PLANE222


2D 4-Node Coupled-Field Solid

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PLANE222 Element Description

PLANE222 supports the following physics combinations:

  • Structural-Thermal

  • Piezoresistive

  • Electrostatic-Structural

  • Piezoelectric

  • Thermal-Electric

  • Structural-Thermoelectric

  • Thermal-Piezoelectric

  • Structural-Diffusion

  • Thermal-Diffusion

  • Electric-Diffusion

  • Thermal-Electric-Diffusion

  • Structural-Thermal-Diffusion

  • Structural-Electric-Diffusion

  • Structural-Thermal-Electric-Diffusion

The element has four nodes with up to five degrees of freedom per node. The element can be used as either a plane element or an axisymmetric element.

Structural capabilities include elasticity, plasticity, hyperelasticity, viscoelasticity, viscoplasticity, creep, large strain, large deflection, and stress-stiffening. It also has mixed formulation capability for simulating deformations of nearly incompressible elastoplastic materials, and fully incompressible hyperelastic materials.

For coupled-field analyses with structural degrees of freedoms, PLANE222 uses by default the full-integration method (also known as the selective reduced integration method). For more information and limitations on this method, see B-Bar Method (Selective Reduced Integration). Enhanced Strain Formulation and Simplified Enhanced Strain Formulation are also supported for structural-thermal, piezoelectric, piezoresistive, structural-diffusion, structural-thermal-diffusion, structural-thermoelectric, and structural-electric-diffusion analyses. For more information about additional degrees of freedom, see Element Technologies.

Piezoresistive capabilities include the piezoresistive effect. Piezoelectric capabilities include direct and converse piezoelectric effects. Electrostatic-structural capabilities include electrostatic force coupling. Thermoelectric capabilities include Seebeck, Peltier, and Thomson effects, as well as Joule heating. In addition to thermal expansion, structural-thermal capabilities include the piezocaloric effect in dynamic analyses. The Coriolis effect is available for analyses with structural degrees of freedom. The thermoplastic and viscoelastic heating effects are available for analyses with structural and thermal degrees of freedom.

The diffusion expansion effect is available for analyses with structural and diffusion degrees of freedom. The thermo-migration effect (Soret effect) and the temperature-dependent saturated concentration effect is available for analyses with thermal and diffusion degrees of freedom. The electro-migration effect is available for analyses with electrical and diffusion degrees of freedom.

The specific heat matrix is diagonalized as described in Lumped Matrices.

See PLANE222 in the Mechanical APDL Theory Reference for more details about this element.

Figure 222.1: PLANE222 Geometry

PLANE222 Geometry

PLANE222 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 222.1: PLANE222 Geometry. The element input data includes four nodes and structural and thermal material properties. For the plane or plane stress case, you can also specify the element thickness (Z depth) by setting KEYOPT(3) to 3 and inputting the real constant THK. The default element coordinate system is along global directions. You may define an element coordinate system using ESYS, which forms the basis for orthotropic material directions.

KEYOPT(1) determines the element degree-of-freedom set and the corresponding force labels and reaction solution. KEYOPT(1) is set equal to the sum of the field keys shown in Table 222.1: PLANE222 Field Keys. KEYOPT(1) is set to 11 for a structural-thermal analysis (structural field key + thermal field key = 1 + 10). For a structural-thermal analysis, UX, UY, and TEMP are the degree-of-freedom labels, and force and heat flow are the reaction solution.

KEYOPT(3) = 3 enables you to define constant or varying thickness via the real constant input. To define varying thickness, input a table name (specified as %tablename% and created via *DIM). Tabular thickness can vary in terms of coordinates (X and Y) or node numbers. Supported primary variables for tabular thickness are X, Y, and NODES. (The Function Tool is a convenient way to define your thickness tables; you can use it to define thickness as a function of global/local coordinates.)

Table 222.1: PLANE222 Field Keys

Field Field Key DOF Label Force Label Reaction Solution
Structural1UX, UY[a] FX, FYForce
Thermal10TEMPHEATHeat Flow
Electric Conduction100VOLTAMPSElectric Current
Electrostatic1000VOLTCHRGElectric Charge
Diffusion100000CONCRATEDiffusion Flow Rate

[a] When KEYOPT(3) is set to 6 for analyses with structural degrees of freedom, ROTY is added to the set of degrees of freedom.


The coupled-field analysis KEYOPT(1) settings, degree-of-freedom labels, force labels, reaction solutions, and analysis types are shown in the following table.

Table 222.2: PLANE222 Coupled-Field Analysis

Coupled-Field Analysis KEYOPT(1) DOF Label Force Label Reaction Solution Analysis Type
Structural-Thermal[a], [b] 11UX, UY, TEMPFX, FY, HEATForce,

Heat Flow

Static,

Full Harmonic,

Full Transient

Piezoresistive101UX, UY, VOLTFX, FY, AMPSForce,

Electric Current

Static,

Full Transient

Electrostatic-Structural1001[c] UX, UY, VOLTFX, FY, CHRGForce, Electric Charge (negative)Static,

Full Transient,

Linear Perturbation Static,

Linear Perturbation Harmonic,

Linear Perturbation Modal

Piezoelectric (Charge-Based)1001[c] UX, UY,

VOLT

FX, FY,

CHRG

Force,

Electric Charge (negative)

Static,

Modal,

Linear Perturbation Modal,

Full, Linear Perturbation, or Mode Superposition Harmonic,

Full or Mode Superposition Transient

Piezoelectric (Current-Based)101UX, UY,

VOLT

FX, FY,

AMPS

Force,

Electric Current

Full Harmonic,

Full Transient

Thermal-Electric110TEMP,

VOLT

HEAT,

AMPS

Heat Flow,

Electric Current

Static,

Full Transient

Structural-Thermoelectric[a] 111UX, UY,

TEMP,

VOLT

FX, FY,

HEAT,

AMPS

Force,

Heat Flow,

Electric Current

Static,

Full Transient

Thermal-Piezoelectric[a], [b] 1011UX, UY,

TEMP,

VOLT

FX, FY,

HEAT,

CHRG

Force,

Heat Flow,

Electric Charge (negative)

