LINK228
3D Coupled-Field Link
LINK228 Element Description
LINK228 is a uniaxial element in 3D space with the following capabilities:
Structural-thermal
Thermal-electric
Structural-thermoelectric
Piezoelectric
The element has two or three nodes with up to five degrees of freedom per node.
See LINK228 in the Mechanical APDL Theory Reference for more details about this element.
LINK228 Input Data
The geometry, node locations, and the coordinate system for this conducting bar are shown in Figure 228.1: LINK228 Geometry. The element is defined by its configuration (two or three nodes, prescribed by setting KEYOPT(4) = 0 or 1, respectively), a cross-sectional area input via the SECTYPE and SECDATA commands, and the material properties.
The element x-axis is oriented along the length of the element from node I toward node J.
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 228.1: LINK228 Field Keys. For example, 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, UZ, and TEMP are the DOF labels, and force and heat flow are the reaction solution variables.
Table 228.1: LINK228 Field Keys
| Field | Field Key | DOF Label | Force Label | Reaction Solution |
|---|---|---|---|---|
| Structural | 1 | UX, UY, UZ | FX, FY, FZ | Force |
| Thermal | 10 | TEMP | HEAT | Heat Flow |
| Electric Conduction | 100 | VOLT | AMPS | Electric Current |
| Electrostatic | 1000 | VOLT | CHRG | Electric Charge |
The coupled-field analysis KEYOPT(1) settings, DOF labels, force labels, reaction solutions, and analysis types are shown in the following table.
Table 228.2: LINK228 Coupled-Field Analysis
| Coupled-Field Analysis | KEYOPT(1) | DOF Label | Force Label | Reaction Solution | Analysis Type |
|---|---|---|---|---|---|
| Structural-Thermal[a][b] | 11 | UX, UY, UZ, TEMP | FX, FY, FZ, HEAT | Force, Heat Flow | Static Full Harmonic Full Transient |
| Thermal-Electric | 110 | TEMP, VOLT | HEAT, AMPS | Heat Flow, Electric Current | Static Full Transient |
| Structural-Thermoelectric[a] | 111 | UX, UY, UZ, TEMP, VOLT | FX, FY, FZ, HEAT, AMPS | Force, Heat Flow, Electric Current | Static Full Transient |
| Piezoelectric (Charge-Based) | 1001 | UX, UY, UZ, VOLT | FX, FY, FZ, 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) | 101 | UX, UY, UZ, VOLT | FX, FY, FZ, AMPS |
Force, Electric Current | Full Harmonic Full Transient |
As shown in the following tables, material property requirements consist of those required for the individual fields (structural, thermal, or electric conduction) and those required for field coupling. Individual material properties are defined via the MP and MPDATA commands. Nonlinear and multiphysics material models are defined via the TB command.
Table 228.3: Structural Material Properties
| Field | Field Key | Material Properties and Material Models |
|---|---|---|
|
Structural | 1 |
EX, PRXY (or NUXY), GXY, DENS, ALPD, BETD, DMPR, DMPS, ALPX (or CTEX or THSX), REFT --- Bilinear isotropic hardening, Bilinear kinematic hardening, Chaboche nonlinear kinematic hardening, Creep, Coefficient of thermal expansion, Damage evolution law, Damage initiation criteria, Density, Elasticity, Hill anisotropy, Prony series constants for viscoelastic materials, Rate-dependent plasticity (viscoplasticity), Rate-independent plasticity, Shift function for viscoelastic materials, Three-network model, Voce isotropic hardening law |
Table 228.4: LINK228 Material Properties and Material Models
| Coupled-Field Analysis | KEYOPT(1) | Material Properties and Material Models | |
|---|---|---|---|
| Structural-Thermal | 11 | Structural | See Table 228.3: Structural Material Properties. |
| Thermal | KXX, DENS, C[a], ENTH | ||
| Coupling | ALPX, REFT, QRATE | ||
| Thermal-Electric[b] | 110 | Thermal | KXX, DENS, C[a], ENTH |
| Electric | RSVX, PERX | ||
| Coupling | SBKX | ||
| Structural-Thermoelectric | 111 | Structural | See Table 228.3: Structural Material Properties. |
| Thermal | KXX, DENS, C[a], ENTH | ||
| Electric | RSVX, PERX | ||
| Coupling | ALPX, REFT, QRATE --- SBKX | ||
| Piezoelectric | 1001 (Charge-Based) 101 (Current-Based) | Structural | See Table 228.3: Structural Material Properties[c]. |
| Electric | PERX, RSVX, LSST | ||
| Coupling | Piezoelectric coefficient (TB,PIEZ) | ||
[a] When thermoelastic damping is active (KEYOPT(9) = 0), the specific heat (C) is considered as the specific heat at constant strain or volume (Cv). Therefore, the conversion between Cp and Cv is ignored for this element. See Thermoelasticity in the Theory Reference.
