∞3 Hierarchy plate theories for thick and thin composite plates: The generalized unified formulation

Each displacement component is expanded along the thickness of the plate by using a powerful compact formulation. Infinite different types of expansions can be independently used for the displacements ux, uy and uz. Therefore, the present formulation here introduced for the first time, leads to the writing, with a single formal theory, of a class of ∞3 theories. These theories can be successfully implemented in a single FEM code, and without changing a single line of the program it is possible to obtain results of all the ∞3 theories. In addition, this formulation allows the user to treat each unknown independently and, therefore, different numerical approaches can be used in the FEM codes based on this generalized unified formulation. This new technique can be very useful in multifield problems such as thermoelastic applications and multilayered composite plates embedding piezo-layers.