# About the Numerical Solution of the Equations of Piezoelectricity

• Martin Kögl
• Lothar Gaul
Part of the International Centre for Mechanical Sciences book series (CISM, volume 433)

## Abstract

In this paper, the numerical solution of piezoelectric problems by means of two discretization methods — the Finite Element Method (FEM) and the Boundary Element Method (BEM) — is described. At first, using the equations of elastostatics, the similarities and differences of the methods are explained and some of their advantages and disadvantages are pointed out. After this, the piezoelectric formulations of both methods are introduced. A numerical example serves to demonstrate the excellent agreement of the FEM and BEM results as well as to show the superiority of the BEM in the calculation of elastic stresses and the electric field.

## Keywords

Boundary Element Boundary Element Method Finite Element Method Computation Piezoelectric Body Dual Reciprocity

## References

1. Allik, H., and Hughes, T. J. R. (1970). Finite element method for piezoelectric vibration. Int. J. Num. Meth. Eng. 2: 151–157.
2. Bathe, K.-J. (1996). Finite element procedures. New Jersey: Prentice-Hall.Google Scholar
3. Brebbia, C., Telles, J., and Wrobel, L. (1984). Boundary element techniques. Berlin: Springer-Verlag.
4. Gaul, L., and Fiedler, C. (1996). Boundary Element Methods in Statics and Dynamics (in German). Braunschweig: Verlag Vieweg.Google Scholar
5. Kögl, M., and Gaul, L. (1999). Dual reciprocity boundary element method for three-dimensional problems of dynamic piezoelectricity. In Boundary Elements XXI, 537–548. Southampton: Computational Mechanics Publications.Google Scholar
6. Kögl, M., and Gaul, L. (2000). A Boundary Element Method for transient piezoelectric analysis. Engineering Analysis with Boundary Elements 24 (7–8): 591–598.
7. Kögl, M. (2000). A Boundary Element Method for Dynamic Analysis of Anisotropic Elastic, Piezoelectric, and Thermoelastic Solids. PhD thesis, Universität Stuttgart.Google Scholar
8. Lerch, R. (1990). Simulation of piezoelectric devices by two-and three-dimensional finite elements. IEEE Transactions on ultrasonics, ferroelectrics, and frequency control 37 (2): 233–247.
9. Partridge, P. W., Brebbia, C. A., and Wrobel, L. C. (1992). The dual reciprocity boundary element method. Southampton: Computational Mechanics Publications.
10. Tiersten, H. F. (1969). Linear piezoelectric plate vibrations. New York: Plenum Press.
11. Zienkiewicz, O. C., and Taylor, R. L. (1991). The finite element method, volume 2. London: McGraw-Hill, fourth edition.Google Scholar
12. Zienkiewicz, O. C., and Taylor, R. L. (1994). The finite element method, volume 1. London: McGraw-Hill, fourth edition.Google Scholar