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

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...

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Bibliographic Details
Published in:Mechanics of solids 2023-08, Vol.58 (4), p.1126-1136
Main Author: Bogdanov, V. R.
Format: Article
Language:English
Subjects:
Classical Mechanics
Elastic half spaces
Integral equations
Linear algebra
Mathematical analysis
Physics
Physics and Astronomy
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Summary: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.
ISSN:0025-6544
1934-7936
DOI:10.3103/S002565442360037X