Optimal design of elastic-plastic structures with post-critical behaviour

This work deals with the optimal design of nonlinear structures where both geometric and path-dependent material nonlinearities are considered. Postcr itical behaviour is allowed. Critical and postcritical constraints are cons idered. Constraints on local and global stability have been introduced. The classical critical load constraint against global instability is given wit h numerical advantage by a new method using a displacement constraint. The total Lagrangian description and a continuum variational formulation are us ed for the response and design sensitivity analysis. A continuation algorit hm is used to implement the post-critical path. The path-dependent sensitiv ity problem is addressed by an incremental strategy. A direct differentiati on approach is used to derive the response sensitivities with respect to bo th cross-section and configuration design. A finite element technique model s the structure. A mathematical programming approach is used for the optimi zation process. Numerical examples are performed on three-dimensional truss structures.