M. Maleki - Mechanical Engineering Department, AmirKabir University of Technology
M. H. Naei - School of Mechanical Engineering, University of Tehran
E. Hosseinian - School of Mechanical Engineering, University of Tehran
A. Babahaji - School of Mechanical Engineering, University of Tehran

This paper considers deformation of a prismatic piezoelectric rod under pure torsion and various boundary conditions. The rod is sufficiently far from torsional load and made up of ADP (Ammonium Dehydrogen Phosphate) or PZT (Lead Zirconate Titanate). The analysis is independent of any assumption such as the assumptions of Saint Venant theory of torsion and how electric potential distributes through the cross section.In previous investigations, torsion of piezoelectric rods has already been discussed based on some simplifications such as linear distribution of electric potential and the Saint Venant assumptions of torsional deformation. In this paper, three dimensional theory of elasticity is applied to obtain exact distributions of electric potential; stress and strain of a piezoelectric rod without any simplification The exact solution of torsion, for any arbitrary cross section is obtained. This is analytically solved for a rectangular cross section rod of ADP and PZT. Additionally, a threedimensional finite element analysis is applied and the results are compared with the analytical solution. It is shown that the Saint Venant theory of torsion is still valid, while the assumption of linearity in electric potential distribution is invalid and leads to remarkable inaccuracy in stress and strain distributions.

Torsion, Piezoelectric, Electric Potential Distribution, Analytical Solution, ADP, PZT