The Elastic Stability of Twisted Plates

Abstract

Since Coulomb’s and Saint-Venant’s fundamental work, many researches have studied the effect of twisting on elastic bodies. The work presented here investigates instabilities that can occur when thin bodies are subject to large twists and extends work by A. E. Green published in 1937. Because large twists are considered, a fully nonlinear plate theory is used. This theory predicts compressive lateral membrane stresses not predicted by Green’s weakly nonlinear theory. These stresses can significantly alter the twist angle at which buckling occurs. Two conditions for the opposing twisted end supports are considered. In one case the supports are held a fixed distance apart and in the other case the force applied to the supports is held fixed during twist. The buckling modes and critical twist angles vary significantly depending on the support condition used.