The anisotropic coupling of one‐dimensional problems in linear elasticity

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)