Structural optimization with a non-smooth buckling load criterion

This work addresses problems in optimal design of structures with a non-smooth buckling load criterion and in particular applications in layout design of plate reinforcements using a material based model and thickness beam optimization problems. Starting with the formulation of the linearized buckling problem, the optimization problem is formulated and the optimal necessary conditions are derived. Considering the possibility of non-differentiability of the objective function, the optimal necessary conditions are stated in terms of generalized gradients for non-smooth functions. The importance of the obtained result is analyzed and directional derivatives of the critical load factor obtained from the generalized gradient set definition, are compared with forward finite difference approximations. Optimization applications, to test the developments done, are presented. They are performed using a mathematical programming code, the Bundle Trust Method, which addresses the non-smoothness of the problem.