First-order shear deformation plate models for functionally graded materials

In this paper, first-order shear deformation plate models for modelling structures made of functionally graded materials are proposed. Identification of transverse shear factors is investigated through these models by energy equivalence. The transverse shear stresses are derived from the expression of membrane stresses and equilibrium equations. Using the obtained transverse shear factor, a numerical analysis is performed on the examples of a simply supported square plate and of a cylindrical bending sandwich plate clamped at both ends. The material properties are assumed to be isotropic at each point and vary through the thickness according to a power law distribution. The numerical results of the static analysis are compared to available solutions from previous studies.