Optimal design of material properties and material distribution for multiple loading conditions

An extension of recent work1 on the simultaneous optimization of material and structure to address the design of structures under multiple loading conditions is presented. Material properties are represented in the most general form possible, namely, as elements of the unrestricted set of positive‐semi‐definite constitutive tensors of a linearly elastic continuum. Existence of solutions can be shown when the objective is a weighted average of compliances and a resource constraint measured as the 2‐norm or the trace of the constitutive tensors is included. The optimized material properties can be derived analytically. The optimization of the layout of the material leads to a sizing problem of structural optimization involving a non‐linear, non‐smooth elasticity analysis. The computational solution of this problem is discussed and illustrated with examples. Copyright © 1995 John Wiley & Sons, Lt