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J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 4, Pages 485–497 (Mi jsfu511)  

Models of deformation of stiffened orthotropic shells under dynamic loading

Alexey A. Semenov

Saint Petersburg State University of Architecture and Civil Engineering, 2nd Krasnoarmeyskaya, 4, Saint Petersburg, 190005, Russia

Abstract: Two models of deformation of reinforced orthotropic shells under dynamic loading are considered in this paper. One such model is in the form of equations of motion and another model is in the form of a system of ordinary differential equations. Mathematical models are based on the hypotheses of the Kirchhoff–Love theory of shells. They take into account the geometric nonlinearity, orthotropic material properties and reinforcement elements. All relations of the models are in general form, and they can be used for a wide range of structures (shallow shells of double curvature, cylindrical, conical, spherical and toroidal shells and panels, etc.). An important feature of the proposed model is the ability to introduce stiffeners both discretely and by the method of constructive anisotropy (MCA) in accordance with their shear and torsional rigidity. The second model is derived by applying the Kantorovich method to the functional of the total energy of deformation of a shell. The resulting initial value problem is easier to solve than the system of equations of motion in partial derivatives.

Keywords: mathematical model, shell, dynamic loading, orthotropy, geometric nonlinearity, the equations of motion, method of constructive anisotropy.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 3801
The work was supported by the Ministry of Education and Science of the Russian Federation (project 3801).


DOI: https://doi.org/10.17516/1997-1397-2016-9-4-485-497

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Bibliographic databases:

UDC: 539.3, 531.3, 001.891.573
Received: 23.03.2016
Received in revised form: 02.08.2016
Accepted: 08.09.2016
Language:

Citation: Alexey A. Semenov, “Models of deformation of stiffened orthotropic shells under dynamic loading”, J. Sib. Fed. Univ. Math. Phys., 9:4 (2016), 485–497

Citation in format AMSBIB
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\by Alexey~A.~Semenov
\paper Models of deformation of stiffened orthotropic shells under dynamic loading
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2016
\vol 9
\issue 4
\pages 485--497
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\crossref{https://doi.org/10.17516/1997-1397-2016-9-4-485-497}
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  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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