Bi-directional evolutionary structural optimization with buckling constraints

Buckling is a critical phenomenon in structural members under compression, which could cause catastrophic failure of a structure. To increase the buckling resistance in structural design, a novel topology optimization approach based on the bi-directional evolutionary structural optimization (BESO) method is proposed in this study with the consideration of buckling constraints. The BESO method benefits from using only two discrete statuses (solid and void) for design variables, thereby alleviating numerical issues associated with pseudo buckling modes. The Kreisselmeier-Steinhauser aggregation function is introduced to aggregate multiple buckling constraints into a differentiable one. An augmented Lagrangian multiplier is developed to integrate buckling constraints into the objective function to ensure computational stability. Besides, a modified design variable update scheme is proposed to control the evolutionary rate after the target volume fraction is reached. Four topology optimization design examples are investigated to demonstrate the effectiveness of the buckling-constrained BESO method. The numerical results show that the developed optimization algorithm with buckling constraints can significantly improve structural stability with a slight increase in compliance.