## General Mechanical

#### Piezoelectric Bimorph Actuator – Meshing and Electrode Issues

• Matthew Davenport
Subscriber

Hello,

I am working to create a Piezoelectric Birmorph Actuator that models a cantileaver beam with a substrate twice as thick as the indivdual layers of Piezoelectric materials on the top and bottom surface. The cantlieaver beam is meant to be an extreme condition where the actuators and substrate are very long compared to their thickness, i.e. 10-40 meters long while 1 to 2 mm thick.

This code is modified from the Ansys APDL manual example of a Piezoelectric Bimorph. I am able to get the model to work fairly well when the lengths are less than or equal to 1 meter, however past this length, I find errors in pairing electrodes across the top and bottom materials.

I do not entirely understand all line items in the code which I modified from the manual, however I believe the areas and meshing are not the issue, but rather something with how I am assigning the electrodes to the top surface. Any help or advice is greeatly appreciated!

/batch,list

/title, Static Analysis of a Piezoelectric Bimorph Beam

/nopr

/com,

/PREP7

!

! Define problem parameters

!

! - Geometry

!

L=.1 ! Length, m

H=0.5e-3 ! One-layer thickness, m

Ls = .1

Hs = 1e-3

Htop = Hs+H

!

!

V=100 ! Electrode voltage, Volt

Uy=10.e-3 ! Tip displacement, m

!

! - Material properties for PVDF

!

E1=2.0e9 ! Young's modulus, N/m^2

NU12=0.29 ! Poisson's ratio

G12=0.775e9 ! Shear modulus, N/m^2

d31=2.2e-11 ! Piezoelectric strain coefficients, C/N

d32=0.3e-11

d33=-3.0e-11

ept33=12 ! Relative permittivity at constant stress

!

! Finite element model of the piezoelectric bimorph beam

!

local,11 ! Coord. system for lower layer: polar axis +Y

local,12,,,,,180 ! Coord. system for upper layer: polar axis -Y

csys,11 ! Activate coord. system 11

rect,0,L,-H,0 ! Create area for lower layer

rect,0,Ls,0,Hs

rect,0,L, Hs,Htop ! Create area for upper layer

aglue,all ! Glue layers

esize,H ! Specify the element length

!

et,1,PLANE223,1001,,0 ! 2-D piezoelectric element, plane stress

et,2,PLANE183

MPTEMP,,,,,,,,

MPTEMP,1,0

MPDATA,EX,2,,228e9

MPDATA,PRXY,2,,0.3

tb,ANEL,1,,,1 ! Elastic compliance matrix

tbda,1,1/E1,-NU12/E1,-NU12/E1

tbda,7,1/E1,-NU12/E1

tbda,12,1/E1

tbda,16,1/G12

tb,PIEZ,1,,,1 ! Piezoelectric strain matrix

tbda,2,d31

tbda,5,d33

tbda,8,d32

tb,DPER,1,,,1 ! Permittivity at constant stress

tbdata,1,ept33,ept33

tblist,all ! List input and converted material matrices

amesh,all

nsel,s,loc,x,L

*get,ntip,node,0,num,min ! Get master node at beam tip

!

nelec = 100 ! Number of electrodes on top surface

*dim,ntop,array,nelec

l1 = 0 ! Initialize electrode locations

l2 = L/nelec

*do,i,1,nelec ! Define electrodes on top surface

nsel,s,loc,y,Htop

nsel,r,loc,x,l1,l2

cp,i,volt,all

*get,ntop(i),node,0,num,min ! Get master node on top electrode

l1 = l2 + Htop/10 ! Update electrode location

l2 = l2 + L/nelec

*enddo

nsel,s,loc,y,-H ! Define bottom electrode

d,all,volt,0 ! Ground bottom electrode

nsel,s,loc,x,0 ! Clamp left end of bimorph

d,all,ux,0,,,,uy

nsel,all

fini

/SOLU ! Actuator simulation

antype,static ! Static analysis

*do,i,1,nelec

d,ntop(i),volt,V ! Apply voltages to top electrodes

*enddo solve

solve

fini

/SOLU ! Sensor simulation

• Erik Kostson
Ansys Employee

Hi

I would recommend to use WB coupled field harmonic or static system.

If you want to use an example though in APDL there are some in our help manual - coupled field analysis.

All the best

Erik

• Matthew Davenport
Subscriber

Hi Erik,

Thank you for your response, I have been using the 2.15 example of a Bimorph in the APDL Coupeled Field Analysis Guide, which this code is based off of. Creating and selecting electrode positions across the top and bottom surfaces seems to be where this code breaks. Any advice on how to use the nsel command?

Thank you,

• Erik Kostson
Ansys Employee

Hi

Is this the exact same 2.15 example as in the apdl manual? if it is it should run

Or is this example something different and not our 2.15 example?

All the best

Erik

• Matthew Davenport
Subscriber

Hi Erik,

This is based off that example, but I have made modifications to represent my problem constraints, which include a substrate material between the actuating surfaces, and different geometry.

The example straight from the manual runs great, but the modifications I have made are resulting in strange errors, and I am unsure how.

• Erik Kostson
Ansys Employee

Hello

There is an error in the line:

*enddo solve is wrong and should be:

```*enddo
solveAnother things is that the pol. direction is opposite in the 2.15 example while you have the same:```

The polarization which is given by these lines and in combination with the material properties given (which are relative the element system):

```local,11                        ! Coord. system for lower layer: polar axis +Y
local,12,,,,,180                ! Coord. system for upper layer: polar axis -Y```
```type,1 \$ esys,11
amesh,1                         ! Generate mesh within the lower layer
type,1 \$ esys,12
amesh,3                         ! Generate mesh within the upper layer```

Erik

• Matthew Davenport
Subscriber

Hi Erik, thank you for the clarification!

Regarding the polarization, are you stating that my code is now, the polarization of the material set by the mat properties is opposite the polarization direction set by the coord system? If so, how could I correct the coordinate system lines of code?

• Matthew Davenport
Subscriber

And a follow up question as I am new to coupeled field elements in ADPL, should the top piezo and bottom piezo be polarized in opposite directions? I am also attempting to create a 3D bimorph cantileaver beam using 226 and 186 elements. Is there a specific way I should handle the polarization and voltages aross the top and bottom piezo volumes in that example?

• Erik Kostson
Ansys Employee

Hi

In the 2.15 example the polarization is opposite on top and bottom piezo patch (so the polarization is given by the material property definition TB command and the element system esys as shown below):

```local,11                        ! Coord. system for lower layer: polar axis +Y
local,12,,,,,180                ! Coord. system for upper layer: polar axis -Y```
```type,1 \$ esys,11
amesh,1                         ! Generate mesh within the lower layer
type,1 \$ esys,12
amesh,3   ```