Two-dimensional sublamination theory for analysis of functionally graded plates

Presented is a two-dimensional sublamination theory for analysis of plates made of functionally graded materials. The sublamination plate theory extends a layer-wise higher-order shear-deformation theory for laminated plates by considering material properties being continuous functions of the thickness coordinate and using a new concept of sublamination to increase the degrees of freedom. The theory accommodates free shear stress conditions on the bonding surfaces, accounts for non-uniform deformation-dependent distributions of transverse shear stresses through the thickness, can be used for evaluating boundary restraint effects, and can be used for analyzing thin and thick plates with any boundary conditions. A sublamination plate element based on this theory is developed and validated for static and dynamic analysis. The degrees of freedom of the element is adaptable. For an element away from boundaries, itʹs degrees of freedom can be reduced at the elemental level without loss of accuracy. Analytical shear warping functions are presented. Moreover, modal analysis of functionally graded plates with different boundary conditions is performed to show the capability and accuracy of the theory.