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<table><tr><td>S4T(S)</td><td>4-node general-purpose shell, finite membrane strains, bilinear temperature in the shell surface</td></tr><tr><td>S4RT</td><td>4-node general-purpose shell, reduced integration with hourglass control, finite membrane strains, bilinear temperature in the shell surface</td></tr><tr><td>S8RT(S)</td><td>8-node thick shell, biquadratic displacement, bilinear temperature in the shell surface</td></tr></table>

# Active degrees of freedom

1, 2, 3, 4, 5, 6 at all nodes

11, 12, 13, etc. (temperatures through the thickness as described in “Choosing a shell element,” Section 29.6.2) at all nodes for S3T, S3RT, S4T, and S4RT; and at the corner nodes only for S8RT

# Additional solution variables

None.

# Nodal coordinates required

and, optionally for shells with displacement degrees of freedom in Abaqus/Standard, $N _ { x } , N _ { y } , N _ { z }$ , the direction cosines of the shell normal at the node.

# Element property definition

<table><tr><td>Input File Usage:</td><td>Use either of the following options for stress/displacement elements:*SHELL SECTION*SHELL GENERAL SECTIONUse the following option for heat transfer or coupled temperature-displacement elements:*SHELL SECTIONIn addition, use the following option for variable thickness shells:*NODAL THICKNESS</td></tr><tr><td>Abaqus/CAE Usage:</td><td>Property module: Create Section: select Shell as the section Category and Homogeneous or Composite as the section Type</td></tr></table>

# 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.

Body forces, centrifugal loads, and Coriolis forces must be given as force per unit area if the equivalent section properties are specified directly as part of the general shell section definition.

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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>BX</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force (give magnitude as force per unit volume) in the global X-direction.</td></tr><tr><td>BY</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force (give magnitude as force per unit volume) in the global Y-direction.</td></tr><tr><td>BZ</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force (give magnitude as force per unit volume) in the global Z-direction.</td></tr><tr><td>BXNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force (give magnitude as force per unit volume) in the global X-direction, with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>BYNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force (give magnitude as force per unit volume) in the global Y-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 (give magnitude as force per unit volume) in the global Z-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> $FL^{-4}$  $(ML^{-3}T^{-2})$ </td><td>Centrifugal load (magnitude defined as  $\rho\omega^{2}$ , where  $\rho$  is the mass density and  $\omega$  is the angular speed).</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 speed).</td></tr></table>

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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> $CORIO^{(S)}$ </td><td>Coriolis force</td><td> $FL^{-4}T (ML^{-3}T^{-1})$ </td><td>Coriolis force (magnitude input ρω, where ρ is the mass density and ω is the angular speed). The load stiffness due to Coriolis loading is not accounted for in direct steady-state dynamics analysis.</td></tr><tr><td>EDLDn</td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>General traction on edge n.</td></tr><tr><td> $EDLDnNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-1}$ </td><td>Nonuniform general traction on edge n with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td>EDMOMn</td><td>Shell edge load</td><td>F</td><td>Moment on edge n.</td></tr><tr><td> $EDMOMnNU^{(S)}$ </td><td>Not supported</td><td>F</td><td>Nonuniform moment on edge n with magnitude supplied via user subroutine UTRACLOAD.</td></tr><tr><td>EDNORn</td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>Normal traction on edge n.</td></tr><tr><td> $EDNORnNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-1}$ </td><td>Nonuniform normal traction on edge n with magnitude supplied via user subroutine UTRACLOAD.</td></tr><tr><td>EDSHRn</td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>Shear traction on edge n.</td></tr><tr><td> $EDSHRnNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-1}$ </td><td>Nonuniform shear traction on edge n with magnitude supplied via user subroutine UTRACLOAD.</td></tr><tr><td>EDTRAn</td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>Transverse traction on edge n.</td></tr><tr><td> $EDTRAnNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-1}$ </td><td>Nonuniform transverse traction on edge n with magnitude supplied via user subroutine UTRACLOAD.</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> $HP^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Hydrostatic pressure applied to the element reference surface and linear in global Z. The pressure is positive in</td></tr></table>

