Dynamic axisymmetric problem of the elasticity theory for a hollow cantilever-fixed cylinder
Published: 25.03.2025
Authors: Shlyakhin D.A., Rakov D.V.
Published in issue: #3(159)/2025
DOI: 10.18698/2308-6033-2025-3-2429
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
The paper presents a new closed solution to the axisymmetric problem for a thick-walled hollow isotropic cylinder in the case of the non-stationary axisymmetric load in the form of the stresses normal to the loading surfaces acting on its end and outer cylindrical surfaces. The cylinder lower face is rigidly fixed (displacements in the radial and axial directions are missing), and the upper face is membrane-fixed in the radial plane. The closed solution is constructed by successively using the one-component integral Fourier transform with respect to the axial variable and the generalized integral transform with respect to the radial coordinate. To implement this approach, the paper uses a procedure of reducing boundary conditions at the ends of the cylinder to the mixed computation relations. The constructed computation algorithm makes it possible to determine the cylinder stress-strain state, as well as to analyze the influence of the loads type and their relations on the displacement and stresses fields.
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