Resolving issues with member buckling in truss topology optimization using a mixed variable approach

Abstract

In this paper, several issues related to member buckling in truss topology optimization are treated. In the conventional formulations, where cross-sectional areas of ground structure members are the design variables, member buckling constraints are known to be very difficult to handle, both numerically and theoretically. Buckling constraints produce a feasible set that is non-connected and non-convex. Furthermore, the so-called jump in the buckling length phenomenon introduces severe difficulties for determining the correct buckling strength of parallel consecutive compression members. These issues are handled in the paper by employing a mixed variable formulation of truss topology optimization problems. In this formulation, member buckling constraints become linear. Parallel consecutive members of the ground structure are identified as chains, and overlapping members are added to the ground structure between each pair of nodes of a chain. Buckling constraints are written for every member, and linear constraints on the binary member existence variables disallow impractical topologies. In the proposed approach, Euler buckling as well as buckling according to various design codes, can be incorporated. Numerical examples demonstrate that the optimum topology depends on whether the buckling constraints are derived from Euler's theory or from design codes.