A refined analysis for the transversely isotropic plate under tangential loads by the 3D Green's function

Composites are applied wildly in the engineering and some of them are composed of the transversely isotropic plate. In this paper, a refined analysis for the transversely isotropic plate under tangential loads is addressed based on the Green's function. The 3D Green's function for the transversely isotropic plate loaded by a tangential point force is derived in Section 2. 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 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 in everywhere of the plate, it is much more refined than that of the traditional plate theory, which is restricted by the thickness of plate. Numerical analysis in Section 3 is given to discuss the efficiency and accuracy of this method and study the stress distributions in the transversely isotropic plate loaded by the tangential point force and the tangential distributed load, respectively.