2-D 4-Node Coupled-Field Solid
PLANE222 Element Description
PLANE222 supports the following physics combination:
Structural-Thermal
The element has four nodes with up to three degrees of freedom per node. The element can be used as either a plane element or as 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. In addition to thermal expansion, structural-thermal capabilities include the piezocaloric and thermoplastic effects. The Coriolis effect is available for analyses with structural degrees of freedom.
PLANE222 uses 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).
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.
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. 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 DOF 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 DOF labels, and force and heat flow are the reaction solution.
Table 222.1: PLANE222 Field Keys
| Field | Field Key | DOF Label | Force Label | Reaction Solution |
|---|---|---|---|---|
| Structural | 1 | UX, UY | FX, FY | Force |
| Thermal | 10 | TEMP | HEAT | Heat Flow |
The coupled-field analysis KEYOPT(1) settings, DOF labels, force labels, reaction solutions, and analysis types are shown in the following table.
As shown in the following tables, material property requirements consist of those required for the individual fields (structural, thermal) and those required for field coupling. Individual material properties are defined via MP and MPDATA. Nonlinear and multiphysics material models are defined via TB.
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 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 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) | Field | Material Properties and Material Models |
|---|---|---|---|
| Structural-Thermal | 11 | Structural | See Table 222.3: Structural Material Properties |
| Thermal | KXX, KYY, DENS, C, ENTH, HF | ||
| Coupling | ALPX, ALPY, ALPZ, REFT, QRATE |
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 Nodal 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.
Table 222.5: PLANE222 Surface and Body Loads
| Coupled-Field Analysis | KEYOPT(1) | Load Type | Load | Command Label | |||
|---|---|---|---|---|---|---|---|
| Structural-Thermal | 11 | Surface |
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| Body |
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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
None
- Material Properties
See Table 222.4: PLANE222 Material Properties and Material Models.
- Surface Loads
- Body Loads
- Special Features
Birth and death Coriolis effect Large deflection Large strain Nonlinear stabilization Stress stiffening Nonlinear adaptivity - KEYOPT(1)
Element degrees of freedom. See Table 222.2: PLANE222 Coupled-Field Analysis.
- KEYOPT(2)
Coupling method between the structural and thermal DOFs:
- 0 --
Strong (matrix) coupling. Produces an unsymmetric matrix. 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.
- KEYOPT(3)
Element behavior:
- 0 --
Plane stress
- 1 --
Axisymmetric
- 2 --
Plane strain
- KEYOPT(9)
Thermoelastic damping (piezocaloric effect) in coupled-field analyses having structural and thermal DOFs. Applicable to harmonic and transient analyses only.
- 0 --
Active
- 1 --
Suppressed (required for frictional heating analyses)
- KEYOPT(11)
Element formulation in coupled-field analyses with structural DOFs:
- 0 --
Pure displacement formulation (default)
- 1 --
Mixed u-P formulation (not valid with plane stress)
PLANE222 Output Data
The solution output associated with the element is in two forms:
Nodal degrees of freedom included in the overall nodal solution
Additional element output as shown in Table 222.6: PLANE222 Element Output Definition
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 number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.
Table 222.6: PLANE222 Element Output Definition
| Name | Definition | O | R |
|---|---|---|---|
| ALL ANALYSES | |||
| EL | Element Number | - | Y |
| NODES | Nodes - I, J, K, L | - | Y |
| MAT | Material number | - | Y |
| VOLU: | Volume | - | Y |
| XC, YC | Location where results are reported | - | 2 |
| ALL ANALYSES WITH A STRUCTURAL FIELD | |||
| S:X, Y, Z, XY | Stresses (SZ = 0.0 for plane stress elements) | - | 1 |
| S:1, 2, 3 | Principal stresses | - | 1 |
| S:EQV | Equivalent stress | - | 1 |
| EPEL:X, Y, Z, XY | Elastic strains | - | 1 |
| EPTH:X, Y, Z, XY | Thermal strains | - | 1 |
| EPTH:EQV | Equivalent thermal strain [3] | - | 1 |
| EPPL:X, Y, Z, XY | Plastic strains | - | 1 |
| EPPL: EQV | Equivalent plastic strain [3] | - | 1 |
| EPCR:X, Y, Z, XY | Creep strains | - | 1 |
| EPCR:EQV | Equivalent creep strain [3] | - | 1 |
| EPTO:X, Y, Z, XY | Total mechanical strains (EPEL + EPPL + EPCR) | - | - |
| EPTO:EQV | Total equivalent mechanical strain (EPEL + EPPL + EPCR) | - | - |
| NL:SEPL | Plastic yield stress [5] | - | Y |
| NL:EPEQ | Accumulated equivalent plastic strain [5] | - | Y |
| NL:CREQ | Accumulated equivalent creep strain [5] | - | Y |
| NL:SRAT | Plastic yielding (1 = actively yielding, 0 = not yielding) [5] | - | Y |
| NL:HPRES | Hydrostatic pressure [5] | - | Y |
| SENE: | Elastic strain energy | - | Y |
| ADDITIONAL OUTPUT FOR STRUCTURAL-THERMAL ANALYSES (KEYOPT(1) = 11) | |||
| TG:X, Y, SUM | Thermal gradient components and vector magnitude | - | 1 |
| TF:X, Y, SUM | Thermal flux components and vector magnitude | - | 1 |
| UE | Elastic strain energy [4] | - | 1 |
| UT | Total strain energy [4] | - | 1 |
| PHEAT | Plastic heat generation rate per unit volume | - | 1 |
Solution values are output only if calculated (based on input values).
Available only at centroid as a *GET item.
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 to 0.5.
For a time-harmonic analysis, elastic (UE) and total strain (UT) energies are time-averaged. Their 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.
Nonlinear solution, output only if the element has a nonlinear material, or if large-deflection effects ae enabled (NLGEOM,ON).
Table 222.7: 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 222.7: PLANE222 Item and Sequence Numbers:
- Name
Output quantity as defined in Table 222.6: PLANE222 Element Output Definition
- Item
Predeterminate Item label for ETABLE
- E
Sequence number for single-valued or constant element data
Table 222.7: PLANE222 Item and Sequence Numbers
| Output Quantity Name | ETABLE Command Input | |
|---|---|---|
| Item | E | |
| UE | NMISC | 1 |
| UT | NMISC | 4 |
| PHEAT | NMISC | 5 |
PLANE222 Assumptions and Restrictions
PLANE222 assumes a unit thickness for the plane stress and plain strain options.
PLANE222 uses 2 x 2 and 1 point integration rules to calculate the element matrices and load vectors for the quad and triangle geometries, respectively.
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.
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 PSTRES.