Products: ABAQUS/Standard ABAQUS/Explicit ABAQUS/CAE
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 23.6.10).
Coordinate 1 is r, coordinate 2 is z. The r-direction corresponds to the global X-direction, and the z-direction corresponds to the global Y-direction. Coordinate 1 should be greater than or equal to zero.
Degree of freedom 1 is 
, degree of freedom 2 is 
, 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.
| SAX1 | 2-node thin or thick linear shell |
| SAX2(S) | 3-node thin or thick quadratic shell |
| DSAX1(S) | 2-node shell |
| DSAX2(S) | 3-node shell |
11, 12, 13, etc. (temperatures through the thickness as described in “Choosing a shell element,” Section 23.6.2)
| SAX2T(S) | 3-node thin or thick shell, quadratic displacement, linear temperature in the shell surface |
1, 2, 6 at all three nodes
11, 12, 13, etc. (temperatures through the thickness as described in “Choosing a shell element,” Section 23.6.2) at the end nodes
r, z, and optionally for shells with displacement degrees of freedom, 
, 
, the direction cosines of the shell normal at the node.
Shell thicknesses, offsets, and section stiffnesses can be defined on an element-by-element basis. See “Assigning element properties on an element-by-element basis,” Section 21.1.5.
| Input File Usage: | Use either of the following options for stress/displacement elements: |
*SHELL SECTION *SHELL GENERAL SECTION 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 |
You cannot define variable thickness shells in ABAQUS/CAE. |
Distributed loads are available for elements with displacement degrees of freedom. They are specified as described in “Distributed loads,” Section 27.4.3.
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.
Load ID (*DLOAD): BR
ABAQUS/CAE Load/Interaction: Body force
Units: FL–3
Description: Body force per unit volume in the radial direction.
Load ID (*DLOAD): BZ
ABAQUS/CAE Load/Interaction: Body force
Units: FL–3
Description: Body force per unit volume in the axial direction.
Load ID (*DLOAD): BRNU
ABAQUS/CAE Load/Interaction: Body force
Units: FL–3
Description: 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.
Load ID (*DLOAD): BZNU
ABAQUS/CAE Load/Interaction: Body force
Units: FL–3
Description: 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.
Load ID (*DLOAD): CENT(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–4 (ML–3T–2)
Description: Centrifugal load (magnitude given as 
, where 
is the mass density and 
is the angular velocity). Since only axisymmetric deformation is allowed, the spin axis must be the z-axis.
Load ID (*DLOAD): CENTRIF(S)
ABAQUS/CAE Load/Interaction: Rotational body force
Units: T–2
Description: Centrifugal load (magnitude is input as 
, where is the angular velocity). Since only axisymmetric deformation is allowed, the spin axis must be the z-axis.
Load ID (*DLOAD): GRAV
ABAQUS/CAE Load/Interaction: Gravity
Units: LT–2
Description: Gravity loading in a specified direction (magnitude input as acceleration).
Load ID (*DLOAD): HP(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–2
Description: 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.
Load ID (*DLOAD): P
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–2
Description: Pressure applied to the element reference surface. The pressure is positive in the direction of the positive element normal.
Load ID (*DLOAD): PNU
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–2
Description: 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.
Load ID (*DLOAD): SBF(E)
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–5T2
Description: Stagnation body force in radial and axial directions.
Load ID (*DLOAD): SP(E)
ABAQUS/CAE Load/Interaction: Pressure
Units: FL–4T2
Description: Stagnation pressure applied to the element reference surface.
Load ID (*DLOAD): TRSHR
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–2
Description: Shear traction on the element reference surface.
Load ID (*DLOAD): TRSHRNU(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–2
Description: Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
Load ID (*DLOAD): TRVEC
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–2
Description: General traction on the element reference surface.
Load ID (*DLOAD): TRVECNU(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–2
Description: Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
Load ID (*DLOAD): VBF(E)
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–4T
Description: Viscous body force in radial and axial directions.
Load ID (*DLOAD): VP(E)
ABAQUS/CAE Load/Interaction: Pressure
Units: FL–3T
Description: Viscous surface pressure. The viscous pressure is proportional to the velocity normal to the element face and opposing the motion.
Foundations are available for ABAQUS/Standard elements with displacement degrees of freedom. They are specified as described in “Element foundations,” Section 2.2.2.
Load ID (*FOUNDATION): F(S)
ABAQUS/CAE Load/Interaction: Elastic foundation
Units: FL–3
Description: Elastic foundation in the direction of the shell normal.
Distributed heat fluxes are available for elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 27.4.4.
Load ID (*DFLUX): BF(S)
ABAQUS/CAE Load/Interaction: Body heat flux
Units: JL–3 T–1
Description: Body heat flux per unit volume.
Load ID (*DFLUX): BFNU(S)
ABAQUS/CAE Load/Interaction: Body heat flux
Units: JL–3 T–1
Description: Nonuniform body heat flux per unit volume with magnitude supplied via user subroutine DFLUX.
Load ID (*DFLUX): SNEG(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: JL–2 T–1
Description: Surface heat flux per unit area into the bottom face of the element.
Load ID (*DFLUX): SPOS(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: JL–2 T–1
Description: Surface heat flux per unit area into the top face of the element.
Load ID (*DFLUX): SNEGNU(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: JL–2 T–1
Description: Nonuniform surface heat flux per unit area into the bottom face of the element with magnitude supplied via user subroutine DFLUX.
