Buckling of Piezoelectric Functionally Graded Material Beams

Buckling analysis of functionally graded material (FGM) beams with surface-bonded piezoelectric layers which are subjected to both mechanical axial loading and constant voltage is studied in this paper. The material non-homogeneous properties of FGM beam are assumed to vary smoothly by distribution of power law through the beam thickness. It is assumed that the applied voltage to the piezoelectric layers is in the thickness direction and the electric field is generated in the thickness direction, too. The Euler-Bernoulli beam theory and nonlinear strain-displacement relation are used to obtain the equilibrium equations of the piezoelectric FGM beam. These equations may be useful for the static analysis of piezoelectric FGM beams. Based on the adjacent criterion, the stability equations for a perfect piezoelectric FGM beam are derived and by the pre-buckling analysis of the beam, buckling force is derived. Six types of boundary conditions with possible combination of simply-supported, clamped, free, and the roller edges are assumed for the beam and closed-form solutions are presented to evaluate the critical buckling load. The effects of the applied actuator voltage, beam geometry, boundary conditions, and power law index of functionally graded material on the buckling load are investigated

Keywords:

buckling , functionally graded materials , piezoelectric layers , Euler-Bernoulli beam theory