On solving static contact problems for a semi-strip stamp on an anisotropic composite

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Abstract

For the first time, the exact solution of the static contact problem of the frictionless action of a rigid die in the form of a semi-strip on an anisotropic multilayer composite material is constructed by the block element method. Previously, these important tasks in structural engineering practice, electronics, physics, and other fields were not solved. The difficulty in solving these contact problems with anisotropy, in comparison with the isotropic case, consists in the difficulty of describing the spectral properties of such mathematical objects as Green's functions and symbols of integral equations. Using existing numerical methods, it is possible to describe the behavior of the concentration of contact stresses at the stamp boundary in cases of isotropic materials. However, it was not possible to construct an accurate solution for the distribution of contact stresses in the anisotropic case under a semi-strip stamp, together with features at the boundary. For the first time, a solution was constructed reflecting the real distribution of contact stresses and their concentrations under the stamp. The solution obtained in the work tends to the solutions obtained for a strip or a quarter of the plane when the semi-strip degenerates into these areas.

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V. A. Babeshko

Kuban State University; Southern Scientific Center of the Russian Academy of Sciences

Author for correspondence.
Email: babeshko41@mail.ru

Academician of the RAS

Russian Federation, Krasnodar; Rostov-on-Don

O. V. Evdokimova

Southern Scientific Center of the Russian Academy of Sciences

Email: babeshko41@mail.ru
Russian Federation, Rostov-on-Don

O. M. Babeshko

Kuban State University

Email: babeshko41@mail.ru
Russian Federation, Krasnodar

V. S. Evdokimov

Kuban State University

Email: babeshko41@mail.ru
Russian Federation, Krasnodar

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2. Fig. 1. The half-strip stamp extends to infinity only on the right.

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3. Fig. 2. Parameter γ of the singularity at the corner point of the stamp for different friction coefficients ε. For comparison with the result of the article, it is necessary to take ε = 0, θ/π = 0.25.

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