On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells

V. A. Krysko, J. Awrejcewicz, M. V. Zhigalov, I. V. Papkova, T. V. Yakovleva, A. V. Krysko

Research Laboratory for 3D Modeling and Industrial Design

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Abstract

Mathematical models of multi-layer orthotropic shells were reconsidered based on the Timoshenko hypothesis. A new mathematical model with ε-regularisation was proposed, and the theorem regarding the existence of a generalised solution to the model was formulated and proved. The algorithms of numerical investigation of models studied with the aid of the variational-difference method were developed. The associated stability problem was also addressed. A comparison of the results yielded by the considered models was carried out and discussed for numerous factors and parameters.

Original language	English
Pages (from-to)	2093-2118
Number of pages	26
Journal	Nonlinear Dynamics
Volume	92
Issue number	4
DOIs	https://doi.org/10.1007/s11071-018-4183-4
Publication status	Published - 1 Jun 2018

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Keywords

Buckling
Finite differences
Shells
Structures
Vibrations

ASJC Scopus subject areas

Control and Systems Engineering
Aerospace Engineering
Ocean Engineering
Mechanical Engineering
Applied Mathematics
Electrical and Electronic Engineering

Cite this

Krysko, V. A., Awrejcewicz, J., Zhigalov, M. V., Papkova, I. V., Yakovleva, T. V., & Krysko, A. V. (2018). On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells. Nonlinear Dynamics, 92(4), 2093-2118. https://doi.org/10.1007/s11071-018-4183-4

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AU - Awrejcewicz, J.

AU - Zhigalov, M. V.

AU - Papkova, I. V.

AU - Yakovleva, T. V.

AU - Krysko, A. V.

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AB - Mathematical models of multi-layer orthotropic shells were reconsidered based on the Timoshenko hypothesis. A new mathematical model with ε-regularisation was proposed, and the theorem regarding the existence of a generalised solution to the model was formulated and proved. The algorithms of numerical investigation of models studied with the aid of the variational-difference method were developed. The associated stability problem was also addressed. A comparison of the results yielded by the considered models was carried out and discussed for numerous factors and parameters.

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KW - Finite differences

KW - Shells

KW - Structures

KW - Vibrations

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Access to Document

10.1007/s11071-018-4183-4