Exact analytical solution for a problem of equilibrium of a composite plate containing prestressed parts made of incompressible elastic materials under superimposed finite strains
https://doi.org/10.22405/2226-8383-2022-23-4-251-261
Abstract
In the article, for the case of large deformations, an exact analytical solution of the problem of the stress-strain state of a composite slab is presented, which is built by connecting two predeformed layers. Each layer is obtained by straightening a cylindrical panel, initially shaped like a sector of a hollow circular cylinder. The cylinders are made of incompressible non-linear-elastic materials — Treloar’s, or neo-Hookean materials. The axes of cylinders before deformation are
orthogonal. After connection, the plate is subjected to biaxial tension or compression in its plane. The problem is formulated on the basis of the theory of superimposed large strains.
An important role in solving the problem is played by the fact that the plate material is incompressible. When solving the problem, as well as when conducting numerical studies, nonlinear effects are investigated. The resulting solution can be used to verify software that is designed to numerically solve problems of the stress-strain state of structural elements made by connecting pre-deformed parts. For the obtained solution of the problem, numerical studies were carried out, the results of which - the dependence of the stress at the ends of the plates
on various deformation parameters - are presented in the work.
About the Authors
Vladimir Anatol’evich Levin
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
Konstantin Moiseevich Zingerman
Tver State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
Anton Eduardovich — Belkin
Tula State University
Russian Federation
Russian Federation
postgraduate student
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Review
For citations:
Levin V.A., Zingerman K.M., Belkin A.E. Exact analytical solution for a problem of equilibrium of a composite plate containing prestressed parts made of incompressible elastic materials under superimposed finite strains. Chebyshevskii Sbornik. 2022;23(4):251-261. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-4-251-261
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