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Active degree of freedom

8

Additional solution variables

None.

Piezoelectric elements 

<table><tr><td>CAX3E(S)</td><td>3-node linear</td></tr><tr><td>CAX4E(S)</td><td>4-node bilinear</td></tr><tr><td>CAX6E(S)</td><td>6-node quadratic</td></tr><tr><td>CAX8E(S)</td><td>8-node biquadratic</td></tr><tr><td>CAX8RE(S)</td><td>8-node biquadratic, reduced integration</td></tr></table>

Active degrees of freedom

1, 2, 9

Additional solution variables

None.

Nodal coordinates required

r, z at

Element property definition

For element types DCCAX2 and DCCAX2D, you must specify the channel thickness of the element in the (r–z) plane. The default is unit thickness if no thickness is given.

For all other elements, you do not need to specify the thickness.

Input File Usage: \*SOLID SECTION

Abaqus/CAE Usage: Property module: Create Section: select Solid as the section Category and Homogeneous as the section Type

Element-based loading

# Distributed loads

Distributed loads are available for all elements with displacement degrees of freedom. They are specified as described in “Distributed loads,” Section 34.4.3. Distributed load magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

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<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>BR</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in radial direction.</td></tr><tr><td>BZ</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in axial direction.</td></tr><tr><td>BRNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in radial direction with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>BZNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in axial direction with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td> $CENT^{(S)}$ </td><td>Not supported</td><td> $FL^{-4}M^{-3}T^{-2}$ </td><td>Centrifugal load (magnitude input as  $\rho\omega^{2}$ , where  $\rho$  is the mass density per unit volume,  $\omega$  is the angular velocity). Not available for pore pressure elements.</td></tr><tr><td> $CENTRIF^{(S)}$ </td><td>Rotational body force</td><td> $T^{-2}$ </td><td>Centrifugal load (magnitude is input as  $\omega^{2}$ , where  $\omega$  is the angular velocity).</td></tr><tr><td>GRAV</td><td>Gravity</td><td> $LT^{-2}$ </td><td>Gravity loading in a specified direction (magnitude is input as acceleration).</td></tr><tr><td> $HPn^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Hydrostatic pressure on face  $n$ , linear in global  $Y$ .</td></tr><tr><td> $Pn$ </td><td>Pressure</td><td> $FL^{-2}$ </td><td>Pressure on face  $n$ .</td></tr><tr><td> $PnNU$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform pressure on face  $n$  with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td> $SBF^{(E)}$ </td><td>Not supported</td><td> $FL^{-5}T^{2}$ </td><td>Stagnation body force in radial and axial directions.</td></tr><tr><td> $SPn^{(E)}$ </td><td>Not supported</td><td> $FL^{-4}T^{2}$ </td><td>Stagnation pressure on face  $n$ .</td></tr></table>

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<table><tr><td>Load ID(*DLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>TRSHRn</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Shear traction on face n.</td></tr><tr><td> $TRSHRnNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform shear traction on face n with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td>TRVECn</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>General traction on face n.</td></tr><tr><td> $TRVECnNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform general traction on face n with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td> $VBF^{(E)}$ </td><td>Not supported</td><td> $FL^{-4}T$ </td><td>Viscous body force in radial and axial directions.</td></tr><tr><td> $VPn^{(E)}$ </td><td>Not supported</td><td> $FL^{-3}T$ </td><td>Viscous pressure on face n, applying a pressure proportional to the velocity normal to the face and opposing the motion.</td></tr></table>

# Foundations

Foundations are available for Abaqus/Standard elements with displacement degrees of freedom. They are specified as described in “Element foundations,” Section 2.2.2.

