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# 29.1.2 GENERAL MEMBRANE ELEMENT LIBRARY

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE

# References

• “Membrane elements,” Section 29.1.1   
• \*NODAL THICKNESS   
• \*MEMBRANE SECTION

# Overview

This section provides a reference to the general membrane elements available in Abaqus/Standard and Abaqus/Explicit.

Element types 

<table><tr><td>M3D3</td><td>3-node triangle</td></tr><tr><td>M3D4</td><td>4-node quadrilateral</td></tr><tr><td>M3D4R</td><td>4-node quadrilateral, reduced integration, hourglass control</td></tr><tr><td> $M3D6^{(S)}$ </td><td>6-node triangle</td></tr><tr><td> $M3D8^{(S)}$ </td><td>8-node quadrilateral</td></tr><tr><td> $M3D8R^{(S)}$ </td><td>8-node quadrilateral, reduced integration</td></tr><tr><td> $M3D9^{(S)}$ </td><td>9-node quadrilateral</td></tr><tr><td> $M3D9R^{(S)}$ </td><td>9-node quadrilateral, reduced integration, hourglass control</td></tr><tr><td colspan="2">Active degrees of freedom</td></tr><tr><td colspan="2">1, 2, 3</td></tr><tr><td colspan="2">Additional solution variables</td></tr><tr><td colspan="2">None.</td></tr><tr><td colspan="2">Nodal coordinates required</td></tr><tr><td colspan="2">X, Y, Z</td></tr><tr><td colspan="2">Element property definition</td></tr></table>

Input File Usage: \*MEMBRANE SECTION

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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 34.4.3.

<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>BX</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in the global X-direction.</td></tr><tr><td>BY</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in the global Y-direction.</td></tr><tr><td>BZ</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in the global Z-direction.</td></tr><tr><td>BXNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in the global X-direction with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>BYNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in the global Y-direction with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>BZNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in the global Z-direction with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>CENT(S)</td><td>Not supported</td><td> $FL^{-4}$  $(ML^{-3}T^{-2})$ </td><td>Centrifugal load (magnitude is input as  $\rho\omega^{2}$ , where  $\rho$  is the mass density per unit volume,  $\omega$  is the angular velocity).</td></tr><tr><td>CENTRIF(S)</td><td>Rotational body force</td><td> $T^{-2}$ </td><td>Centrifugal load (magnitude is input as  $\omega^{2}$ , where  $\omega$  is the angular velocity).</td></tr></table>

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<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $CORIO^{(S)}$ </td><td>Coriolis force</td><td> $FL^{-4}T (ML^{-3}T^{-1})$ </td><td>Coriolis force (magnitude is input as  $\rho\omega$ , where  $\rho$  is the mass density per unit volume,  $\omega$  is the angular velocity). The load stiffness due to Coriolis loading is not accounted for in direct steady-state dynamic analysis.</td></tr><tr><td>GRAV</td><td>Gravity</td><td> $LT^{-2}$ </td><td>Gravity loading in a specified direction (magnitude is input as acceleration).</td></tr><tr><td> $HP^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>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.</td></tr><tr><td>P</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Pressure applied to the element reference surface. The pressure is positive in the direction of the positive element normal.</td></tr><tr><td>PNU</td><td>Not supported</td><td> $FL^{-2}$ </td><td>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.</td></tr><tr><td> $ROTA^{(S)}$ </td><td>Rotational body force</td><td> $T^{-2}$ </td><td>Rotary acceleration load (magnitude is input as  $\alpha$ , where  $\alpha$  is the rotary acceleration).</td></tr><tr><td> $ROTDYNF^{(S)}$ </td><td>Not supported</td><td> $T^{-1}$ </td><td>Rotordynamic load (magnitude is input as  $\omega$ , where  $\omega$  is the angular velocity).</td></tr><tr><td> $SBF^{(E)}$ </td><td>Not supported</td><td> $FL^{-5}T^{2}$ </td><td>Stagnation body force in global X-, Y-, and Z-directions.</td></tr></table>

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<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $SP^{(E)}$ </td><td>Not supported</td><td> $FL^{-4}T^{2}$ </td><td>Stagnation pressure applied to the element reference surface.</td></tr><tr><td>TRSHR</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Shear traction on the element reference surface.</td></tr><tr><td> $TRSHRNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td>TRVEC</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>General traction on the element reference surface.</td></tr><tr><td> $TRVECNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td> $VBF^{(E)}$ </td><td>Not supported</td><td> $FL^{-4}T$ </td><td>Viscous body force in global X-, Y-, and Z-directions.</td></tr><tr><td> $VP^{(E)}$ </td><td>Not supported</td><td> $FL^{-3}T$ </td><td>Viscous surface pressure applied to the element reference surface. The pressure is proportional to the velocity normal to the element face and opposing the motion.</td></tr></table>

# Foundations

Foundations are available only in Abaqus/Standard and are specified as described in “Element foundations,” Section 2.2.2.

