On the prediction of extremal material properties for the optimal design of topology, shape and material

This paper describes some recent developments that treat the simultaneous optimization of material and structure for minimum compliance. The basic idea is to represent the material properties for a linear elastic continuum in the most general form possible, namely as the unrestricted set of elements of positive semi-definite constitutive tensors. The cost of resource is measured through certain invariants of the tensors, here the 2-norm or the trace of the tensors. The advantage of this general formulation is that analytical forms for the optimized material properties can be derived and that effective methods for computational solution can be devised for the resulting reduced structural optimization problem. (author)