Static,

Full Harmonic,

Full Transient,

Structural-Diffusion[a] 100001UX, UY,

CONC

FX, FY,

RATE

Force,

Diffusion Flow Rate

Static,

Full Transient

Thermal-Diffusion[a] 100010TEMP,

CONC

HEAT,

RATE

Heat Flow,

Diffusion Flow Rate

Static,

Full Transient

Electric-Diffusion[a] 100100VOLT,

CONC,

AMPS,

RATE

Electric Current,

Diffusion Flow Rate

Static,

Full Transient

Thermal-Electric-Diffusion[a] 100110TEMP,

VOLT,

CONC

HEAT,

AMPS,

RATE

Heat Flow,

Electric Current,

Diffusion Flow Rate

Static,

Full Transient

Structural-Thermal-Diffusion[a] 100011UX, UY,

TEMP,

CONC

FX, FY,

HEAT,

RATE

Force,

Heat Flow,

Diffusion Flow Rate

Static,

Full Transient

Structural-Electric-Diffusion[a] 100101UX, UY,

VOLT,

CONC

FX, FY,

AMPS,

RATE

Force,

Electric Current,

Diffusion Flow Rate,

Static,

Full Transient

Structural-Thermal-Electric-Diffusion[a] 100111UX, UY,

TEMP,

VOLT,

CONC

FX, FY,

HEAT,

AMPS,

RATE

Force,

Heat Flow,

Electric Current,

Diffusion Flow Rate

Static,

Full Transient

[a] For static and full transient analyses, KEYOPT(2) can specify a strong (matrix) or weak (load vector) structural-thermal, structural-diffusion, thermal-diffusion, and electric diffusion coupling.

[b] For harmonic analyses, only strong coupling (KEYOPT(2) = 0) applies.

[c] The electrostatic-structural analysis available with KEYOPT(1) = 1001 defaults to electrostatic force coupling. To turn off the electrostatic force coupling, you can set KEYOPT(4) = 2 for elastic air or KEYOPT(4) = 4 for solid dielectrics, respectively. Alternatively, to do an uncoupled structural-electrostatic analysis, you can specify a negligible piezoelectric coefficient using TBDATA with TB,PIEZ.


As shown in the following tables, material property requirements consist of those required for the individual fields (structural, thermal, electric conduction, electrostatic, or diffusion) and those required for field coupling. Individual material properties are defined via MP and MPDATA. Nonlinear and multiphysics material models are defined via the TB command.

Table 222.3: Structural Material Properties

Field Field Key Material Properties and Material Models

Structural

1

EX, EY, EZ, PRXY, PRYZ, PRXZ (or NUXY, NUYZ, NUXZ), GXY, GYZ, GXZ, DENS, ALPD, BETD, DMPR, DMPS

ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ, or THSX, THSY, THSZ), REFT

---

Anisotropic hyperelasticity, Anisotropic elasticity, Bergstrom-Boyce, Bilinear isotropic hardening, Bilinear kinematic hardening, Cast iron, Chaboche nonlinear kinematic hardening, Creep, Elasticity, Extended Drucker-Prager, Gurson pressure-dependent plasticity, Hill anisotropy, Hyperelasticity, Mullins effect, Voce isotropic hardening law, Plasticity, Prony series constants for viscoelastic materials, Rate-dependent plasticity (viscoplasticity), Rate-independent plasticity, Material-dependent alpha and beta damping (Rayleigh damping), Material-dependent structural damping, Shift function for viscoelastic materials, Shape memory alloy, Uniaxial stress-strain relation


Table 222.4: PLANE222 Material Properties and Material Models

Coupled-Field Analysis KEYOPT(1) Material Properties and Material Models
Structural-Thermal11StructuralSee Table 222.3: Structural Material Properties
ThermalKXX, KYY, DENS, C, ENTH, HF
CouplingALPX, ALPY, ALPZ, REFT, QRATE
Piezoresistive[a] 101StructuralSee Table 222.3: Structural Material Properties
ElectricRSVX, RSVY, PERX, PERY
Coupling Piezoresistivity
Electrostatic-Structural1001StructuralSee Table 222.3: Structural Material Properties
ElectricPERX, PERY

---

Anisotropic electric permittivity

Piezoelectric1001

(Charge-Based)

101

(Current-Based)

StructuralSee Table 222.3: Structural Material Properties [b]

---

Anisotropic viscosity

---

Anisotropic elastic loss tangent

ElectricPERX, PERY, LSST (and/or RSVX, RSVY)

---

Anisotropic electric permittivity

---

Anisotropic dielectric loss tangent

Coupling Piezoelectric matrix
Thermal-Electric[a] 110ThermalKXX, KYY, DENS, C, ENTH, HF
ElectricRSVX, RSVY, PERX, PERY
CouplingSBKX, SBKY
Structural-Thermoelectric111StructuralSee Table 222.3: Structural Material Properties
ThermalKXX, KYY, DENS, C, ENTH, HF
ElectricRSVX, RSVY, PERX, PERY
CouplingALPX, ALPY, ALPZ, REFT, QRATE

---

SBKX, SBKY

---

Piezoresistivity

Thermal-Piezoelectric1011StructuralSee Table 222.3: Structural Material Properties [b]
ThermalKXX, KYY, DENS, C, ENTH, HF
ElectricPERX, PERY, LSST (and/or RSVX, RSVY)

---

Anisotropic electric permittivity

CouplingALPX, ALPY, ALPZ, REFT

---

Piezoelectric matrix

Structural-Diffusion[a] 100001StructuralSee Table 222.3: Structural Material Properties
DiffusionDXX, DYY, CSAT
CouplingBETX, BETY, CREF
Thermal-Diffusion[a] 100010ThermalKXX, KYY, DENS, C, ENTH, HF
DiffusionDXX, DYY, CSAT
CouplingTemperature-dependent CSAT

