Abstract
A new method for analysis of stress-strain state in elastic cylindrical toroidal shells is put forward, whereby forces and displacements are chosen as unknown functions. The method enables a study of the bend ovalization phenomenon that occurs when three-dimensional bending moments are applied. The authors have derived geometrical equations relating displacement components and strains, and introduced smallness hypothesis, which makes it possible to neglect some combinations of displacements during the shell deformation analysis. The Karman hypothesis of nondeformability of a pipe median surface is demonstrated to be applicable only after the circumferential force is excluded from equilibrium equations. The authors have established the limits of applicability of the solutions obtained, depending on the order of approximation of the flexibility parameter. Beam differential equations have been derived for a curvilinear bar, which relate angles of rotation and center-line displacements with applied loading factors. The results obtained are compared to those reported elsewhere.
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Orynyak, I.V., Radchenko, S.A. A Mixed-Approach Analysis of Deformations in Pipe Bends. Part 1. Saint-Venant Three-Dimensional Bending. Strength of Materials 36, 238–259 (2004). https://doi.org/10.1023/B:STOM.0000035758.63004.07
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DOI: https://doi.org/10.1023/B:STOM.0000035758.63004.07