Stress-constrained topology optimization of multi-scale structures made of triply periodic minimal surface (TPMS) lattices

AbstractThis paper proposes a method for the stress-constrained topology optimization of structures made of sheet-network, triply periodic minimal surface (TPMS) lattices that can be realized through Additive Manufacturing (AM). The proposed method simultaneously designs the topology of the macro component and the thickness distribution for the lattice. To efficiently predict the stress in the TPMS lattice, we employ surrogates of the stress for TPMS lattices, which enables the use of a solid mesh made of a homogenized material for the analysis of the component. The surrogates consist of an ensemble of polynomial approximations of the stress components in the unit cell of the lattice subject to unit loads. Using linear superposition, the stresses at each element centroid of the component mesh are subsequently used in conjunction with the surrogates to obtain the element stresses for a unit cell. As in aggregation techniques used in stress-constrained topology optimization, the maximum stress is obtained via a differentiable approximation. The aggregation is performed at two levels: one to obtain the maximum unit cell stress for each element of the component mesh, and another to obtain the largest stress in the component. To validate the proposed method, the proposed method is used to design 2-dimensional and 3-dimensional structures made of TPMS lattices. The results show that the proposed method can effectively create lightweight designs while satisfying the imposed stress limits.