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).
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.
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) 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
Element-Based Loading
Distributed Loads
Distributed loads are available for elements with displacement degrees of freedom. They are specified as described in Distributed Loads.
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.
*dload
Load ID (*DLOAD): BR
Body force
FL−3
Body force per unit volume in the radial direction.
Load ID (*DLOAD): BZ
Body force
FL−3
Body force per unit volume in the axial direction.
Load ID (*DLOAD): 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.
Load ID (*DLOAD): 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.
Load ID (*DLOAD): CENT(S)
Not supported
FL−4 (ML−3T−2)
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)
Rotational body force
T−2
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
Gravity
LT−2
Gravity loading in a specified direction (magnitude input as acceleration).
Load ID (*DLOAD): 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.
Load ID (*DLOAD): P
Pressure
FL−2
Pressure applied to the element reference surface. The pressure is positive in the direction of the positive element normal.
Load ID (*DLOAD): 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.
Load ID (*DLOAD): SBF(E)
Not supported
FL−5T2
Stagnation body force in radial and axial directions.
Load ID (*DLOAD): SP(E)
Not supported
FL−4T2
Stagnation pressure applied to the element reference surface.
Load ID (*DLOAD): TRSHR
Surface traction
FL−2
Shear traction on the element reference surface.
Load ID (*DLOAD): TRSHRNU(S)
Not supported
FL−2
Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
Load ID (*DLOAD): TRVEC
Surface traction
FL−2
General traction on the element reference surface.
Load ID (*DLOAD): TRVECNU(S)
Not supported
FL−2
Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
Load ID (*DLOAD): VBF(E)
Not supported
FL−4T
Viscous body force in radial and axial directions.
Load ID (*DLOAD): VP(E)
Not supported
FL−3T
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.
*foundation
Load ID (*FOUNDATION): F(S)
Elastic foundation
FL−3
Elastic foundation in the direction of the 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.
*dflux
Load ID (*DFLUX): BF(S)
Body heat flux
JL−3 T−1
Body heat flux per unit volume.
Load ID (*DFLUX): BFNU(S)
Body heat flux
JL−3 T−1
Nonuniform body heat flux per unit volume with magnitude supplied via user subroutine DFLUX.
Load ID (*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): SPOS(S)
Surface heat flux
JL−2 T−1
Surface heat flux per unit area into the top face of the element.
Load ID (*DFLUX): 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.
Load ID (*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.
*film
Load ID (*FILM): FNEG(S)
Surface film condition
JL−2 T −1−1
Film coefficient and sink temperature (units of ) provided on the bottom face of the element.
Load ID (*FILM): FPOS(S)
Surface film condition
JL−2 T−1−1
Film coefficient and sink temperature (units of ) provided on the top face of the element.
Load ID (*FILM): FNEGNU(S)
Not supported
JL−2 T−1−1
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)
Not supported
JL−2 T−1−1
Nonuniform film coefficient and sink temperature (units of ) provided on the top face of the element with magnitude supplied via user subroutine FILM.
Radiation Types
Radiation conditions are available for elements with temperature degrees of freedom. They are specified as described in Thermal Loads.
*radiate
Load ID (*RADIATE): RNEG(S)
Surface radiation
Dimensionless
Emissivity and sink temperature (units of ) provided for the bottom face of the shell.
Load ID (*RADIATE): RPOS(S)
Surface radiation
Dimensionless
Emissivity and sink temperature (units of ) 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.
Distributed load magnitudes are per unit area or per unit volume. They do not need to be multiplied by .
*dsload
Load ID (*DSLOAD): 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.
Load ID (*DSLOAD): P
Pressure
FL−2
Pressure on the element reference surface. The pressure is positive in the direction opposite to the surface normal.
Load ID (*DSLOAD): 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): SP(E)
Pressure
FL−4T2
Stagnation pressure applied to the element reference surface.
Load ID (*DSLOAD): TRSHR
Surface traction
FL−2
Shear traction on the element reference surface.
Load ID (*DSLOAD): TRSHRNU(S)
Surface traction
FL−2
Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
Load ID (*DSLOAD): TRVEC
Surface traction
FL−2
General traction on the element reference surface.
Load ID (*DSLOAD): TRVECNU(S)
Surface traction
FL−2
Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
Load ID (*DSLOAD): VP(E)
Pressure
FL−3T
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.
*dsflux
Load ID (*DSFLUX): S(S)
Surface heat flux
JL−2 T−1
Surface heat flux per unit area into the element surface.
Load ID (*DSFLUX): 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.
*sfilm
Load ID (*SFILM): F(S)
Surface film condition
JL−2 T−1−1
Film coefficient and sink temperature (units of ) provided on the element surface.
Load ID (*SFILM): FNU(S)
Surface film condition
JL−2 T−1−1
Nonuniform film coefficient and sink temperature (units of ) provided on the element surface with magnitude supplied via user subroutine FILM.
Radiation Types
Surface-based radiation conditions are available for elements with temperature degrees of freedom. They are specified as described in Thermal Loads.
*sradiate
Load ID (*SRADIATE): R(S)
Surface radiation
Dimensionless
Emissivity and sink temperature (units of ) 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. 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.