OPTIMAL-DESIGN OF MATERIAL PROPERTIES AND MATERIAL DISTRIBUTION FOR MULTIPLE LOADING CONDITIONS

An extension of recent work(1) on the simultaneous optimization of mat erial 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 unrestri cted set of positive-semi-definite constitutive tensors of a linearly elastic continuum. Existence of solutions can be shown when the object ive is a weighted average of compliances and a resource constraint mea sured as the 2-norm or the trace of the constitutive tensors is includ ed. 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 elastici ty analysis. The computational solution of this problem is discussed a nd illustrated with examples.