Anisotropic and Refined Plate Theories
- 286 Downloads
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...
KeywordsRefined Plate Theory Monoclinic Plates Monoclinic Material Compliance Matrix Simple Shear Stress
- Ambartsumyan SA (1970) Theory of anisotropic plates: strength, stability, vibration. Technomic Publishing Company, StamfordGoogle Scholar
- Huber MT (1929) Probleme der Statik technisch wichtiger orthotroper Platten. Gebethner & Wolff, WarsawGoogle Scholar
- Jones RM (1975) Mechanics of composite materials, vol 193. Scripta Book Company, Washington, DCGoogle Scholar
- Lekhnitskii S (1968) Anisotropic plates. Gordon and Breach, Cooper Station, New YorkGoogle Scholar
- 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
- 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
- Vekua I (1985) Shell theory: general methods of construction. Monographs, advanced texts and surveys in pure and applied mathematics. Wiley, New YorkGoogle Scholar