Non-stationary contact of a cylindrical shell and perfectly rigid elliptic paraboloid

Аuthors

Mitin A. Y.^1*, Tarlakovsky D. V.^2**, Fedotenkov G. V.^3***

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Institute of Mechanics Lomonosov Moscow State University, 1, Michurinsky prospect, Moscow, 119192, Russia
3. ,

*e-mail: mitin232@hotmail.com
**e-mail: tdvhome@mail.ru
***e-mail: greghome@mail.ru

Abstract

The article studies a strain-stress state of a circular cylindrical shell of the Tymoshenko type and perfectly rigid cylindrical paraboloid in the process of their collision at the supersonic stage of interaction. The process of vertical impact is being considered, where the shell movement is regarded in Cartesian coordinate system. The contact occurs in free sliding conditions.

The problem setting includes equations of the shell motion, and equations of the elliptic paraboloid as a perfectly rigid body, boundary and initial conditions. To solve the problem, influence functions are used for a circular cylindrical shell, which represents normal displacement and is a solution to the initial-boundary problem of the impact on the surface of an elastic shell of normal pressure, given as a product of Dirac delta functions.

A numerical-analytical algorithm for solving the system associated with the inversion of Fourier-Laplace integral transformations, which is based on the bond of Fourier integral with decomposition into a Fourier series on a variable interval, was developed and implemented. Examples of computations are presented.

The goal of the work consists in formulating a spatial non-stationary contact problem for perfectly rigid impactors and a circular cylindrical shell of the Tymoshenko type.

The relevance of the research topic is stipulated in theoretical terms by the small number of studies of spatial non-stationary contact problems. From a practical viewpoint, it is associated with the need to determine the stress-strain state in the process of collision of an perfectly rigid body with a shell structure.

Keywords:

non-stationary contact problems, cylindrical shell of Timoshenko type, integral equations, influence functions

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