Multicriteria optimization that minimizes maximum stress and maximizes stiffness

In presenting and discussing structural analysis and design an engineer/analyst is always emphasizing the importance of strength and stiffness and endeavoring to get a balance between them both that suits the design in hand. It seems logical therefore in presenting structural optimization that both these crucial items be objectives of the process rather than having one as the objective and the other as a constraint as has traditionally been the case. It initially feels more appropriate to be trying to maximize stiffness whilst simultaneously maximize the strength. Also the goal of maximizing strength of a structure should, to the authors mind, be in the form of minimizing the maximum stress under all load cases. Traditionally structural optimization has targeted stress equalization or the achievement of “fully stressed” design as the stress objective/constraint. The authors consider that such an objective, especially coupled in with FEA still can lead to high localized stresses which therefore do not improve the strength of the structure. This paper aims at exploring the application of the evolutionary structural optimization method to such multicriteria design problems. To evaluate the overall effect on the design of material variation due to these two optimality criteria, a weighting scheme is adopted, whereby the weight factors emphasize and/or balance the stiffness and stress criteria. The work can accommodate various situations involving shape and topology design with multiple criteria. Also the important practical aspects of possible multiple peak stresses and multiple load cases are taken into account. A number of examples demonstrate the capabilities of the proposed method for solving multicriteria design optimization structural design problems.