ANALYSIS OF THE STRESS-STRAIN STATE OF A CANTILEVER PLATE WITH A LINEAR BEARING CONNECTION
Abstract
A methodology for solving a spatial problem of elasticity theory for a slab with a rigid embedded cylindrical fixation and a bearing connection is proposed. The computational model is represented as a layer with a longitudinal cylindrical cavity and a longitudinal cylindrical thick-walled pipe. Stresses are specified at the upper and lower boundaries of the layer, displacements are specified on the surface of the cavity, and contact-type conditions are specified on the inner surface of the pipe. The layer and the pipe are rigidly connected to each other. The solution to the problem is presented in the form of the Lamé equation in different coordinate systems: the layer is considered in the Cartesian system, the cavity and the pipe in the local cylindrical system. To combine the basic solutions of the Lamé equation between different coordinate systems, the generalized Fourier method is used. The infinite system of integro-algebraic equations arising from the boundary conditions is analytically reduced to linear algebraic equations of the second kind, which allows us to apply the method of reduction to it. When solving it numerically, the accuracy of the results directly depends on the degree of approximation of the boundary surfaces to each other and the order of the system of equations. By solving the system of equations, the unknown Lamé equations are found, which makes it possible to obtain displacements and stresses at any point of the body with high accuracy. A numerical analysis of the stress-strain state was performed, during which the stress distribution was obtained in places of their concentration: around the cavity, pipe, at the upper and lower boundaries of the layer. The results give an idea of the load on the bearing mechanism, the distribution of stresses along them, and the dependence on the layer material. From the numerical studies, it can be concluded that a slab with dimensions in width and length greater than the distance from the support to the cantilever load can be represented by the proposed model. The developed method allows engineers to obtain highly accurate results of the stress-strain state when calculating the strength of bearing assemblies with different materials and geometries. This makes it possible to optimize structures and ensure their reliability.
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Miroshnikov, V. Yu., Pelykh, V. P., & Denshchykov, O. Yu. (2024). Analysis of the stress state of a layer with two cylindrical swivel joints and a cylindrical cavity. Journal of Mechanical Engineering – Problemy Mashynobuduvannia, 27(2), 25–35. https://doi.org/10.15407/pmach2024.02.025
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Denshchykov, O. Yu., Pelykh, V. P., Hrebeniuk, Ya. V., & Mirosh¬nikov, V. Yu. (2024). First Basic Problem of Elasticity Theory for a Composite Layer with Two Thick-Walled Tubes. Journal of Mechanical Engineering – Problemy Mashynobuduvannia, 27(4), 40–50. https://doi.org/10.15407/pmach2024.04.040
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DOI: https://doi.org/10.32620/oikit.2025.104.06
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