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Applicability ranges for four approaches to determination of bending stiffness of multilayer plates

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Abstract

A linear static problem of bending of a multilayer plate with homogeneous isotropic layers is considered. The deflection is assumed to have harmonic shape in the tangential directions. For calculation of the bending stiffness we introduce two dimensionless parameters: a small thickness parameter equal to the ratio of the thickness to the deformation wavelength in the tangential directions, and a large inhomogeneity parameter equal to the ratio of the maximum and minimum Young’s moduli of the layers. The plane of these parameters is split into four regions, in which different models are available for calculating the bending stiffness. The first of these is the Kirchhoff - Love model based on the hypothesis of straight non-deformable normal. In the second region, the Timoshenko - Reissner model with a shear parameter is used, calculated by an asymptotic formula of the second order of accuracy. The third region is based on assumptions on inextensible normal fiber and large heterogeneity. Finally, in the fourth region, compression of the normal is taken into account, and an approximate formula for bending stiffness is proposed for a three-layer plate. Error estimation of the models is carried out on test examples by comparison with the exact numerical solution of the three-dimensional problem of the elasticity theory. The possibility of suitability of the bending stiffness for calculating the plate eigenfrequencies is discussed.

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Acknowledgements

Support of Russian Foundation for Basic Research is acknowledged, projects 18-01-00884a, 19-01-00208a, 20-51-S52001 MHT-a.

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Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    Nikita F. Morozov & Petr E. Tovstik

  2. Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, St.Petersburg, Russia

    Alexander K. Belyaev & Tatiana P. Tovstik

Authors
  1. Nikita F. Morozov
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  2. Alexander K. Belyaev
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  3. Petr E. Tovstik
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  4. Tatiana P. Tovstik
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Correspondence to Tatiana P. Tovstik.

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Communicated by Marcus Aßmus, Victor A. Eremeyev and Andreas Öchsner.

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Morozov, N.F., Belyaev, A.K., Tovstik, P.E. et al. Applicability ranges for four approaches to determination of bending stiffness of multilayer plates. Continuum Mech. Thermodyn. 33, 1659–1673 (2021). https://doi.org/10.1007/s00161-021-00996-3

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