Optimum material design of minimum structural compliance under seepage constraint

In filtration and chemical engineering industry the load carrying capacity and seepage performances are very important for a successful filter design. We study a two-scale structural design optimization problem to minimize structural compliance under given seepage flow rate and material porosity constraints. Structural size, shape and topology are given because of other functional requirements. Structural material used is macro homogeneous porous material with periodic microstructure and is to be designed. Since structural compliance and seepage performances in macro-scale are implicit functions of material microstructural topology, it becomes a two-scale design optimization problem. The cross scale sensitivities are derived by the adjoint method. A new volume preserving nonlinear density filter is proposed which makes the process of optimization iteration more stable. The optimization problem is solved by Globally Convergent Method of Moving Asymptotes (GCMMA). Examples under the equality constraints of different seepage flow rate are presented to illustrate the effectiveness of two-scale design optimization formulation and solution approach.