# 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 output: Contribution to journalArticle

1 Citation (Scopus)

### 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 2093-2118 26 Nonlinear Dynamics 92 4 https://doi.org/10.1007/s11071-018-4183-4 Published - 1 Jun 2018

### Fingerprint

Multilayer
Shell
Mathematical Model
Mathematical models
Generalized Solution
Numerical Investigation
Variational Methods
Difference Method
Regularization
Model
Theorem

### 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

On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells. / Krysko, V. A.; Awrejcewicz, J.; Zhigalov, M. V.; Papkova, I. V.; Yakovleva, T. V.; Krysko, A. V.

In: Nonlinear Dynamics, Vol. 92, No. 4, 01.06.2018, p. 2093-2118.

Research output: Contribution to journalArticle

Krysko, VA, Awrejcewicz, J, Zhigalov, MV, Papkova, IV, Yakovleva, TV & Krysko, AV 2018, 'On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells', Nonlinear Dynamics, vol. 92, no. 4, pp. 2093-2118. https://doi.org/10.1007/s11071-018-4183-4
Krysko, V. A. ; Awrejcewicz, J. ; Zhigalov, M. V. ; Papkova, I. V. ; Yakovleva, T. V. ; Krysko, A. V. / On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells. In: Nonlinear Dynamics. 2018 ; Vol. 92, No. 4. pp. 2093-2118.
@article{8280cdedd10e47dab8c8fa2982f58f63,
title = "On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells",
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.",
keywords = "Buckling, Finite differences, Shells, Structures, Vibrations",
author = "Krysko, {V. A.} and J. Awrejcewicz and Zhigalov, {M. V.} and Papkova, {I. V.} and Yakovleva, {T. V.} and Krysko, {A. V.}",
year = "2018",
month = "6",
day = "1",
doi = "10.1007/s11071-018-4183-4",
language = "English",
volume = "92",
pages = "2093--2118",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Netherlands",
number = "4",

}

TY - JOUR

T1 - On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells

AU - Krysko, V. A.

AU - Awrejcewicz, J.

AU - Zhigalov, M. V.

AU - Papkova, I. V.

AU - Yakovleva, T. V.

AU - Krysko, A. V.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

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.

KW - Buckling

KW - Finite differences

KW - Shells

KW - Structures

KW - Vibrations

UR - http://www.scopus.com/inward/record.url?scp=85043711151&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043711151&partnerID=8YFLogxK

U2 - 10.1007/s11071-018-4183-4

DO - 10.1007/s11071-018-4183-4

M3 - Article

AN - SCOPUS:85043711151

VL - 92

SP - 2093

EP - 2118

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 4

ER -