Adaptive load incrementation in elastic-plastic finite element analysis - Tracey, Dennis M.; Freese, Colin E. (Computers & structures, 1981)
The paper presents a strategy to control load path discretization error in elastic-perfectly plastic finite element analysis. The load path discretization is included as part of the nonlinear problem, using the strategy. At each stage in the incrementation, the load step size is treated as a variable which is forced to adapt to the current structural stiffness gradient. The step size is determined during the numerical solution, using a selection criterion which restricts changes in yield surface stress state at points within the plastic zone. The strategy has been developed for a particular, assumed displacement, “incremental secant stiffness” formulation. The formulation per se is not new; it has been presented by Rice and Tracey [1]. Average stiffnesses are used to account for elastic-plastic boundary and flow rule changes during the step. The formulation is examined in detail, to allow discussion of the approximations which are made and also to guide implementation. The 2D problems of plane stress, plane strain and axisymmetric deformation are considered. Simple test solutions are used to demonstrate that solution error can be effectively monitored by the yield surface deviatoric stress change, and this suggests the step size selection criterion that is employed. A new solution algorithm for adaptive incrementation is the major contribution of the paper. With the algorithm, the nonlinear incremental secant equilibrium equation is solved subject to the selection criterion which is viewed as a constraint condition on the nodal variables. It appears that the algorithm could be used to advantage in other structural mechanics problem areas.