Axisymmetric Shell Element Library

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).

This page discusses:

Conventions

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 ur, degree of freedom 2 is uz, 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.

 

See Also
About Shell Elements
Choosing a Shell Element
*NODAL THICKNESS
*SHELL GENERAL SECTION
*SHELL SECTION

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)

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) at the end nodes

Additional Solution Variables

None.

Nodal Coordinates Required

r, z, and optionally for shells with displacement degrees of freedom, Nr, Nz, 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 2⁢π.

Body forces and centrifugal loads must be given as force per unit area if a general shell section is used.

*dload
  1. Load ID (*DLOAD): BR
  2. FL−3

  3. Body force per unit volume in the radial direction.

  1. Load ID (*DLOAD): BZ
  2. FL−3

  3. Body force per unit volume in the axial direction.

  1. Load ID (*DLOAD): BRNU
  2. FL−3

  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.

  1. Load ID (*DLOAD): BZNU
  2. FL−3

  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.

  1. Load ID (*DLOAD): CENT(S)
  2. FL−4 (ML−3T−2)

  3. Centrifugal load (magnitude given as ρω​2, where ρ is the mass density and ω is the angular velocity). Since only axisymmetric deformation is allowed, the spin axis must be the z-axis.

  1. Load ID (*DLOAD): CENTRIF(S)
  2. T−2

  3. Centrifugal load (magnitude is input as ω2, where ω is the angular velocity). Since only axisymmetric deformation is allowed, the spin axis must be the z-axis.

  1. Load ID (*DLOAD): GRAV
  2. LT−2

  3. Gravity loading in a specified direction (magnitude input as acceleration).

  1. Load ID (*DLOAD): HP(S)
  2. FL−2

  3. 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.

  1. Load ID (*DLOAD): P
  2. FL−2

  3. Pressure applied to the element reference surface. The pressure is positive in the direction of the positive element normal.

  1. Load ID (*DLOAD): PNU
  2. FL−2

  3. 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.

  1. Load ID (*DLOAD): SBF(E)
  2. FL−5T2

  3. Stagnation body force in radial and axial directions.

  1. Load ID (*DLOAD): SP(E)
  2. FL−4T2

  3. Stagnation pressure applied to the element reference surface.

  1. Load ID (*DLOAD): TRSHR
  2. FL−2

  3. Shear traction on the element reference surface.

  1. Load ID (*DLOAD): TRSHRNU(S)
  2. FL−2

  3. Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DLOAD): TRVEC
  2. FL−2

  3. General traction on the element reference surface.

  1. Load ID (*DLOAD): TRVECNU(S)
  2. FL−2

  3. Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DLOAD): VBF(E)
  2. FL−4T

  3. Viscous body force in radial and axial directions.

  1. Load ID (*DLOAD): VP(E)
  2. FL−3T

  3. 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
  1. Load ID (*FOUNDATION): F(S)
  2. FL−3

  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
  1. Load ID (*DFLUX): BF(S)
  2. JL−3 T−1

  3. Body heat flux per unit volume.

  1. Load ID (*DFLUX): BFNU(S)
  2. JL−3 T−1

  3. Nonuniform body heat flux per unit volume with magnitude supplied via user subroutine DFLUX.

  1. Load ID (*DFLUX): SNEG(S)
  2. JL−2 T−1

  3. Surface heat flux per unit area into the bottom face of the element.

  1. Load ID (*DFLUX): SPOS(S)
  2. JL−2 T−1

  3. Surface heat flux per unit area into the top face of the element.

  1. Load ID (*DFLUX): SNEGNU(S)
  2. JL−2 T−1

  3. Nonuniform surface heat flux per unit area into the bottom face of the element with magnitude supplied via user subroutine DFLUX.

  1. Load ID (*DFLUX): SPOSNU(S)
  2. JL−2 T−1

  3. 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
  1. Load ID (*FILM): FNEG(S)
  2. JL−2 T −1θ−1

  3. Film coefficient and sink temperature (units of θ) provided on the bottom face of the element.

  1. Load ID (*FILM): FPOS(S)
  2. JL−2 T−1θ−1

  3. Film coefficient and sink temperature (units of θ) provided on the top face of the element.

  1. Load ID (*FILM): FNEGNU(S)
  2. JL−2 T−1θ−1

  3. Nonuniform film coefficient and sink temperature (units of θ) provided on the bottom face of the element with magnitude supplied via user subroutine FILM.

  1. Load ID (*FILM): FPOSNU(S)
  2. JL−2 T−1θ−1

  3. Nonuniform film coefficient and sink temperature (units of θ) 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
  1. Load ID (*RADIATE): RNEG(S)
  2. Dimensionless

  3. Emissivity and sink temperature (units of θ) provided for the bottom face of the shell.

  1. Load ID (*RADIATE): RPOS(S)
  2. Dimensionless

  3. 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.

Distributed load magnitudes are per unit area or per unit volume. They do not need to be multiplied by 2⁢π.

*dsload
  1. Load ID (*DSLOAD): HP(S)
  2. FL−2

  3. Hydrostatic pressure on the element reference surface and linear in global Z. The pressure is positive in the direction opposite the surface normal.

  1. Load ID (*DSLOAD): P
  2. FL−2

  3. Pressure on the element reference surface. The pressure is positive in the direction opposite to the surface normal.

  1. Load ID (*DSLOAD): PNU
  2. FL−2

  3. 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.

  1. Load ID (*DSLOAD): SP(E)
  2. FL−4T2

  3. Stagnation pressure applied to the element reference surface.

  1. Load ID (*DSLOAD): TRSHR
  2. FL−2

  3. Shear traction on the element reference surface.

  1. Load ID (*DSLOAD): TRSHRNU(S)
  2. FL−2

  3. Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DSLOAD): TRVEC
  2. FL−2

  3. General traction on the element reference surface.

  1. Load ID (*DSLOAD): TRVECNU(S)
  2. FL−2

  3. Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DSLOAD): VP(E)
  2. FL−3T

  3. 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
  1. Load ID (*DSFLUX): S(S)
  2. JL−2 T−1

  3. Surface heat flux per unit area into the element surface.

  1. Load ID (*DSFLUX): SNU(S)
  2. JL−2 T−1

  3. 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
  1. Load ID (*SFILM): F(S)
  2. JL−2 T−1θ−1

  3. Film coefficient and sink temperature (units of θ) provided on the element surface.

  1. Load ID (*SFILM): FNU(S)
  2. JL−2 T−1θ−1

  3. Nonuniform film coefficient and sink temperature (units of θ) 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
  1. Load ID (*SRADIATE): R(S)
  2. Dimensionless

  3. Emissivity and sink temperature (units of θ) 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.

HFL1

Heat flux in the meridional direction.

HFL2

Heat flux in the thickness direction.

Node Ordering on Elements



 

Numbering of Integration Points for Output