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Modeling of anisotropic boundary layer effects in plate theory
Author(s) -
Schneider Patrick,
Kienzler Reinhold
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800397
Subject(s) - mathematics , plate theory , isotropy , uniqueness , mathematical analysis , order theory , a priori and a posteriori , boundary value problem , series (stratigraphy) , reduction (mathematics) , displacement field , truncation (statistics) , displacement (psychology) , convergence (economics) , boundary (topology) , order (exchange) , finite element method , geometry , physics , psychology , paleontology , philosophy , statistics , epistemology , quantum mechanics , economics , psychotherapist , biology , economic growth , thermodynamics , finance
The modeling of a Reissner‐type plate theory for elastic, monoclinic material is presented. The basic theory is derived using the a‐priori‐assumption free uniform‐approximation approach, which is based upon series expansions of the displacement field and a structured truncation of the elastic potential that gives rise to a hierarchy of approximating theories. An a‐priori estimate for the approximation error shows that higher‐order theories have indeed a higher rate of convergence with respect to the relative slenderness of the plate. Using a pseudo‐reduction approach, the number of PDEs to be solved is reduced significantly. The resulting first‐order theory is the classical monoclinic plate theory, whereas, the second order theory is not determined uniquely by the approach. Uniqueness is achieved by introduction of an orthogonal decomposition of higher‐order gradients of the in‐plane displacements. The final second‐order theory coincides with the Reissner‐Mindlin theory for the special case of isotropic material.