Alternative II Theory Solution for a Thick Rectangular Anisotropic Plate Under in-Plane and Lateral Loads

This work investigated the application of the Alternative II refined plate theory in the analysis of an anisotropic plate subjected to in-plane and lateral loads. The kinematic equations developed from the Alternative II Refined plate theory were used together with a complete three-dimensional constitutive relation to obtain the total potential energy of an anisotropic plate under lateral and in-plane loads. General variation of the total potential energy was done, a governing equation and two compatibility equations were obtained. A polynomial displacement function was obtained by solving the governing and compatibility equations. This was used to obtain peculiar displacement functions by satisfying the boundary conditions of any plate. The stiffness coefficients were obtained using the displacement function. With the displacement functions and the stiffness coefficients, the equations for the in-plane normal and shear stresses as well as the transverse normal and shear stresses were determined for any applied lateral load when the applied in-plane load is a fraction of the buckling load. Also, the equations for the displacements of the plate were determined. Numerical values of the stresses and displacement parameters were determined for span to thickness ratios of 5, 10, 20 and 100 at angle of fiber orientations of 0 and aspect ratios of 1, 1.5 and 2.0 when the ratio of applied in-plane load to buckling load are 0, 0.25 and 0.5. Using simple percentage difference, the results from this work were compared with the works of previous researchers.