A bidirectional B-spline finite point method for the analysis of piezoelectric laminated composite plates and its application in material parameter identification

The bidirectional B-spline finite point method (BB-sFPM) can be used to construct a direction problem solver with good accuracy and little computational cost. To improve the performance of a piezoelectric structural system, we propose a parameter identification process with BB-sFPM for the analysis of a laminated composite plate with piezoelectric layers bonded to its upper and lower surfaces. The displacement and electric potential fields in the proposed method are approximated by using B-spline interpolation functions in x and y directions. And the displacement and stress solutions of the BB-sFPM are derived for a piezoelectric laminated composite plate (PLCP). The performance of the proposed method is assessed with some numerical examples available in published literature. The numerical results show that the proposed method has very good capability in the analysis of a thin-to-moderately thick PLCP. As an application, the displacements obtained by the BB-sFPM are applied to the material parameter identification of the PLCP. The parameter identification problem is formulated as an objective function minimization problem, defined as a square sum of differences between the measured displacement and the computed displacement by the BB-sFPM. The minimization problem is solved by using Levenberg–Marquardt method in which the sensitivity calculation is based on the differentiation of the governing equations of the BB-sFPM. Numerical examples are given to illustrate the validity of the proposed algorithm for the material parameter identification of the PLCP.