# 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 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 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.

Load ID (*DLOAD)	Abaqus/CAE Load/Interaction	Units	Description
BR	Body force	$FL^{-3}$	Body force per unit volume in the radial direction.
BZ	Body force	$FL^{-3}$	Body force per unit volume in the axial direction.
BRNU	Body force	$FL^{-3}$	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.
BZNU	Body force	$FL^{-3}$	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.
$CENT^{(S)}$	Not supported	$FL^{-4}$ $(ML^{-3}T^{-2})$	Centrifugal load (magnitude given as $\rho\omega^{2}$ , where $\rho$ is the mass density and $\omega$ is the angular velocity). Since only

Load ID (*DLOAD)	Abaqus/CAE Load/Interaction	Units	Description
CENTRIF(S)	Rotational body force	$T^{-2}$	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.
GRAV	Gravity	$LT^{-2}$	Gravity loading in a specified direction (magnitude input as acceleration).
HP(S)	Not supported	$FL^{-2}$	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.
P	Pressure	$FL^{-2}$	Pressure applied to the element reference surface. The pressure is positive in the direction of the positive element normal.
PNU	Not supported	$FL^{-2}$	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.
SBF(E)	Not supported	$FL^{-5}T^2$	Stagnation body force in radial and axial directions.
SP(E)	Not supported	$FL^{-4}T^2$	Stagnation pressure applied to the element reference surface.
TRSHR	Surface traction	$FL^{-2}$	Shear traction on the element reference surface.
TRSHRNU(S)	Not supported	$FL^{-2}$	Nonuniform shear traction on the element reference surface with

Load ID(*DLOAD)	Abaqus/CAELoad/Interaction	Units	Description
			magnitude and direction supplied via user subroutine UTRACLOAD.
TRVEC	Surface traction	$FL^{-2}$	General traction on the element reference surface.
$TRVECNU^{(S)}$	Not supported	$FL^{-2}$	Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
$VBF^{(E)}$	Not supported	$FL^{-4}T$	Viscous body force in radial and axial directions.
$VP^{(E)}$	Not supported	$FL^{-3}T$	Viscous surface pressure. The viscous pressure is proportional to the velocity normal to the element face and opposing the motion.

# 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.

Load ID(*FOUNDATION)	Abaqus/CAELoad/Interaction	Units	Description
$F^{(S)}$	Elasticfoundation	$FL^{-3}$	Elastic foundation in the direction ofthe shell normal.

# 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.

Load ID(*DFLUX)	Abaqus/CAELoad/Interaction	Units	Description
$BF^{(S)}$	Body heat flux	$JL^{-3} \ T^{-1}$	Body heat flux per unit volume.
$BFNU^{(S)}$	Body heat flux	$JL^{-3} \ T^{-1}$	Nonuniform body heat flux per unit volume with magnitude supplied via user subroutine DFLUX.
$SNEG^{(S)}$	Surface heat flux	$JL^{-2} \ T^{-1}$	Surface heat flux per unit area into the bottom face of the element.

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

# 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.

Load ID(*FILM)	Abaqus/CAE Load/Interaction	Units	Description
$FNEG^{(S)}$	Surface film condition	$JL^{-2} T^{-1} \theta^{-1}$	Film coefficient and sink temperature (units of $\theta$ ) provided on the bottom face of the element.
$FPOS^{(S)}$	Surface film condition	$JL^{-2} T^{-1} \theta^{-1}$	Film coefficient and sink temperature (units of $\theta$ ) provided on the top face of the element.
$FNEGNU^{(S)}$	Not supported	$JL^{-2} T^{-1} \theta^{-1}$	Nonuniform film coefficient and sink temperature (units of $\theta$ ) provided on the bottom face of the element with magnitude supplied via user subroutine $\text{FILM}$ .
$FPOSNU^{(S)}$	Not supported	$JL^{-2} T^{-1} \theta^{-1}$	Nonuniform film coefficient and sink temperature (units of $\theta$ ) provided on the top face of the element with magnitude supplied via user subroutine $\text{FILM}$ .

# 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.

Load ID(*RADIATE)	Abaqus/CAELoad/Interaction	Units	Description
RNEG(S)	Surface radiation	Dimensionless	Emissivity and sink temperature (units of θ) provided for the bottom face of the shell.
RPOS(S)	Surface radiation	Dimensionless	Emissivity and sink temperature (units of θ) provided for the top face of the shell.

# 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 .

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

# 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.

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

# 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.

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

# 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.

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

# 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:

S11	Meridional stress.
S22	Hoop (circumferential) stress.

# 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.

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.

# Section strains, curvature changes, and transverse shear strains 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.

# 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 

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Simple line diagram with two labeled points (1 and 2) connected by a straight line (no additional text or symbols)

2 - node element 

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1 2 3

3 - node element