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In the current work, a four-node rectangular finite element with assumed natural shear strains, based on the exact neutral surface position and new higher-order shear deformation theory is employed to perform mechanical buckling and free vibration analysis of functionally graded plates. The present theory has only five unknowns and satisfies zero transverse shear stress at the top and bottom surfaces of the plate, therefore a shear correction factor is not necessary. The accuracy of the proposed formulation is evaluated by comparing the obtained results with those available in the literature.

A novel trigonometric shear deformation theory for the buckling and free vibration analysis of functionally graded plates