Load ID(*DLOAD)	Units	Description
TRSHR	$FL^{-2}$	Shear traction on the element reference surface.
$TRSHRNU^{(S)}$	$FL^{-2}$	Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
TRVEC	$FL^{-2}$	General traction on the element reference surface.
$TRVECNU^{(S)}$	$FL^{-2}$	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)	Units	Description
F	$FL^{-3}$	Elastic foundation.

# Surface-based loading # Distributed loads Surface-based distributed loads are specified as described in “Distributed loads,” Section 34.4.3.

Load ID(*DSLOAD)	Units	Description
HP	$FL^{-2}$	Hydrostatic pressure on the element reference surface and linear in global Z. The pressure is positive in the direction opposite to the surface normal.
P	$FL^{-2}$	Pressure on the element reference surface. The pressure is positive in the direction opposite to the surface normal.
PNU	$FL^{-2}$	Nonuniform pressure on the element reference surface with magnitude supplied

Load ID(*DSLOAD)	Units	Description
		via user subroutine DLOAD. The pressure is positive in the direction opposite to the surface normal.
TRSHR	$FL^{-2}$	Shear traction on the element reference surface.
$TRSHRNU^{(S)}$	$FL^{-2}$	Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
TRVEC	$FL^{-2}$	General traction on the element reference surface.
$TRVECNU^{(S)}$	$FL^{-2}$	Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

# Element output If a local orientation (“Orientations,” Section 2.2.5) is not used with the element, the stress/strain components are expressed in the default directions on the surface defined by the convention given in “Conventions,” Section 1.2.2. If a local orientation is used with the element, the stress/strain components are in the surface directions defined by the orientation. In large-displacement problems the local directions defined in the reference configuration are rotated into the current configuration by the average material rotation. See “State storage,” Section 1.5.4 of the Abaqus Theory Guide, for details. # 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 11 direct stress.
S22	Local 22 direct stress.
S12	Local 12 shear stress.

# Section thickness STH Current thickness. # Node ordering and face numbering on elements 

flowchart

```mermaid graph TD 1 --> 2 2 --> 3 3 --> 4 4 --> 6 6 --> 1 ```

6-node element 

flowchart

```mermaid graph TD 1 --> 2 2 --> 3 3 --> 4 4 --> 7 5 --> 6 6 --> 7 7 --> 8 8 --> 9 9 --> 2 ```

