A non-linear thin-walled beam theory

Abstract

A non-linear thin-walled beam theory for elastic beams of open section is presented. The theory takes into account geometric non-linearities and longitudinal deformations caused by large cross-sectional rotation of the beam. The non-linear differential equations are derived by the minimum potential energy principle. The boundary conditions associated with the differential equations are obtained. It is shown that the set of equations reduces to the linear theory of Vlasov if non-linear terms are neglected. Also, the set of equations admits a simple solution in the special cases of large uniform torsion of thin-walled members of open cross-section. The torque-rotation relationship and axial strain-rotation relationship thus obtained are identical to the results obtained by Cullimore and Gregory.