Symmetrical saddle algorithms in fem analysis of the compound piezoelectric devices

O. N. Akopov ; O. A. Belokon ; K. A. Nadolin ; A. V. Nasedkin ; A. S. Skaliukh ; A. N. Soloviev

Matematičeskoe modelirovanie, Tome 13 (2001) no. 2, pp. 51-60

Résumé

The mathematical modeling by FEM of the piezoelectric modules of technical devices is considered. Continual formulations of the dynamical problems in compound domains with different physical and mechanical properties (piezoelectric, elastic and acoustic) are given. By applying semi-discrete FEM approximations of the solution to the governing equations in weak form the variational FEM equations with symmetrical saddle matrices are derived. A set of algorithms, which use the symmetrical saddle matrices to create and solve the FEM equations, are proposed for static and dynamic problems. Thus the Newmark method without velocities and accelerations node values is used for step-by-step time integration scheme and modified Chollessky decomposition method is used for linear system solver. All procedures that we need in FEM manipulations (the degree of freedom rotations, mechanical and electric boundary condition settings, etc.) are provided also in symmetrical form. On the base of above-mentioned algorithms the computer program ACELAN has been developed. ACELAN provides the opportunity to do analysis of compound piezoelectric axially symmetric or 2D devices. It had been tested carefully and the results had been compared with the analogous that were obtained by a wellknown computer program ANSYS. The numerical experiments showed that ACELAN and its' algorithms are effective enough and give accurate results.