An Efficient Scaled Boundary Finite Element Approach In Bending And Bucking Analysis Of Functionally Graded Piezoelectric Plates

Based on the three-dimensional (3D) linear elastic theory without enforcing any plate assumptions, the scaled boundary finite element method (SBFEM) is proposed to solve the solution of the displacements, electrical potentials, critical buckling loads and buckling modes in functionally graded piezoelectric (FGP) plate. The electroelastic properties are realized by transitioning material phase in the form of exponential function across the thickness direction. According to the constitutive equation of FGP materials and considering the coupling of elastic and electrical effects, the SBFEM model is established. The principle of virtual work in conjunction with the Green's theorem is applied to obtain the SBFEM governing equations with respect to the displacement domains and piezoelectric effects. By placing the scaling center of the SBFEM at infinity, the two-dimensional (2D) mesh can be translated along the thickness to obtain the 3D plate geometry, which can reduce the dimension of the model as well as calculation cost and greatly improve the computational efficiency. The bottom surface of the FGP plate is discretized by 2D higher-order spectral elements because of their high accuracy and fast convergence speed. The radial solution can be expressed analytically as a matrix exponential function, which can be solved accurately by the Pade ' expansion, and a simple and effective stiffness matrix can be obtained. By comparing several numerical examples with the reference solutions, the results indicate that the present analysis has good accuracy and rapid convergence. It is worth mentioning that this method is free of shear-locking and is applicable in the case of deformed grids. The influences of geometric variables, material composition, boundary conditions as well as load forms on the bending and bucking response are investigated.