The refined theory and the decomposed theorem of a transversely isotropic elastic plate

The refined theory of a transversely isotropic elastic plate is analysed. Based on the transversely isotropic elastic theory, a refined theory for bending thick plates is derived using the Elliott–Lodge’s solution and Lur'e method without ad hoc assumptions. First, the expressions for all of the displacements and stress components of a transversely isotropic elastic plate were obtained in terms of the mid-plane displacement and its derivatives. Based on the refined theory, the exact equation for the plate without transverse surface loadings consists of three governing differential equations: the bi-harmonic equation, the shear equation and the transcendental equation. Using basic mathematical methods and the refined theory, the decomposed form of a transversely isotropic elasticity plate was obtained. The interior state, the shear state and the transcendental states of the decomposed form can be derived directly from the three equations of the refined theory. Finally, the equations for the plate under general loadings are derived directly from the refined theory.