---

Migration Model

Electric-Diffusion[a] 100100ElectricRSVX, RSVY, PERX, PERY
DiffusionDXX, DYY, CSAT
Coupling Migration Model
Thermal-Electric-Diffusion[a] 100110ThermalKXX, KYY, DENS, C, ENTH, HF
ElectricRSVX, RSVY, PERX, PERY
DiffusionDXX, DYY, CSAT
CouplingSBKX, SBKY

---

Temperature-dependent CSAT

---

Migration Model

Structural-Thermal-Diffusion[a] 100011StructuralSee Table 222.3: Structural Material Properties
ThermalKXX, KYY, DENS, C, ENTH, HF
DiffusionDXX, DYY, CSAT
CouplingALPX, ALPY, ALPZ, REFT, QRATE

---

BETX, BETY, CREF

---

Temperature-dependent CSAT

---

Migration Model

Structural-Electric-Diffusion[a] 100101StructuralSee Table 222.3: Structural Material Properties
ElectricRSVX, RSVY, PERX, PERY
DiffusionDXX, DYY, CSAT
CouplingBETX, BETY, CREF

---

Migration Model

Structural-Thermal-Electric-Diffusion[a] 100111StructuralSee Table 222.3: Structural Material Properties
ThermalKXX, KYY, DENS, C, ENTH, HF
ElectricRSVX, RSVY, PERX, PERY
DiffusionDXX, DYY, CSAT
CouplingALPX, ALPY, ALPZ, REFT, QRATE

---

BETX, BETY, CREF

---

SBKX, SBKY

---

Temperature-dependent CSAT

---

Migration Model

[a] For this analysis type, some of the material properties can be defined as a function of primary variables by using tabular input on the MP command. For more information, see Defining Linear Material Properties Using Tabular Input in the Material Reference.

[b] For piezoelectric and thermal-piezoelectric analyses (KEYOPT(1) = 101, 1001, or 1011 with TB,PIEZ), only elastic material properties and material models are valid.


Various combinations of nodal loading are available for this element (depending on the KEYOPT(1) value). Nodal loads are defined with D and F. Nodal forces, if any, should be input per unit of depth for a plane analysis and on a full 360° basis for an axisymmetric analysis.

Element loads are described in Element Loading. Surface loads may be input on the element faces indicated by the circled numbers in Figure 222.1: PLANE222 Geometry using SF and SFE. Positive pressures act into the element. Body loads may be input at the element's nodes or as a single element value using BF and BFE.

PLANE222 surface and body loads are given in the following table.

Most surface and body loads can be defined as a function of primary variables by using tabular input. For more information, see Applying Loads Using Tabular Input in the Basic Analysis Guide and the individual surface or body load command description in the Command Reference.

Table 222.5: PLANE222 Surface and Body Loads

Coupled-Field Analysis KEYOPT(1) Load Type Load Command Label
Structural-Thermal11SurfacePressurePRES
Convection

Heat Flux

Radiation (See View Factor Updating at the Substep Level for a Coupled-Field Analysis Including Large-deflection Effects in the Thermal Analysis Guide)

CONV

HFLUX

RDSF

BodyForce DensityFORC
Heat Generation -- Nodes I through LHGEN
Piezoresistive and Piezoelectric (Current-Based)101SurfacePressurePRES
BodyForce DensityFORC
Temperature -- Nodes I through LTEMP
Electrostatic-Structural and Piezoelectric (Charge-Based)1001SurfacePressure

Surface Charge Density

PRES

CHRGS[a]

BodyForce DensityFORC
Temperature -- Nodes I through LTEMP
Volume Charge Density -- Nodes I through LCHRGD[a]
Thermal-Electric110SurfaceConvection

Heat Flux

Radiation

CONV

HFLUX

RDSF

BodyHeat Generation -- Nodes I through LHGEN
Structural-Thermoelectric111SurfacePressurePRES
Convection

Heat Flux

Radiation (See View Factor Updating at the Substep Level for a Coupled-Field Analysis Including Large-deflection Effects in the Thermal Analysis Guide)

CONV

HFLUX

RDSF

BodyForce DensityFORC
Heat Generation -- Nodes I through LHGEN
Thermal-Piezoelectric1011SurfacePressure

Surface Charge Density

PRES

CHRGS[a]

Convection

Heat Flux

Radiation

CONV

HFLUX

RDSF

BodyForce DensityFORC
Heat Generation -- Nodes I through LHGEN
Volume Charge Density -- Nodes I through LCHRGD[a]
Structural-Diffusion 100001SurfacePressurePRES
Diffusion FluxDFLUX
BodyForce DensityFORC
Temperature -- Nodes I through LTEMP
Diffusing Substance Generation --Nodes I through LDGEN
Thermal-Diffusion100010SurfaceConvection

Heat Flux

Radiation

CONV

HFLUX

RDSF

Diffusion FluxDFLUX
BodyHeat Generation -- Nodes I through LHGEN
Diffusing Substance Generation – Nodes I through LDGEN
Electric-Diffusion100100SurfaceDiffusion FluxDFLUX
BodyDiffusing Substance Generation – Nodes I through LDGEN
Temperature -- Nodes I through LTEMP
Thermal-Electric-Diffusion100110SurfaceConvection

Heat Flux

Radiation

CONV

HFLUX

RDSF

Diffusion FluxDFLUX
BodyHeat Generation – Nodes I through LHGEN
Diffusing Substance Generation – Nodes I through LDGEN
Structural-Thermal-Diffusion100011SurfacePressurePRES
Convection

Heat Flux

Radiation (See View Factor Updating at the Substep Level for a Coupled-Field Analysis Including Large-deflection Effects in the Thermal Analysis Guide)

