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Higher Order Theory of Functionally Graded Shells

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  • First Online:
Encyclopedia of Continuum Mechanics

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Synonyms

Curved rod; Higher order theory; Legendre polynomial; Micropolar elasticity

Definition

Higher order theory for functionally graded (FG) shells based on the expansion of the 3-D equations of elasticity for functionally graded materials (FGMs) into Fourier series in terms of Legendre’s polynomials. Higher order theory of the axisymmetric shell of revolution. The first order theory of the FG axisymmetric cylindrical plate and spherical shell.

Introduction

In recent years, a new type of composite materials, the so-called FGMs, has been introduced and applied in a wide range of engineering sciences. The FGMs are heterogeneous materials in which the elastic properties change from one surface to the other, gradually and continuously to achieve the required properties. They especially attract attention because of their distinctive material properties, which vary continuously in one (or more) direction(s), in the case of plates and shells usually in the thickness direction (Shen 2009)....

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References

  • Brischetto S, Carrera E (2010) Advanced mixed theories for bending analysis of functionally graded plates. Comput Struct 88:1474–1483

    Article  Google Scholar 

  • Carrera E, Brischetto S, Nali P (2011) Plates and shells for smart structures. Classical and advanced theories for modeling and analysis. Wiley, New Delhi

    Book  Google Scholar 

  • Carrera E, Cinefra M, Petrolo M, Zappino M (2014) Finite element analysis of structures through unified formulation. Wiley, New Delhi

    Book  Google Scholar 

  • Novozhilov VV (1964) Thin shell theory, 2nd edn. Noordhoff, Groningen

    Google Scholar 

  • Pelekh BL (1973) The theory of shells with finite shear rigidity. Naukova dumka, Kiev

    Google Scholar 

  • Shen H-S (2009) Functionally graded materials: nonlinear analysis of plates and shells. CRC Press/Taylor & Francis Group, Boca Raton

    Book  Google Scholar 

  • Vekua IN (1986) Shell theory, general methods of construction. Pitman Advanced Pub. Program, Boston

    Google Scholar 

  • Zozulya VV (2013) A high-order theory for functionally graded axially symmetric cylindrical shells. Arch Appl Mech 83(3):331–343

    Article  Google Scholar 

  • Zozulya VV (2017) A higher order theory for functionally graded beams based on Legendre’s polynomial expansion. Mech Adv Mater Struct 24(9):745–760

    Article  Google Scholar 

  • Zozulya VV, Zhang C (2012) A high order theory for functionally graded axisymmetric cylindrical shells. Int J Mech Sci 60(1):12–22

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Departamento de Materiales, Centro de Investigacion Cientifica de Yucatan, Merida, Yucatan, Mexico

    V. V. Zozulya

Authors
  1. V. V. Zozulya
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Corresponding author

Correspondence to V. V. Zozulya .

Editor information

Editors and Affiliations

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

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, Queensland, Australia

    Andreas Öchsner

Section Editor information

  1. MUL2 Group, Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, Italy

    Erasmo Carrera

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Zozulya, V.V. (2018). Higher Order Theory of Functionally Graded Shells. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_272-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_272-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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