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Some Two-dimensional Non-classical Models of Anisotropic Plates. / Belyaev, Alexander K. ; Morozov, Nikita F. ; Tovstik, Peter E. ; Tovstik, Tatyana P. .

Analysis of Plates, Shells and Beams: A State of the Art Report. ed. / Holm Altenbach; Natalia Chinchaladze; Reinhold Kienzler; Wolfgang H. Müller. Vol. 134 Springer Nature, 2020. p. 75-94 (Advanced Structured Materials; Vol. 134).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Harvard

Belyaev, AK, Morozov, NF, Tovstik, PE & Tovstik, TP 2020, Some Two-dimensional Non-classical Models of Anisotropic Plates. in H Altenbach, N Chinchaladze, R Kienzler & WH Müller (eds), Analysis of Plates, Shells and Beams: A State of the Art Report. vol. 134, Advanced Structured Materials, vol. 134, Springer Nature, pp. 75-94. https://doi.org/10.1007/978-3-030-47491-1_5

APA

Belyaev, A. K., Morozov, N. F., Tovstik, P. E., & Tovstik, T. P. (2020). Some Two-dimensional Non-classical Models of Anisotropic Plates. In H. Altenbach, N. Chinchaladze, R. Kienzler, & W. H. Müller (Eds.), Analysis of Plates, Shells and Beams: A State of the Art Report (Vol. 134, pp. 75-94). (Advanced Structured Materials; Vol. 134). Springer Nature. https://doi.org/10.1007/978-3-030-47491-1_5

Vancouver

Belyaev AK, Morozov NF, Tovstik PE, Tovstik TP. Some Two-dimensional Non-classical Models of Anisotropic Plates. In Altenbach H, Chinchaladze N, Kienzler R, Müller WH, editors, Analysis of Plates, Shells and Beams: A State of the Art Report. Vol. 134. Springer Nature. 2020. p. 75-94. (Advanced Structured Materials). https://doi.org/10.1007/978-3-030-47491-1_5

Author

Belyaev, Alexander K. ; Morozov, Nikita F. ; Tovstik, Peter E. ; Tovstik, Tatyana P. . / Some Two-dimensional Non-classical Models of Anisotropic Plates. Analysis of Plates, Shells and Beams: A State of the Art Report. editor / Holm Altenbach ; Natalia Chinchaladze ; Reinhold Kienzler ; Wolfgang H. Müller. Vol. 134 Springer Nature, 2020. pp. 75-94 (Advanced Structured Materials).

BibTeX

@inbook{8ae58d2f780943a6a0489084ecfc6bd8,
title = "Some Two-dimensional Non-classical Models of Anisotropic Plates",
abstract = "Thin elastic plates made of an anisotropic material (with 21 elastic moduli) and heterogeneous in the thickness direction (in partial, multilayered) are considered. A short overview of various 2D models describing deformations and vibrations of a plate is given. The classical Kirchhoff–Love and the Timoshenko–Reissner models are discussed and compared in cases of isotropic and transversely isotropic materials. A correspondence of boundary conditions of these models is established. A multilayered plate with alternating soft and hard layers is considered. By using an asymptotic expansion of the solution in a series in small thickness parameter, the 2D equations of second-order accuracy are delivered. From these equations the correct choice of parameters of the single-layered Timoshenko–Reissner model is derived, which is equivalent to a given multilayered plate. In the case of general anisotropy, a model of second-order accuracy is presented as well, and the main properties of the harmonic solutions for static problems and for free vibrations of a plate are briefly described.",
keywords = "2D MODEL OF SECOND-ORDER ACCURACY, ANISOTROPIC MULTILAYERED PLATES, TIMOSHENKO-REISSNER MODEL, TRANSVERSAL SHEAR INFLUENCE, Anisotropic multilayered plates, Timoshenko–Reissner model, Transversal shear influence, 2D model of second-order accuracy",
author = "Belyaev, {Alexander K.} and Morozov, {Nikita F.} and Tovstik, {Peter E.} and Tovstik, {Tatyana P.}",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.",
year = "2020",
doi = "10.1007/978-3-030-47491-1_5",
language = "English",
isbn = "9783030474904",
volume = "134",
series = "Advanced Structured Materials",
publisher = "Springer Nature",
pages = "75--94",
editor = "Altenbach, {Holm } and Chinchaladze, {Natalia } and Kienzler, {Reinhold } and M{\"u}ller, {Wolfgang H. }",
booktitle = "Analysis of Plates, Shells and Beams",
address = "Germany",

}

RIS

TY - CHAP

T1 - Some Two-dimensional Non-classical Models of Anisotropic Plates

AU - Belyaev, Alexander K.

AU - Morozov, Nikita F.

AU - Tovstik, Peter E.

AU - Tovstik, Tatyana P.

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2020.

PY - 2020

Y1 - 2020

N2 - Thin elastic plates made of an anisotropic material (with 21 elastic moduli) and heterogeneous in the thickness direction (in partial, multilayered) are considered. A short overview of various 2D models describing deformations and vibrations of a plate is given. The classical Kirchhoff–Love and the Timoshenko–Reissner models are discussed and compared in cases of isotropic and transversely isotropic materials. A correspondence of boundary conditions of these models is established. A multilayered plate with alternating soft and hard layers is considered. By using an asymptotic expansion of the solution in a series in small thickness parameter, the 2D equations of second-order accuracy are delivered. From these equations the correct choice of parameters of the single-layered Timoshenko–Reissner model is derived, which is equivalent to a given multilayered plate. In the case of general anisotropy, a model of second-order accuracy is presented as well, and the main properties of the harmonic solutions for static problems and for free vibrations of a plate are briefly described.

AB - Thin elastic plates made of an anisotropic material (with 21 elastic moduli) and heterogeneous in the thickness direction (in partial, multilayered) are considered. A short overview of various 2D models describing deformations and vibrations of a plate is given. The classical Kirchhoff–Love and the Timoshenko–Reissner models are discussed and compared in cases of isotropic and transversely isotropic materials. A correspondence of boundary conditions of these models is established. A multilayered plate with alternating soft and hard layers is considered. By using an asymptotic expansion of the solution in a series in small thickness parameter, the 2D equations of second-order accuracy are delivered. From these equations the correct choice of parameters of the single-layered Timoshenko–Reissner model is derived, which is equivalent to a given multilayered plate. In the case of general anisotropy, a model of second-order accuracy is presented as well, and the main properties of the harmonic solutions for static problems and for free vibrations of a plate are briefly described.

KW - 2D MODEL OF SECOND-ORDER ACCURACY

KW - ANISOTROPIC MULTILAYERED PLATES

KW - TIMOSHENKO-REISSNER MODEL

KW - TRANSVERSAL SHEAR INFLUENCE

KW - Anisotropic multilayered plates

KW - Timoshenko–Reissner model

KW - Transversal shear influence

KW - 2D model of second-order accuracy

UR - https://www.elibrary.ru/item.asp?id=43296123

UR - http://www.scopus.com/inward/record.url?scp=85086124701&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-47491-1_5

DO - 10.1007/978-3-030-47491-1_5

M3 - Chapter

SN - 9783030474904

VL - 134

T3 - Advanced Structured Materials

SP - 75

EP - 94

BT - Analysis of Plates, Shells and Beams

A2 - Altenbach, Holm

A2 - Chinchaladze, Natalia

A2 - Kienzler, Reinhold

A2 - Müller, Wolfgang H.

PB - Springer Nature

ER -

ID: 62491196