Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Anisotropic and Refined Plate Theories

Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_136-1




A solid is called heterogeneous if the material properties differ in different points of the solid, e.g., if the solid consists of different materials. If the material properties do not depend on the location in the solid it is called homogeneous.


A material is called anisotropic, if the material properties are direction dependent, i.e., if two probes cut out of the solid with different orientations will react with different mechanical responses to the same load; otherwise, the material is called isotropic.

Anisotropic Materials in Practice

It is possible to manufacture solids (even with macroscopic dimensions) which are single crystals. These monocrystalline solids can be treated as a homogeneous continuum and have a natural anisotropy which stems from the...


Refined Plate Theory Monoclinic Plates Monoclinic Material Compliance Matrix Simple Shear Stress 
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  1. Altenbach J, Altenbach H, Eremeyev V (2010) On generalized cosserat-type theories of plates and shells: a short review and bibliography. Arch Appl Mech 80(1):73–92. https://doi.org/10.1007/s00419-009-0365-3 CrossRefGoogle Scholar
  2. Ambartsumyan SA (1970) Theory of anisotropic plates: strength, stability, vibration. Technomic Publishing Company, StamfordGoogle Scholar
  3. Friedrichs K, Dressler R (1961) A boundary-layer theory for elastic plates. Commun Pure Appl Math 14(1):1–33.  https://doi.org/10.1002/cpa.3160140102 MathSciNetCrossRefGoogle Scholar
  4. Huber MT (1926) Einige Anwendungen der Biegungstheorie orthotroper Platten. ZAMM – Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 6(3):228–231.  https://doi.org/10.1002/zamm.19260060306 CrossRefGoogle Scholar
  5. Huber MT (1929) Probleme der Statik technisch wichtiger orthotroper Platten. Gebethner & Wolff, WarsawGoogle Scholar
  6. Hwu C (2016) Anisotropic elastic plates, 2nd edn. Springer, New YorkzbMATHGoogle Scholar
  7. Jones RM (1975) Mechanics of composite materials, vol 193. Scripta Book Company, Washington, DCGoogle Scholar
  8. Kirchhoff GR (1850) Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Journal für die reine und angewandte Mathematik 39:51–88. http://eudml.org/doc/147439 CrossRefGoogle Scholar
  9. Lekhnitskii S (1968) Anisotropic plates. Gordon and Breach, Cooper Station, New YorkGoogle Scholar
  10. Mindlin RD (1951) Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. J Appl Mech 18:31–38zbMATHGoogle Scholar
  11. Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis. CRC press, LondonCrossRefGoogle Scholar
  12. Reissner E (1944) On the theory of bending of elastic plates. J Math Phys 23:184–191MathSciNetCrossRefGoogle Scholar
  13. Schneider P, Kienzler R (2014) Comparison of various linear plate theories in the light of a consistent second-order approximation. Math Mech Solids 20(7):871–882. https://doi.org/10.1177/1081286514554352 MathSciNetCrossRefGoogle Scholar
  14. Schneider P, Kienzler R (2017) A Reissner-type plate theory for monoclinic material derived by extending the uniform-approximation technique by orthogonal tensor decompositions of nth-order gradients. Meccanica 52(9):2143–2167. https://doi.org/10.1007/s11012-016-0573-1 MathSciNetCrossRefGoogle Scholar
  15. Schneider P, Kienzler R, Böhm M (2014) Modeling of consistent second-order plate theories for anisotropic materials. ZAMM – Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 94(1–2):21–42.  https://doi.org/10.1002/zamm.201100033 MathSciNetCrossRefGoogle Scholar
  16. Szabó I (1977) Geschichte der Mechanischen Prinzipien. Birkhäsuser, Basel. https://doi.org/10.1007/978-3-0348-9288-9 CrossRefGoogle Scholar
  17. Ting T (1996) Anisotropic elasticity: theory and applications, vol 45. Oxford University Press, New YorkzbMATHGoogle Scholar
  18. Vekua I (1985) Shell theory: general methods of construction. Monographs, advanced texts and surveys in pure and applied mathematics. Wiley, New YorkGoogle Scholar

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Institute for Lightweight Construction and Design (KLuB)Technische Universität DarmstadtDarmstadtGermany

Section editors and affiliations

  • Karam Sab
    • 1
  1. 1.Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTARUniversité Paris-EstMarne-la-ValléeFrance