Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory

Model of the FGM beams is first put forward by using on physical neutral surface and high-order shear deformation theory. Nonlinear von Kármán strain–displacement relationships are adopted, and material properties are assumed to be temperature dependent and vary along the thickness. 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 beams. The validity of physical neutral surface higher-order shear deformation beam theory can be confirmed by comparison with related researchers’ results. Nonlinear bending approximate solutions are given out using Ritz method. Physical neutral surface theory has many merits in the engineering application due to its easiness and simplicity.