Geodesic
Exact analytical solution for a problem of equilibrium of a composite plate containing prestressed parts made of incompressible elastic materials under superimposed finite strains
Čebyševskij sbornik, Tome 23 (2022) no. 4, pp. 251-261

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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 pre-deformed 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.
Keywords: predeformed layers, Treloar material, large deformations, nonlinear effects. 
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     author = {V. A. Levin and K. M. Zingerman and A. E. Belkin},
     title = {Exact analytical solution for a problem of equilibrium of a composite plate containing prestressed parts made of incompressible elastic materials under superimposed finite strains},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {251--261},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a21/}
}
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V. A. Levin; K. M. Zingerman; A. E. Belkin. Exact analytical solution for a problem of equilibrium of a composite plate containing prestressed parts made of incompressible elastic materials under superimposed finite strains. Čebyševskij sbornik, Tome 23 (2022) no. 4, pp. 251-261. http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a21/