THICK AND THIN PLATE ELEMENTS WITH ANISOTROPIC MATERIALS BASED ON ANALYTICAL TRIAL FUNCTIONS

In this paper, the Kirchhoff thin plate theory is applied to derive serial analytical trial functions of the plate with anisotropic materials. Then these functions are used to construct a quadrilateral hybrid stress plate element. Firstly, the deflection w of an anisotropic materials plate is derived from the differential equations of thin plate theory. Secondly, the analytical trial functions of generalized displacements/strains/stresses of thin plate theory are obtained from the general characteristics solution of w. Thirdly, the generalized shear stresses are derived from the generalized stresses according to the equations of equilibrium. Finally, a quadrilateral hybrid stress plate element ATF-PH4 is constructed with the analytical trial functions of generalized stresses and generalized shear stresses. The numerical examples show that the element thusly constructed has high precision, good convergence, and is not sensitive to the mesh distortion. And it fits to both thick and thin plate problems.