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On the Problem of Solvability of Nonlinear Boundary Value Problems for Arbitrary Isotropic Shallow Shells of the Timoshenko Type with Free Edges

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Abstract

In the Timoshenko shear model, we investigate the solvability of a geometrically nonlinear boundary value problem for arbitrary inhomogeneous isotropic shallow elastic shells with free edges. Our method is based on integral representations for generalized displacements containing arbitrary holomorphic functions. The holomorphic functions are found from some boundary conditions on the generalized displacements. We reduce the problem to a nonlinear operator equation for generalized displacements in the Sobolev space and, with the help of the principle of contraction mappings, establish its solvability.

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Authors and Affiliations

  1. Kazan State University of Architecture and Engineering, 1 Zelenaya str., 420043, Kazan, Russia

    S. N. Timergaliev

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  1. S. N. Timergaliev
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Correspondence to S. N. Timergaliev.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 4, pp. 90–107.

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Timergaliev, S.N. On the Problem of Solvability of Nonlinear Boundary Value Problems for Arbitrary Isotropic Shallow Shells of the Timoshenko Type with Free Edges. Russ Math. 65, 81–97 (2021). https://doi.org/10.3103/S1066369X21040071

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  • DOI: https://doi.org/10.3103/S1066369X21040071

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