Optimal material layout for 3D elastic structures: Fid-Bau Portal

Optimal material layout for 3D elastic structures

Diaz, A. / Lipton, R.

The optimal layout of two linearly elastic materials in a three-dimensional domain is considered. The goal is to find the least compliant design subject to a constraint on the amount of available stiff material. For reasons of well-posedness and computational tractability, it is known that problems of this type require relaxation. It follows from the theory that relaxation is needed as optimal designs are frequently approached by minimizing sequences of layouts possessing infinitely fine layerings of two materials (see Cherkaev and Lurie 1986; Murat and Tartar 1985). For the three-dimensional elasticity problem a partial relaxation strategy was presented by Suzuki and Kikuchi (1991). There, the parameterization of the design space was achieved using three variables to characterize the local anisotropy of the material. The optimization problem consisted of finding the optimum spatial distribution of these variables subject to a constraint on the total amount of material. The formulation presented here has the advantage of using only one local design variable per element in the global problem. Its main disadvantage is that a six-dimensional local optimization problem must be solved for each element in the model. Fortunately, however, experience suggests that it may be possible to predict the solution to the local problem by studying constraint activity. This would result in significant savings in computations. Work in this area and in the solution of problems with multiple load cases is in progress.