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# 30.1 Point mass elements

• “Point masses,” Section 30.1.1   
• “Mass element library,” Section 30.1.2

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# 30.1.1 POINT MASSES

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE

# References

• “Mass element library,” Section 30.1.2   
• \*MASS   
• “Defining point mass and rotary inertia,” Section 33.3 of the Abaqus/CAE User’s Guide, in the HTML version of this guide

# Overview

Mass elements:

• allow the introduction of concentrated mass that is either isotropic or anisotropic at a point;   
• are associated with the three translational degrees of freedom at a node.

If rotary inertia is also required (for example, to represent a rigid body), use element type ROTARYI (“Rotary inertia,” Section 30.2.1).

In addition to point masses, Abaqus provides a convenient nonstructural mass definition that can be used to smear mass from features that have negligible structural stiffness over a region that is typically adjacent to the nonstructural feature. The nonstructural mass can be specified in the form of a total mass value, a mass per unit volume, a mass per unit area, or a mass per unit length (see “Nonstructural mass definition,” Section 2.7.1).

# Defining the isotropic mass value

You specify a mass magnitude, which is associated with the three translational degrees of freedom at the node of the element. Specify mass, not weight. You must associate this mass with a region of your model.

Input File Usage: \*MASS, ELSET=name

mass magnitude

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

Abaqus/CAE Usage: Property or Interaction module: Special→Inertia→Create: Point

mass/inertia: select point: Magnitude: Isotropic: mass magnitude

# Defining the mass matrix explicitly in Abaqus/Standard

You can define a general mass matrix explicitly in Abaqus/Standard if the introduction of individual terms on and off the diagonal of the mass matrix is desired. See “User-defined elements,” Section 32.17.1, for details.

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Input File Usage: Use both of the following options:

\*USER ELEMENT

\*MATRIX

Abaqus/CAE Usage: Defining the mass matrix explicitly is not supported in Abaqus/CAE.

# Defining the anisotropic mass tensor

You can specify the mass as anisotropic by giving the three principal values and the principal directions. When the orientation of the principal directions is not specified, they are assumed to coincide with the global axes. In a large-displacement analysis the local axes of the anisotropic mass rotate with the rotation, if active, of the node to which the anisotropic mass is attached. The rotation degree of freedom is active at a node if that node is connected to a beam, a conventional shell, a rotary inertia element, or a rigid body. You can specify mass proportional loads such as gravitation on an anisotropic mass. Damping and mass scaling can also be used with an anisotropic mass.

Specify mass, not weight. You must associate this mass with a region of your model.

Input File Usage: $* { \mathrm { M A S S , ~ E L S E T } } { = } n a m e , { \mathrm { ~ T Y P E = A N I S O T R O P I C , } }$

ORIENTATION=orientation\_name

$M _ { 1 1 } , M _ { 2 2 } , M _ { 3 3 }$

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

Abaqus/CAE Usage: Property or Interaction module: Special→Inertia→Create: Point

mass/inertia: select point: Magnitude: Anisotropic: $M _ { 1 1 } , M _ { 2 2 }$ , and $M _ { 3 3 }$

# Defining damping for MASS elements

In Abaqus/Standard you can define mass proportional damping for direct-integration dynamic analysis or composite damping for modal dynamic analysis. Although both damping definitions can be specified for a set of MASS elements, only the damping that is relevant to the particular dynamic analysis procedure will be used.

In Abaqus/Explicit mass proportional damping can be defined for MASS elements.

# Dynamics

You can define inertia proportional damping for MASS elements in direct-integration dynamic analysis or explicit dynamic analysis. See “Material damping,” Section 26.1.1, for details.

Input File Usage: \*MASS, ALPHA=

Abaqus/CAE Usage: Property or Interaction module: Special→Inertia→Create: Point

mass/inertia: select point: Damping: Alpha: $\alpha _ { R }$

# Modal dynamics

You can define the fraction of critical damping to be used with the MASS elements when calculating composite damping factors for the modes when used in modal dynamic analysis. See “Material damping,” Section 26.1.1, for details.

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Input File Usage: \*MASS, COMPOSITE=

Abaqus/CAE Usage: Property or Interaction module: Special→Inertia→Create: Point mass/inertia: select point: Damping: Composite:

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# 30.1.2 MASS ELEMENT LIBRARY

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE

# References

• “Point masses,” Section 30.1.1   
• \*MASS

# Overview

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

# Element type

MASS

Point mass

Active degrees of freedom 1, 2, 3

Additional solution variables None.

# Nodal coordinates required

X, Y, Z

# Element property definition

Input File Usage: \*MASS

Abaqus/CAE Usage: Not supported

# 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/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $\text{CENTRIF}^{(S)}$ </td><td>Not supported</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/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>GRAV</td><td>Not supported</td><td> $LT^{-2}$ </td><td>Gravity loading in a specified direction.</td></tr><tr><td> $ROTA^{(S)}$ </td><td>Not supported</td><td> $T^{-2}$ </td><td>Rotary acceleration load (magnitude is input as  $\alpha$ , where  $\alpha$  is the rotary acceleration).</td></tr></table>

Element output

ELKE Element kinetic energy (available only from Abaqus/Standard).

Nodes associated with the element

1 node.

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# 30.2 Rotary inertia elements

• “Rotary inertia,” Section 30.2.1   
• “Rotary inertia element library,” Section 30.2.2

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