HRBF meshless method for buckling analysis of piezoelectric laminate plates

Radial basis function is simple in form, isotropic etc., and has made great progress in recent years. The bending and buckling of plates belong to high-order boundary value problems. Therefore the displacement and the rotation angles on the boundary are compulsive as essential condition. In order to ensure the accuracy of solution, a new Hermite Radial Basis Functions (HRBF) interpolation is introduced. The shape functions and their derivatives obtained by the HRBF interpolation have all the properties of Kronecker delta. Although the point collocation method is of high efficiency, its stability is bad. However, the Galerkin meshless method has high accuracy, good stability and so on. So, in this paper the Galerkin method is adopted for the discrete scheme. Based on the plate stability theory, the theory of piezoelectric laminates and HRBF meshless method, the discretization characteristic equation for the stability of piezoelectric laminated plates is derived. The simulation of a rectangular elastic plate demonstrates the effectiveness and precision of the method. The stability of a rectangular piezoelectric laminated plate under the action of in-plane load and electric field is considered and the stability domain is obtained.