On Member Buckling in Truss Topology Optimization

Abstract

In this paper, member buckling in truss topology optimization is addressed. A solution to the so-called jump in the buckling length phenomenon is proposed. The method relies on binary variables that control the existence of ground structure members. Parallel consecutive members of the ground structure are identified as chains, and overlapping members are added to the ground structure between each pair of points of the chain. Buckling constraints are written for every chain member, and linear constraints on the member existence variables disallow impractical configurations. The proposed approach is demonstrated on an example problem, where the buckling constraints are formulated according to both Euler buckling and the design rules of Eurocode 3. The problem shows that the optimum topology depends on the buckling constraint type.