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![](images/page-991_b2d402356245d2d6d069c4dad191279e0615724e2a502bab2b4cfd6c672cbfda.jpg)

<details>
<summary>text_image</summary>

3
×1
1
2
</details>

3 - node element

![](images/page-991_1c836da5c7c30aeea51bdff689ee6bb1e5ab6c38df802a7a138582b24d4c7b4c.jpg)

<details>
<summary>flowchart</summary>

```mermaid
graph TD
    1 -->|x1| 4
    1 -->|x1| 6
    2 -->|x| 3
    2 -->|x| 5
    3 -->|x| 6
    4 -->|x| 5
    5 -->|x| 3
```
</details>

6 - node element

![](images/page-991_3dc2f4f7241e881402726a7e40ab0621906d245262a6ef24914a95126bae1558.jpg)

<details>
<summary>text_image</summary>

4
×3
4×
×1
2×
1
2
3
</details>

4 - node element

![](images/page-991_097370ac61afe77f2cdf1bc09e25c8465b21f095d23bcb4b9689c11f12dc1a10.jpg)

<details>
<summary>text_image</summary>

4
×1
1
2
3
</details>

4 - node reduced integration element

![](images/page-991_dfc14373a5ab18651267ab9e1347033ef4d808cab8b66bf91b1e2b226d7b3544.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-991_7a5365e3ec20cdaaf2e9b69198c5ba6042f185556777d484c0385298b8767079.jpg)

<details>
<summary>text_image</summary>

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

8 - node reduced integration element

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# 32.7.3 CYLINDRICAL SURFACE ELEMENT LIBRARY

Product: Abaqus/Standard

# References

• “Surface elements,” Section 32.7.1   
• \*SURFACE SECTION   
• \*REBAR LAYER

# Overview

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

# Element types

SFMCL6 6-node cylindrical surface SFMCL9 9-node cylindrical surface

Active degrees of freedom

1, 2, 3

Additional solution variables

None.

# Nodal coordinates required

X, Y, Z

# Element property definition

Input File Usage:

Use the following option to define surface element properties:

\*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

<!-- source-page: 994 -->

# Distributed loads

Distributed loads are specified as described in “Distributed loads,” Section 34.4.3. Gravity, centrifugal, rotary acceleration, and Coriolis force loads apply only if the surface elements have rebar defined or if the elements have a defined density.

<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> $FL^{-2}$ </td><td>Body force in the global Y-direction.</td></tr><tr><td>BZ</td><td> $FL^{-2}$ </td><td>Body force in the global Z-direction.</td></tr><tr><td>BXNU</td><td> $FL^{-2}$ </td><td>Nonuniform body force in the global X-direction with magnitude supplied via user subroutine DLOAD.</td></tr><tr><td>BYNU</td><td> $FL^{-2}$ </td><td>Nonuniform body force in the global Y-direction with magnitude supplied via user subroutine DLOAD.</td></tr><tr><td>BZNU</td><td> $FL^{-2}$ </td><td>Nonuniform body force in the global Z-direction with magnitude supplied via user subroutine DLOAD.</td></tr><tr><td>CENT</td><td> $FL^{-3}(ML^{-2} T^{-2})$ </td><td>Centrifugal load (magnitude is input as  $\rho\omega^{2}$ , where  $\rho$  is the mass density per unit area,  $\omega$  is the angular speed).</td></tr><tr><td>CENTRIF</td><td> $T^{-2}$ </td><td>Centrifugal load (magnitude is input as  $\omega^{2}$ , where  $\omega$  is the angular speed).</td></tr><tr><td>CORIO</td><td> $FL^{-3}T (ML^{-2} T^{-1})$ </td><td>Coriolis force (magnitude is input as  $\rho\omega$ , where  $\rho$  is the mass density per unit area,  $\omega$  is the angular speed). The load stiffness due to Coriolis loading is not accounted for in direct steady-state dynamics analysis.</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</td></tr></table>

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<table><tr><td>Load ID (*DLOAD)</td><td>Units</td><td>Description</td></tr><tr><td></td><td></td><td>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.</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>TRSHR</td><td> $FL^{-2}$ </td><td>Shear traction on the element reference surface.</td></tr><tr><td> $TRSHRNU^{(S)}$ </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> $FL^{-2}$ </td><td>General traction on the element reference surface.</td></tr><tr><td> $TRVECNU^{(S)}$ </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></table>