9-node element # Numbering of integration points for output 

flowchart

```mermaid graph TD 3 --> 5 5 --> 2 2 --> 1 1 --> 6 6 --> 4 4 --> 3 3 --> 2 2 --> 1 1 --> 2 2 --> 3 3 --> 4 4 --> 6 6 --> 1 3 -->|× 3| 2 2 -->|× 2| 3 1 -->|× 1| 4 ```

6-node element 

text_image

3 7 ×6 ×5 4 6 ×4 9 ×2 ×3 8 1 2 5

9-node element # 29.1.4 AXISYMMETRIC MEMBRANE ELEMENT LIBRARY Products: Abaqus/Standard Abaqus/CAE # References • “Membrane elements,” Section 29.1.1 • \*MEMBRANE SECTION • \*NODAL THICKNESS # Overview This section provides a reference to the axisymmetric membrane elements available in Abaqus/Standard. # Conventions Coordinate 1 is $\boldsymbol { r } ,$ 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 $u _ { r }$ , degree of freedom 2 is $u _ { z }$ . Generalized axisymmetric elements with twist have an additional degree of freedom, 5, corresponding to the twist angle $\phi$ (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 Nodal coordinates required R, Z Element property definition

Input File Usage:	*MEMBRANE SECTIONIn addition, use the following option for variable thickness membranes:*NODAL THICKNESS
Abaqus/CAE Usage:	Property module:Create Section:select Shell as the sectionCategory and Membrane as the section TypeYou cannot define variable thickness membranes in Abaqus/CAE.

Element-based loading Distributed loads Distributed loads are specified as described in “Distributed loads,” Section 34.4.3.

Load ID (*DLOAD)	Abaqus/CAE Load/Interaction	Units	Description
BR	Body force	$FL^{-3}$	Body force in the radial (1 or $r$ ) direction.
BZ	Body force	$FL^{-3}$	Body force in the axial (2 or $z$ ) direction.
BRNU	Body force	$FL^{-3}$	Nonuniform body force in the radial direction with magnitude supplied via user subroutine DLOAD.
BZNU	Body force	$FL^{-3}$	Nonuniform body force in the axial direction with magnitude supplied via user subroutine DLOAD.
CENT	Not supported	$FL^{-4}$ $(ML^{-3}T^{-2})$	Centrifugal load (magnitude is input as $\rho\omega^{2}$ , where $\rho$ is the mass density per unit volume, $\omega$ is the angular

Load ID (*DLOAD)	Abaqus/CAE Load/Interaction	Units	Description
			velocity). Since only axisymmetric deformation is allowed, the spin axis must be the z-axis.
CENTRIF	Rotational body force	$T^{-2}$	Centrifugal load (magnitude is input as $\omega^2$ , where $\omega$ is the angular velocity). Since only axisymmetric deformation is allowed, the spin axis must be the z-axis.
GRAV	Gravity	$LT^{-2}$	Gravity loading in a specified direction (magnitude input as acceleration).
HP	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.
P	Pressure	$FL^{-2}$	Pressure applied to the element reference surface. The pressure is positive in the direction of the positive element normal.
PNU	Not supported	$FL^{-2}$	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.
TRSHR	Surface traction	$FL^{-2}$	Shear traction on the element reference surface.
$TRSHRNU^{(S)}$	Not supported	$FL^{-2}$	Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
TRVEC	Surface traction	$FL^{-2}$	General traction on the element reference surface.
$TRVECNU^{(S)}$	Not supported	$FL^{-2}$	Nonuniform general traction on the element reference surface with

Load ID (\*DLOAD) Abaqus/CAE Load/Interaction Units Description magnitude and direction supplied via user subroutine UTRACLOAD. # Foundations Foundations are specified as described in “Element foundations,” Section 2.2.2. Load ID(\*FOUNDATION) Abaqus/CAE Load/Interaction Units Description F Elastic foundation FL−3 Elastic foundation. For MGAX elements the elastic foundations are applied to degrees of freedom $u _ { r }$ and $u _ { z }$ only. # Surface-based loading # Distributed loads Surface-based distributed loads are specified as described in “Distributed loads,” Section 34.4.3.

Load ID(*DSLOAD)	Abaqus/CAELoad/Interaction	Units	Description
HP	Pressure	$FL^{-2}$	Hydrostatic pressure on the element reference surface and linear in global Z. The pressure is positive in the direction opposite to the surface normal.
P	Pressure	$FL^{-2}$	Pressure on the element reference surface. The pressure is positive in the direction opposite to the surface normal.
PNU	Pressure	$FL^{-2}$	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.
TRSHR	Surface traction	$FL^{-2}$	Shear traction on the element reference surface.

Load ID(*DSLOAD)	Abaqus/CAELoad/Interaction	Units	Description
$TRSHRNU^{(S)}$	Surface traction	$FL^{-2}$	Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
TRVEC	Surface traction	$FL^{-2}$	General traction on the element reference surface.
$TRVECNU^{(S)}$	Surface traction	$FL^{-2}$	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 and shock loads,” Section 34.4.6. 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 11 direct stress.
S22	Local 22 direct stress.
S12	Local 12 shear stress. Only available for generalized axisymmetric membrane elements.

# Section thickness STH Current thickness. # Node ordering on elements 

natural_image

Simple diagonal line with two labeled points (1 and 2) at endpoints (no additional text or symbols)

2 - node element 

flowchart

```mermaid graph TD 1 --> 2 2 --> 3 ```

3 - node element # Numbering of integration points for output 

text_image

1 + 1 2

2 - node element 

flowchart

```mermaid graph TD 1["1"] -->|×| 1 1 -->|×| 2["2"] 2 -->|×| 2 2 -->|×| 3["3"] ```

3 - node element