A Mathematically Consistent Vector-Matrix Representation of Generalized Hooke’s Law for Shear-Rigid Plates

The present contribution is dedicated to the mathematical consistent expression of constitutive relations needed for efficient computational treatment of thin-walled structural elements within a geometrically and physically linear framework, as usually used by engineers. Hereby, the direct approach for homogeneous plates is taken as a basis. We confine our research to shear-rigid plates. We further on do not restrict ourselves by material symmetry classes and consider an aelotropic material. Based on the fully coupled constitutive equations, we introduce an approach by applying normalized bases to decay into a vector-matrix representation. It is thus possible to formulate the tensorial quantities in form of vector-matrix equations which are mathematically consistent. The key advantages of this approach are disclosed.