Toward the problem of static deformations in curvilinear rods
The article presents expressions for deformation tensor components, potential energy, differential equations, and boundary conditions as applied to a curvilinear rod with axis curved along a circle of given radius and subject to the effect of concentrated tensile and bending loads. Analytical solutions of three boundary value problems on bending and tension of a cantilever rod with axially constant cross section are given under some simplifying assumptions. Characteristics of the stress-strain state of curvilinear rods are noted for various methods of loading.
KeywordsBoundary Condition Differential Equation Potential Energy Static Deformation Tensor Component
Unable to display preview. Download preview PDF.
- 1.L. D. Magomaev, “Toward the theory of rods with curvilinear axis,” Prikl. Mekh.,20, No. 4, 68–74 (1984).Google Scholar
- 2.Yu. S. Vorob'ev and B. F. Shorr, The Theory of Rods in Torsion [in Russian], Naukova Dumka, Kiev (1983).Google Scholar
- 3.Yu. S. Vorob'ev, “Bending of a rod by accounting for warping under shear and torsion,” Din. Prochn. Mash., Issue 1, 125–131 (1965).Google Scholar
- 4.L. D. Magomaev, “Toward determination of deformation parameters of prismatic rods,” Probl. Prochn., No. 10, 82–90 (1986).Google Scholar
- 5.A. I. Lur'e, The Theory of Elasticity [in Russian], Nauka, Moscow (1970).Google Scholar