ON THE PREDICTION OF MATERIAL PROPERTIES AND TOPOLOGY FOR OPTIMAL CONTINUUM STRUCTURES

A new formulation is presented for mathematical modelling to predict m aterial properties for the optimal design of continuum structures. The method is based on an extended form of an already established charact erization for continuum design, where the material properties tensor f or an arbitrary structural continuum appears as the design variable. T he extension is comprised of means to represent an independently speci fied unit relative cost factor, which appears simply as a weighting fu nction in the argument of the isoperimetric (cost) constraint of the o riginal model. A procedure is demonstrated where optimal black/white t opology is predicted out of a sequence of solutions to material proper ties design problems having this generalized cost formulation form. A systematic adjustment is made in the unit relative cost field for each subsequent solution step in the sequence, and at the stage identified with final topology, no more than a small fraction of a percent of th e total element area in the system has material property density off t he bounding ''black'' or ''white'' levels. This technique is effective for the prediction of optimal black/white topology design for design around obstacles of arbitrary shape, as well as the more unusual topol ogy design problems. Results are presented for 2D examples of both typ es of problem. In addition to the treatment for (the usual) minimum co mpliance design, an alternate formulation of the design problem is pre sented as well, one that provides for the prediction of optimum topolo gy with a generalized measure of compliance as the objective.