[b] 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.
Various combinations of nodal loading are available for this element (depending upon the KEYOPT(1) value). Nodal loads are defined with the D and the F commands.
Element loads are described in Element Loading. Body loads may be input at the element's nodes or as a single element value using the BF and BFE commands.
Most 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 228.5: LINK228 Body Loads
| Coupled-Field Analysis | KEYOPT(1) | Load Type | Load | Command Label |
|---|---|---|---|---|
| Structural-Thermal | 11 | Body | Heat Generation – Nodes I, J for KEYOPT(4) = 0 Nodes I, J, K for KEYOPT(4) = 1 | HGEN |
| Thermal-Electric | 110 | Body | Heat Generation – Nodes I, J for KEYOPT(4) = 0 Nodes I, J, K for KEYOPT(4) = 1 | HGEN |
| Structural-Thermoelectric | 111 | Body | Heat Generation – Nodes I, J for KEYOPT(4) = 0 Nodes I, J, K for KEYOPT(4) = 1 | HGEN |
| Piezoelectric | 1001 (Charge-Based) 101 (Current-Based) | Body | Temperature – Nodes I, J for KEYOPT(4) = 0 Nodes I, J, K for KEYOPT(4) = 1 | TEMP |
A summary of the element input is given in "LINK228 Input Summary". A general description of element input is given in Element Input.
LINK228 Input Summary
- Nodes
I, J for KEYOPT(4) = 0 I, J, K for KEYOPT(4) = 1 - Degrees of Freedom
Set by KEYOPT(1). See Table 228.2: LINK228 Coupled-Field Analysis.
- Real Constants
None
- Material Properties
See Table 228.4: LINK228 Material Properties and Material Models.
- Surface Loads
None
- Body Loads
- Special Features
Birth and death Large deflection Large strain Nonlinear stabilization Stress stiffening Linear perturbation: available for piezoelectric analysis (KEYOPT(1) = 1001) - KEYOPT(1)
Element degrees of freedom. See Table 228.2: LINK228 Coupled-Field Analysis.
- KEYOPT(2)
Coupling method between the DOFs for the structural-thermal coupling:
- 0 --
Strong (matrix) coupling. May produce 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)
Cross-section scaling (applies only when structural DOFs and large-deflection effects [NLGEOM,ON] are specified):
- 0 --
Enforce incompressibility; cross-section is scaled as a function of axial stretch (default).
- 1 --
Section is assumed to be rigid.
- KEYOPT(4)
Specify 2-node or 3-node element:
- 0 --
2-node element (default)
- 1 --
3-node element
- 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).
LINK228 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 228.6: LINK228 Element Output Definitions.