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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></td><td></td><td></td><td>the direction of the positive element normal.</td></tr><tr><td>P</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Pressure applied to the element reference surface. The pressure is positive in the direction of the positive element normal.</td></tr><tr><td>PNU</td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform pressure applied to the element reference surface with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit. The pressure is positive in the direction of the positive element normal.</td></tr><tr><td> $\text{ROTA}^{(S)}$ </td><td>Rotational body force</td><td> $T^{-2}$ </td><td>Rotary acceleration load (magnitude is input as  $\alpha$ , where  $\alpha$  is the rotary acceleration).</td></tr><tr><td> $\text{ROTDYNF}^{(S)}$ </td><td>Not supported</td><td> $T^{-1}$ </td><td>Rotordynamic load (magnitude is input as  $\omega$ , where  $\omega$  is the angular velocity).</td></tr><tr><td> $\text{SBF}^{(E)}$ </td><td>Not supported</td><td> $FL^{-5}T$ </td><td>Stagnation body force in global X-, Y-, and Z-directions.</td></tr><tr><td> $\text{SP}^{(E)}$ </td><td>Not supported</td><td> $FL^{-4}T^{2}$ </td><td>Stagnation pressure applied to the element reference surface.</td></tr><tr><td>TRSHR</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Shear traction on the element reference surface.</td></tr><tr><td> $\text{TRSHRNU}^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform shear traction on the element reference 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 reference surface.</td></tr><tr><td> $\text{TRVECNU}^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform general traction on the element reference surface with</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></td><td></td><td></td><td>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 global X-, Y-, and Z-directions.</td></tr><tr><td> $VP^{(E)}$ </td><td>Not supported</td><td> $FL^{-3}T$ </td><td>Viscous surface pressure. The viscous pressure is proportional to the velocity normal to the element 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/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $F^{(S)}$ </td><td>Elasticfoundation</td><td> $FL^{-3}$ </td><td>Elastic foundation in the direction of the shell normal.</td></tr></table>

# Distributed heat fluxes

Distributed heat fluxes are available for elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4.

<table><tr><td>Load ID(*DFLUX)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $BF^{(S)}$ </td><td>Body heat flux</td><td> $JL^{-3}$   $T^{-1}$ </td><td>Body heat flux per unit volume.</td></tr><tr><td> $BFNU^{(S)}$ </td><td>Body heat flux</td><td> $JL^{-3}$   $T^{-1}$ </td><td>Nonuniform body heat flux per unit volume with magnitude supplied via user subroutine DFLUX.</td></tr><tr><td> $SNEG^{(S)}$ </td><td>Surface heat flux</td><td> $JL^{-2}$   $T^{-1}$ </td><td>Surface heat flux per unit area into the bottom face of the element.</td></tr><tr><td> $SPOS^{(S)}$ </td><td>Surface heat flux</td><td> $JL^{-2}$   $T^{-1}$ </td><td>Surface heat flux per unit area into the top face of the element.</td></tr><tr><td> $SNEGNU^{(S)}$ </td><td>Not supported</td><td> $JL^{-2}$   $T^{-1}$ </td><td>Nonuniform surface heat flux per unit area into the bottom face of the element with magnitude supplied via user subroutine DFLUX.</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> $SPOSNU^{(S)}$ </td><td>Not supported</td><td> $JL^{-2} \ T^{-1}$ </td><td>Nonuniform surface heat flux per unit area into the top face of the element with magnitude supplied via user subroutine DFLUX.</td></tr></table>

# Film conditions

Film conditions are available for 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> $FNEG^{(S)}$ </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 bottom face of the element.</td></tr><tr><td> $FPOS^{(S)}$ </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 top face of the element.</td></tr><tr><td> $FNEGNU^{(S)}$ </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 the bottom face of the element with magnitude supplied via user subroutine  $FILM$ .</td></tr><tr><td> $FPOSNU^{(S)}$ </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 the top face of the element with magnitude supplied via user subroutine  $FILM$ .</td></tr></table>

# Radiation types

Radiation conditions are available for 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>RNEG(S)</td><td>Surface radiation</td><td>Dimensionless</td><td>Emissivity and sink temperature (units of θ) provided for the bottom face of the shell.</td></tr></table>

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<table><tr><td>Load ID(*RADIATE)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $RPOS^{(S)}$ </td><td>Surface radiation</td><td>Dimensionless</td><td>Emissivity and sink temperature (units of  $\theta$ ) provided for the top face of the shell.</td></tr></table>

Surface-based loading   
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.

