23.1.4 Axisymmetric membrane element library

**Products: **ABAQUS/Standard ABAQUS/CAE

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 are required 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.

Input File Usage: | *MEMBRANE SECTION |

In addition, use the following option for variable thickness membranes: *NODAL THICKNESS |

ABAQUS/CAE Usage: | Property module: |

You cannot define variable thickness membranes in ABAQUS/CAE. |

Distributed loads

Distributed loads are specified as described in “Distributed loads,” Section 27.4.3.

**Load ID (*DLOAD):** BR**ABAQUS/CAE Load/Interaction:** **Body force****Units:** FL^{–3}**Description: **Body force in the radial (1 or *r*) direction.

**Load ID (*DLOAD):** BZ**ABAQUS/CAE Load/Interaction:** **Body force****Units:** FL^{–3}**Description: **Body force in the axial (2 or *z*) direction.

**Load ID (*DLOAD):** BRNU**ABAQUS/CAE Load/Interaction:** **Body force****Units:** FL^{–3}**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^{–3}**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^{–4} (ML^{–3}T^{–2})**Description: **Centrifugal load (magnitude is input as , where is the mass density per unit volume, 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^{–3}**Description: **Elastic foundation. For MGAX elements the elastic foundations are applied to degrees of freedom and only.

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 on 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 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`. The pressure is positive in the direction opposite of 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:** **Pressure****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 loads are available. They are specified as described in “Acoustic loads,” Section 27.4.5. If the incident wave field includes a reflection off a plane outside the boundaries of the mesh, this effect can be included.

The default local material directions are such that local material direction 1 lies along the line of the element and local material direction 2 is the hoop direction.

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 | Local direct stress. |

S22 | Local direct stress. |

S12 | Local shear stress. Only available for generalized axisymmetric membrane elements. |