Two-scale optimization of graded lattice structures respecting buckling on micro- and macroscale

Abstract

Interest in components with detailed structures increased with the progress in advanced manufacturing techniques in recent years. Parts with graded lattice elements can provide interesting mechanical, thermal, and acoustic properties compared to parts where only coarse features are included. One of these improvements is better global buckling resistance of the component. However, thin features are prone to local buckling. Normally, analyses with high-computational effort are conducted on high-resolution finite element meshes to optimize parts with good global and local stability. Until recently, works focused only on either global or local buckling behavior. We use two-scale optimization based on asymptotic homogenization of elastic properties and local buckling behavior to reduce the effort of full-scale analyses. For this, we present an approach for concurrent local and global buckling optimization of parameterized graded lattice structures. It is based on a worst-case model for the homogenized buckling load factor, which acts as a safeguard against pure local buckling. Cross-modes residing on both scales are not detected. We support our theory with numerical examples and validations on dehomogenized designs, which show the capabilities of our method, and discuss the advantages and limitations of the worst-case model.

Bisection Constraint Method for Multiple-Loading Conditions in Structural Topology Optimization

“…The application of this method to TO was proposed by Jaouadi in 2015 [58]. In a recent study from 2023, Hübner et al [59] employed the epsilon-constraint method to solve multi-objective two-scale sizing optimization problems. However, in the epsilon-constraint method, the necessity of giving the epsilon values by users, which requires a certain understanding of all scenarios of the problems, leads to difficulty in method implementation, and the method remains somewhat subjective.…”