Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Continuum Mechanics pp 1–14Cite as

Axiomatic/Asymptotic Method and Best Theory Diagram for Composite Plates and Shells

  • 295 Accesses

Synonyms

2D structural models; Axiomatic/asymptotic method (AAM); Best theory diagram (BTD); Carrera unified formulation (CUF); Theory of structures

Definitions

Plates and shells are 2D structural models; in fact, the unknown, primary variables depend on two coordinates and are assumed along the third one. Plates and shells can model the structural behavior of 3D bodies in which the third dimension – the thickness, h – is much smaller than the other two. To define a plate or shell is useful to use segments of height h and the surface containing the midpoints of the segments, namely, the mid-surface. In plates, the mid-surface is flat; in shells the mid-surface is curved. Figure 1 shows the geometry of a shell, the mid-surface, or reference surface embodies the 3D features of the structure. From a mathematical standpoint, in plates and shells, expansions of the thickness coordinate (z) defines the behavior of the unknown variables along the thickness. Each term of the expansion is a...

This is a preview of subscription content, access via your institution.

References

  • Carrera E (2001) Developments, ideas and evaluations based upon the Reissner’s mixed variational theorem in the modeling of multilayered plates and shells. Appl Mech Rev 54:301–329

    Google Scholar 

  • Carrera E (2003) Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch Comput Meth Eng 10(3):216–296

    Google Scholar 

  • Carrera E, Miglioretti F (2012) Selection of appropriate multilayered plate theories by using a genetic like algorithm. Compos Struct 94(3):1175–1186. https://doi.org/10.1016/j.compstruct.2011.10.013

  • Carrera E, Petrolo M (2010) Guidelines and recommendation to contruct theories for metallic and composite plates. AIAA J 48(12):2852–2866. https://doi.org/10.2514/1.J050316

  • Carrera E, Petrolo M (2011) On the effectiveness of higher-order terms in refined beam theories. J Appl Mech 78. https://doi.org/10.1115/1.4002207

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

    CrossRef  MATH  Google Scholar 

  • Cicala P (1965) Systematic approximation approach to linear shell theory. Levrotto e Bella, Torino

    Google Scholar 

  • Filippi M, Petrolo M, Valvano S, Carrera E (2016) Analysis of laminated composites and sandwich structures by trigonometric, exponential and miscellaneous polynomials and a mitc9 plate element. Compos Struct 150:103–114

    CrossRef  Google Scholar 

  • Gol’denweizer AL (1961) Theory of thin elastic shells. International series of monograph in aeronautics and astronautics. Pergamon Press, New York

    Google Scholar 

  • Kirchhoff G (1850) Uber das gleichgewicht und die bewegung einer elastischen scheibe. Journal fur reins und angewandte Mathematik 40:51–88

    CrossRef  Google Scholar 

  • Mindlin RD (1951) Influence of rotatory inertia and shear in flexural motions of isotropic elastic plates. J Appl Mech 18:1031–1036

    MATH  Google Scholar 

  • Murakami H (1986) Laminated composite plate theory with improved in-plane response. J Appl Mech 53:661–666

    CrossRef  MATH  Google Scholar 

  • Pandya B, Kant T (1988) Finite element analysis of laminated compiste plates using high-order displacement model. Compos Sci Technol 32:137–155

    CrossRef  Google Scholar 

  • Reissner E (1945) The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech 12:69–76

    MathSciNet  MATH  Google Scholar 

  • Varadan T, Bhaskar K (1991) Bending of laminated orthotropic cylindrical shells – an elasticity approach. Compos Struct 17:141–156. https://doi.org/10.1016/j.compstruct.2011.10.013

    CrossRef  Google Scholar 

  • Washizu K (1968) Variational methods in elasticity and plasticity. Pergamon, Oxford

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Erasmo Carrera & Marco Petrolo

Authors
  1. Erasmo Carrera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marco Petrolo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erasmo Carrera .

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

    Prof. Dr. Andreas Öchsner

Section Editor information

  1. Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    Erasmo Carrera

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer-Verlag GmbH Germany

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Carrera, E., Petrolo, M. (2018). Axiomatic/Asymptotic Method and Best Theory Diagram for Composite Plates and Shells. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_140-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53605-6_140-1

  • Published:

  • 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

search

Navigation