Viscoplastic plane‐strain analysis of infinite solids using elastic supports

Abstract

SUMMARYA highly efficient novel Finite Element Boundary Element Method (FEBEM) is proposed for the elastoviscoplastic plane-strain analysis of displacements and stresses in infinite solids. The proposed method takes advantage of both the Finite Element Method (FEM) and the Boundary Element Method (BEM) to achieve higher efficiency and accuracy by using the concept of elastic supports to simulate the effects of unbounded solid mass surrounding the region of interest. The BEM is used to compute the stiffnesses of elastic supports and to estimate the location of the truncation boundary for the finite element model. As compared to the conventional coupled FEBEM, the proposed method has three main computational advantages. Firstly, the symmetrical and highly banded form of the standard finite element stiffness matrix is not disturbed. Secondly, the proposed technique may be implemented simply by using standard codes for elasto-viscoplastic finite element analysis and elastic boundary element analysis. Thirdly, the yielded zone is approximately located in advance by using the BEM and hence, an unnecessarily large extent of the domain does not have to be discretized for the finite element modelling. The efficiency and accuracy of the proposed method are demonstrated by computing elastic and elasto-plastic displacements and stresses around 'deep' underground openings in rock mass subject to hydrostatic and non-hydrostatic in situ stresses. Results obtained by the proposed method are compared with 'exact' solutions and with those obtained by using a BEM and a coupled FEBEM.