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+
+# 29.6.9 AXISYMMETRIC SHELL ELEMENT LIBRARY
+
+Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE
+
+# References
+
+• “Shell elements: overview,” Section 29.6.1   
+• “Choosing a shell element,” Section 29.6.2   
+• \*NODAL THICKNESS   
+• \*SHELL GENERAL SECTION   
+• \*SHELL SECTION
+
+# Overview
+
+This section provides a reference to the axisymmetric shell elements available in Abaqus/Standard and Abaqus/Explicit. For axisymmetric shell geometries in which nonaxisymmetric behavior is expected, use the SAXA elements available in Abaqus/Standard (see “Axisymmetric shell elements with nonlinear, asymmetric deformation,” Section 29.6.10).
+
+# Conventions
+
+Coordinate 1 is r, coordinate 2 is z. The r-direction corresponds to the global X-direction, and the zdirection corresponds to the global Y-direction. Coordinate 1 should be greater than or equal to zero.
+
+Degree of freedom 1 is $u _ { r }$ , degree of freedom 2 is $u _ { z }$ , and degree of freedom 6 is rotation in the r–z plane.
+
+Abaqus does not automatically apply any boundary conditions to nodes located along the symmetry axis. You should apply radial or symmetry boundary conditions on these nodes if desired.
+
+Point loads and concentrated fluxes should be given as the value integrated around the circumference (that is, the load on the complete ring).
+
+The meridional direction is the direction that is tangent to the element in the r–z plane; that is, the meridional direction is along the line that is rotated about the axis of symmetry to generate the full three-dimensional body.
+
+The circumferential or hoop direction is the direction normal to the r–z plane.
+
+# Element types
+
+# Stress/displacement elements
+
+SAX1 2-node thin or thick linear shell   
+SAX2(S) 3-node thin or thick quadratic shell
+
+<!-- source-page: 502 -->
+
+Active degrees of freedom
+
+1, 2, 6
+
+Additional solution variables
+
+None.
+
+# Heat transfer elements
+
+DSAX1(S)
+
+2-node shell
+
+DSAX2(S)
+
+3-node shell
+
+Active degrees of freedom
+
+11, 12, 13, etc. (temperatures through the thickness as described in “Choosing a shell element,” Section 29.6.2)
+
+Additional solution variables
+
+None.
+
+# Coupled temperature-displacement element
+
+SAX2T(S)
+
+3-node thin or thick shell, quadratic displacement, linear temperature in the shell surface
+
+Active degrees of freedom
+
+1, 2, 6 at all three nodes
+
+11, 12, 13, etc. (temperatures through the thickness as described in “Choosing a shell element,” Section 29.6.2) at the end nodes
+
+Additional solution variables
+
+None.
+
+# Nodal coordinates required
+
+r, z, and optionally for shells with displacement degrees of freedom, , , the direction cosines of the shell normal at the node.
+
+# Element property definition
+
+Input File Usage:
+
+Use either of the following options for stress/displacement elements:
+
+\*SHELL SECTION
+
+\*SHELL GENERAL SECTION
+
+<!-- source-page: 503 -->
+
+Use the following option for heat transfer or coupled temperature-displacement elements:
+
+\*SHELL SECTION
+
+In addition, use the following option for variable thickness shells:
+
+\*NODAL THICKNESS
+
+Abaqus/CAE Usage: Property module: Create Section: select Shell as the section Category and Homogeneous or Composite as the section Type
+
+# Element-based loading
+
+# Distributed loads
+
+Distributed loads are available for 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 .
+
+Body forces and centrifugal loads must be given as force per unit area if a general shell section is used.
