A refined analysis for the transversely isotropic plate under normal loads with the 3D Green’s function

Many composite plates behave transversely isotropic. An accurate and efficient 3D analysis for the transversely isotropic plate will contribute much to the accurate design and quality promotion of this kind of structure. In this paper, a refined analysis for the transversely isotropic plate under normal loads is addressed based on the 3D Green’s function. The 3D Green’s function for the transversely isotropic plate loaded by a normal point force is derived. By adopting the general solution for the transversely isotropic material, a new harmonic function which contains undetermined constants is constructed. All stress components can be obtained by substituting the harmonic function into the general solution. The constants can be determined by considering the equilibrium and boundary conditions of the plate. For the reason that this solution satisfies the 3D governing equations rigorously everywhere in the plate, it is much more refined than that of the traditional plate theory, which is restricted by the thickness of the plate. Numerical analysis is given to discuss the efficiency and accuracy of this method and study the stress distributions in the transversely isotropic plate loaded by a normal point force and a normal distributed load, respectively.