3D topology optimization of sandwich structures with anisotropic shells

Abstract

The development of a density-based 3D minimum compliance topology optimization approach for sandwich structures with anisotropic shells is presented. A constant thickness shell is enforced at the interface of a base structure through a two-step filtering approach. Homogenous effective properties of a cellular material are assigned to the base structure while the shell is treated as a constant stiffness laminate with anisotropic properties. Local shell normal vectors are obtained from the density gradient introduced in the second filtering step and local material orientations in the shell’s tangent plane are approximated based on the fabrication process of the structure. Simple approximating strategies using the Gauss map are presented for a fabric draping process and the fused filament fabrication additive manufacturing process. The effect of material anisotropy on the optimal topology is studied on the Messerschmitt Bölkow Blohm beam benchmark problem. An application to composite structures is then presented where a square, simply supported laminate is reinforced on one face by a topology optimized sandwich structure. Though manufacturability cannot be ensured in the current implementation, careful consideration of the optimization parameters allow to constrain the problem towards manufacturable solutions using additively manufactured cores.