Wavelet Collocation Precise Integration Method For Piezoelectric Laminated Plates

In the Hamilton canonical equation theory of elasticity, stress and displacement are usually set as unknown variables to be solved. The use of such method to solve the problem of piezoelectric laminates indicates that this type of mixed variables has unique advantages.On the other hand, the method of solving differential equations based on the wavelet theory is high-efficient. In this paper, the goal is to solve the static problem of piezoelectric laminated rectangular plates by combinating the Hamilton canonical equation theory and the wavelet collocation precise integration method. The main work is as follows:Firstly, all the analytical methods of piezoelectric laminates, wavelet collocation method and precise integration method are summarized systematically based on the three-dimensional problem, thus it lays the foundation for solving piezoelectric laminates problems by combinating the Hamilton canonical equation theory and the wavelet collocation precise integration method.Hamilton canonical equation(or mixed state equation) is deduced from the basic elastic equation and the H-R variational principle of the piezoelectric materials.For rectangular plates, the discrete equation which is discrete in plane and continuum along the thickness is obtained by introducing Shannon wavelet collocation method and Quasi-Shannon wavelet collocation method into the Hamilton canonical equation.Then the process of solving the discrete equation according to the precise integration method is deduced in detail. Numerical analysis program is written based on Mathematic Programming Language. Examples include single-layer, multi-layer and mixed multi-layer piezoelectric rectangular plates with four sides clamped. Numerical results are compared with the solution of ANSYS Software, and show that the current approach is correct.Since this method is based on the three-dimensional problem and doesn't introduce any simplifying assumptions like other general plate theories, its solutions are accurate and reliable. This method can be used to inspect the effectiveness of various plate theories. This work provides a new method of analyzing the statics problems of rectangular piezoelectric laminated plates.