Variational design sensitivity analysis in the context of structural optimization and configurational mechanics

Variational design sensitivity analysis is a branch of structural optimization. We consider variations of the material configuration and we are interested in the change of the state variables and the objective functional due to these variations. In the same manner in configurational mechanics we are interested in changes of the material body. In this paper, we derive the physical and material residual problem by using standard optimization procedures and we investigate sensitivity relations for the physical and material problem. These sensitivity relations are used in order to solve the coupled physical and material problem. Both problems are coupled by the pseudo load operator, which play an important role for the solution of structural optimization problems. Furthermore, we derive explicit formulations for the variations of the physical and material problem and propose different solution algorithms for the coupled problem.