A symmetric formulation in non-associated plasticity

Abstract

An elastoplastic model with a non-associated law is used in the analysis of many structural problems. In non-associated plasticity the system of equations of the tangential stiffness method is non-symmetric. This inconvenience can be overcome by denning a new material, with associated law, equivalent to the initial one. In this case the system of equations becomes symmetric. In the method presented here this symmetric system is modified, with the nonlinear part of the stiffness matrix being transferred to the load vector, and the resulting system being solved by an iterative process. A numerical example is given and the results obtained by this method are compared with those given by the initial stiffness method. Comparisons are also made in terms of CPU time, showing that the method presented uses considerably less time than does the initial stiffness method.