Piezoelectric elements

This problem contains basic test cases for one or more Abaqus elements and features.

Piezoelectric elements have both displacements and electric potentials as degrees of freedom. These elements include truss, plane stress, plane strain, axisymmetric, or three-dimensional continuum. The elements are identical to the basic stress/displacement elements except for the coupling between the stress field and the electrical potential gradients. The mechanical loads are tested for these elements but are not reported here since they are identical to those reported in the section for continuum stress/displacement elements. Only the additional loads associated with body and distributed charges are reported in this section.

This page discusses:

Truss elements
Plane stress and plane strain elements
Axisymmetric elements
Three-dimensional solids

ProductsAbaqus/Standard

Truss elements

Problem description

Model:


Length	1.0
Area	0.1
Centrifugal axis of rotation	(0, 1, 0) through (.5, 0, 0)
Gravitational load vector	(0, −1, 0)

Material:


Young's modulus	3 × 10⁶
Coefficient of thermal expansion	.0001
Density	5 × 10⁻⁵
Piezoelectric coupling matrix	$[\begin{matrix} 15.08 & 0 & 0 \\ - 5.207 & 0 & 0 \\ - 5.207 & 0 & 0 \\ 0 & 12.710 & 0 \\ 0 & 0 & 12.710 \\ 0 & 0 & 0 \end{matrix}]$
Dielectric term	5.872 × 10⁻⁹

Initial conditions


Initial temperature	ALL, −10.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

T2D2E element load tests:

et22efdf.inp: BX, BY, GRAV, CENT, CENTRIF, EBF.
et22efdr.inp: ROTA.

T3D2E element load tests:

et32efdf.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, EBF.
et32efdr.inp: ROTA.

T2D3E element load tests:

et23efdf.inp: BX, BY, GRAV, CENT, CENTRIF, EBF.
et23efdr.inp: ROTA.

T3D3E element load tests:

et33efdf.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, EBF.
et33efdr.inp: ROTA.

Plane stress and plane strain elements

Problem description

Model:


Square dimensions	7 × 7
Thickness	1.0
Centrifugal axis of rotation	(0, 1, 0) through origin
Gravitational load vector	(0, −1, 0)

Material:


Young's modulus	3 × 10⁶
Poisson's ratio	0.3
Coefficient of thermal expansion	.0001
Density	5 × 10⁻⁵
Piezoelectric coupling matrix	$[\begin{matrix} 15.08 & 0 & 0 \\ - 5.207 & 0 & 0 \\ - 5.207 & 0 & 0 \\ 0 & 12.710 & 0 \\ 0 & 0 & 12.710 \\ 0 & 0 & 0 \end{matrix}]$
Dielectric term	5.872 × 10⁻⁹

Initial conditions


Initial temperature	ALL, −10.0
Hydrostatic pressure datum	lower-order elements: 7.0
	higher-order elements: 3.0
Hydrostatic pressure elevation	0.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

CPS3E element load tests:

ecs3efdf.inp: BX, BY, GRAV, CENT, CENTRIF, P1, P2, P3, HP1, HP2, HP3, EBF, ES1, ES2, ES3.
ecs3efdr.inp: ROTA.
ecs3efdm.inp: ES, HP, P.

CPE3E element load tests:

ece3efdf.inp: BX, BY, GRAV, CENT, CENTRIF, P1, P2, P3, HP1, HP2, HP3, EBF, ES1, ES2, ES3.
ece3efdr.inp: ROTA.
ece3efdm.inp: ES, HP, P.

CPS4E element load tests:

ecs4efdf.inp: BX, BY, GRAV, CENT, CENTRIF, P1, P2, P3, P4, HP1, HP2, HP3, HP4, EBF, ES1, ES2, ES3, ES4.
ecs4efdr.inp: ROTA.
ecs4efdm.inp: ES, HP, P.

CPE4E element load tests:

ece4efdf.inp: BX, BY, GRAV, CENT, CENTRIF, P1, P2, P3, P4, HP1, HP2, HP3, HP4, EBF, ES1, ES2, ES3, ES4.
ece4efdr.inp: ROTA.
ece4efdm.inp: ES, HP, P.

CPS6E element load tests:

ecs6efdf.inp: BX, BY, GRAV, CENT, CENTRIF, P1, P2, P3, HP1, HP2, HP3, EBF, ES1, ES2, ES3.
ecs6efdr.inp: ROTA.
ecs6efdm.inp: ES, HP, P.

CPE6E element load tests:

ece6efdf.inp: BX, BY, GRAV, CENT, CENTRIF, P1, P2, P3, HP1, HP2, HP3, EBF, ES1, ES2, ES3.
ece6efdr.inp: ROTA.
ece6efdm.inp: ES, HP, P.

CPS8E element load tests:

ecs8efdf.inp: BX, BY, GRAV, CENT, CENTRIF, P1, P2, P3, P4, HP1, HP2, HP3, HP4, EBF, ES1, ES2, ES3, ES4.
ecs8efdr.inp: ROTA.
ecs8efdm.inp: ES, HP, P.

CPE8E element load tests:

ece8efdf.inp: BX, BY, GRAV, CENT, CENTRIF, P1, P2, P3, P4, HP1, HP2, HP3, HP4, EBF, ES1, ES2, ES3, ES4.
ece8efdr.inp: ROTA.
ece8efdm.inp: ES, HP, P.

CPS8RE element load tests:

ecs8erdf.inp: BX, BY, GRAV, CENT, CENTRIF, P1, P2, P3, P4, HP1, HP2, HP3, HP4, EBF, ES1, ES2, ES3, ES4.
ecs8erdr.inp: ROTA.
ecs8erdm.inp: ES, HP, P.

