15.1.4 Axisymmetric membrane element library

Products: ABAQUS/Standard ABAQUS/CAE

References

Conventions

Coordinate 1 is , coordinate 2 is . At , the -direction corresponds to the global -direction and the -direction corresponds to the global -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.

Element types

Regular axisymmetric membranes

MAX1 2-node linear, without twist
MAX2 3-node quadratic, without twist

Active degrees of freedom

1, 2

Additional solution variables

None.

Generalized axisymmetric membranes

MGAX1 2-node linear, with twist
MGAX2 3-node quadratic, with twist

Active degrees of freedom

1, 2, 5

Additional solution variables

None.

Nodal coordinates required

Element property definition

Input File Usage:	*MEMBRANE SECTION
	In addition, use the following option for variable thickness membranes: *NODAL THICKNESS

ABAQUS/CAE Usage:	Property module: Create Section: select Shell as the section Category and Membrane as the section Type
	You cannot define variable thickness membranes in ABAQUS/CAE.

Element-based loading

Distributed loads

Distributed loads are specified as described in “Distributed loads,” Section 19.4.3.

Load ID (*DLOAD):  BR

ABAQUS/CAE Load/Interaction:  Body force

Units:  FL^–3

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

Load ID (*DLOAD):  BZ

ABAQUS/CAE Load/Interaction:  Body force

Units:  FL^–3

Description:  Body force in the axial (2 or ) 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 (“DLOAD,” Section 25.2.5).

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 (“DLOAD,” Section 25.2.5).

Load ID (*DLOAD):  CENT

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–4 (ML^–3T^–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 -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 -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 . 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 (“DLOAD,” Section 25.2.5). 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 (“UTRACLOAD,” Section 25.2.41).

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 (“UTRACLOAD,” Section 25.2.41).

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.

Surface-based loading

Distributed loads

Surface-based distributed loads are specified as described in “Distributed loads,” Section 19.4.3.

Load ID (*DSLOAD):  HP

ABAQUS/CAE Load/Interaction:  Pressure

Units:  FL^–2

Description:  Hydrostatic pressure on the element reference surface and linear in global . 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 (“DLOAD,” Section 25.2.5). 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 (“UTRACLOAD,” Section 25.2.41).

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 (“UTRACLOAD,” Section 25.2.41).

Incident wave loading

Surface-based incident wave loads are available. They are specified as described in “Acoustic loads,” Section 19.4.5. If the incident wave field includes a reflection off a plane outside the boundaries of the mesh, this effect can be included.

Element output

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.

Section thickness

STH	Current thickness.