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

Nonlinear Dynamics, Mar 2018

Mathematical models of multi-layer orthotropic shells were reconsidered based on the Timoshenko hypothesis. A new mathematical model with $\varepsilon$-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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V. A. Krysko, J. Awrejcewicz, M. V. Zhigalov, I. V. Papkova, T. V. Yakovleva, A. V. Krysko. On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells, Nonlinear Dynamics, 2018, 1-26, DOI: 10.1007/s11071-018-4183-4