<table><tr><td>Load ID(*FOUNDATION)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $F^{(S)}$ </td><td>Elasticfoundation</td><td> $FL^{-3}$ </td><td>Elastic foundation.</td></tr></table>

# Surface-based loading

# Distributed loads

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

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<table><tr><td>Load ID(*DSLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>HP(S)</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Hydrostatic pressure on the element reference surface and linear in global Z. The pressure is positive in the direction opposite to the surface normal.</td></tr><tr><td>P</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Pressure on the element reference surface. The pressure is positive in the direction opposite to the surface normal.</td></tr><tr><td>PNU</td><td>Pressure</td><td> $FL^{-2}$ </td><td>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.</td></tr><tr><td>SP(E)</td><td>Pressure</td><td> $FL^{-4}T^{2}$ </td><td>Stagnation pressure applied to the element reference surface.</td></tr><tr><td>TRSHR</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Shear traction on the element reference surface.</td></tr><tr><td>TRSHRNU(S)</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td>TRVEC</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>General traction on the element reference surface.</td></tr><tr><td>TRVECNU(S)</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td>VP(E)</td><td>Pressure</td><td> $FL^{-3}T$ </td><td>Viscous surface pressure applied to the element reference surface. The pressure is proportional to the velocity normal to the element surface and opposing the motion.</td></tr></table>

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# 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

If a local orientation (“Orientations,” Section 2.2.5) is not used with the element, the stress/strain components are 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:

<table><tr><td>S11</td><td>Local 11 direct stress.</td></tr><tr><td>S22</td><td>Local 22 direct stress.</td></tr><tr><td>S12</td><td>Local 12 shear stress.</td></tr></table>

# Section thickness

STH Current thickness.

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![](images/page-257_ad33898c4fadfd56f0b8a1023aacdd4377f8a69be7408ac5c952ba03f3904907.jpg)

<details>
<summary>text_image</summary>

1
2
3
</details>

3 - node element

![](images/page-257_97ab4f946cfa57099d3b8c369c032abdfffbe986e1a5163dbbd9be74c1c395c1.jpg)

<details>
<summary>text_image</summary>

1
2
3
4
</details>

4 - node element

![](images/page-257_08e4a1a1e6f1c6a7c961f859b8da233b9d13cc46974b515ca9f3d85725efc54f.jpg)

<details>
<summary>flowchart</summary>

```mermaid
graph TD
    1 --> 2
    1 --> 4
    2 --> 3
    3 --> 4
    3 --> 5
    4 --> 5
```
</details>

6 - node element

![](images/page-257_1bc11f28aefedb255365e561ae59ad1c2660a825af77f094cb930786e215eafe.jpg)

<details>
<summary>flowchart</summary>

```mermaid
graph TD
    1 --> 2
    1 --> 5
    1 --> 8
    2 --> 3
    2 --> 6
    3 --> 7
    3 --> 6
    4 --> 7
    4 --> 8
    5 --> 8
    6 --> 7
    7 --> 8
```
</details>

8 - node element

![](images/page-257_142a0ed70ecc4d3a72c0355790195278dc6441b6d154b6fe0c2227300f0c1a60.jpg)

<details>
<summary>flowchart</summary>

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

9 - node element

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# Numbering of integration points for output

![](images/page-258_981aa086dc6411d089a9bc695efefbd15af00a9ac2c8b37ba4cc9101da9d44cf.jpg)

<details>
<summary>text_image</summary>

3
× 1
1
2
</details>

3 - node element

![](images/page-258_09658b57e8b3b53dfbf4d46a7e9a555abac9fb34fb4e2b3801aed0dc93c8a48f.jpg)

<details>
<summary>flowchart</summary>

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

6 - node element

![](images/page-258_d0e0a4b6e3859472aa78ea7466271b6d51bf976bd66b1bfcad4fa3962ec9458c.jpg)

<details>
<summary>text_image</summary>

4 ×3 3
×1 2×
1 2
</details>

4 - node element

![](images/page-258_a7483de4d1ba24214d033a6b80497a44878876a70f9e519121f1e9953fc991d1.jpg)

<details>
<summary>text_image</summary>

4
×1
1
3
2
</details>

4 - node reduced integration element

![](images/page-258_67aa286609b9c72b142e2055b45b49ba28875c3bd2db918524716beee7539cb0.jpg)

