The derivation of a thick and thin plate formulation without ad hoc assumptions
For the plate formulation, appropriate three-dimensional elasticity solution representations for isotropic materials are constructed. No a priori assumptions for stress or displacement distributions over the thickness of the plate are made. The strategy used in the derivation is to separate functions of the thickness variable \(z\) from functions of the coordinates \(x\) and \(y\) lying in the midplane of the plate. Real and complex three-dimensional elasticity solution representations are used to obtain three types of functions of the coordinates \(x\), \(y\) and the corresponding differential equations.
homogeneous and nonhomogeneous boundary conditions
three-dimensional elasticity solution representations
scientific article; zbMATH DE number 147033