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One Approach to the Plane Problem on Impact of Timoshenko-Type Shells on Elastic Half-Space

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Abstract

The article presents an attempt to solve the plane problem on the impact of an elastic Timoshenko shell on an elastic half-space using the method of reducing problems of dynamics to the solution of a Volterra’s infinite system of integral equations (ISIE) of the second kind. It is shown that such an approach is not acceptable. When discretizing the reduced Volterra’s ISIE of the second kind, a poorly defined system of linear algebraic equations is obtained: as the reduction order increases, the determinant of such a system tends to infinity. This circumstance shows the limitations of this approach.

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Authors and Affiliations

  1. Progressive Research Solutions Pty Ltd, Sydney, Australia

    V. R. Bogdanov

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Correspondence to V. R. Bogdanov.

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Translated by A. Borimova

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Bogdanov, V.R. One Approach to the Plane Problem on Impact of Timoshenko-Type Shells on Elastic Half-Space. Mech. Solids 58, 1126–1136 (2023). https://doi.org/10.3103/S002565442360037X

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  • DOI: https://doi.org/10.3103/S002565442360037X

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