CONV

HFLUX

RDSF

Diffusion FluxDFLUX
BodyForce DensityFORC
Heat Generation -- Nodes I through LHGEN
Diffusing Substance Generation – Nodes I through LDGEN
Structural-Electric-Diffusion100101SurfacePressurePRES
Diffusion FluxDFLUX
BodyForce DensityFORC
Diffusing Substance Generation – Nodes I through LDGEN
Temperature -- Nodes I through LTEMP
Structural-Thermal-Electric-Diffusion100111SurfacePressurePRES
Convection

Heat Flux

Radiation (See View Factor Updating at the Substep Level for a Coupled-Field Analysis Including Large-deflection Effects in the Thermal Analysis Guide)

CONV

HFLUX

RDSF

Diffusion FluxDFLUX
BodyForce DensityFORC
Heat Generation – Nodes I through LHGEN
Diffusing Substance Generation --Nodes I through LDGEN

[a] CHRGS and CHRGD are interpreted as negative surface charge density and negative volume charge density, respectively.1. CHRGS and CHRGD are interpreted as negative surface charge density and negative volume charge density, respectively.


Automatic element technology selections are given in the following table (for more information, see Automatic Selection of Element Technologies and Formulations).

Table 222.6: Automatic Element Technology Selection

Coupled-Field Analysis Stress State ETCONTROL Command Suggestions/Resettings
All analyses with structural and thermal fields  KEYOPT(2) = 1 for elastoplastic or hyperelastic materials
Analyses with a structural field that support the enhanced strain (KEYOPT(6) = 2) or simplified enhanced strain (KEYOPT(6) = 3) formulationsPlane stress

(KEYOPT(3) = 0 or KEYOPT(3) = 3)

KEYOPT(6) = 2 for linear materials

KEYOPT(6) = 2 for elastoplastic materials[a]

KEYOPT(6) = 0 for hyperelastic materials only

Not plane stress

KEYOPT(6) = 3 for linear materials with Poisson’s ratio ν ≤ 0.49 only

KEYOPT(6) = 2 for linear materials with Poisson’s ratio ν > 0.49 or anisotropic materials only

KEYOPT(6) = 2 for elastoplastic materials[b]

KEYOPT(6) = 0 for hyperelastic materials only

[a] Hyperelastic materials may be present.

[b] Hyperelastic materials may be present.


A summary of the element input is given in "PLANE222 Input Summary". A general description of element input is given in Element Input. For axisymmetric applications, see Harmonic Axisymmetric Elements.

PLANE222 Input Summary

Nodes

I, J, K, L

Degrees of Freedom

Set by KEYOPT(1). See Table 222.2: PLANE222 Coupled-Field Analysis.

Real Constants
THK - Thickness if KEYOPT (3) = 3
Material Properties

See Table 222.4: PLANE222 Material Properties and Material Models.

Surface Loads

See Table 222.5: PLANE222 Surface and Body Loads.

Body Loads

See Table 222.5: PLANE222 Surface and Body Loads.

Special Features

Note:  Linear perturbation is available for the following coupled analyses: electrostatic-structural and piezoelectric analyses (KEYOPT(1) = 1001).


KEYOPT(1)

Element degrees of freedom. See Table 222.2: PLANE222 Coupled-Field Analysis.

KEYOPT(2)

Coupling method between the degrees of freedom for the following types of coupling: structural-thermal, structural-diffusion, thermal-diffusion, thermal-electric, and electric-diffusion:

0 -- 

Strong (matrix) coupling. May produce an unsymmetric matrix (see note [1]). In a linear analysis, a coupled response is achieved after one iteration.

1 -- 

Weak (load vector) coupling. Produces a symmetric matrix and requires at least two iterations to achieve a coupled response. (See note [2].)


Note:  

  1. In addition to unsymmetric constitutive equations, temperature-dependent thermal conductivity, electrical resistivity, and diffusivity produce unsymmetric matrices. Effects associated with the temperature-dependent material properties are not taken into account with the weak coupling option (KEYOPT(2) = 1).

  2. The weak coupling option (KEYOPT(2) = 1) can be used in a coupled electrostatic-structural analysis (KEYOPT(1) = 1001) to produce legacy element behavior. In this case, the reaction solution for the VOLT degree of freedom is positive charge (CHRG), and the analysis types are limited to static and full transient analyses. Linear perturbation analyses are not supported.


KEYOPT(3)

Element behavior:

0 -- 

Plane or plane stress

1 -- 

Axisymmetric

2 -- 

Plane strain

3 -- 

Plane or plane stress with thickness input

6 -- 

Axisymmetric with torsion


Note:  For the plane/plane stress options (KEYOPT(3) = 0 or 3), the element behavior is plane stress for analyses with structural degrees of freedom. The plane strain (KEYOPT(3) = 2) and axisymmetric with torsion (KEYOPT(3) = 6) options are valid only for analyses with structural degrees of freedom.


KEYOPT(4)

Electrostatic force coupling in electrostatic-structural analysis (KEYOPT(1) = 1001):

0 -- 

Applied to every element node. Used to model electrostatic or electromagnetic force coupling in solids.

1 -- 

Applied to the air-structure interface or to element nodes that have constrained structural degrees of freedom. Produces a symmetric electrostatic force coupling matrix by ignoring some terms associated with the nodes interior to the air domain. Recommended for models with a single layer of elastic air elements without midside nodes.

2 -- 

Not applied. Recommended for elastic air elements not directly attached to the air-structure interface to make the solution more efficient.

3 -- 

Applied to the air-structure interface or to element nodes that have constrained structural degrees of freedom. Compared to KEYOPT(4) = 1, all terms of the electrostatic force coupling matrix are retained, which produces an unsymmetric matrix. Recommended for models with multiple layers of elastic air elements.

