1. Example: Radially Polarized Tube

2. Introduction This is a 2D static axisymmetric piezoelectric benchmark problem A radially polarized piezoelectric tube is modeled Radially Polarized Tube

3. Radially Polarized Tube – Problem Definition Height: 0.62 mm Inner radius: 0.38 mm Outer radius: 0.62 mm Geometry

4. Domain Equations Radially Polarized Tube – Problem Definition The axisymmetric constitutive equations:

5. Domain Equations Radially Polarized Tube – Problem Definition The governing field equations, in the absences of volume electric charges and neglecting body or inertia forces:

6. Boundary Conditions Radially Polarized Tube – Problem Definition Structural mechanics application: First and second case: The bottom surface is constrained from moving in the axial direction (z-direction). Second case: An internal fluid pressure of 0.1 MPa is added. Electrostatics application: First case: A 1V potential difference is applied between the inner and outer surfaces of the tube. Second case: The inner and outer surfaces of the tube are grounded.

7. Results Radially Polarized Tube – Results The deformed shape and radial displacement due to the radial electric field for the first case.

8. Results Radially Polarized Tube – Results The deformed shape, radial displacement and potential as function of tube thickness to due an internal pressure of 0.1 MPa (second case) A comparison of the results with Peelamedu et al shows a good agreement.