Piezoelectric Analysis

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

They are widely used for a variety of applications such as load cells, hearing aids, accelerometers, pressure-sensors, MEMS (Micro Electromechanical systems) in industries such as Acoustics, Aerospace, Automotive, Biomedical, Oil and Gas among others.
Figure 1. (a) A piezoelectric material subject to structural loading (applied stress) generates electric potential. Conversely, (b) when electric potential is applied, it induces mechanical strain


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.

Supported analysis types:
  • Linear and Nonlinear Static (SMDISP)
  • Normal Modes
  • Direct Complex Eigenvalue
  • Direct and Modal Frequency Response
  • Linear and Nonlinear Transient (SMDISP)
Supported element types:
Element Type
Order
Solids
1st and 2nd order
Note: This support limitation is applicable only to the elements whose properties refer to piezoelectric material entries. The model can still have other element types for non-piezoelectric material definitions.

Input

Input file entries for piezoelectric coupling definition.

Bulk Data Entries - Material Definitions

Note: Other entities of Structural Analysis (for example, MAT1) also need to be defined in addition to these.
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

Note: Other entities of Structural Analysis (for example, structural loads, SPCs) can be defined in addition to these.
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 section of an input file to demonstrate modeling piezoelectric coupling:
$ *************************************************************
$ 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.