4 -- 

Not applied. Can be used to turn off the default electrostatic or electromagnetic force coupling in solids. Compared to KEYOPT(4) = 2, elements with KEYOPT(4) = 4 can be subject to electrostatic or electromagnetic force coupling when connected to an elastic air element.


Note:  KEYOPT(4) = 1, 2, and 3 are used to identify elastic air elements during the automatic detection of the air-structure interface. The electrostatic or electromagnetic force coupling:

  • Will not be applied to the element nodes connected to another elastic air element.

  • Will be applied to the element nodes connected to a structure, that is, any element with structural degrees of freedom except for the elastic air elements.


For more information, see Electrostatic-Structural Analysis in the Coupled-Field Analysis Guide and Electroelasticity in the Mechanical APDL Theory Reference.

KEYOPT(6)

Element technology:

0 -- 

Full integration with method (default).

2 -- 

Enhanced strain formulation. (Available for the coupled analyses listed in the note.)

3 -- 

Simplified enhanced strain formulation. (Available for the coupled analyses listed in the note.)


Note:  The enhanced strain and simplified enhanced strain formulations are available for the following coupled analyses:

Structural-thermal (KEYOPT(1) = 11) with thermoelastic damping turned off (KEYOPT(9)=1)
Piezoelectric (KEYOPT(1) = 1001)
Piezoresistive (KEYOPT(1) = 101)
Structural-diffusion (KEYOPT(1) = 100001)
Structural-thermal-diffusion (KEYOPT(1) = 100011)
Structural-thermoelectric (KEYOPT(1) = 111)
Structural-electric-diffusion (KEYOPT(1) = 100101)

KEYOPT(9)

Thermoelastic damping (piezocaloric effect) in coupled-field analyses having structural and thermal degrees of freedom.

0 -- 

Active. Evaluated at the reference temperature. Applicable to harmonic and transient analyses.

1 -- 

Suppressed (required for frictional heating analyses).

2 -- 

Active. Evaluated at the actual temperature. Applicable to a transient analysis.

KEYOPT(10)

Damping matrix in coupled-field analyses having the diffusion degree of freedom (CONC).

0 -- 

Consistent

1 -- 

Diagonalized

KEYOPT(11)

Element formulation in coupled-field analyses with structural degrees of freedom:

0 -- 

Pure displacement formulation (default)

1 -- 

Mixed u-P formulation (not valid with plane stress)

KEYOPT(15)

Perfectly matched layers (PML) absorbing condition in a harmonic piezoelectric analysis (KEYOPT(1) = 1001):

0 -- 

Do not include the PML absorbing condition (default)

1 -- 

Include the PML absorbing condition

PLANE222 Output Data

The solution output associated with the element is in two forms:

The element output directions are parallel to the element coordinate system. A general description of solution output is given in Solution Output. See the Basic Analysis Guide for ways to view results.

The Element Output Definitions table uses the following notation:

A colon (:) in the Name column indicates that the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file jobname.out. The R column indicates the availability of the items in the results file.

In either the O or R columns, “Y” indicates that the item is always available, a letter or number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

