Stable optimal design of two-dimensional elastic structures

We study optimal layout of piece-wise periodic structures of linearly elastic materials. The effective tensors of these structures are constant within pre-specified regions, the optimality is understood as the minimum of complementary energy. The suggested formulation leads to a construction that is stable under variation of the loading and which does not degenerates into checkerboard type structures. We derive necessary conditions of optimality of such layouts and analyse them. Numerically, we fins optimal structures for a number of examples, which are analyzed.