CPE8RE element load tests:

ece8erdf.inp: BX, BY, GRAV, CENT, CENTRIF, P1, P2, P3, P4, HP1, HP2, HP3, HP4, EBF, ES1, ES2, ES3, ES4.
ece8erdr.inp: ROTA.
ece8erdm.inp: ES, HP, P.

Axisymmetric elements

Problem description

Model:


Planar dimensions	3 × 3
Inside radius	1.0
Outside radius	4.0
Centrifugal axis of rotation	(0, 1, 0) through origin
Gravitational load vector	(0, −1, 0)

Material:


Young's modulus	3 × 10⁶
Poisson's ratio	0.3
Coefficient of thermal expansion	.0001
Density	5 × 10⁻⁵
Piezoelectric coupling matrix	$[\begin{matrix} 15.08 & 0 & 0 \\ - 5.207 & 0 & 0 \\ - 5.207 & 0 & 0 \\ 0 & 12.710 & 0 \\ 0 & 0 & 12.710 \\ 0 & 0 & 0 \end{matrix}]$
Dielectric term	5.872 × 10⁻⁹

Initial conditions


Hydrostatic pressure datum	3.0
Hydrostatic pressure elevation	0.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

CAX3E element load tests:

eca3efdf.inp: BZ, GRAV, CENT, P1, P2, P3, HP1, HP2, HP3, EBF, ES1, ES2, ES3.
eca3efdm.inp: ES, HP, P.

CAX4E element load tests:

eca4efdf.inp: BZ, GRAV, CENT, P1, P2, P3, P4, HP1, HP2, HP3, HP4, EBF, ES1, ES2, ES3, ES4.
eca4efdm.inp: ES, HP, P.

CAX6E element load tests:

eca6efdf.inp: BZ, GRAV, CENT, P1, P2, P3, HP1, HP2, HP3, EBF, ES1, ES2, ES3.
eca6efdm.inp: ES, HP, P.

CAX8E element load tests:

eca8efdf.inp: BZ, GRAV, CENT, P1, P2, P3, P4, HP1, HP2, HP3, HP4, EBF, ES1, ES2, ES3, ES4.
eca8efdm.inp: ES, HP, P.

CAX8RE element load tests:

eca8erdf.inp: BZ, GRAV, CENT, P1, P2, P3, P4, HP1, HP2, HP3, HP4, EBF, ES1, ES2, ES3, ES4.
eca8erdm.inp: ES, HP, P.

Three-dimensional solids

Problem description

Model:


Cubic dimensions	7 × 7 × 7
Centrifugal axes of rotation	(0, 1, 0) through (−1000, 3.5, −3.5)
Gravitational load vector	(1, 0, 0)

Material:


Young's modulus	3 × 10⁶
Poisson's ratio	0.3
Coefficient of thermal expansion	.0001
Density	10.0
Piezoelectric coupling matrix	$[\begin{matrix} 15.08 & 0 & 0 \\ - 5.207 & 0 & 0 \\ - 5.207 & 0 & 0 \\ 0 & 12.710 & 0 \\ 0 & 0 & 12.710 \\ 0 & 0 & 0 \end{matrix}]$
Dielectric term	5.872 × 10⁻⁹

Initial conditions


Initial temperature	ALL, −10.0
Hydrostatic pressure datum	0.0
Hydrostatic pressure elevation	−7.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

C3D4E element load tests:

ec34efdf.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P1, P2, P3, P4, HP1, HP2, HP3, HP4, EBF, ES1, ES2, ES3, ES4.
ec34efdr.inp: ROTA.
ec34efdm.inp: ES, HP, P.

C3D6E element load tests:

ec36efdf.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P1, P2, P3, P4, P5, HP1, HP2, HP3, HP4, HP5, EBF, ES1, ES2, ES3, ES4, ES5.
ec36efdr.inp: ROTA.
ec36efdm.inp: ES, HP, P.

C3D8E element load tests:

ec38efdf.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P1, P2, P3, P4, P5, P6, HP1, HP2, HP3, HP4, HP5, HP6, EBF, ES1, ES2, ES3, ES4, ES5, ES6.
ec38efdr.inp: ROTA.
ec38efdm.inp: ES, HP, P.

C3D10E element load tests:

ec3aefdf.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P1, P2, P3, P4, HP1, HP2, HP3, HP4, EBF, ES1, ES2, ES3, ES4.
ec3aefdr.inp: ROTA.
ec3aefdm.inp: ES, HP, P.

C3D15E element load tests:

ec3fefdf.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P1, P2, P3, P4, P5, HP1, HP2, HP3, HP4, HP5, EBF, ES1, ES2, ES3, ES4, ES5.
ec3fefdr.inp: ROTA.
ec3fefdm.inp: ES, HP, P.

C3D20E element load tests:

ec3kefdf.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P1, P2, P3, P4, P5, P6, HP1, HP2, HP3, HP4, HP5, HP6, EBF, ES1, ES2, ES3, ES4, ES5, ES6.
ec3kefdr.inp: ROTA.
ec3kefdm.inp: ES, HP, P.

C3D20RE element load tests:

ec3kerdf.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P1, P2, P3, P4, P5, P6, HP1, HP2, HP3, HP4, HP5, HP6, EBF, ES1, ES2, ES3, ES4, ES5, ES6.
ec3kerdr.inp: ROTA.
ec3kerdm.inp: ES, HP, P.