An analytical model to predict optimal material properties in the context of optimal structural design

This paper deals with the simultaneous optimization of material and structure for minimum compliance. Material properties are represented in the most general form possible for a (locally) linear elastic continuum, namely the unrestricted set of elements of positive semi-definite constitutive tensors and cost measures based on certain invariants of the tensors. Analytical forms are derived for the optimized material properties. These results, which apply in general, indicate that the optimized material is orthotropic with the directions of orthotropy following the directions of principal strains. The analysis for optimization of the material leads to a reduced structural optimization problem, for which the existence of solutions can be shown and for which effective methods for computational solution can be devised.