26.7.4 Axisymmetric surface element library

Products: ABAQUS/Standard  ABAQUS/CAE  

References

Conventions

Coordinate 1 is r, coordinate 2 is z. At , the r-direction corresponds to the global X-direction and the z-direction corresponds to the global Y-direction. This is important when data must be given in global directions. Coordinate 1 should be greater than or equal to zero.

Degree of freedom 1 is , degree of freedom 2 is . Generalized axisymmetric elements with twist have an additional degree of freedom, 5, corresponding to the twist angle (in radians).

ABAQUS/Standard does not automatically apply any boundary conditions to nodes located along the symmetry axis. You must apply radial or symmetry boundary conditions on these nodes if desired.

Point loads and moments should be given as the value integrated around the circumference; that is, the total value on the ring.

Element types

Regular axisymmetric surface elements

SFMAX12-node linear, without twist
SFMAX23-node quadratic, without twist

Active degrees of freedom

1, 2

Additional solution variables

None.

Generalized axisymmetric surface elements

SFMGAX12-node linear, with twist
SFMGAX23-node quadratic, with twist

Active degrees of freedom

1, 2, 5

Additional solution variables

None.

Nodal coordinates required

R, Z

Element property definition

Input File Usage:           Use the following option to define surface elements:
*SURFACE SECTION

If rebar are being defined, use the following option in conjunction with the *SURFACE SECTION option:

*REBAR LAYER

Use the following option to define a mass density per unit area:

*SURFACE SECTION, DENSITY=number

ABAQUS/CAE Usage: 

Property module: Create Section: select Shell as the section Category and Surface as the section Type, Rebar Layers (optional)


You cannot define the mass per unit area for a surface section in ABAQUS/CAE.

Element-based loading

Distributed loads

Distributed loads are specified as described in Distributed loads, Section 27.4.3. Gravity and centrifugal loads apply only if the surface elements have rebar defined or if the elements have a defined density.


Load ID (*DLOAD):  BR

ABAQUS/CAE Load/Interaction:  Body force

Units:  FL–2

Description:  Body force in the radial (1 or r) direction.


Load ID (*DLOAD):  BZ

ABAQUS/CAE Load/Interaction:  Body force

Units:  FL–2

Description:  Body force in the axial (2 or z) direction.


Load ID (*DLOAD):  BRNU

ABAQUS/CAE Load/Interaction:  Body force

Units:  FL–2

Description:  Nonuniform body force in the radial direction with magnitude supplied via user subroutine DLOAD.


Load ID (*DLOAD):  BZNU

ABAQUS/CAE Load/Interaction:  Body force

Units:  FL–2

Description:  Nonuniform body force in the axial direction with magnitude supplied via user subroutine DLOAD.


Load ID (*DLOAD):  CENT

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL–3 (ML–2T–2)

Description:  Centrifugal load (magnitude is input as , where is the mass density per unit area, is the angular velocity). Since only axisymmetric deformation is allowed, the spin axis must be the z-axis.


Load ID (*DLOAD):  CENTRIF

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

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. The pressure is positive in the direction of the positive element normal.


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.

Foundations

Foundations are specified as described in Element foundations, Section 2.2.2.


Load ID (*FOUNDATION):  F

ABAQUS/CAE Load/Interaction:  Elastic foundation

Units:  FL–2

Description:  Elastic foundation. For SFMGAX1 and SFMGAX2 elements the elastic foundations are applied to degrees of freedom and only.

Surface-based loading

Distributed loads

Surface-based distributed loads are specified as described in Distributed loads, Section 27.4.3.


Load ID (*DSLOAD):  HP

ABAQUS/CAE Load/Interaction:  Pressure

Units:  FL–2

Description:  Hydrostatic pressure applied to the element reference surface and linear in global Z. The pressure is positive in the direction opposite to the surface normal.


Load ID (*DSLOAD):  P

ABAQUS/CAE Load/Interaction:  Pressure

Units:  FL–2

Description:  Pressure applied to 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 applied to the element reference surface with magnitude supplied via user subroutine DLOAD. The pressure is positive in the direction opposite to the surface normal.


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.

Incident wave loading

Surface-based incident wave loading is also available for these elements. See Acoustic loads, Section 27.4.5.

Element output

Output is currently available only when the surface element is used to carry rebar layers. See Defining reinforcement, Section 2.2.3, for details.

Node ordering on elements

Numbering of integration points for output