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 228.6: LINK228 Element Output Definitions
| Name | Definition | O | R |
|---|---|---|---|
| ALL ANALYSES | |||
| EL | Element Number | Y | Y |
| NODES | Nodes - I, J for KEYOPT(4) = 0 Nodes - I, J, K for KEYOPT(4) = 1 | Y | Y |
| MAT | Material number | Y | Y |
| SECID | Section Number | - | Y |
| VOLU: | Volume | Y | Y |
| AREA | Cross-sectional area | Y | Y |
| XC, YC, ZC | Location where results are reported | Y | [a] |
| ALL ANALYSES WITH A STRUCTURAL FIELD | |||
| FORCE | Member force in the element coordinate system | Y | Y |
| Sxx | Axial stress | - | Y |
| EPELxx | Axial elastic strain | - | Y |
| EPTOxx | Total mechanical strain (EPEL + EPPL + EPCR) | - | - |
| EPEQ | Plastic equivalent strain | - | [b] |
| Cur.Yld.Flag | Current yield flag | - | [b] |
| Plwk | Plastic strain energy density | - | [b] |
| Creq | Creep equivalent strain | - | [b] |
| Crwk_Creep | Creep strain energy density | - | [b] |
| EPPLxx | Axial Plastic strains | - | [b] |
| EPCRxx | Axial Creep strains | - | [b] |
| EPTHxx | Axial Thermal strains | - | [c] |
| EPTTxx | Total strain (EPEL + EPPL + EPCR + EPTH) | - | [d] |
| NL:SEPL | Plastic yield stress | - | [e] |
| NL:SRAT | Plastic yielding (1 = actively yielding, 0 = not yielding) | - | [e] |
| NL:EPEQ | Accumulated equivalent plastic strain | - | [e] |
| NL:CREQ | Accumulated equivalent creep strain | - | [e] |
| NL:PLWK | Plastic work per unit volume | - | [e] |
| NL:HPRES | Hydrostatic pressure | - | [e] |
| SENE: | Elastic strain energy | - | Y |
| ADDITIONAL OUTPUT FOR STRUCTURAL-THERMAL ANALYSES (KEYOPT(1) = 11) [f] | |||
| TGxx | Axial thermal gradient | - | Y |
| TFxx | Axial thermal flux | - | Y |
| UE | Elastic strain energy[g] | - | Y |
| UT | Total strain energy[h] | - | Y |
| PHEAT | Plastic heat generation rate per unit volume | - | [b] |
| VHEAT | Plastic heat generation rate per unit volume | - | [b] |
| THERMAL-ELECTRIC ANALYSES (KEYOPT(1) = 110) | |||
| TGxx | Axial thermal gradient | - | Y |
| TFxx | Axial thermal flux | - | Y |
| EFxx | Axial electric field | - | Y |
| JCxx | Axial conduction current density | - | Y |
| JSxx | Axial current density | - | Y |
| JHEAT | Joule heat generation per unit volume[i] | - | Y |
| ADDITIONAL OUTPUT FOR STRUCTURAL-THERMOELECTRIC ANALYSES (KEYOPT(1) = 111)[f] | |||
| TGxx | Axial thermal gradient | - | Y |
| TFxx | Axial thermal flux | - | Y |
| EFxx | Axial electric field | - | Y |
| JCxx | Axial conduction current density | - | Y |
| JSxx | Axial current density | - | Y |
| JHEAT | Joule heat generation per unit volume[i] | - | Y |
| UE | Elastic strain energy | - | Y |
| UT | Total strain energy[h] | - | Y |
| PHEAT | Plastic heat generation rate per unit volume | - | [b] |
| VHEAT | Viscoelastic heat generation rate per unit volume | - | [b] |
| ADDITIONAL OUTPUT FOR PIEZOELECTRIC ANALYSES (KEYOPT(1) = 1001 and KEYOPT(1) = 101)[f] | |||
| TEMP | Input temperatures | - | Y |
| EFxx | Axial electric field | - | Y |
| Dxx | Axial electric flux density. Available only for charge-based analysis (KEYOPT(1) = 1001) | - | Y |
| JCxx | Axial conduction current density. Available only for current-based analysis (KEYOPT(1) = 101) | - | Y |
| JSxx | Axial element current density[j] | - | Y |
| JHEAT | Joule heat generation per unit volume[i][k] | - | Y |
| UE, UM, UD | Elastic, mutual, and dielectric energies[g] | - | Y |
| UT | Total strain energy[h] | - | Y |
| SENE | Sum of elastic and dielectric energies (UE+UD)[g] | - | Y |
| DENE | Damping energy[g] | - | Y |
| KENE | Kinetic energy[g] | - | Y |
| P:X, Y, Z, SUM | Element Poynting vector components (X, Y, Z) and vector magnitude[g] | - | Y |
[a] Available only at centroid as a *GET item.
[b] Available if the element has an appropriate nonlinear material.