<details>
<summary>text_image</summary>

4
×7 ×8 ×9
8 ×4 ×5 ×6
×1 ×2 ×3
1 5 2
3
6
</details>

8 - node element

![](images/page-258_b6fb581d652573c3cec8c12921c231426d5eaf780772ac11f697bf819cc98c40.jpg)

<details>
<summary>text_image</summary>

4
×3
7
4×
3
8
×1
1
5
2×
6
2
</details>

8 - node reduced integration element

![](images/page-258_dce2e5e9332412c92a37b939a5a565c66c3cd4d981d31dba53ba7cee63d2d399.jpg)

<details>
<summary>text_image</summary>

4
×7
7
×8
×9
3
8
×4
9
×6
6
×1
×2
×3
1
5
2
</details>

9 - node element

![](images/page-258_be3219b45e31ae4d78bdf107a5f018a07a153b8c0ad10921e4b04c56e6a2b21a.jpg)

<details>
<summary>text_image</summary>

4
×3
7
3
4×
8
9
6
×1
2×
1
5
2
</details>

9 - node reduced integration element

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# 29.1.3 CYLINDRICAL MEMBRANE ELEMENT LIBRARY

Product: Abaqus/Standard

References

• “Membrane elements,” Section 29.1.1   
• \*MEMBRANE SECTION

Overview

This section provides a reference to the cylindrical membrane elements available in Abaqus/Standard.

Element types 

<table><tr><td>MCL6</td><td>6-node cylindrical membrane</td></tr><tr><td>MCL9</td><td>9-node cylindrical membrane</td></tr></table>

Active degrees of freedom

1, 2, 3

Additional solution variables

None.

Nodal coordinates required

X, Y, Z

Element property definition

Input File Usage: \*MEMBRANE SECTION

Element-based loading

Distributed loads

Distributed loads are specified as described in “Distributed loads,” Section 34.4.3.

<table><tr><td>Load ID(*DLOAD)</td><td>Units</td><td>Description</td></tr><tr><td>BX</td><td> $FL^{-3}$ </td><td>Body force in the global X-direction.</td></tr><tr><td>BY</td><td> $FL^{-3}$ </td><td>Body force in the global Y-direction.</td></tr><tr><td>BZ</td><td> $FL^{-3}$ </td><td>Body force in the global Z-direction.</td></tr></table>

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<table><tr><td>Load ID (*DLOAD)</td><td>Units</td><td>Description</td></tr><tr><td>BXNU</td><td> $FL^{-3}$ </td><td>Nonuniform body force in the global X-direction with magnitude supplied via user subroutine DLOAD.</td></tr><tr><td>BYNU</td><td> $FL^{-3}$ </td><td>Nonuniform body force in the global Y-direction with magnitude supplied via user subroutine DLOAD.</td></tr><tr><td>BZNU</td><td> $FL^{-3}$ </td><td>Nonuniform body force in the global Z-direction with magnitude supplied via user subroutine DLOAD.</td></tr><tr><td>CENT</td><td> $FL^{-4}(ML^{-3} T^{-2})$ </td><td>Centrifugal load (magnitude is input as  $\rho\omega^{2}$ , where  $\rho$  is the mass density per unit volume,  $\omega$  is the angular velocity).</td></tr><tr><td>CENTRIF</td><td> $T^{-2}$ </td><td>Centrifugal load (magnitude is input as  $\omega^{2}$ , where  $\omega$  is the angular velocity).</td></tr><tr><td>CORIO</td><td> $FL^{-4}T (ML^{-3} T^{-1})$ </td><td>Coriolis force (magnitude is input as  $\rho\omega$ , where  $\rho$  is the mass density per unit volume,  $\omega$  is the angular velocity).</td></tr><tr><td>GRAV</td><td> $LT^{-2}$ </td><td>Gravity loading in a specified direction (magnitude is input as acceleration).</td></tr><tr><td>HP</td><td> $FL^{-2}$ </td><td>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.</td></tr><tr><td>P</td><td> $FL^{-2}$ </td><td>Pressure applied to the element reference surface. The pressure is positive in the direction of the positive element normal.</td></tr><tr><td>PNU</td><td> $FL^{-2}$ </td><td>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.</td></tr><tr><td>ROTA</td><td> $T^{-2}$ </td><td>Rotary acceleration load (magnitude is input as  $\alpha$ , where  $\alpha$  is the rotary acceleration.</td></tr><tr><td> $ROTDYNF^{(S)}$ </td><td> $T^{-1}$ </td><td>Rotordynamic load (magnitude is input as  $\omega$ , where  $\omega$  is the angular velocity).</td></tr></table>
