Distortional analysis of thin walled beams

Abstract

A general solution for the stress-deformation analysis of interconnected plates subjected to general loading conditions is developed. The solution is based on the assumptions of thin-walled plate theory and is limited to combinations of straight plates made of linearly elastic isotropic material. The principle of stationary potential energy is used in conjunction with series expansion for the displacement fields to formulate the equilibrium conditions and boundary conditions. In general, the differential equilibrium equations are coupled. A quasi-closed form solution for the displacement fields is nonetheless provided. The solution developed is successfully adopted to solve several example problems. Three of the problems involve individual plates, while six involve multiply connected plates. Comparisons with established finite element solutions demonstrate the ability of the model to accurately capture the behaviour with a remarkably small number of degrees of freedoms.