<table><tr><td>Load ID(*DSLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>EDLD</td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>General traction on edge-based surface.</td></tr><tr><td> $EDLDNU^{(S)}$ </td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>Nonuniform general traction on edge-based surface with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td>EDMOM</td><td>Shell edge load</td><td>F</td><td>Moment on edge-based surface.</td></tr><tr><td> $EDMOMNU^{(S)}$ </td><td>Shell edge load</td><td>F</td><td>Nonuniform moment on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.</td></tr><tr><td>EDNOR</td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>Normal traction on edge-based surface.</td></tr><tr><td> $EDNORNU^{(S)}$ </td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>Nonuniform normal traction on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.</td></tr><tr><td>EDSHR</td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>Shear traction on edge-based surface.</td></tr><tr><td> $EDSHRNU^{(S)}$ </td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>Nonuniform shear traction on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.</td></tr><tr><td>EDTRA</td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>Transverse traction on edge-based surface.</td></tr></table>

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<table><tr><td>Load ID(*DSLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $EDTRANU^{(S)}$ </td><td>Shell edge load</td><td> $FL^{-1}$ </td><td>Nonuniform transverse traction on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.</td></tr><tr><td> $HP^{(S)}$ </td><td>Pressure</td><td> $FL^{-2}$ </td><td>Hydrostatic pressure on the element reference surface and linear in global Z. The pressure is positive in the direction opposite to the surface normal.</td></tr><tr><td>P</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Pressure on the element reference surface. The pressure is positive in the direction opposite to the surface normal.</td></tr><tr><td>PNU</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Nonuniform pressure on the element reference surface with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit. The pressure is positive in the direction opposite to the surface normal.</td></tr><tr><td> $SP^{(E)}$ </td><td>Pressure</td><td> $FL^{-4}T^{2}$ </td><td>Stagnation pressure applied to the element reference surface.</td></tr><tr><td>TRSHR</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Shear traction on the element reference surface.</td></tr><tr><td> $TRSHRNU^{(S)}$ </td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Nonuniform shear traction on the element reference 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 reference surface.</td></tr><tr><td> $TRVECNU^{(S)}$ </td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr></table>

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<table><tr><td>Load ID(*DSLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>VP(E)</td><td>Pressure</td><td> $FL^{-3}T$ </td><td>Viscous surface pressure. The viscous pressure is proportional to the velocity normal to the element face and opposing the motion.</td></tr></table>

# Distributed heat fluxes

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

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

# Film conditions

Surface-based film conditions are available for 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> $F^{(S)}$ </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 elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4.

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<table><tr><td>Load ID(*SRADIATE)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $R^{(S)}$ </td><td>Surface radiation</td><td>Dimensionless</td><td>Emissivity and sink temperature (units of  $\theta$ ) provided for the element surface.</td></tr></table>

# Incident wave loading

Surface-based incident wave loads are available. They are specified as described in “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1. If the incident wave field includes a reflection off a plane outside the boundaries of the mesh, this effect can be included.

# Element output

If a local coordinate system is not assigned to the element, the stress/strain components, as well as the section forces/strains, are in the default directions on the surface defined by the convention given in “Conventions,” Section 1.2.2. If a local coordinate system is assigned to the element through the section definition (“Orientations,” Section 2.2.5), the stress/strain components and the section forces/strains are in the surface directions defined by the local coordinate system.

In large-displacement problems with elements that allow finite membrane strains in Abaqus/Standard and in all problems in Abaqus/Explicit, the local directions defined in the reference configuration are rotated into the current configuration by the average material rotation.

# 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:

<table><tr><td>S11</td><td>Local 11 direct stress.</td></tr><tr><td>S22</td><td>Local 22 direct stress.</td></tr><tr><td>S12</td><td>Local 12 shear stress.</td></tr></table>

# Section forces, moments, and transverse shear forces

Available for elements with displacement degrees of freedom.

<table><tr><td>SF1</td><td>Direct membrane force per unit width in local 1-direction.</td></tr><tr><td>SF2</td><td>Direct membrane force per unit width in local 2-direction.</td></tr><tr><td>SF3</td><td>Shear membrane force per unit width in local 1–2 plane.</td></tr><tr><td>SF4</td><td>Transverse shear force per unit width in local 1-direction (available only for S3/S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R, and S8RT).</td></tr><tr><td>SF5</td><td>Transverse shear force per unit width in local 2-direction (available only for S3/S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R, and S8RT).</td></tr></table>
