1.4.10 Piezoelectric elements

Product: ABAQUS/Standard

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.

I. 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
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.

II. 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
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.

III. 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
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.

IV. 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
Dielectric term	5.872 × 10^–9