Thickness optimization of circular annular plate at buckling

This work deals with thickness optimization of a circular annular plate at buckling. The plate is loaded with uniform, axially symmetric, in-plane loads on the inner and outer edge. The variable thickness of the plate is approximated by a function of radial coordinates and design variables. An optimization problem is defined to find optimal sets of design variables which maximize buckling loads at constant weight/volume of the plate. The required buckling loads are determined according to the standard linear buckling equations, and the material is modelled by the small strain J₂ flow and deformation theories of plasticity where an elastic linear hardening rheological model is considered. Optimal thickness functions are determined for different support and load cases and the numerical results show that buckling loads can be increased significantly.