Study of constrained torsion of thin-walled open profile rods using the asymptotic splitting method

The problem of constrained torsion of thin-walled rods under the action of an end torque is considered. Using the asymptotic splitting method, a system of resolving equations was obtained that describes the combined torsion, tension-compression, and bending of the rod. To test the resulting model using the example of typical sections, a comparison was made of the stress-strain state in the rod, determined in the calculation using the developed model and three-dimensional numerical calculation by the finite element method. The resulting mathematical model was analyzed and its advantages compared to the widely used Vlasov theory were revealed. It is shown that the developed model does not contain the restrictions imposed by the hypotheses in the Vlasov theory, such as the non-deformability of the transverse contour and the absence of shear deformations on the middle surface. In a number of cases, the resulting model makes it possible to more accurately determine the emerging stress-strain state. In particular, it is shown that the developed model takes into account the presence of a boundary layer near the embedment, which arises during torsion of corner sections and makes a significant contribution to longitudinal stresses, while Vlasov's theory does not allow one to restore the arising longitudinal stresses.