<table><tr><td>Load ID(*FOUNDATION)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $Fn^{(S)}$ </td><td>Elastic foundation</td><td> $FL^{-3}$ </td><td>Elastic foundation on face n. For CGAX elements the elastic foundations are applied to degrees of freedom  $u_r$  and  $u_z$  only.</td></tr></table>

# Distributed heat fluxes

Distributed heat fluxes are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4. Distributed heat flux magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

<table><tr><td>Load ID(*DFLUX)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>BF</td><td>Body heat flux</td><td> $JL^{-3}T^{-1}$ </td><td>Heat body flux per unit volume.</td></tr></table>

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<table><tr><td>Load ID(*DFLUX)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>BFNU</td><td>Body heat flux</td><td> $JL^{-3}T^{-1}$ </td><td>Nonuniform heat body flux per unit volume with magnitude supplied via user subroutineDFLUXin Abaqus/Standard andVDFLUXin Abaqus/Explicit.</td></tr><tr><td>Sn</td><td>Surface heat flux</td><td> $JL^{-2}T^{-1}$ </td><td>Heat surface flux per unit area into face n.</td></tr><tr><td>SnNU</td><td>Not supported</td><td> $JL^{-2}T^{-1}$ </td><td>Nonuniform heat surface flux per unit area into face n with magnitude supplied via user subroutineDFLUXin Abaqus/Standard andVDFLUXin Abaqus/Explicit.</td></tr></table>

# Film conditions

Film conditions are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4.

<table><tr><td>Load ID (*FILM)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>Fn</td><td>Surface film condition</td><td> $JL^{-2}T^{-1}\theta^{-1}$ </td><td>Film coefficient and sink temperature (units of  $\theta$ ) provided on face n.</td></tr><tr><td>FnNU(S)</td><td>Not supported</td><td> $JL^{-2}T^{-1}\theta^{-1}$ </td><td>Nonuniform film coefficient and sink temperature (units of  $\theta$ ) provided on face n with magnitude supplied via user subroutine FILM.</td></tr></table>

# Radiation types

Radiation conditions are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4.

<table><tr><td>Load ID(*RADIATE)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>Rn</td><td>Surface radiation</td><td>Dimensionless</td><td>Emissivity and sink temperature provided for face n.</td></tr></table>

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# Distributed flows

Distributed flows are available for all elements with pore pressure degrees of freedom. They are specified as described in “Pore fluid flow,” Section 34.4.7. Distributed flow magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

<table><tr><td>Load ID (*FLOW)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $Qn^{(S)}$ </td><td>Not supported</td><td> $F^{-1}L^{3}T^{-1}$ </td><td>Seepage coefficient and reference sink pore pressure (units of  $FL^{-2}$ ) provided on face n.</td></tr><tr><td> $QnD^{(S)}$ </td><td>Not supported</td><td> $F^{-1}L^{3}T^{-1}$ </td><td>Drainage-only seepage coefficient provided on face n.</td></tr><tr><td> $QnNU^{(S)}$ </td><td>Not supported</td><td> $F^{-1}L^{3}T^{-1}$ </td><td>Nonuniform seepage coefficient and reference sink pore pressure (units of  $FL^{-2}$ ) provided on face n with magnitude supplied via user subroutine FLOW.</td></tr><tr><td>Load ID (*DFLOW)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $Sn^{(S)}$ </td><td>Surface pore fluid</td><td> $LT^{-1}$ </td><td>Prescribed pore fluid effective velocity (outward from the face) on face n.</td></tr><tr><td> $SnNU^{(S)}$ </td><td>Not supported</td><td> $LT^{-1}$ </td><td>Nonuniform prescribed pore fluid effective velocity (outward from the face) on face n with magnitude supplied via user subroutine DFLOW.</td></tr></table>

# Distributed impedances

Distributed impedances are available for all elements with acoustic pressure degrees of freedom. They are specified as described in “Acoustic and shock loads,” Section 34.4.6.

<table><tr><td>Load ID(*IMPEDANCE)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>In</td><td>Not supported</td><td>None</td><td>Name of the impedance property that defines the impedance on face n.</td></tr></table>

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# Electric fluxes

Electric fluxes are available for piezoelectric elements. They are specified as described in “Piezoelectric analysis,” Section 6.7.2.

<table><tr><td>Load ID(*DECHARGE)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $EBF^{(S)}$ </td><td>Body charge</td><td> $CL^{-3}$ </td><td>Body flux per unit volume.</td></tr><tr><td> $ESn^{(S)}$ </td><td>Surface charge</td><td> $CL^{-2}$ </td><td>Prescribed surface charge on face n.</td></tr></table>

# Distributed electric current densities

Distributed electric current densities are available for coupled thermal-electrical elements. They are specified as described in “Coupled thermal-electrical analysis,” Section 6.7.3.

