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The anisotropic coupling of one‐dimensional problems in linear elasticity
Author(s) -
Schneider Patrick,
Kienzler Reinhold
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410118
Subject(s) - orthotropic material , elasticity (physics) , anisotropy , homogeneous , monoclinic crystal system , linear elasticity , coupling (piping) , symmetry (geometry) , reflection symmetry , mathematical analysis , mathematics , geometry , physics , materials science , structural engineering , statistical physics , optics , composite material , engineering , finite element method , quantum mechanics , molecule
We investigate the coupling of the four one‐dimensional problems of linear elasticity (i.e., the rod‐, the two beam‐ and the shaft‐problem), for the case of a cross section that has two orthogonal axes of reflectional symmetry. An analytical proof is given, that the problems are decoupled for a homogeneous orthotropic material and the coupling behavior is given for monoclinic materials in dependence of the orientation of the symmetry plane. For a general anisotropic (aelotropic) material all four problems are coupled. We also identify the driving forces for the four problems, leading to a detailed definition of the admissible load‐cases for the classical problems, so that any three‐dimensional load‐case can be uniquely decomposed into the driving forces of the four problems. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)