Multi geometrical scale optimization for porous structure and material with multi-objective of structural compliance and thermal deformation

A new multi-objective optimization formulation is developed for the multi geometrical scale topology optimization of the load carrying spacecraft structures composed of porous ceramic materials, which combines high stiffness with low thermal expansion in a predefined domain. The objective function is composed of two items. One is to minimize the structural compliance when only the mechanical loads are applied on structures, while the other is to minimize the thermal expansion of the outer spacecraft structure surface when only the thermal loads are applied. The two items are both normalized and then jointed through weighted coefficients to form a multi-objective function. The independent macro and micro densities are introduced as the design variables and penalization approaches are adopted in both scales, i.e. SIMP (Solid Isotropic Material Penalization) in micro material scale and PAMP (Porous Anisotropic Material Penalization) in macro structure scale. Optimizations of the two geometrical scales are integrated into one system through homogenization theory. The volume preserving nonlinear density filtering based on Heaviside step function is used to prevent checkerboard patterns and to obtain a clear design. We apply the proposed multi-objective optimization model to a sandwich elliptically curved shell to investigate the concurrent multi-scale design of structure configuration and microstructure of porous ceramic. The numerical examples demonstrate that the porous material is conducive to enhance the multi-objective performances of curve shell structure when the available amount of material is insufficiently given. And an optimum material volume fraction is observed for the multi-objective optimization problem. The influence of thickness of surface sheets on the optimal design is investigated at last.