Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell

In this paper, the size-dependent formulation of shear deformable functionally graded piezoelectric (FGP) cylindrical nanoshells is developed based on a new modified couple stress theory. After the general formulation, the buckling of FGP cylindrical nanoshells under pressure is investigated by using the first order shear deformable shell model. The material properties are assumed to be varied along thickness direction according to the power law distribution. The equilibrium equations and boundary conditions are obtained by using the minimum potential energy principle. A buckling analysis of simply-supported FGP cylindrical nanoshells under uniform lateral external pressure is carried out and the effects of different parameters on the critical pressure are examined. The effects of geometrical, electrical and material properties, such as material length scale parameter, length, thickness, external electric voltage and material property gradient index, on the critical pressure are illustrated. It is indicated that the critical pressure is significantly size-dependent.