On variational sensitivity analysis and configurational mechanics

This contribution is concerned with the application of variational design sensitivity analysis in the context of structural optimization and configurational mechanics. In both disciplines we consider variations of the material configuration and we use techniques from variational sensitivity analysis in order to solve these problems. We derive the physical and material residual problem in one step by using standard optimization procedures. Furthermore, we investigate the sensitivity of the physical as well as the material residual problem and obtain the coupled saddle point problem based on these sensitivities. Both problems are coupled by the pseudo load operator, which plays an important role by the solution of structural optimization problems. By means of computational examples from mesh optimization and shape optimization, we demonstrate the capability of the proposed theoretical framework.