Worst shapes of imperfections for space trusses with many simultaneously buckling members

Abstract

Optimally designed truss type structures whose joints do not transmit moments often have a large number of coincident buckling modes. Each mode corresponds to the buckling of an individual member. Due to the interaction between various simultaneous modes, such trusses can be sensitive to imperfections. This problem is analysed using the Lyapunov-Schmidt-Koiter decomposition and asymptotic expansion technique. The shape of the imperfection that maximizes the load drop is determined from the postbifurcated equilibrium branch of the perfect structure on which the load drops most rapidly. It is shown that this branch is obtained by minimizing a homogeneous quadratic form subject to linear inequality constraints. The general theory is illustrated by several examples involving two- and three-dimensional trusses.