### Abstract

A two-dimensional model describing the multilayered anisotropic plate deformations is proposed. The plate is assumed to consist of some orthotropic layers with arbitrary orientation of axes relative to the plate frame. The studied multilayered plate is replaced by the equivalent plate composed of a monoclinic material with piecewise elastic modules. An asymptotic solution is constructed for long-wave deformations. This problem was solved earlier in the first approximation; however, the obtained solution is not applicable for the case in which the stiffness of layers differs essentially from each other. The second asymptotic approximation is constructed in the present paper. It takes into account the effects of transversal shear and the normal fibers extension. Some special cases resulting in simple equations are studied in detail. The asymptotic solution error is estimated by comparison with the exact three-dimensional solutions for some test examples.

Original language | English |
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Pages (from-to) | 2891-2904 |

Journal | Acta Mechanica |

Volume | 230 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1 Aug 2019 |

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### Scopus subject areas

- Computational Mechanics
- Mechanical Engineering

### Cite this

*Acta Mechanica*,

*230*(8), 2891-2904. https://doi.org/10.1007/s00707-019-02405-y

}

*Acta Mechanica*, vol. 230, no. 8, pp. 2891-2904. https://doi.org/10.1007/s00707-019-02405-y

**Two-dimensional linear models of multilayered anisotropic plates.** / Belyaev, A. K.; Morozov, N. F.; Tovstik, P. E.; Tovstik, T. P.

Research output

TY - JOUR

T1 - Two-dimensional linear models of multilayered anisotropic plates

AU - Belyaev, A. K.

AU - Morozov, N. F.

AU - Tovstik, P. E.

AU - Tovstik, T. P.

N1 - Belyaev, A.K., Morozov, N.F., Tovstik, P.E. et al. Two-dimensional linear models of multilayered anisotropic plates. Acta Mech 230, 2891–2904 (2019) doi:10.1007/s00707-019-02405-y

PY - 2019/8/1

Y1 - 2019/8/1

N2 - A two-dimensional model describing the multilayered anisotropic plate deformations is proposed. The plate is assumed to consist of some orthotropic layers with arbitrary orientation of axes relative to the plate frame. The studied multilayered plate is replaced by the equivalent plate composed of a monoclinic material with piecewise elastic modules. An asymptotic solution is constructed for long-wave deformations. This problem was solved earlier in the first approximation; however, the obtained solution is not applicable for the case in which the stiffness of layers differs essentially from each other. The second asymptotic approximation is constructed in the present paper. It takes into account the effects of transversal shear and the normal fibers extension. Some special cases resulting in simple equations are studied in detail. The asymptotic solution error is estimated by comparison with the exact three-dimensional solutions for some test examples.

AB - A two-dimensional model describing the multilayered anisotropic plate deformations is proposed. The plate is assumed to consist of some orthotropic layers with arbitrary orientation of axes relative to the plate frame. The studied multilayered plate is replaced by the equivalent plate composed of a monoclinic material with piecewise elastic modules. An asymptotic solution is constructed for long-wave deformations. This problem was solved earlier in the first approximation; however, the obtained solution is not applicable for the case in which the stiffness of layers differs essentially from each other. The second asymptotic approximation is constructed in the present paper. It takes into account the effects of transversal shear and the normal fibers extension. Some special cases resulting in simple equations are studied in detail. The asymptotic solution error is estimated by comparison with the exact three-dimensional solutions for some test examples.

KW - Anisotropy

KW - Deformation

KW - Shear flow

UR - http://www.scopus.com/inward/record.url?scp=85066619634&partnerID=8YFLogxK

U2 - 10.1007/s00707-019-02405-y

DO - 10.1007/s00707-019-02405-y

M3 - Article

AN - SCOPUS:85066619634

VL - 230

SP - 2891

EP - 2904

JO - Acta Mechanica

JF - Acta Mechanica

SN - 0001-5970

IS - 8

ER -