STUDY ON HIGHER-ORDER SHEAR DEFORMATION THEORIES OF THICK-PLATE

It is still necessary to study the thick plate theory and higher-order shear deformation models with a lot of published work. Starting with the definition of average rotation and the free shear stress condition at the bottom and top surfaces, the displacements on the neutral plane are suggested with a unified higher-order shear deformation model, and then expressed in the orthogonal form. On this basis, the generalized stresses are defined, then the generalized strains are obtained in light of the work conjugate, and the constitutive relations are established for the plate theory. The objectivity of the principle of virtual work in the plate theory is proved for different definitions of rotation, as well as the identity to three-dimensional elasticity theory. Based on the principle of virtual work, the variationally consistent higherorder plate theory and the variationally asymptotic lower-order plate theory are respectively established by deriving the corresponding equilibrium equations and boundary conditions, and then compared with the existing plate theories. The current work originally presents the equilibrium equations of the plate theory in terms of the generalized stresses, and clarifies some fundamental problems such as the relations of different definitions of rotation, the relation between the higher-order plate theory and the lower-order plate theory, and the evaluation of the shear factor. The current plate theory is finally validated by solving the Saint-Venant torsion problem.