Semi-analytical solution of B-spline wavelet-based finite element for piezoelectric lamina

Some static problems of hybrid laminated plates with composite and piezoelectricity can be expediently solved by taking the advantage of wavelet finite element methods. Based on the features of laminated structures，the scale function of B-spline wavelet on the interval (BSWI) was employed to discretize the domain in-plane of structure，and the BSWI element formula of Hamilton canonical equation for piezoelectric materials was established by employing the modified mixed H-R( Hellinger-Reissner) variational principle for piezoelectric materials. One of the main characteristics of the BSWI element is the analytical form in the direction with respect to thickness. For the solution of the specific problem to ensure the interlaminar continuity of the electricity and mechanics variables，the transfer matrix technique was used. Numerical examples show that the BSWI element presented in the paper is successful. Employing the approach to deriving the BSWI element formula for piezoelectric materials can be extended to establish the analogous BSWI element formula for magnetoelectroelastic materials.