Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

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

  • Erasmo Carrera
  • Marco Petrolo
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_140-1

Synonyms

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...
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References

  1. 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 54:301–329Google Scholar
  2. 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):216–296Google Scholar
  3. 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
  4. 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
  5. 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
  6. Carrera E, Cinefra M, Petrolo M, Zappino E (2014) Finite element analysis of structures through unified formulation. Wiley, ChichesterCrossRefzbMATHGoogle Scholar
  7. Cicala P (1965) Systematic approximation approach to linear shell theory. Levrotto e Bella, TorinoGoogle Scholar
  8. 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 150:103–114CrossRefGoogle Scholar
  9. Gol’denweizer AL (1961) Theory of thin elastic shells. International series of monograph in aeronautics and astronautics. Pergamon Press, New YorkGoogle Scholar
  10. Kirchhoff G (1850) Uber das gleichgewicht und die bewegung einer elastischen scheibe. Journal fur reins und angewandte Mathematik 40:51–88CrossRefGoogle Scholar
  11. Mindlin RD (1951) Influence of rotatory inertia and shear in flexural motions of isotropic elastic plates. J Appl Mech 18:1031–1036zbMATHGoogle Scholar
  12. Murakami H (1986) Laminated composite plate theory with improved in-plane response. J Appl Mech 53:661–666CrossRefzbMATHGoogle Scholar
  13. Pandya B, Kant T (1988) Finite element analysis of laminated compiste plates using high-order displacement model. Compos Sci Technol 32:137–155CrossRefGoogle Scholar
  14. Reissner E (1945) The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech 12:69–76MathSciNetzbMATHGoogle Scholar
  15. 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 CrossRefGoogle Scholar
  16. Washizu K (1968) Variational methods in elasticity and plasticity. Pergamon, OxfordzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.MUL2 Group, Department of Mechanical and Aerospace EngineeringPolitecnico di TorinoTorinoItaly

Section editors and affiliations

  • Erasmo Carrera
    • 1
  1. 1.Mechanical and Aerospace EngineeringPolitecnico di TorinoTorinoItaly