[c] Available if the element temperatures differ from the reference temperature.
[d] Same as EPTO if there is no thermal effect.
[e] Available 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), 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 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] Calculated Joule heat generation rate per unit volume (JHEAT) may be made available for a subsequent thermal analysis with companion thermal elements. For piezoelectric analysis, the heat generation rate output as JHEAT is produced by both the supported structural and electrical losses.
[j] JS represents the sum of element conduction and displacement current densities.
[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.
Table 228.7: LINK228 Item and Sequence Numbers lists output available through the ETABLE command 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 228.7: LINK228 Item and Sequence Numbers:
- Name
output quantity as defined in Table 228.6: LINK228 Element Output Definitions
- Item
- E
sequence number for single-valued or constant element data
Table 228.7: LINK228 Item and Sequence Numbers
| Output Quantity Name | ETABLE and ESOL Command Input | |||
|---|---|---|---|---|
| Item | E | I | J | |
| ALL ANALYSES WITH A STRUCTURAL FIELD | ||||
| Sxx | LS | - | 1 | 2 |
| EPELxx | LEPEL | - | 1 | 2 |
| EPTOxx | LEPTO[a] | - | 1 | 2 |
| EPTHxx | LEPTH | - | 1 | 2 |
| EPPLxx | LEPPL | - | 1 | 2 |
| EPCRxx | LEPCR | - | 1 | 2 |
| NL:SEPL | NLIN | 1 | - | - |
| NL:SRAT | NLIN | 2 | - | - |
| NL:HPRES | NLIN | 3 | - | - |
| NL:EPEQ | NLIN | 4 | - | - |
| NL:CREQ | NLIN | 5 | - | - |
| NL:PLWK | NLIN | 6 | - | - |
| STRUCTURAL-THERMAL ANALYSES (KEYOPT(1) = 11) | ||||
| FORCE | SMISC | - | 1 | 2 |
| Average HEAT RATE | SMISC | 3 | - | - |
| UE | NMISC | 1 | - | - |
| UT | NMISC | 4 | - | - |
| PHEAT | NMISC | 5 | - | - |
| VHEAT | NMISC | 6 | - | - |
| AREA | NMISC | - | 11 | 12 |
| THERMAL-ELECTRIC ANALYSES (KEYOPT(1) = 110) | ||||
| Average HEAT RATE | SMISC | 3 | - | - |
| AREA | NMISC | - | 11 | 12 |
| STRUCTURAL-THERMOELECTRIC ANALYSES (KEYOPT(1) = 111) | ||||
| FORCE | SMISC | - | 1 | 2 |
| Average HEAT RATE | SMISC | 3 | - | - |
| UE | NMISC | 1 | ||
| UT | NMISC | 4 | ||
| PHEAT | NMISC | 5 | ||
| VHEAT | NMISC | 6 | ||
| AREA | NMISC | - | 11 | 12 |
| PIEZOELECTRIC ANALYSES (KEYOPT(1) = 1001 and KEYOPT(1) = 101) | ||||
| FORCE | SMISC | - | 1 | 2 |
| UE | NMISC | 1 | - | - |
| UD | NMISC | 2 | - | - |
| UM | NMISC | 3 | ||
| UT | NMISC | 4 | ||
| PX | NMISC | 5 | ||
| PY | NMISC | 6 | ||
| PZ | NMISC | 7 | ||
| PSUM | NMISC | 8 | ||
| AREA | NMISC | - | 11 | 12 |
LINK228 Assumptions and Restrictions
The element must not have a zero length, so nodes I and J must not be coincident.
The cross-sectional area must be greater than zero.
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 DOF.
Stress stiffening is always included in geometrically nonlinear (NLGEOM,ON) coupled-field analyses with structural degrees of freedom.
For coupled-field analyses with structural degrees of freedom, a nonlinear iterative solution method is necessary to simulate the tension-/compression-only options.
Heat and current are assumed to flow in the longitudinal element directions only.
A free end of the element (that is, not adjacent to another element and not subjected to a boundary constraint) is assumed to be adiabatic.
When the link works as a rigid constraint, for example in the case of a free swinging pendulum, the rigid cross section option is recommended (KEYOPT(3) = 1).