Multi-Scale Topological Design of Structural Materials: An Integrated Approach

The present dissertation aims at addressing multiscale topology optimization problems. For this purpose, the concept of topology derivative in conjunction with the computational homogenization method is considered. In this study, the topological derivative algorithm, which is non standard in topology optimization, and the optimality conditions are first introduced in order to a provide a better insight. Then, a precise treatment of the interface elements is proposed to reduce the numerical instabilities and the time-consuming computations that appear when using the topological derivative algorithm. The resulting strategy is examined and compared with current methodologies collected in the literature by means of some numerical tests of different nature.