II. How To Use ATILA

3.3 Multilayer (Homework 5)
2D Multilayer


PROBLEM - 2D 8-Layer, PZT4, Width 5 mm x layer thickness 1 mm, Interdigital Electrode


  • Composite of two different polarization layers, with an interdigital electrode configuration
  • Learn the internal stress distribution
1.
Calculate the potential and stress distributions in a 2D piezoelectric PZT4 multilayer actuator with the following dimensions under a static and a dynamic drive: width 5 mm x 8 layers of 1 mm thick each layer with an interdigital electrode configuration (0.5 mm embedded from the surface).
2.
Show the displacement motion of this actuator (show the non-uniform surface motion of the actuator) under static (100 Hz) drive.
3.
Calculate the Admittance Spectrum around 190 kHz.
4.
Discuss the deformation/stress distribution difference between the off-resonance (100 Hz) and the resonance mode (190 kHz).

 
HINT:

GEOMETRY/DRAWING
Create Surface

Geometry -> Create -> Object -> Rectangle -> Enter first corner point -> 0,0 -> Enter second corner point -> 5,1 -> Enter

Divide Surface

Geometry -> Edit -> Divide -> Surfaces -> Near point -> Select the Surface -> Choose NURBS sense -> Input -> Near Points -> 0.5, 0 & 4.5, 0

Create Multilayer Copy mode

Utilities -> Copy -> Surfaces -> Translate by 1 mm (No Extrude) -> Select

MATERIAL ASSIGMENT
Piezoelectric Materials

Data -> Materials -> Piezoelectric -> PZT4 -> Assign -> Surfaces

BOUNDARY CONDITIONS
Polarization/Local Axes

Data -> Conditions -> Surfaces -> Geometry -> Polarization (Cartesian) -> Define Polarization (P1) (0,0,1) direction
Choose 3PointsXZ -> Define X axis by putting (1,0,0) -> Then define Z axis by putting (0,0,1) -> Escape
Assign Polarization (Local-Axes P1) -> Choose every two layer surfaces -> Finish

Data -> Conditions -> Surfaces -> Geometry -> Polarization (Cartesian) -> Define Polarization (P2) (0,0,-1) direction
Choose 3PointsXZ -> Define X axis by putting (1,0,0) -> Then define Z axis by putting (0,0,-1) -> Escape
Assign Polarization (Local-Axes P2) -> Choose every two layer surfaces -> Finish

Potential

Data -> Conditions -> lines -> Potential 0.0 (or Ground in ATILA 5.2.4 or higher version) -> Assign every two layer line-> Forced Potential 1.0 -> Assign every two layer line

MESHING

Mapped Mesh

Meshing -> Structured -> Surfaces -> Select all surfaces -> Then Cancel the further process
Meshing -> Structured -> Lines -> Enter number to divide line -> Choose necessary numbers -> Generate

PROBLEM TYPE
Data -> Problem data -> 2D & Plane Strain, Harmonic, Click both Compute Stress and Include Losses

FREQUENCY
Data -> Interval data Interval 1 (100 Hz), Interval 2 (180000-200000 Hz)

CALCULATION

Calculate -> Calculate window -> Start

POST PROCESS/VIEW RESULTS
Click for Opening the Post Calculation (Flavia) Domain
Notice the new Toolbar appearance

Click Admittance/Impedance Result
Admittance Peak Point : 190000 Hz -> This peak corresponds to the First Resonance
View Animation - Vibration Mode at a Particular Frequency
View results -> Default Analysis/Step -> Harmonic-Magnitude -> Set a Frequency
(100 Hz for Off-Resonance Mode: Peak Point : 190000 Hz for Resonance Mode)
Double Click

100 Hz Off-Resonance
190000Hz Resonance