Topology optimization of continuum structures for buckling resistance using a floating projection method

Buckling resistance is crucial in structural design. This study addresses challenges associated with enhancing buckling resistance through topology optimization, focusing on avoiding incorrect buckling analyses and reducing reliance on parameter tuning. To eliminate pseudo buckling modes in low-density elements, this research employs a linear material model and a stress relaxation function, demonstrating its effectiveness in mitigating pseudo modes. Additionally, a novel local stress relief strategy is proposed to avoid spurious localized modes caused by stress singularities or concentrations, particularly near applied loads and constrained nodes. The study also introduces a reformulated problem statement for buckling-constrained optimization that separates the critical buckling load factor (BLF) from the aggregation function, allowing the use of a small aggregation factor for the Kreisselmeier‐Steinhauser function. This reformulation effectively prevents the influence of aggregation parameters on the accuracy of the critical BLF approximation and enhances optimization stability by avoiding mode switching. The effectiveness of the proposed algorithm is validated through both BLF maximization and buckling-constrained problems. A series of 2D and 3D examples demonstrate that the proposed algorithm requires minimal parameter tuning across various challenging cases, achieving stable convergence and satisfactory objective values while accurately meeting constraints. Additionally, the algorithm produces smooth designs that are conducive to manufacturing.