Layout and shape optimization of elastoplastic disks with bounds on deformation and displacement

A design method is presented for layout optimization of linearly elastic-perfectly plastic disks subjected to multi-parameter loading. The method is based on the static theorem of shakedown analysis and on the concept of porous material, where the material distribution of the discretized structure is described by the densities of the finite elements that are considered design variables. In addition to shakedown, two further compliance constraints are applied: bounds for the complementary strain energy of the residual stresses, and for the residual displacements. By the proper choice of these bounds the plastic behavior of the disk can be controlled and in special cases the elastic and fully plastic optimal solutions can be determined. The formulation of this problem yields to nonlinear mathematical programing. The application is illustrated by numerical examples. The method can also be applied to trusses, frames, and plates.