Worst shapes of imperfections for space trusses with multiple global and local buckling modes

Abstract

The initial postbuckling behavior and imperfection sensitivity of truss-type structures in which the joints do not transmit moments is determined by means of the Lyapunov-Schmidt-Koiter approach. Such structures possess local buckling modes involving the buckling of individual members, and global modes involving axial deformations of all members but no member buckling. Of particular interest is the case in which through optimization (or otherwise) a number of local and global modes are coincident. The worst shape of imperfection for this case is determined from the bifurcated equilibrium branch on which the load drops most rapidly. It is shown that this critical bifurcated branch initially involves the buckling of one member only. The general theory is illustrated by a number of examples involving two- and three-dimensional lattice columns. The leading order asymptotic results for these examples are compared to exact results obtained by tracking the appropriate equilibrium branch numerically.