Lattice structure design optimization under localized linear buckling constraints

Abstract

An optimization method for the design of multi-lattice structures satisfying local buckling constraints is proposed in this study. In order to resolve the highly nonlinear large-scale optimization problem, a consecutive numerical approach is devised: macro-field optimization and microstructure embedding. The macro-field optimization finds an optimal elasticity tensor distribution among all feasible elastic continua based on a concept of free material optimization (FMO), which largely extends the design space compared with density-based topology optimization. After this, by an inverse design approach that approximates the elasticity tensor under local buckling constraint, an appropriate lattice structure is able to be embedded within each macro-element, where the local stress tensors are considered in particular to produce more reasonable microstructures. During the process, a machine learning approach is also devised to significantly reduce the number of material/lattice types and thus the overall computational costs. Ultimately, a lattice structure under requirements of overall stiffness and local buckling resistance is produced, as demonstrated via numerical examples.