Abstract:
We study the existence of solutions of a boundary value problem for a system of nonlinear second-order partial differential equations for the generalized displacements under given nonlinear boundary conditions that describes the equilibrium state of elastic nonshallow isotropic inhomogeneous shells of zero Gaussian curvature with free edges in the framework of the Timoshenko shear model. The research method is based on integral representations for generalized displacements containing arbitrary functions that allow the original boundary value problem to be reduced to a nonlinear operator equation for generalized displacements in the Sobolev space. The solvability of the operator equation is established using the contraction mapping principle.
Keywords:
nonshallow Timoshenko-type shell of zero Gaussian curvature, nonlinear boundary value problem, partial differential equations, generalized solution, holomorphic function, operator equation, existence theorem.
Citation:
S. N. Timergaliev, “On the existence of solutions of nonlinear boundary value problems for nonshallow Timoshenko-type shells with free edges”, Sib. Zh. Ind. Mat., 26:4 (2023), 160–179; J. Appl. Industr. Math., 17:4 (2023), 874–891
\Bibitem{Tim23}
\by S.~N.~Timergaliev
\paper On the existence of solutions of nonlinear boundary value problems for nonshallow Timoshenko-type shells with free edges
\jour Sib. Zh. Ind. Mat.
\yr 2023
\vol 26
\issue 4
\pages 160--179
\mathnet{http://mi.mathnet.ru/sjim1267}
\crossref{https://doi.org/10.33048/SIBJIM.2023.26.411}
\transl
\jour J. Appl. Industr. Math.
\yr 2023
\vol 17
\issue 4
\pages 874--891
\crossref{https://doi.org/10.1134/S1990478923040154}
Linking options:
https://www.mathnet.ru/eng/sjim1267
https://www.mathnet.ru/eng/sjim/v26/i4/p160
This publication is cited in the following 1 articles:
S. N. Timergaliev, “SOLVABILITY OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR DIFFERENTIAL EQUILIBRIUM EQUATIONS OF NON-FLAT TIMOSHENKO TYPE SHELLS OF NON-ZERO GAUSSIAN CURVATURE IN ISOMETRIC COORDINATES”, Differencialʹnye uravneniâ, 60:12 (2024), 1685
Citation in format AMSBIB
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