Elasto‐plastic analysis of an underground opening by FEM and coupled FEBEM

Abstract

SUMMARYThe elasto-plastic analysis of a circular underground opening using the finite element method (FEM), the coupled finite element and the boundary element method (FEBEM) is presented. The coupling procedure and elasto-plastic formulation are discussed. The effect of in situ stress ratio on yielded zone, displaced shape and principal stresses is presented. The results of FEBEM analysis are compared with those obtained from FEM. The computation time and the number of iterations as required by FEBEM and FEM are compared.

Viscoplastic plane‐strain analysis of infinite solids using elastic supports

“…For other quantities, there was practically no difference in the results obtained by the two methods. For s"1)0, as shown in Table IV, the present results were more accurate than those reported in [7] and therefore, the minor difference in results is also due to errors in the coupled FEBEM. One main factor contributing to the higher accuracy of the proposed FEBEM is the fact that the stiffness matrix remains symmetrical and highly banded and, therefore, there is lesser propagation of error in the repetitive solution of equation (8).…”

“…Furthermore, minor errors in the computation of stiffnesses of elastic supports at the truncation boundary had an insignificant effect on the results for displacements and stresses obtained by using the proposed FEBEM. The results obtained by using the proposed FEBEM were found to be almost 'identical' to the 'exact' solutions for all the cases analysed (Tables I and II For the elasto-plastic analysis, the example problem was chosen such that the results obtained by the proposed method could be compared with 'exact' solutions and with other available results [7]. The function ( ) was normalized in terms of the equivalent yield stress as follows: The Mohr-Coulomb yield criterion was used for which the yield function and the equivalent yield stress are expressed as…”

“…The proposed FEBEM results obtained by using d/R"1)0 and 3)0 are compared with those in [7]. For s"1)0, these results are also compared with the 'exact' solutions ( Figure 9).…”

“…The results for displacements and principal stresses obtained by the proposed FEBEM were also compared with those obtained by using the coupled FEBEM [7] (Tables V and VI). The proposed FEBEM results correspond to those obtained by using d/R"3)0 and t"0)0076 s.…”

Nonlinear analysis of NATM tunnel construction with the boundary element method

“…The usual approach consists in using the FEM to simulate the tunnel lining and the zones around the tunnel which undergo plastic deformation and in using the BEM to simulate the elastic zones of the rock mass. However, most of this work focuses on 2D modelling only [22,26,29]. Furthermore, the use of the BEM for the nonlinear zone and the direct coupling of the boundary elements with the finite elements for the tunnel lining has -to the best of the authors' knowledge -never been discussed in 3D.…”