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The torsion of the conical layered elastic cone

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Abstract

An infinite conic layered cone which represents the sequence of conical adjacent funnels, inserted one into another, is considered. Each of these funnels differs by their shear modulus. Conditions of an ideal contact are fulfilled between the adjacent conical surfaces. An external conical surface is loaded by tangent torsion stress. An exact solution of the corresponding one-dimensional boundary problem is constructed in the domain of Mellin’s transformation, which is applied directly to the torsion equation. A formulation of boundary conditions in matrix form allows to obtain recurrent-type relations for unknown constants of a general solution for each layer. The proposed solving method leads to the exact solution which is independent of the layers’ number. Mellin’s transformation is inversed to finish the construction of the formulas for displacements and stress. The detailed elaboration of the proposed approach is done for two particular cases: a cone without stratification and a two-layered cone.

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Authors and Affiliations

  1. Institute of Mathematics, Economics and Mechanics, Odessa Mechnikov University, str. Dvoryanskaya, 2, Odessa, 65082, Ukraine

    G. Popov & N. Vaysfel’d

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  1. G. Popov
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  2. N. Vaysfel’d
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Correspondence to N. Vaysfel’d.

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Popov, G., Vaysfel’d, N. The torsion of the conical layered elastic cone. Acta Mech 225, 67–76 (2014). https://doi.org/10.1007/s00707-013-0957-4

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  • DOI: https://doi.org/10.1007/s00707-013-0957-4

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