Abstract
This paper has presented an exact analytical solution of the flat pure bending problem of a multilayer wedge-shaped console consisting of an arbitrary number of wedge-shaped rigidly connected layers. It is assumed that the console is deformed elastically, and its layers are made of orthotropic or isotropic homogeneous materials. The problem is solved by the methods of linear theory of elasticity using a continuous approach, in which the multilayer console is considered as a continuous body with variable in the transverse direction mechanical characteristics of the material. This has allowed to obtain generalized relations for the components of the stress-strain state immediately for the whole package of layers. The solution of the problem is reduced to the definition of an unknown continuous function of tangential stress distribution in cylindrical cross-sections of the console. The defining equation is obtained for this function, the main types of solutions for homogeneous orthotropic and isotropic layers are investigated. As a special case, a homogeneous orthotropic and isotropic wedge is studied, for which closed relations for stresses and displacements are obtained. The correspondence to the known solution for a homogeneous isotropic wedge is shown. The obtained solution can be directly used to predict strength and stiffness of multilayer beams of variable cross-section, to solve other bending problems of such elements, as well as to verify the accuracy of approximate calculation methods.
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Koval’chuk, S., Goryk, O., Antonets, A. (2023). Exact Analytical Solution of the Pure Bending Problem of a Multilayer Wedge-Shaped Console. In: Altenbach, H., et al. Advances in Mechanical and Power Engineering . CAMPE 2021. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-18487-1_18
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DOI: https://doi.org/10.1007/978-3-031-18487-1_18
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