A novel shear correction factor for stress and modal analyses of annular FGM plates with non-uniform inclined tractions and non-uniform elastic foundations

•Shear correction factors are presented for the annular functionally graded plates.•The plate is subjected to non-uniform normal and shear tractions.•Effects of the non-uniform Winkler–Pasternak foundation are considered as well.•The solutions are derived using the analytical Taylor׳s transformation method.•3D elasticity is used instead of the constitutive-equation-based approach.

Only simple tractions and material properties have been considered in derivation of the available shear correction factors, e.g., they have been developed for homogeneous isotropic plates and/or assuming that no shear tractions are imposed on the top or bottom surfaces of the plate. In the present research, the more general case of an annular functionally graded plate subjected to both normal and shear non-uniform tractions and/or resting on a non-uniform Winkler–Pasternak elastic foundation is considered. Instead of using approximate numerical methods, the solutions are derived using the analytical Taylor׳s transformation method. Instead of using the traditional constitutive-equation-based approach, the most accurate equilibrium-equation-based 3D elasticity approach is used. To enhance modeling of variations of the material properties, Mori–Tanka micromechanical-based model is chosen instead of the traditional rule of mixtures. The proposed analytical correction factor and the resulting elasticity-based formulation are evaluated for both the modal and the stress analyses. Results reveal that the resulting accuracies are comparable to those of the elasticity theory.