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

Abstract

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.

Keywords

• topology optimization
• linearized buckling
• buckling constraint
• design-dependent loads