Table 222.7: PLANE222 Element Output Definitions

Name Definition O R
ALL ANALYSES
ELElement Number-Y
NODESNodes - I, J, K, L-Y
MATMaterial number-Y
VOLU:Volume-Y
XC, YCLocation where results are reported- [a]
ALL ANALYSES WITH A STRUCTURAL FIELD
THICKThickness-Y
S:X, Y, Z, XY[b] Stresses (SZ = 0.0 for plane stress elements)- [c]
S:1, 2, 3Principal stresses- [c]
S:EQVEquivalent stress- [c]
EPEL:X, Y, Z, XY[b] Elastic strains- [c]
EPTH:X, Y, Z, XY[b] Thermal strains- [c]
EPTH:EQVEquivalent thermal strain[d] - [c]
EPPL:X, Y, Z, XY[b] Plastic strains- [c]
EPPL:EQVEquivalent plastic strain[d] - [c]
EPCR:X, Y, Z, XY[b] Creep strains- [c]
EPCR:EQVEquivalent creep strain[d] - [c]
EPTO:X, Y, Z, XY[b] Total mechanical strains (EPEL + EPPL + EPCR)Y-
EPTO:EQVTotal equivalent mechanical strain (EPEL + EPPL + EPCR)--
EPTT:X, Y, Z, XY[b] Total mechanical, thermal, and diffusion strains (EPEL + EPPL + EPCR + EPTH + EPDI)--
EPTT:EQVTotal equivalent mechanical strain (EPEL + EPPL + EPCR + EPTH + EPDI)--
NL:SEPLPlastic yield stress[e] -Y
NL:EPEQAccumulated equivalent plastic strain[e] -Y
NL:CREQAccumulated equivalent creep strain[e] -Y
NL:SRATPlastic yielding (1 = actively yielding, 0 = not yielding)[e] -Y
NL:HPRESHydrostatic pressure[e] -Y
SENE:Elastic strain energy-Y
ADDITIONAL OUTPUT FOR STRUCTURAL-THERMAL ANALYSES (KEYOPT(1) = 11) [f]
TG:X, Y, SUMThermal gradient components and vector magnitude- [c]
TF:X, Y, SUMThermal flux components and vector magnitude- [c]
UEElastic strain energy[g] - [c]
UTTotal strain energy[h] - [c]
PHEAT Plastic heat generation rate per unit volume- [c]
VHEATViscoelastic heat generation rate per unit volume- [c]
ADDITIONAL OUTPUT FOR PIEZORESISTIVE ANALYSES (KEYOPT(1) = 101) [f]
TEMPInput temperatures-Y
EF:X, Y, SUMElectric field components (X, Y) and vector magnitude- [c]
JC:X, Y, SUMConduction current density components (X, Y) and vector magnitude- [c]
JS:X, Y, SUMCurrent density components (in the global Cartesian coordinate system) (X, Y) and vector magnitude[i] - [c]
JHEATJoule heat generation per unit volume[j] - [c]
ADDITIONAL OUTPUT FOR ELECTROSTATIC-STRUCTURAL ANALYSES (KEYOPT(1) = 1001) [f]
TEMPInput temperatures-Y
EF:X, Y, SUMElectric field components (X, Y) and vector magnitude- [c]
D:X, Y, SUMElectric flux density components (X, Y) and vector magnitude- [c]
FMAG:X, Y, SUMElectrostatic force components (X, Y) and vector magnitude- [c]
JS:X, Y, SUMElement current density components (X, Y) in the global Cartesian coordinate system and vector magnitude [i]-[c]
JHEATJoule heat generation per unit volume[j], [k]-[c]
UE, UM, UDElastic, mutual, and dielectric energies[g]- [c]
SENESum of elastic and dielectric energies (UE+UD)[g]-[c]
DENEDamping energy[g]-[c]
KENEKinetic energy[g]-[c]
ADDITIONAL OUTPUT FOR PIEZOELECTRIC ANALYSES (KEYOPT(1) = 1001 and 101) [f]
TEMPInput temperatures-Y
EF:X, Y, SUMElectric field components (X, Y) and vector magnitude- [c]
D:X, Y, SUMElectric flux density components (X, Y) and vector magnitude; available only for charge-based analysis (KEYOPT(1) = 1001)- [c]
JC:X, Y, SUMConduction current density components (X, Y) and vector magnitude; available only for current-based analysis (KEYOPT(1) = 101)- [c]
JS:X, Y, SUMElement current density components (X, Y) in the global Cartesian coordinate system and vector magnitude[i] - [c]
JHEATJoule heat generation per unit volume[j], [k] - [c]
UE, UM, UDElastic, mutual, and dielectric energies[g] - [c]
UTTotal strain energy[h] - [c]
SENESum of elastic and dielectric energies (UE + UD)[g] - [c]
DENEDamping energy[g] - [c]
KENEKinetic energy[g] - [c]
P:X, Y, SUMElement Poynting vector components (X, Y) and vector magnitude[g] - [c]
THERMAL-ELECTRIC ANALYSES (KEYOPT(1) = 110)
TG:X, Y, SUMThermal gradient components and vector magnitude- [c]
TF:X, Y, SUMThermal flux components and vector magnitude- [c]
EF:X, Y, SUMElectric field components and vector magnitude - [c]
JC:X, Y, SUMConduction current density components and vector magnitude- [c]
JS:X, Y, SUMCurrent density components (in the global Cartesian coordinate system) and vector magnitude[i] - [c]
JHEATJoule heat generation per unit volume[j], [k] - [c]
ADDITIONAL OUTPUT FOR STRUCTURAL-THERMOELECTRIC ANALYSES (KEYOPT(1) = 111) [f]
TG:X, Y, SUMThermal gradient components and vector magnitude- [c]
TF:X, Y, SUMThermal flux components and vector magnitude- [c]
EF:X, Y, SUMElectric field components and vector magnitude- [c]
JC:X, Y, SUMConduction current density components and vector magnitude- [c]
JS:X, Y, SUMCurrent density components (in the global Cartesian coordinate system) and vector magnitude [i] - [c]
JHEATJoule heat generation per unit volume [j], [k] - [c]
UEElastic strain energy- [c]
UTTotal strain energy [h] - [c]
PHEAT Plastic heat generation rate per unit volume- [c]
VHEATViscoelastic heat generation rate per unit volume- [c]
ADDITIONAL OUTPUT FOR THERMAL-PIEZOELECTRIC ANALYSES (KEYOPT(1) = 1011) [f]
TG:X, Y, SUMThermal gradient components and vector magnitude- [c]
TF:X, Y, SUMThermal flux components and vector magnitude- [c]
EF:X, Y, SUMElectric field components and vector magnitude- [c]
D:X, Y, SUMElectric flux density components and vector magnitude- [c]
JHEATJoule heat generation per unit volume[j], [k] - [c]
UE, UM, UDElastic, mutual, and dielectric energies [g] - [c]
UTTotal strain energy [h] - [c]
PHEAT Plastic heat generation rate per unit volume- [c]
VHEATViscoelastic heat generation rate per unit volume- [c]
ADDITIONAL OUTPUT FOR STRUCTURAL-DIFFUSION ANALYSES (KEYOPT(1) = 100001) [f]
TEMPInput temperatures-Y
EPDI:X, Y, Z, XYDiffusion strains- [c]
CG:X, Y, SUMConcentration gradient components and vector magnitude- [c]
DF:X, Y, SUMDiffusion flux components and vector magnitude- [c]
CONCElement concentration [l] - [c]
DFC:X,Y,SUM Pure diffusion flux components (X,Y) and vector magnitude -[c]
DFS:X,Y,SUM Stress migration flux components (X,Y) and vector magnitude -[c]
THERMAL-DIFFUSION ANALYSES (KEYOPT(1) = 100010)
TG:X, Y, SUMThermal gradient components and vector magnitude- [c]
TF:X, Y, SUMThermal flux components and vector magnitude- [c]
CG:X, Y, SUMConcentration gradient components and vector magnitude- [c]
DF:X, Y, SUMDiffusion flux components and vector magnitude- [c]
CONCElement concentration[l] - [c]
DFC:X,Y,SUMPure diffusion flux components (X,Y) and vector magnitude -[c]
DFT:X,Y,SUMThermal migration flux components (X,Y) and vector magnitude -[c]
ELECTRIC-DIFFUSION ANALYSES (KEYOPT(1) = 100100)
TEMPInput temperatures-Y
EF:X, Y, SUMElectric field components and vector magnitude- [c]
JC:X, Y, SUMConduction current density components and vector magnitude- [c]
JS:X, Y, SUMCurrent density components (in the global Cartesian coordinate system) and vector magnitude [i] - [c]
CG:X, Y, SUMConcentration gradient components and vector magnitude- [c]
DF:X, Y, SUMDiffusion flux components and vector magnitude- [c]
CONCElement concentration[l] - [c]
DFC:X,Y,SUMPure diffusion flux components (X,Y) and vector magnitude -[c]
DFE:X,Y,SUMElectric migration flux components (X,Y) and vector magnitude -[c]
THERMAL-ELECTRIC-DIFFUSION ANALYSES (KEYOPT(1) = 100110)
TG:X, Y, SUMThermal gradient components and vector magnitude- [c]
TF:X, Y, SUMThermal flux components and vector magnitude- [c]
EF:X, Y, SUMElectric field components and vector magnitude- [c]
JC:X, Y, SUMConduction current density components and vector magnitude- [c]
JS:X, Y, SUMCurrent density components (in the global Cartesian coordinate system) and vector magnitude[i] - [c]
JHEATJoule heat generation per unit volume[j], [k] - [c]
CG:X, Y, SUMConcentration gradient components and vector magnitude- [c]
DF:X, Y, SUMDiffusion flux components and vector magnitude- [c]
CONCElement concentration[l]Co- [c]
DFC:X,Y,SUMPure diffusion flux components (X,Y) and vector magnitude-[c]
DFT:X,Y,SUMThermal migration flux components (X,Y) and vector magnitude -[c]
DFE:X,Y,SUMElectric migration flux components (X,Y) and vector magnitude -[c]
ADDITIONAL OUTPUT FOR STRUCTURAL-ELECTRIC-DIFFUSION ANALYSES (KEYOPT(1) = 100101) [f]
TEMPInput temperatures-Y
EPDI:X, Y, Z, XYDiffusion strains- [c]
EF:X, Y, SUMElectric field components and vector magnitude- [c]
JC:X, Y, SUMConduction current density components and vector magnitude- [c]
JS:X, Y, SUMConduction current density components and vector magnitude- [c]
JHEATJoule heat generation per unit volume[j], [k] - [c]
CG:X, Y, SUMConcentration gradient components and vector magnitude- [c]
DF:X, Y, SUMDiffusion flux components and vector magnitude- [c]
CONCElement concentration[l] - [c]
DFC:X,Y,SUMPure diffusion flux components (X,Y) and vector magnitude-[c]
DFS:X,Y,SUMStress migration flux components (X,Y) and vector magnitude -[c]
DFE:X,Y,SUMElectric migration flux components (X,Y) and vector magnitude -[c]
ADDITIONAL OUTPUT FOR STRUCTURAL-THERMAL-DIFFUSION ANALYSES (KEYOPT(1) = 100011) [f]
EPDI:X, Y, Z, XYDiffusion strains- [c]
TG:X, Y, SUMThermal gradient components and vector magnitude- [c]
TF:X, Y, SUMThermal flux components and vector magnitude- [c]
CG:X, Y, SUMConcentration gradient components and vector magnitude- [c]
DF:X, Y, SUMDiffusion flux components and vector magnitude- [c]
CONCElement concentration[l] - [c]
DFC:X,Y,SUMPure diffusion flux components (X,Y) and vector magnitude -[c]
DFS:X,Y,SUMStress migration flux components (X,Y) and vector magnitude -[c]
DFT:X,Y,SUMThermal migration flux components (X,Y) and vector magnitude -[c]
PHEAT Plastic heat generation rate per unit volume- [c]
VHEATViscoelastic heat generation rate per unit volume- [c]
ADDITIONAL OUTPUT FOR STRUCTURAL-THERMAL-ELECTRIC-DIFFUSION ANALYSES (KEYOPT(1) = 100111) [f]
EPDI:X, Y, Z, XYDiffusion strains- [c]
TF:X, Y, SUMThermal flux components and vector magnitude- [c]
EF:X, Y, SUMElectric field components and vector magnitude- [c]
JC:X, Y, SUMConduction current density components and vector magnitude- [c]
JS:X, Y, SUMConduction current density components and vector magnitude- [c]
JHEATJoule heat generation per unit volume [j], [k] - [c]
CG:X, Y, SUMConcentration gradient components and vector magnitude- [c]
DF:X, Y, SUMDiffusion flux components and vector magnitude- [c]
CONCElement concentration[l] - [c]
DFC:X,Y,SUMPure diffusion flux components (X,Y) and vector magnitude -[c]
DFS:X,Y,SUMStress migration flux components (X,Y) and vector magnitude -[c]
DFT:X,Y,SUMThermal migration flux components (X,Y) and vector magnitude -[c]
DFE:X,Y,SUMElectric migration flux components (X,Y) and vector magnitude -[c]
PHEAT Plastic heat generation rate per unit volume- [c]
VHEATViscoelastic heat generation rate per unit volume- [c]

