Topology Optimization for Minimum Compliance with Material Volume and Buckling Constraints under Design-Dependent Loads

Stability is a critical factor in structural design. Although buckling-constrained topology optimization has been investigated in previous work, the problem has not been considered under design-dependent loads. In this study, a model of buckling constraints in topology optimization problems under design-dependent loads was proposed to solve the above problem. First, the Kreisselmeier-Steinhauser aggregation function was employed to reduce multiple constraints to a single constraint. Then, the problem was sequentially approximated using the optimality criteria method tailored to update the variables. After that, a gradient-based optimization algorithm was established based on finite element and sensitivity analyses for the topology optimization problem with design-dependent loads. Finally, four numerical examples with design-dependent loads were comparatively analyzed, with and without bucking-constrained solutions. The calculation results proved the effectiveness and reliability of the optimization algorithm. Therefore, in this study, it was suggested that the developed optimization algorithm gained improved applicability.

Automated summary

Stability is critical in structural design. This study proposes a model to solve the problem of buckling-constrained topology optimization under design-dependent loads. The Kreisselmeier-Steinhauser aggregation function is used to reduce multiple constraints to a single one. The proposed optimization algorithm, based on finite element and sensitivity analyses, is proven effective and reliable through numerical examples.