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![](images/page-541_b95a48139e9564284332789867c6b281a0b40c2e5656fba6ff579a98a59281f9.jpg)

<details>
<summary>text_image</summary>

n
4
3
1
2
face SPOS
face SNEG
n
1
2
3
Z
Y
X
</details>

Figure 30.3.1–2 Positive normals for R3D3 and R3D4 elements.

# Defining rigid elements

Rigid elements must always be part of a rigid body. See “Rigid body definition,” Section 2.4.1, for complete details on the definition of a rigid body.

Input File Usage: \*RIGID BODY, ELSET=name

where the ELSET parameter refers to a set of rigid elements.

Abaqus/CAE Usage: Interaction module: Create Constraint: Rigid body: Body (elements)

# Mass distribution

In Abaqus/Standard rigid elements do not contribute mass to the rigid body to which they are assigned. The mass distribution on the rigid surface can be accounted for by using point mass (“Point masses,” Section 30.1.1) and rotary inertia elements (“Rotary inertia,” Section 30.2.1) on the nodes connected to the rigid elements.

By default in Abaqus/Explicit, rigid elements do not contribute mass to the rigid body to which they are assigned. To define the mass distribution, you can specify the density of all rigid elements in a rigid body. When a nonzero density and thickness are specified, mass and rotary inertia contributions to the rigid body from rigid elements will be computed in an analogous manner to structural elements.

Input File Usage: Use the following option in Abaqus/Explicit to specify the density of rigid elements:

\*RIGID BODY, DENSITY=density

Abaqus/CAE Usage: You cannot specify the density of rigid elements in Abaqus/CAE.

# Geometry in Abaqus/Explicit

In Abaqus/Explicit you can specify the cross-sectional area or thickness for all of the rigid elements that are part of a rigid body. Abaqus/Explicit assumes a default zero cross-sectional area or thickness if you do not specify one.

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To account for a continuously varying thickness of a surface formed by rigid elements in Abaqus/Explicit, you can specify the thickness of the rigid elements at the nodes.

Specifying a nonzero thickness for rigid elements that form a rigid surface in a contact pair definition can be used to account for the effect of surface thickness in the contact constraint. It also enables the use of the double-sided surface contact feature with rigid surfaces formed by rigid elements.

Input File Usage: Use the following option in Abaqus/Explicit to specify the cross-sectional area or thickness for all rigid elements in a rigid body:

\*RIGID BODY cross-sectional area or thickness

Use both of the following options to specify a continuously varying thickness for a surface formed by rigid elements:

\*NODAL THICKNESS \*RIGID BODY, NODAL THICKNESS

Abaqus/CAE Usage: You cannot specify the cross-sectional area or thickness of rigid elements in Abaqus/CAE.

# Offset in Abaqus/Explicit

In Abaqus/Explicit you can define the distance (measured as a fraction of the rigid element’s thickness) from the rigid element’s midsurface to the reference surface containing the element’s nodes. The positive values of the offset are in the direction of the element normal. When the offset distance is 0.5, the top surface is the reference surface. When the offset distance is −0.5, the bottom surface is the reference surface. The default offset distance is 0, which indicates that the middle surface of the rigid element is the reference surface. You can specify a value for the offset distance that is greater in magnitude than half the rigid element’s thickness.

Since no element-level calculations are performed for rigid elements, a specified offset affects only the handling of contact pairs with rigid surfaces formed by rigid elements (see “Element-based surface definition,” Section 2.3.2). Mass and rotary inertia contributions to the rigid body from rigid elements defined with an offset are computed as if the offset is zero.

Input File Usage: Use the following option in Abaqus/Explicit to specify a surface offset for a rigid element:

\*RIGID BODY, OFFSET=offset

The OFFSET parameter accepts a value or a label (SPOS or SNEG). Specifying SPOS is equivalent to specifying a value of 0.5; specifying SNEG is equivalent to specifying a value of −0.5.

Abaqus/CAE Usage: You cannot specify an offset for rigid elements in Abaqus/CAE.

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# 30.3.2 RIGID ELEMENT LIBRARY

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE

# References

• “Rigid elements,” Section 30.3.1   
• \*RIGID BODY

# Overview

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

# Element types

# 2D rigid elements

R2D2 2-node, linear link (for use in plane strain or plane stress)

RAX2 2-node, linear link (for use in axisymmetric planar geometries)

RB2D2(S) 2-node, rigid beam

# Slave kinematic variables

R2D2 and RAX2: 1, 2

RB2D2: 1, 2, 6

# Master degrees of freedom

R2D2, RAX2, and RB2D2: 1, 2, 6 at the rigid body reference node

Additional solution variables

None.

