Topology optimization of trusses considering global stability and member buckling

Abstract

Ensuring stability in the practical application of optimized trusses is essential. Conventional optimization formulations use cross-sectional areas and axial force of members as design variables, but imposing member buckling constraints results in a concave feasible set, making the problem challenging to solve. Additionally, unstable nodes within continuous parallel compressive members complicate the determination of buckling strength. Here, we present an algorithm named evolutionary truss optimization (ETO) to address both global instability and member buckling issues. Initially, a convex semidefinite constraint is integrated into the optimization framework to ensure global stability and resolve challenges posed by unstable nodes, ensuring accurate buckling lengths of members. Subsequently, the concave optimization problem is transformed into a series of convex optimization problems by iteratively linearizing member buckling constraints, mitigating convergence issues. Optimization results from two numerical examples show that the proposed method ensures both the global stability and member stability. Its effectiveness is validated through comparisons with results from existing algorithms.