[a] Available only at centroid as a *GET item.

[b] Also YZ and XZ when used with the axisymmetric with torsion option (KEYOPT(3) = 6). Stress/strain outputs have six components with the same meanings as the 3D solid element outputs. To better understand the solution results, you can plot them in 3D space (/ESHAPE,1) when PowerGraphics is enabled (/GRAPHICS,POWER).

[c] Solution values are output only if calculated (based on input values).

[d] The equivalent strains use an effective Poisson's ratio: for elastic and thermal this value is set by the user (MP,PRXY); for plastic and creep this value is set at 0.5.

[e] Nonlinear solution, output only if the element has a nonlinear material, or if large-deflection effects are enabled (NLGEOM,ON).

[f] Output listed for this coupled analysis is in addition to the structural field output at the beginning of this table.

[g] For time-harmonic and modal analyses, the following values are time-averaged: elastic (UE), mutual (UM), and dielectric (UD) energies, the sum of elastic and dielectric energies (SENE), damping energy (DENE), kinetic energy (KENE), and the Poynting vector (P). The real part of the UE, UM, UD, and SENE records represents the average energy, while the imaginary part represents the average energy loss. The real part of the Poynting vector represents the average power flow. For more information, see Piezoelectrics and Electroelasticity in the Mechanical APDL Theory Reference.

