A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations

A new trigonometric shear deformation plate theory involving only four unknown functions, as against five functions in case of other shear deformation theories, is developed for flexural analysis of Functionally Graded Material (FGM) plates resting on an elastic foundation. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. In the analysis, the two-parameter Pasternak and Winkler foundations are considered. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Governing equations are derived from the principle of virtual displacements. The accuracy of the present theory is demonstrated by comparing the results with solutions derived from other higher-order models found in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded plates.