<table><tr><td>Load ID(*DECURRENT)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $CBF^{(S)}$ </td><td>Body current</td><td> $CL^{-3}T^{-1}$ </td><td>Volumetric current source density.</td></tr><tr><td> $CSn^{(S)}$ </td><td>Surface current</td><td> $CL^{-2}T^{-1}$ </td><td>Current density on face n.</td></tr></table>

# Distributed concentration fluxes

Distributed concentration fluxes are available for mass diffusion elements. They are specified as described in “Mass diffusion analysis,” Section 6.9.1.

<table><tr><td>Load ID (*DFLUX)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $BF^{(S)}$ </td><td>Body concentration flux</td><td> $PT^{-1}$ </td><td>Concentration body flux per unit volume.</td></tr><tr><td> $BFNU^{(S)}$ </td><td>Body concentration flux</td><td> $PT^{-1}$ </td><td>Nonuniform concentration body flux per unit volume with magnitude supplied via user subroutine DFLUX.</td></tr><tr><td> $Sn^{(S)}$ </td><td>Surface concentration flux</td><td> $PLT^{-1}$ </td><td>Concentration surface flux per unit area into face n.</td></tr><tr><td> $SnNU^{(S)}$ </td><td>Surface concentration flux</td><td> $PLT^{-1}$ </td><td>Nonuniform concentration surface flux per unit area into face n with magnitude supplied via user subroutine DFLUX.</td></tr></table>

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# Distributed loads

Surface-based distributed loads are available for all elements with displacement degrees of freedom. They are specified as described in “Distributed loads,” Section 34.4.3. Distributed load magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

<table><tr><td>Load ID(*DSLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>HP(S)</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Hydrostatic pressure on the element surface, linear in global Y.</td></tr><tr><td>P</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Pressure on the element surface.</td></tr><tr><td>PNU</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Nonuniform pressure on the element surface with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>SP(E)</td><td>Pressure</td><td> $FL^{-4}T^{2}$ </td><td>Stagnation pressure on the element surface.</td></tr><tr><td>TRSHR</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Shear traction on the element surface.</td></tr><tr><td>TRSHRNU(S)</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Nonuniform shear traction on the element surface with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td>TRVEC</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>General traction on the element surface.</td></tr><tr><td>TRVECNU(S)</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Nonuniform general traction on the element surface with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td>VP(E)</td><td>Pressure</td><td> $FL^{-3}T$ </td><td>Viscous pressure applied on the element surface. The viscous pressure is proportional to the velocity normal to the face and opposing the motion.</td></tr></table>

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# Distributed heat fluxes

Surface-based heat fluxes are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4. Distributed heat flux magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

<table><tr><td>Load ID(*DSFLUX)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>S</td><td>Surface heat flux</td><td> $JL^{-2}T^{-1}$ </td><td>Heat surface flux per unit area into the element surface.</td></tr><tr><td>SNU</td><td>Surface heat flux</td><td> $JL^{-2}T^{-1}$ </td><td>Nonuniform heat surface flux per unit area into the element surface with magnitude supplied via user subroutine DFLUX in Abaqus/Standard and VDFLUX in Abaqus/Explicit.</td></tr></table>

# Film conditions

Surface-based film conditions are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4.

<table><tr><td>Load ID(*SFILM)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>F</td><td>Surface film condition</td><td> $JL^{-2}T^{-1}\theta^{-1}$ </td><td>Film coefficient and sink temperature (units of  $\theta$ ) provided on the element surface.</td></tr><tr><td> $FNU^{(S)}$ </td><td>Surface film condition</td><td> $JL^{-2}T^{-1}\theta^{-1}$ </td><td>Nonuniform film coefficient and sink temperature (units of  $\theta$ ) provided on the element surface with magnitude supplied via user subroutine  $FILM$ .</td></tr></table>

# Radiation types

Surface-based radiation conditions are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4.

