Accounting of cross-sectional deformation of the contour in the calculation of thin-walled rods

Abstract

One of the main hypotheses in the calculation of thin-walled rods theory is the assumption that there is no deformation of the contour of the cross section. However, studies have shown that the denial of the contour deformation in many cases leads to significant errors in the calculations. It is also known that a significant influence on the stress-strain state of thin-walled rods’s section contour has warping. The article describes the general approach for the accounting of these two phenomena, which is based on the formation of the two systems of orthogonal functions that are approximating functions for solvation of the problem by Kantorovich-Vlasov, which allows to determine the stress- strain state of thin-walled rod, taking into account the deformation and warping of section contour. The resulting generalized longitudinal and transverse movements allow to find a force of stress and strain in the rods of any profile.