A scaled boundary finite element method for bending analysis of fiber-reinforced piezoelectric laminated composite plates

Abstract

The main purpose of this study is to develop a high performance numerical model for the analysis of the coupled electromechanical effects of the fiber-reinforced piezoelectric laminated composite plate under the mechanical or electric loading. Considering that the piezoelectric laminated plate is made of N orthotropic layers with the material axes oriented arbitrarily with respect to the laminate coordinate, the three-dimensional (3D) theory of elasticity for the kth orthotropic (piezoelectric) lamina is applied for the establishment of the mathematic model by using the elastic displacements and the electric potential as the nodal degree of freedom. The scaled boundary finite element method (SBFEM) coupling with the precise integration technique (PIT) are used to obtain the solution. Under the formulations of the SBFEM, only the in-plane of the plate structure is discretized into two-dimensional (2D) elements thus the spatial dimension is reduced by one. By introducing a dual vector of the internal nodal force, the SBFEM governing equation is described as an analytic formulation along the through-thickness with a matrix exponential function which can be estimated with high accuracy using the PIT. In addition, the high order spectral element is applied for the description of the basic variables so that the laminate with the complicated curved boundaries can be accurately determined. At the same time, assuming that the generalized displacement field is a quadratic function with respect to the thickness coordinate of each layer, then the generalized strain and stress fields can be determined directly based on the strain-displacement relations and the constitutive relations in the scaled boundary coordinate system. Numerical results show that a good agreement can be achieved with few discrete nodes for both the thin and moderately thick piezoelectric laminated plate under different types of loads through comparison with the 3D exact solutions and good performance has also been validated. Moreover, two numerical examples including a square piezoelectric laminated plate with the complex configuration (involving the fiber orientation and the distribution of piezoelectric layers) and a circular/annular piezoelectric laminated plate are further discussed to demonstrate the applicability of the present formulations.