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 st ructure for minimum compliance. Material properties are represented in the most general form possible for a (locally) linear elastic continu um, 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 p roperties. These results, which apply in general, indicate that the op timized material is orthotropic with the directions of orthotropy foll owing the directions of principal strains. The analysis for optimizati on of the material leads to a reduced structural optimization problem, for which the existence of solutions can be shown and for which effec tive methods for computational solution can be devised.