We are concerned with shape optimal design of composite materials with periodic microstructures. The homogenization approach is applied to obtain the computationally feasible macromodel. The microstructural geometrical details of the microcells (such as lengths and widths of the different layers forming the cell walls) are considered as design parameters. Our purpose is to find the best material-and-shape combination in order to achieve the optimal performance of the materials. Our PDE constrained optimization routine is based on the elasticity problem as a state equation and additional equality and inequality constraints which are technically or physically motivated. The discretization of the PDE constrained optimization problem typically gives rise to a large-scale nonlinear programming problem. Primal-dual Newton-type interior-point methods are used for the numerical solution. Numerical experiments are presented and discussed.

(Seminar CMUC-LCM)