An improved approach for determining the optimal orientation of orthotropic material

Abstract

Several approaches for determining the optimal orientation in the topological optimization process are discussed in this paper. It is shown that the use of a strain based method may give an even worse result than the case in which the discrete orientational variables are fixed in the optimization process, because strong couplings exist among the orientational variables when the strain field is used. The stress field is less sensitive than the strain field with respect to the variations of the orientational variables. Therefore, the coupling between the orientational variables is relatively weak when the stress field is used. This explains why the stress based approaches (e.g. Suzuki and Kikuchi 1991; Díaz and Bendsøe 1992) are more efficient than the strain based method. This kind of approach will be generalized to deal with more general optimization problems. It will be shown that the new approach can not only obtain the best result for the problem as compared to the other methods, but also has the generality for various optimization problems. Several examples will be presented to support the above statements.