[h] For a time-harmonic analysis, total strain (UT) energy is time-averaged. The real part represents the average energy, while the imaginary part represents the average energy loss. For more information, see Thermoelasticity in the Mechanical APDL Theory Reference.

[i] JS represents the sum of element conduction and displacement current densities.

[j] Calculated Joule heat generation rate per unit volume (JHEAT) may be made available for a subsequent thermal analysis with companion thermal elements. For piezoelectric and electrostatic-structural analyses, the heat generation rate output as JHEAT is produced by both the supported structural and electrical losses.

[k] For a time-harmonic analysis, Joule losses (JHEAT) are time-averaged. These values are stored in both the real and imaginary data sets. For more information, see Quasistatic Electric Analysis in the Mechanical APDL Theory Reference.

[l] With the normalized concentration approach, CONC is the actual concentration obtained by multiplying the saturated concentration (MP,CSAT) and the normalized concentration evaluated at the element centroid. For more information, see Normalized Concentration Approach in the Theory Reference.


Table 222.8: PLANE222 Item and Sequence Numbers lists output available through ETABLE using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 222.8: PLANE222 Item and Sequence Numbers:

Name

output quantity as defined in Table 222.7: PLANE222 Element Output Definitions

Item

predetermined Item label for ETABLE

E

sequence number for single-valued or constant element data

Table 222.8: PLANE222 Item and Sequence Numbers

Output Quantity Name ETABLE Command Input
Item E
Analyses that include DIFFUSION (KEYOPT(1) = 100001, 100010, 100100, 100110, 100011, 100101, and 100111)
CONCSMISC1
DFCXSMISC2
DFCYSMISC3
DFCSUMSMISC5
DFSXSMISC6
DFSYSMISC7
DFSSUMSMISC9
DFTXSMISC10
DFTYSMISC11
DFTSUMSMISC13
DFEXSMISC14
DFEYSMISC15
DFESUMSMISC17
STRUCTURAL-THERMAL ANALYSES (KEYOPT(1) = 11)
UENMISC1
UTNMISC4
PHEATNMISC5
VHEATNMISC6
ELECTROSTATIC-STRUCTURAL ANALYSES (KEYOPT(1) = 1001)
UENMISC1
UDNMISC2
UMNMISC3
PIEZOELECTRIC ANALYSES (KEYOPT(1) = 1001 and 101)
UENMISC1
UDNMISC2
UMNMISC3
UTNMISC4
PXNMISC5
PYNMISC6
PSUMNMISC8
STRUCTURAL-THERMOELECTRIC ANALYSES (KEYOPT(1) = 111)
UTNMISC4
PHEATNMISC5
VHEATNMISC6
THERMAL-PIEZOELECTRIC ANALYSES (KEYOPT(1) = 1011)
UENMISC1
UDNMISC2
UMNMISC3
UTNMISC4
PHEATNMISC5
VHEATNMISC6
Analyses that include a STRUCTURAL field
(KEYOPT(1) = 11, 111, 1001, 100001, 100011, 100101, and 100111)
THICKNMISC9

PLANE222 Assumptions and Restrictions

  • The element assumes a unit thickness for plane strain (KEYOPT(3) = 2) calculations.

  • In a piezoelectric or electrostatic-structural analysis, electric charge loading is interpreted as negative electric charge or negative charge density.

  • Optimized nonlinear solution defaults are applied in coupled-field analyses with structural degrees of freedom using this element.

  • The element must lie in a global X-Y plane as shown in Figure 222.1: PLANE222 Geometry and the Y-axis must be the axis of symmetry for axisymmetric analyses.

  • An axisymmetric structure should be modeled in the +X quadrants.

  • This element may not be compatible with other elements with the VOLT degree of freedom. To be compatible, the elements must have the same reaction solution for the VOLT degree of freedom. Elements that have an electric charge reaction solution must all have the same electric charge reaction sign. For more information, see Element Compatibility in the Low-Frequency Electromagnetic Analysis Guide.

  • When using mixed formulation (KEYOPT(11) = 1), use the sparse solver (default).

  • Stress stiffening is always included in geometrically nonlinear (NLGEOM,ON) coupled-field analyses with structural degrees of freedom. Prestress effects can be activated via the PSTRES command.

  • Graphical Solution Tracking (/GST) is not supported for analyses with CONC DOFs (KEYOPT(1) = 100001, 100010, 100011, 100100, 100101, 100110, and 100111).

  • Reaction forces are not available for electrostatic-structural (KEYOPT(1) = 1001) analyses with the elastic air option (KEYOPT(4) = 1).

  • In a plane stress piezoelectric analysis (KEYOPT(1) = 1001 and KEYOPT(3) = 0) with anisotropic structural damping (TB,AVIS or TB,ELST), the plane stress state is approximated by setting both the elastic and viscous (or imaginary) components of out-of-plane stress to zero.

  • The following are true for the axisymmetric with torsion option (KEYOPT(3) = 6):

    • It can be used only with surface element SURF153 with KEYOPT(3) = 1.

    • Rezoning and nonlinear adaptivity are not supported.

    • Results of analyses using the axisymmetric with torsion option can be displayed using the /ESHAPE command.

    • Enhanced strain (KEYOP(6) = 2) and simplified enhanced strain (KEYOPT(6) = 3) formulations are not supported.

  • The stress-migration effect (specified via TB,MIGR) is not supported in an analysis with structural and diffusion degrees of freedom.

  • Tabular thickness input (KEYOPT(3) = 3) is supported only when structural degrees of freedom are present within the element.

  • The film coefficient (if any) is evaluated at average film temperature (TS + TB)/2 for the coupled-thermal analyses (KEYOPT(1) = 11, 110, 111, 1011, 100010, 100110, 100011, and 100111).

PLANE222 Product Restrictions

There are no product-specific restrictions for this element.