ABSTRACT
Starting with the elastoplastic boundary element formulation introduced by Swedlow and Cruse (1971), the first two-dimensional elastoplastic analysis was developed by Riccardella (1973), the first viscoplastic analyses by Kumar and Mukherjee (1975) and Chaudonneret (1977), the first three-dimensional analyses by Banerjee et al. (1979), and the first axisymmetric analysis by Cathie and Banerjee (1980). Since then these formulations have been improved by many researchers. These early elastoplastic BEM formulations were all based on iterative procedures which work successfully, but often take an unduly large number of iterations to converge to the correct solution, particularly
in problems involving a high degree of non-linearity such as the loading close to the collapse state of stress when a significant amount of plastic zones develop. For this reason, Banerjee and Raveendra (1986) developed an advanced implementation of the iterative algorithm (Banerjee et al., 1979; Banerjee and Davies, 1984) which has a time saving feature which reduces the number of iterations needed for convergence by utilising the past history of initial stress rates to estimate the value of the initial stress rates for the next load increment. The method was found to reduce substantially the time needed for iteration and this procedure has been adopted in the iterative results presented in this chapter. Nevertheless, the iterative procedure still often has trouble converging to a correct solution for a crude mesh, particularly close to the collapse state of stress. It is to this end that Raveendra (1984) and Banerjee and Raveendra (1987) presented the first direct or ‘non-iterative’, two-dimensional elastoplastic analysis which is comparable to the variable stiffness method in finite element analysis. The method proved successful and has recently been extended to axisymmetric analysis by Henry and Banerjee (1988a) and to the three-dimensional case by Banerjee and Henry (1987) and Banerjee et al. (1988a).