+
+<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 per unit volume in the radial direction.</td></tr><tr><td>BZ</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force per unit volume in the axial direction.</td></tr><tr><td>BRNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force per unit volume in the radial direction, with the 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 per unit volume in the global z-direction, with the 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 given as  $\rho\omega^{2}$ , where  $\rho$  is the mass density and  $\omega$  is the angular velocity). Since only</td></tr></table>
+
+<!-- source-page: 504 -->
+
+<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>CENTRIF(S)</td><td>Rotational body force</td><td> $T^{-2}$ </td><td>axisymmetric deformation is allowed, the spin axis must be the z-axis. Centrifugal load (magnitude is input as  $\omega^2$ , where  $\omega$  is the angular velocity). Since only axisymmetric deformation is allowed, the spin axis must be the z-axis.</td></tr><tr><td>GRAV</td><td>Gravity</td><td> $LT^{-2}$ </td><td>Gravity loading in a specified direction (magnitude 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 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>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>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>TRSHRNU(S)</td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform shear traction on the element reference surface with</td></tr></table>
+
+<!-- source-page: 505 -->
+
+<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>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>Not supported</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><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> $VP^{(E)}$ </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 ofthe 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></table>
+
+<!-- source-page: 506 -->
+
+<table><tr><td>Load ID(*DFLUX)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</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><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  $\text{FILM}$ .</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  $\text{FILM}$ .</td></tr></table>
+
+<!-- source-page: 507 -->
+
+# 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><tr><td>RPOS(S)</td><td>Surface radiation</td><td>Dimensionless</td><td>Emissivity and sink temperature (units of θ) provided for the top face of the shell.</td></tr></table>
+
+# Surface-based loading
+
+# Distributed loads
+
+Surface-based distributed loads are available for 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 reference surface and linear in global Z. The pressure is positive in the direction opposite 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></table>
+
+<!-- source-page: 508 -->
+
+<table><tr><td>Load ID(*DSLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</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><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 surface and opposing the motion.</td></tr></table>
+
+# Distributed heat fluxes
+
+Surface-based 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.
+
+<!-- source-page: 509 -->
+
+<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 subroutineFILM.</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.
+
+<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
+
+# 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>Meridional stress.</td></tr><tr><td>S22</td><td>Hoop (circumferential) stress.</td></tr></table>
+
+# Section forces, moments, and transverse shear forces
+
+Available for elements with displacement degrees of freedom.
+
+SF1 Membrane force per unit width in the meridional direction.
+
+SF2 Membrane force per unit width in the hoop direction.
+
+<!-- source-page: 510 -->
+
+<table><tr><td>SF3</td><td>Transverse shear force per unit width in the meridional direction (available only from Abaqus/Standard).</td></tr><tr><td>SF4</td><td>Integrated stress in the thickness direction; always zero (available only from Abaqus/Standard).</td></tr><tr><td>SM1</td><td>Bending moment per unit width about the hoop direction.</td></tr><tr><td>SM2</td><td>Bending moment per unit width about the meridional direction.</td></tr></table>
+
+# Section strains, curvature changes, and transverse shear strains
+
+Available for elements with displacement degrees of freedom.
+
+<table><tr><td>SE1</td><td>Membrane strain in the meridional direction.</td></tr><tr><td>SE2</td><td>Membrane strain in the hoop direction.</td></tr><tr><td>SE3</td><td>Transverse shear strain in the meridional direction (available only from Abaqus/Standard).</td></tr><tr><td>SE4</td><td>Strain in the thickness direction (available only from Abaqus/Standard).</td></tr><tr><td>SK1</td><td>Curvature change about the hoop direction.</td></tr><tr><td>SK2</td><td>Curvature change about the meridional direction.</td></tr></table>
+
+# Shell thickness
+
+STH Shell thickness, which is the current thickness for SAX1, SAX2, and SAX2T elements.
+
+# Heat flux components
+
+Available for elements with temperature degrees of freedom.
+
+HFL1 Heat flux in the meridional direction.
+
+HFL2 Heat flux in the thickness direction.
+
+# Node ordering on elements
+
+![](images/page-510_d94856119d1788a3dcbbc010490723eaa6463a8f2e18090e8848f42fcd72c09e.jpg)
+
+<details>
+<summary>natural_image</summary>
+
+Simple line diagram with two labeled points (1 and 2) connected by a straight line (no additional text or symbols)
+</details>
+
+2 - node element
+
+![](images/page-510_47002b0daab6e6f3551d5c88d1c06590c414d0b50076b2132247abf9c686b3a9.jpg)
+
+<details>
+<summary>text_image</summary>
+
+1
+2
+3
+</details>
+
+3 - node element