A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis

Abstract This paper presents a new simple four-unknown shear and normal deformations theory (sSNDT) for static, dynamic and buckling analyses of functionally graded material (FGM) isotropic and sandwich plates. The fully three-dimensional material matrix is used in the relation between stress and strain. The present theory uses only four independent unknowns although it is additionally accounted for a deformation in the axial direction. In comparison with the first and higher order shear deformation theories, the number of independent unknowns of the present theory retains four degrees of freedom per node. The shear stress free surface conditions are naturally satisfied so that the shear correction factors are no longer required. The discrete system of equations is derived from the Galerkin weak form and numerically solved by isogeometric analysis (IGA). This discrete form requires the C 1 -continuity of the displacement field. Therefore, NURBS basis functions in IGA can easily satisfy this condition. Several examples are given to demonstrate the efficiency of the present method.