<table><tr><td>Load ID(*SRADIATE)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>R</td><td>Surface radiation</td><td>Dimensionless</td><td>Emissivity and sink temperature provided for the element surface.</td></tr></table>

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# Distributed flows

Surface-based distributed flows are available for all elements with pore pressure degrees of freedom. They are specified as described in “Pore fluid flow,” Section 34.4.7. Distributed flow magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

<table><tr><td>Load ID(*SFLOW)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $Q^{(S)}$ </td><td>Not supported</td><td> $F^{-1}L^{3}T^{-1}$ </td><td>Seepage coefficient and reference sink pore pressure (units of  $FL^{-2}$ ) provided on the element surface.</td></tr><tr><td> $QD^{(S)}$ </td><td>Not supported</td><td> $F^{-1}L^{3}T^{-1}$ </td><td>Drainage-only seepage coefficient provided on the element surface.</td></tr><tr><td> $QNU^{(S)}$ </td><td>Not supported</td><td> $F^{-1}L^{3}T^{-1}$ </td><td>Nonuniform seepage coefficient and reference sink pore pressure (units of  $FL^{-2}$ ) provided on the element surface with magnitude supplied via user subroutine FLOW.</td></tr><tr><td>Load ID(*DSFLOW)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $S^{(S)}$ </td><td>Surface pore fluid</td><td> $LT^{-1}$ </td><td>Prescribed pore fluid effective velocity outward from the element surface.</td></tr><tr><td> $SNU^{(S)}$ </td><td>Surface pore fluid</td><td> $LT^{-1}$ </td><td>Nonuniform prescribed pore fluid effective velocity outward from the element surface with magnitude supplied via user subroutine DFLOW.</td></tr></table>

# Distributed impedances

Surface-based impedances are available for all elements with acoustic pressure degrees of freedom. They are specified as described in “Acoustic and shock loads,” Section 34.4.6.

# Incident wave loading

Surface-based incident wave loads are available for all elements with displacement degrees of freedom or acoustic pressure degrees of freedom. They are specified as described in “Acoustic and shock loads,” Section 34.4.6. If the incident wave field includes a reflection off a plane outside the boundaries of the mesh, this effect can be included.

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# Electric fluxes

Surface-based electric fluxes are available for piezoelectric elements. They are specified as described in “Piezoelectric analysis,” Section 6.7.2.

<table><tr><td>Load ID(*DSECHARGE)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $ES^{(S)}$ </td><td>Surface charge</td><td> $CL^{-2}$ </td><td>Prescribed surface charge on the element surface.</td></tr></table>

# Distributed electric current densities

Surface-based electric current densities are available for coupled thermal-electrical elements. They are specified as described in “Coupled thermal-electrical analysis,” Section 6.7.3.

<table><tr><td>Load ID(*DSECURRENT)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $CS^{(S)}$ </td><td>Surface current</td><td> $CL^{-2}T^{-1}$ </td><td>Current density on the element surface.</td></tr></table>

# Element output

Output is in global directions unless a local coordinate system is assigned to the element through the section definition (“Orientations,” Section 2.2.5) in which case output is in the local coordinate system (which rotates with the motion in large-displacement analysis). See “State storage,” Section 1.5.4 of the Abaqus Theory Guide, for details. For regular axisymmetric elements, the local orientation must be in the –z plane with being a principal direction. For generalized axisymmetric elements with twist, the local orientation can be arbitrary.

# Stress, strain, and other tensor components

Stress and other tensors (including strain tensors) are available for elements with displacement degrees of freedom. All tensors have the same components. For example, the stress components are as follows:

For elements with displacement degrees of freedom without twist:

<table><tr><td>S11</td><td>Stress in the radial direction or in the local 1-direction.</td></tr><tr><td>S22</td><td>Stress in the axial direction or in the local 2-direction.</td></tr><tr><td>S33</td><td>Hoop direct stress.</td></tr><tr><td>S12</td><td>Shear stress.</td></tr></table>

For elements with displacement degrees of freedom with twist:

<table><tr><td>S11</td><td>Stress in the radial direction or in the local 1-direction.</td></tr><tr><td>S22</td><td>Stress in the axial direction or in the local 2-direction.</td></tr></table>
