Bending, buckling and free vibration analysis of incompressible functionally graded plates using higher order shear and normal deformable plate theory

Abstract

• Incompressible functionally graded rectangular thick plates are studied. • Material properties vary through the thickness based on the power law function. • Higher order shear and normal deformable plate theory is developed. • Legendre polynomials are used in the expansion of displacement field components. • Bending, buckling and free vibration are investigated for simply supported plates . In the present study, higher order shear and normal deformable plate theory is developed for analysis of incompressible functionally graded rectangular thick plates. Also, The effect of incompressibility is studied on the static, dynamic and stability responses of thick plate. It is assumed that plate is incompressible and the incompressibility condition is considered in addition to the governing equations for determining the unknowns. Since the plate is thick, higher order shear and normal deformable theory is applied so that the Legendre polynomials are used for expansion of displacement field components in the thickness direction. Also, it is supposed that material properties vary through the thickness based on the power law function. Utilizing the variational approach, governing equations for static, stability and dynamic analysis of plate are derived. Resulted equations are solved analytically for simply supported plates. Finally, the effects of material properties and dimensions on the response of incompressible plates are investigated in details.