# 3D rigid elements

R3D3 3-node, triangular facet

R3D4 4-node, bilinear quadrilateral

RB3D2(S) 2-node, rigid beam

# Slave kinematic variables

R3D3 and R3D4: 1, 2, 3

RB3D2: 1, 2, 3, 4, 5, 6

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# Master degrees of freedom

1, 2, 3, 4, 5, 6 at the rigid body reference node

Additional solution variables

None.

# Nodal coordinates required

R2D2 and RB2D2: X, Y

RAX2: r, z

R3D3, R3D4, and RB3D2: X, Y, Z

# Element property definition

For R2D2, RB2D2, and RB3D2 elements you can specify the cross-sectional area of the element. In Abaqus/Standard if no area is given, unit area is assumed; the area is required in Abaqus/Explicit.

For RAX2, R3D3, and R3D4 elements you can specify the thickness of the element. In Abaqus/Standard if no thickness is given, unit thickness is assumed; the thickness is required in Abaqus/Explicit.

The cross-sectional area or element thickness is used for the purpose of defining body forces, which are given in units of force per unit volume, and, in Abaqus/Explicit, determining the total mass.

Input File Usage: \*RIGID BODY

Abaqus/CAE Usage: Interaction module: Create Constraint: Rigid body: Body (elements)

# Element-based loading

# Distributed loads

Distributed loads are available for elements with displacement degrees of freedom. They are specified as described in “Distributed loads,” Section 34.4.3.

Available for R2D2 elements only:

<table><tr><td>Load ID(*DLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>BX(S)</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in global X-direction.</td></tr><tr><td>BY(S)</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in global Y-direction.</td></tr><tr><td>BXNU(S)</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in global X-direction with magnitude supplied via user subroutine DLOAD.</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> $BYNU^{(S)}$ </td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in global Y-direction with magnitude supplied via user subroutine DLOAD.</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 and  $\omega$  is the angular velocity).</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 and  $\omega$  is the angular velocity). The load stiffness due to Coriolis loading is not accounted for in direct steady-state dynamics analysis.</td></tr><tr><td> $P^{(E)}$ </td><td>Pressure</td><td> $FL^{-2}$ </td><td>Pressure on the element surface. The pressure is positive in the direction of the positive element normal.</td></tr><tr><td> $PNU^{(E)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform pressure on the element surface with magnitude supplied via user subroutine VDLOAD. The pressure is positive in the direction of the positive element normal.</td></tr></table>

Available for RAX2 elements only: 

<table><tr><td>Load ID(*DLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $BR^{(S)}$ </td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force per unit volume in the radial direction.</td></tr><tr><td> $BZ^{(S)}$ </td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force per unit volume in the axial direction.</td></tr><tr><td> $BRNU^{(S)}$ </td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force per unit volume in the radial direction, with the magnitude supplied via user subroutine DLOAD.</td></tr></table>

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<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td></td><td>Description</td></tr><tr><td> $BZNU^{(S)}$ </td><td>Body force</td><td> $FL^{-3}$ </td><td></td><td>Nonuniform body force per unit volume in the z-direction, with the magnitude supplied via user subroutine DLOAD.</td></tr><tr><td> $CENT^{(S)}$ </td><td>Not supported</td><td> $FL^{-4}$  $^3T^{-2}$ </td><td> $(ML^{-}$ </td><td>Centrifugal load (magnitude given as  $\rho\omega^2$ , where  $\rho$  is the mass density and  $\omega$  is the angular speed). Since only axisymmetric deformation is allowed, the spin axis must be the z-axis.</td></tr><tr><td> $HP^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td></td><td>Hydrostatic pressure on the element 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></td><td>Pressure on the element 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></td><td>Nonuniform pressure on the element surface with the 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>TRSHR</td><td>Surface traction</td><td> $FL^{-2}$ </td><td></td><td>Shear traction on the element surface.</td></tr><tr><td> $TRSHRNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td></td><td>Nonuniform shear traction on the element 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></td><td>General traction on the element surface.</td></tr><tr><td> $TRVECNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td></td><td>Nonuniform general traction on the element surface with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr></table>

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Available for R3D3 and R3D4 elements only: 

