Structural topology optimization for maximum linear buckling loads by using a moving iso-surface threshold method

This paper investigates topology design optimization for maximizing critical buckling loads of thin-walled structures using a moving iso-surface threshold (MIST) method. Formulation for maximizing linear buckling loads with additional constraints on load-path continuity and lower bound of eigenvalue is firstly presented. New physical response functions are proposed and expressed in terms of the strain energy densities determined in the two-steps of finite element buckling analysis. A novel approach by introducing a connectivity coefficient is developed to ensure continuity of effective load-path in optimum topology. The lower bound of eigenvalue is defined to eliminate spurious localized buckling modes. The MIST algorithm and its interfaces with commercial finite element (FE) software are given in detail. Numerical results are presented for topology optimization of plate-like structures to maximize critical buckling forces or displacements considering in-plane and out-of-plane buckling respectively. The FE analyses of the re-meshed final solid topologies with and without void material reveal that the presence of the void material has a significant effect on the out-of-plane buckling loads and a minor influence on the in-plane buckling loads.