On the prediction of material properties and topology for optimal continuum structures

A new formulation is presented for mathematical modelling to predict material properties for the optimal design of continuum structures. The method is based on an extended form of an already established characterization for continuum design, where the material properties tensor for an arbitrary structural continuum appears as the design variable. The extension is comprised of means to represent an independently specified unit relative cost factor , which appears simply as a weighting function in the argument of the isoperimetric (cost) constraint of the original model. A procedure is demonstrated where optimal black/white topology is predicted out of a sequence of solutions to material properties 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 the total element area in the system has material property density off the 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 topology design problems. Results are presented for 2D examples of both types of problem. In addition to the treatment for (the usual) minimum compliance design, an alternate formulation of the design problem is presented as well, one that provides for the prediction of optimum topology with a generalized measure of compliance as the objective.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46075/1/158_2005_Article_BF01812523.pd