# Foundations

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

<table><tr><td>Load ID(*FOUNDATION)</td><td>Units</td><td>Description</td></tr><tr><td>F</td><td> $FL^{-2}$ </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>Units</td><td>Description</td></tr><tr><td>HP</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> $FL^{-2}$ </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> $FL^{-2}$ </td><td>Nonuniform pressure on the element reference surface with magnitude supplied via user subroutine DLOAD. The pressure is positive in the direction opposite to the surface normal.</td></tr><tr><td>TRSHR</td><td> $FL^{-2}$ </td><td>Shear traction on the element reference surface.</td></tr><tr><td> $TRSHRNU^{(S)}$ </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> $FL^{-2}$ </td><td>General traction on the element reference surface.</td></tr><tr><td> $TRVECNU^{(S)}$ </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></table>

# Incident wave loading

Surface-based incident wave loading is also available for these elements. See “Acoustic and shock loads,” Section 34.4.6.

# 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.

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# Node ordering and face numbering on elements

![](images/page-997_3a7ecc46a69f20ef9f2db5fa1a5fd7da1f17f58f53ac0966cf66758e4c01056a.jpg)

<details>
<summary>flowchart</summary>

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

6-node element

![](images/page-997_be7b54a5862b382398e052274383ef3a6c9a9072c9ebad97aa35fcb0d9752553.jpg)

<details>
<summary>flowchart</summary>

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

9-node element

# Numbering of integration points for output

![](images/page-997_e778f1e3bfc2bd6ec89e289ac8767f7ae697c723c9b22444b6fce8af9e57f477.jpg)

<details>
<summary>flowchart</summary>

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

6-node element

![](images/page-997_7d992b1d088fb3885741701e8b82bacf163acaa37d18568ea360db68a874e6c0.jpg)

<details>
<summary>text_image</summary>

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

9-node element

<!-- source-page: 998 -->

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# 32.7.4 AXISYMMETRIC SURFACE ELEMENT LIBRARY

Products: Abaqus/Standard Abaqus/CAE

# References

• “Surface elements,” Section 32.7.1   
• \*SURFACE SECTION   
• \*REBAR LAYER

# Overview

This section provides a reference to the axisymmetric surface elements available in Abaqus/Standard.

# 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 $u _ { r }$ , degree of freedom 2 is $u _ { z }$ . Generalized axisymmetric elements with twist have an additional degree of freedom, 5, corresponding to the twist angle (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

<table><tr><td>SFMAX1</td><td>2-node linear, without twist</td></tr><tr><td>SFMAX2</td><td>3-node quadratic, without twist</td></tr></table>

Active degrees of freedom

1, 2

Additional solution variables

None.

# Generalized axisymmetric surface elements

<table><tr><td>SFMGAX1</td><td>2-node linear, with twist</td></tr><tr><td>SFMGAX2</td><td>3-node quadratic, with twist</td></tr></table>

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Active degrees of freedom

1, 2, 5

Additional solution variables

None.

Nodal coordinates required

R, Z

Element property definition 

<table><tr><td>Input File Usage:</td><td>Use the following option to define surface elements:*SURFACE SECTIONIf rebar are being defined, use the following option in conjunction with the *SURFACE SECTION option:*REBAR LAYERUse the following option to define a mass density per unit area:*SURFACE SECTION, DENSITY=number</td></tr><tr><td>Abaqus/CAE Usage:</td><td>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.</td></tr><tr><td colspan="2">Element-based loading</td></tr></table>

# Distributed loads

Distributed loads are specified as described in “Distributed loads,” Section 34.4.3. Gravity and centrifugal loads apply only if the surface elements have rebar defined or if the elements have a defined density.

<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>BR</td><td>Body force</td><td> $FL^{-2}$ </td><td>Body force in the radial (1 or  $r$ ) direction.</td></tr><tr><td>BZ</td><td>Body force</td><td> $FL^{-2}$ </td><td>Body force in the axial (2 or  $z$ ) direction.</td></tr><tr><td>BRNU</td><td>Body force</td><td> $FL^{-2}$ </td><td>Nonuniform body force in the radial direction with magnitude supplied via user subroutine DLOAD.</td></tr></table>
