Modeling and analysis of FGM rectangular plates based on physical neutral surface and high order shear deformation theory

In this paper, model of the FGM plate is successfully constructed by physical neutral surface and high-order shear deformation theory. Material properties are assumed to be temperature-dependent, while Poisson's ratio depends weakly on temperature change and position and is assumed to be a constant. It is worth noting that physical neutral surface will be changed with temperature. Therefore, the displacements have special forms, there are no stretching–bending couplings in constitutive equations, and governing equations have the simple forms, so the solution procedure is similar as homogeneous isotropic plate. The validity of physical neutral surface higher-order shear deformation plate theory can be confirmed by comparison with related researchers' results. Using this new model, post-buckling, nonlinear bending and vibration approximate solutions are given out using Ritz method, and influences played by different supported boundaries, thermal environmental conditions and volume fraction index are discussed in detail. Physical neutral surface theory has many merits in the engineering application due to its easiness and simplicity.

► A new model of the FGM rectangle plate is successfully constructed.
► Both physical neutral surface and high order shear deformation theory are adopted.
► Stretching–bending couplings are eliminated in constitutive equations.
► The material properties are temperature dependent.
► Nonlinear problems of FGM rectangle plates are solved by Ritz method.