency. A new form of Newton–Raphson algorithm in nonlinear BEM is established in which the formation of the right hand side terms in each iteration is accurately represented. In this new algorithm, only the equations related to the yielded nodes need Gaussian elimination, at each load step. This advantage combined with the sub-region technique now makes BEM a viable tool for multi-region elastoplastic analyses. A combined analytical and numerical integration of boundary and volume integrals have been performed for both two- and three-dimensional analyses. Whenever the geometry of the volume cells meets the straight line or flat surface requirements, the analytical integration is faster and more accurate than numerical integration.The numerical results using the above formulation have been presented for some two- and three-dimensional practical problems commonly encountered in structural and geotechnical engineering and compared with other available solutions.