Topology optimization for maximizing buckling strength using a linear material model

Buckling resistance has gained significant attention in topology optimization due to its profound implications for structural designs. Despite considerable research on buckling-constrained topology optimization, maximizing the critical buckling load factor (BLF) still remains a challenging topic. In this study, an innovative algorithm that utilizes a linear material interpolation scheme is introduced to maximize the buckling resistance of structures. The linear material model offers several advantages, such as obviating the need to select the penalization schemes and penalty values, facilitating straightforward sensitivity analysis, and removing the ambiguous physical meaning of penalization for the stress stiffness matrix. The accuracy of the linear material model for buckling analysis is systematically examined, and the avoidance of stress singularities in low-density regions is investigated. The effectiveness and efficiency of the proposed approach are supported by four buckling optimization design examples, which also demonstrate substantial improvements compared to the existing algorithms.