Viscoplastic plane-strain analysis of infinite solids using elastic supports

A highly e¦cient novel Finite Element Boundary Element Method (FEBEM) is proposed for the elastoviscoplastic plane-strain analysis of displacements and stresses in inÞnite solids. The proposed method takes advantage of both the Finite Element Method (FEM) and the Boundary Element Method (BEM) to achieve higher e¦ciency and accuracy by using the concept of elastic supports to simulate the e¤ects of unbounded solid mass surrounding the region of interest. The BEM is used to compute the sti¤nesses of elastic supports and to estimate the location of the truncation boundary for the Þnite 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 Þnite element sti¤ness matrix is not disturbed. Secondly, the proposed technique may be implemented simply by using standard codes for elasto-viscoplastic Þnite 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 Þnite element modelling. The e¦ciency and accuracy of the proposed method are demonstrated by computing elastic and elasto-plastic displacements and stresses around ÔdeepÕ underground openings in rock mass subject to hydrostatic and non-hydrostatic in situ stresses. Results obtained by the proposed method are compared with ÔexactÕ solutions and with those obtained by using a BEM and a coupled FEBEM.