# Piezoelectric Analysis

Piezoelectric materials are a class of materials in which structural deformation triggers electrical potential and vice versa.

## Piezoelectric Analysis in OptiStruct

Piezoelectric Analysis in OptiStruct involves two-way coupling in which a mechanical excitation will generate an electrical response. Conversely, an electrical excitation will generate a mechanical response. The coupling is strong, which means that both mechanical and electrical responses are solved simultaneously.

### Support Information

Piezoelectricity phenomenon is not modeled by a separate analysis type. It is modeled by structural materials, piezoelectric materials, and a coupling definition between the two domains in a structural analysis.

- Linear and Nonlinear Static (SMDISP)
- Normal Modes
- Direct Complex Eigenvalue
- Direct and Modal Frequency Response
- Linear and Nonlinear Transient (SMDISP)

**Element Type****Order**- Solids
- 1
^{st}and 2^{nd}order

## Input

Input file entries for piezoelectric coupling definition.

### Bulk Data Entries - Material Definitions

**Entry****Purpose**- MAT1PT
- Defines isotropic permittivity and damping for dielectric materials.
- MAT2PT
- Defines anisotropic permittivity and damping for dielectric materials.
- MATPZO
- Defines the piezoelectric coupling matrix between dielectric and structural components.
- MATT1PT
- Defines a temperature dependent version of MAT1PT.
- MATT2PT
- Defines a temperature dependent version of MAT2PT.
- MATTPZO
- Defines a temperature dependent version of MATPZO.

### Bulk Data Entries - Loads, Constraints, and Boundary Conditions

**Entry****Purpose**- CHARGE
- Defines a point charge.
- CHGAREA
- Defines charge density over an area.
- CHGVOL
- Defines charge density over a volume.
- SPC
- Can be used to define a zero electric potential, by setting
C='V'.This can also be used with other DoF components for the structural domain as well. For example,
`$--1---><---2--><---3--><---4--><--5---><--6---><---7--><--8---><---9--> SPC 1 261 V 10.0 SPC 2 261 123V 1000.0`

- SPCD
- Can be used to define a prescribed electric potential, by setting
C='V'.This can also be used with other DoF components for the structural domain as well. For example,
`$--1---><---2--><---3--><---4--><--5---><--6---><---7--><--8---><---9--> SPCD 10 261 V 10.0 SPCD 20 261 123V 1000.0`

- MPC
- Can be used to model an electric conductive surface, by setting C='V'.
- TLOAD1/TLOAD2
- Can be used to define a dynamic load.
- When TYPE=LOAD, it can point to CHARGE, CHGARE or CHGVOL
- When TYPE=DISP, it can point to SPCD with C=’V’

- RLOAD1/RLOAD2
- Can be used to define a dynamic load.
- When TYPE=LOAD, it can point to CHARGE, CHGARE or CHGVOL
- When TYPE=DISP, it can point to SPCD with C=’V’

### Bulk Data Entries - Miscellaneous

**Entry****Purpose**- PARAM, VAPMTV
- Defines the vacuum permittivity for piezoelectric materials. This is required when relative permittivity is defined in MAT1PT or MAT2PT.

### Problem Setup

```
$ *************************************************************
$ EXAMPLE: LINEAR STATIC ANALYSIS WITH PIEZOELECTRIC COUPLING
$ ************************************************************
DISPLACEMENT = ALL
SPCFORCE = ALL
GPFORCE = ALL
OLOAD = ALL
SUBCASE 1
ANALYSIS STATIC
SPC = 2
LOAD = 3
BEGIN BULK
$--1---><---2--><---3--><---4--><--5---><--6---><---7--><--8---><---9-->
PSOLID 1 2
MAT4 2 1000.0
MAT1PT 2 1000.0
CHARGE 3 163 1.0
SPC 2 2890 V 0.0
SPC 2 2875 V 0.0
..
```

## Output

Currently, results are only available in H3D format.

### Supported Output Requests

**Entry****Purpose**- DISPLACEMENT
- Electric potential results.
- OLOAD
- Applied charge results.
- GPFORCE
- Grid charge results.
It can be used to check whether the results are reasonable. At the grids without applied load or applied potential, grid charge should be close to zero.

- SPCFORCE
- Reaction charge results.
It is non-zero only at the grids where SPC with C=V is applied.

- STRAIN
- Electric field results.
It is the gradient of electric potential.

- STRESS
- Electric displacement results.
It is electric flux, both mechanical strain and electric field will produce electric displacement.