Abstract
The problem of elasticity theory for the transversely isotropic hollow cylinder with mixed conditions on the side surface is considered in the paper. Transcendental equations are obtained regarding the eigenvalues of the problem. The roots of the characteristic equations are studied thoroughly. The study of the eigenvalues allowed to establish the essential characteristics of the stress-strain state of an anisotropic shell in comparison with isotropic shells. Homogeneous solutions were built here.
Highlights
The modern theory of shells is deeply developed section of the mechanics of a deformable solid
The calculation of shells on the basis of three-dimensional equations of the theory of elasticity is associated with considerable mathematical difficulties
Suppose that the boundary conditions are given at the cylinder side surface ur = 0, τ rz = 0 for r = rs (s = 1, 2)
Summary
The modern theory of shells is deeply developed section of the mechanics of a deformable solid. The asymptotic methods of integrating the equations of two-dimensional shell theory obtained the great development in A. In the first one the solution of the elasticity problem for thin bodies is carried out by means of direct integration of elasticity equations with the help of two iterative processes. This direction is developed in the works of A.L. Goldenveiser, M.I. HuseynZade, A.V. Kolos [11], [12] and L.A. Agalovyan [13]. Lidski [26] and their followers [27], [28], [29], [13], [30], [31], has made significant contribution to the development of the theory of Magomed Farman Mekhtiyev et al.: The Asymptotic Analysis of the Solution of an Elasticity Theory Problem for a Transversely Isotropic Hollow Cylinder with Mixed Boundary Conditions on the Side Surface plates and shells
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