A novel integral parabolic plate theory incorporating stretching effects for the bending analysis of advanced FG plates resting on Winkler–Pasternak foundations

This paper presents a novel parabolic shear deformation plate theory incorporating the stretching effect for bending analysis of simply supported advanced functionally graded plates resting on a Winkler-Pasternak elastic foundation. The theory considers a parabolic distribution of transverse shear strains and satisfies zero traction boundary conditions on the plate surfaces without requiring shear correction factors. This theory involves only five unknowns, fewer than those in other shear and normal deformation theories. The originality of the present work lies in the introduction of a new displacement field based on undetermined integral variables that simultaneously incorporates both shear and stretching effects, providing a more accurate yet simple formulation compared to existing theories. Material properties are assumed to vary through the thickness direction following a simple power law distribution based on the volume fractions of the constituents. The accuracy of the proposed theory is validated by comparing its results with those available in the literature. The effects of the volume fraction index of the functionally graded material, the side-to-thickness ratio, and the Winkler-Pasternak elastic foundation on the bending responses of functionally graded plates are investigated. The study concludes that the proposed theory is both accurate and straightforward in predicting the bending responses of functionally graded plates, considering the stretching effect on an elastic foundation.