Two-Dimensional Large Deflection Analysis of Beam with Initial Shape

Abstract

Two-dimensional large deflection of the initially deformed beam is theoretically and numerically analyzed. Effects of the geometrical non-linearity due to thickness and radius of the beam are considered on the derivation of the strain equation. The equilibrium equations are derived by applying non-extensional assumption at the neutral axis as used in the Elastica. The numerical examples are performed to investigate the effects of the ratio of thickness to radius on the total deformations and the ratio of non-dimensional maximum stress of proposed analysis to that of Elastica. The deformation of the beam calculated by the proposed analysis becomes smaller and non-dimensional stress ratio calculated by the proposed analysis becomes larger for larger ratio of thickness to radius.