Speaker
Description
We present a novel numerical method for optimal design problems in the setting of the Kirchhoff-Love model, where the mechanical behaviour of the domain is modeled with fourth order elliptic
equation, and we restrict ourselves to domains filled with two isotropic elastic materials.
Since the classical solution usually does not exist, we use homogenization theory to prove general existence theorems and to provide efficient numerical algorithm for their
computation.
Moreover, we give an explicit calculation of the Hashin-Shtrikman bounds on the complementary energy. They are of a great significance in optimal design problems, since the necessary conditions of optimality are easily derived and expressed via lower Hashin-Shtrinkman bound on the complementary energy. This enables a development of the optimality criteria method for finding an approximate solution.
