Analysis and Continuum Topology Optimization of Periodic Solids with Linearized Elastic Buckling Criterion

摘要

A methodology for a linearized elastic buckling analysis based on a two-scale asymptotic method for periodic materials is generalized to three-dimensional case and implemented at microscale level. The present two-scale method provides a set of uncoupled problems for the linearized elastic stability analysis at the macroscale and the microscale material levels respectively. For the micro-scale level problem, it is considered an infinite and periodic structured medium for a given average (at the macroscale level) strain. Using the Floquet-Bloch wave theory within the finite element method and a continuum topology optimization problem, implicitly assuming repetitive cells, the minimum critical budding strain is obtained and maximized while the cell volume fraction is kept constant. The performance of the implemented methodology is tested for different cases. Results obtained with finite repetitive medium for periodic open cells versus closed cells keeping the same cell volume fraction are discussed.