Load ID (*DFLUX): SPOSNU(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: JL–2 T–1
Description: Nonuniform surface heat flux per unit area into the top face of the element with magnitude supplied via user subroutine DFLUX.
Film conditions are available for elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 27.4.4.
Load ID (*FILM): FNEG(S)
ABAQUS/CAE Load/Interaction: Surface film condition
Units: JL–2 T –1
–1
Description: Film coefficient and sink temperature (units of ) provided on the bottom face of the element.
Load ID (*FILM): FPOS(S)
ABAQUS/CAE Load/Interaction: Surface film condition
Units: JL–2 T–1–1
Description: Film coefficient and sink temperature (units of ) provided on the top face of the element.
Load ID (*FILM): FNEGNU(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: JL–2 T–1–1
Description: Nonuniform film coefficient and sink temperature (units of ) provided on the bottom face of the element with magnitude supplied via user subroutine FILM.
Load ID (*FILM): FPOSNU(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: JL–2 T–1–1
Description: Nonuniform film coefficient and sink temperature (units of ) provided on the top face of the element with magnitude supplied via user subroutine FILM.
Radiation conditions are available for elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 27.4.4.
Load ID (*RADIATE): RNEG(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: Dimensionless
Description: Emissivity and sink temperature (units of ) provided for the bottom face of the shell.
Load ID (*RADIATE): RPOS(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: Dimensionless
Description: Emissivity and sink temperature (units of ) provided for the top face of the shell.
Surface-based distributed loads are available for elements with displacement degrees of freedom. They are specified as described in “Distributed loads,” Section 27.4.3.
Distributed load magnitudes are per unit area or per unit volume. They do not need to be multiplied by .
Load ID (*DSLOAD): HP(S)
ABAQUS/CAE Load/Interaction: Pressure
Units: FL–2
Description: Hydrostatic pressure on the element reference surface and linear in global Z. The pressure is positive in the direction opposite the surface normal.
Load ID (*DSLOAD): P
ABAQUS/CAE Load/Interaction: Pressure
Units: FL–2
Description: Pressure on the element reference surface. The pressure is positive in the direction opposite to the surface normal.
Load ID (*DSLOAD): PNU
ABAQUS/CAE Load/Interaction: Pressure
Units: FL–2
Description: 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.
Load ID (*DSLOAD): SP(E)
ABAQUS/CAE Load/Interaction: Pressure
Units: FL–4T2
Description: Stagnation pressure applied to the element reference surface.
Load ID (*DSLOAD): TRSHR
ABAQUS/CAE Load/Interaction: Surface traction
Units: FL–2
Description: Shear traction on the element reference surface.
Load ID (*DSLOAD): TRSHRNU(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–2
Description: Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
Load ID (*DSLOAD): TRVEC
ABAQUS/CAE Load/Interaction: Surface traction
Units: FL–2
Description: General traction on the element reference surface.
Load ID (*DSLOAD): TRVECNU(S)
ABAQUS/CAE Load/Interaction: Not supported
Units: FL–2
Description: Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
Load ID (*DSLOAD): VP(E)
ABAQUS/CAE Load/Interaction: Pressure
Units: FL–3T
Description: Viscous surface pressure. The viscous pressure is proportional to the velocity normal to the element surface and opposing the motion.
Surface-based heat fluxes are available for elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 27.4.4.
Load ID (*DSFLUX): S(S)
ABAQUS/CAE Load/Interaction: Surface heat flux
Units: JL–2 T–1
Description: Surface heat flux per unit area into the element surface.
Load ID (*DSFLUX): SNU(S)
ABAQUS/CAE Load/Interaction: Surface heat flux
Units: JL–2 T–1
Description: Nonuniform surface heat flux per unit area into the element surface with magnitude supplied via user subroutine DFLUX.
Surface-based film conditions are available for elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 27.4.4.
Load ID (*SFILM): F(S)
ABAQUS/CAE Load/Interaction: Surface film condition
Units: JL–2 T–1–1
Description: Film coefficient and sink temperature (units of ) provided on the element surface.
Load ID (*SFILM): FNU(S)
ABAQUS/CAE Load/Interaction: Surface film condition
Units: JL–2 T–1–1
Description: Nonuniform film coefficient and sink temperature (units of ) provided on the element surface with magnitude supplied via user subroutine FILM.
Surface-based radiation conditions are available for elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 27.4.4.
Load ID (*SRADIATE): R(S)
ABAQUS/CAE Load/Interaction: Surface radiation to ambient
Units: Dimensionless
Description: Emissivity and sink temperature (units of ) provided for the element surface.
Surface-based incident wave loads are available. They are specified as described in “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.9.1. If the incident wave field includes a reflection off a plane outside the boundaries of the mesh, this effect can be included.
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:
S11 | Meridional stress. |
S22 | Hoop (circumferential) stress. |
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. |
SF3 | Transverse shear force per unit width in the meridional direction (available only from ABAQUS/Standard). |
SF4 | Integrated stress in the thickness direction; always zero (available only from ABAQUS/Standard). |
SM1 | Bending moment per unit width about the hoop direction. |
SM2 | Bending moment per unit width about the meridional direction. |
Available for elements with displacement degrees of freedom.
SE1 | Membrane strain in the meridional direction. |
SE2 | Membrane strain in the hoop direction. |
SE3 | Transverse shear strain in the meridional direction (available only from ABAQUS/Standard). |
SE4 | Strain in the thickness direction (available only from ABAQUS/Standard). |
SK1 | Curvature change about the hoop direction. |
SK2 | Curvature change about the meridional direction. |