<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>BX(S)</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in the global X-direction.</td></tr><tr><td>BY(S)</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in the global Y-direction.</td></tr><tr><td>BZ(S)</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in the global Z-direction.</td></tr><tr><td>BXNU(S)</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.</td></tr><tr><td>BYNU(S)</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.</td></tr><tr><td>BZNU(S)</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.</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 and  $\omega$  is the angular velocity).</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 and  $\omega$  is the angular velocity). The load stiffness due to Coriolis loading is not accounted for in direct steady-state dynamics analysis.</td></tr><tr><td>HP(S)</td><td>Not supported</td><td> $FL^{-2}$ </td><td>Hydrostatic pressure on the element 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 on the element 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 on the element surface with magnitude supplied via user subroutine DLOAD in</td></tr></table>

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<table><tr><td>Load ID(*DLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td></td><td></td><td></td><td>Abaqus/Standard and VDLOAD in Abaqus/Explicit. The pressure is positive in the direction of the positive element normal.</td></tr><tr><td>TRSHR</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Shear traction on the element surface.</td></tr><tr><td> $TRSHRNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform shear traction on the element 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 surface.</td></tr><tr><td> $TRVECNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform general traction on the element surface with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr></table>

# Abaqus/Aqua loads

Abaqus/Aqua loads are specified as described in “Abaqus/Aqua analysis,” Section 6.11.1.

Available for R3D3 and R3D4 elements only:

<table><tr><td>Load ID(*CLOAD/*DLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>PB(A)</td><td>Not supported</td><td> $FL^{-2}$ </td><td>Buoyancy force.</td></tr></table>

Available for RB2D2 and RB3D2 elements only:

<table><tr><td>Load ID(*CLOAD/*DLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $FDD^{(A)}$ </td><td>Not supported</td><td> $FL^{-1}$ </td><td>Transverse fluid drag force.</td></tr><tr><td> $FD1^{(A)}$ </td><td>Not supported</td><td>F</td><td>Fluid drag force on the first end of the rigid link (node 1).</td></tr><tr><td> $FD2^{(A)}$ </td><td>Not supported</td><td>F</td><td>Fluid drag force on the second end of the rigid link (node 2).</td></tr></table>

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<table><tr><td>Load ID(*CLOAD/*DLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $FDT^{(A)}$ </td><td>Not supported</td><td> $FL^{-1}$ </td><td>Tangential fluid drag load.</td></tr><tr><td> $FI^{(A)}$ </td><td>Not supported</td><td> $FL^{-1}$ </td><td>Transverse fluid inertia load.</td></tr><tr><td> $FI1^{(A)}$ </td><td>Not supported</td><td>F</td><td>Fluid inertia load on the first end of the rigid link (node 1).</td></tr><tr><td> $FI2^{(A)}$ </td><td>Not supported</td><td>F</td><td>Fluid inertia load on the second end of the rigid link (node 2).</td></tr><tr><td> $PB^{(A)}$ </td><td>Not supported</td><td> $FL^{-1}$ </td><td>Buoyancy force (with closed-end condition).</td></tr><tr><td> $WDD^{(A)}$ </td><td>Not supported</td><td> $FL^{-1}$ </td><td>Transverse wind drag force.</td></tr><tr><td> $WD1^{(A)}$ </td><td>Not supported</td><td>F</td><td>Wind drag force on the first end of the rigid link (node 1).</td></tr><tr><td> $WD2^{(A)}$ </td><td>Not supported</td><td>F</td><td>Wind drag force on the second end of the rigid link (node 2).</td></tr></table>

# Surface-based loading

# Distributed loads

Surface-based distributed loads are available for elements with displacement degrees of freedom. They are specified as described in “Distributed loads,” Section 34.4.3.

Available for RAX2, R3D3, and R3D4 elements only:

<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 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 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 surface with the magnitude supplied via user subroutine DLOAD in</td></tr></table>

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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></td><td></td><td></td><td>Abaqus/Standard and VDLOAD in Abaqus/Explicit. The pressure is positive in the direction opposite to the surface normal.</td></tr><tr><td>TRSHR</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Shear traction on the element surface.</td></tr><tr><td> $TRSHRNU^{(S)}$ </td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Nonuniform shear traction on the element 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 surface.</td></tr><tr><td> $TRVECNU^{(S)}$ </td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Nonuniform general traction on the element surface with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr></table>

# Element output

None.
