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Three-Dimensional Exact Analysis of Functionally Graded Laminated Composite Plates

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Shell and Membrane Theories in Mechanics and Biology

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 45))

Abstract

A paper focuses on the implementation of the method of sampling surfaces (SaS) to three-dimensional (3D) exact solutions for functionally graded (FG) laminated composite plates. According to the SaS method, we introduce inside the \(n\)th layer \({I}_{n}\) not equally spaced SaS parallel to the middle surface of the plate in order to choose the displacements of these surfaces as basic plate variables. This permits the presentation of the proposed FG laminated plate formulation in a very compact form. It is important that the SaS are located inside each layer at Chebyshev polynomial nodes. This fact allows one to uniformly minimize the error due to Lagrange interpolation, i.e. the use of Lagrange polynomials of high degree becomes possible. As a result, the SaS method can be applied efficiently to 3D exact solutions of elasticity for FG laminated plates with a specified accuracy utilizing the sufficient number of SaS.

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Acknowledgments

This work was supported by Russian Ministry of Education and Science under Grant No. 9.137.2014K and by Russian Foundation for Basic Research under Grant No 13-01-00155.

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Authors and Affiliations

  1. Tambov State Technical University, Sovetskaya Street, 106, Tambov, 392000, Russia

    Gennady M. Kulikov & Svetlana V. Plotnikova

Authors
  1. Gennady M. Kulikov
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  2. Svetlana V. Plotnikova
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Correspondence to Gennady M. Kulikov .

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Editors and Affiliations

  1. Lehrstuhl für Technische Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Department of Bio- and Nanomechanics, Belarusian State University, Minsk, Belarus

    Gennadi I. Mikhasev

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Kulikov, G.M., Plotnikova, S.V. (2015). Three-Dimensional Exact Analysis of Functionally Graded Laminated Composite Plates. In: Altenbach, H., Mikhasev, G. (eds) Shell and Membrane Theories in Mechanics and Biology. Advanced Structured Materials, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-02535-3_13

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  • DOI: https://doi.org/10.1007/978-3-319-02535-3_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02534-6

  • Online ISBN: 978-3-319-02535-3

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