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A consistent second‐order plate theory for monotropic material
Author(s) -
Schneider Patrick,
Kienzler Reinhold
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110128
Subject(s) - isotropy , homogenization (climate) , plate theory , shear (geology) , homogeneous , first order , classical mechanics , physics , mathematics , materials science , mathematical analysis , composite material , optics , statistical physics , boundary value problem , biodiversity , ecology , biology
Mathematical homogenization (or averaging) of composite materials, such as fibre laminates, often leads to non‐isotropic homogenized (averaged) materials. Especially the upcoming importance of these materials increases the need for accurate mechanical models of non‐isotropic shell‐like structures. We present a second‐order (or: Reissner‐type) theory for the elastic deformation of a plate with constant thickness for a homogeneous monotropic material. It is equivalent to Kirchhoff's plate theory as a first‐order theory for the special case of isotropy and, furthermore, shear‐deformable and equivalent to R. Kienzler's theory as a second‐order theory for isotropy, which implies further equivalences to established shear‐deformable theories, especially the Reissner‐Mindlin theory and Zhilin's plate theory. Details of the derivation of the theory will be published in a forthcoming paper [3]. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)