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A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2019-7pp.1030-1041

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V.L. Prisekin and G.I. Rastorguev, "Bending and Cramped Torsion of Thin-Walled Rods," Mech. Solids. 54 (7), 1030-1041 (2019)
Year 2019 Volume 54 Number 7 Pages 1030-1041
DOI 10.3103/S0025654419070045
Title Bending and Cramped Torsion of Thin-Walled Rods
Author(s) V.L. Prisekin (Novosibirsk State Technical University, pr. K. Marksa 20, Novosibirsk, 630073 Russia)
G.I. Rastorguev (Novosibirsk State Technical University, pr. K. Marksa 20, Novosibirsk, 630073 Russia, rastorguev@adm.nstu.ru)
Abstract The derivation of the equilibrium equations of bending and torsion of a thin-walled rod with an arbitrary contour of the cross section is given. The structural elements of the rod, represented by longeron and stringer belts, have tensile-compressive rigidity, and the panels perceive only shear. Panels connect the belts, which ensures joint deformation of all elements of the rod. The movement of the belts is determined by the hypothesis of flat sections. With tight torsion, the movements of the belts depend on the geometric parameters and may not coincide with the plane of the cross section. Only the torque acts on the rod, in this case, the internal forces in the belts satisfy the equations: the sum of the forces and the sum of the bending moments are zero. The rank of the matrix of equations is three, therefore, it is proposed in the work to form groups with a different number of belts, and for each of them to form equilibrium equations for the constrained torsion of a thin-walled rod. This is a peculiar form of belt equilibrium equations. Examples of rod’s torsion are considered.
Keywords wing, thin-walled rod, the hypothesis of plane sections, the hypothesis of nondeformability of the contour of the cross section, deplanation, the equation of equilibrium, bending, constrained torsion
Received 05 October 2018
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