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# 2.8.1 DISTRIBUTION DEFINITION

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE

# References

• “Orientations,” Section 2.2.5   
• “Material library: overview,” Section 21.1.1   
• “Material data definition,” Section 21.1.2   
• “Combining material behaviors,” Section 21.1.3   
• “Density,” Section 21.2.1   
• “Linear elastic behavior,” Section 22.2.1   
• “Thermal expansion,” Section 26.1.2   
• “Solid (continuum) elements,” Section 28.1.1   
• “Membrane elements,” Section 29.1.1   
• “Using a shell section integrated during the analysis to define the section behavior,” Section 29.6.5   
• “Using a general shell section to define the section behavior,” Section 29.6.6   
• “Connectors: overview,” Section 31.1.1   
• “Controlling initial contact status for general contact in Abaqus/Explicit,” Section 36.4.4   
• “Boundary conditions in Abaqus/CFD,” Section 34.3.2   
• \*DISTRIBUTION   
• \*DISTRIBUTION TABLE   
• Chapter 63, “The Discrete Field toolset,” of the Abaqus/CAE User’s Guide

# Overview

# A distribution:

• is a spatially varying field defined over elements, nodes, or element faces in an Abaqus model;   
• can be used to define shell thicknesses on an element-by-element basis for shell elements with displacement degrees of freedom;   
• can be used to define shell stiffness on an element-by-element basis;   
• can be used to define local coordinate systems on solid continuum and shell elements on an elementby-element basis;   
• can be used to define orientation angles on the layers of composite shell elements that have displacement degrees of freedom;   
• can be used to define orientation angles for connector elements;   
• can be used to define thicknesses on the layers of conventional composite shell elements;   
• can be used to specify initial contact clearances;

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• can be used to specify pressure that varies with the total volume of fluid crossing a surface in an Abaqus/CFD analysis; and   
• in an Abaqus/Standard analysis can be used to define mass density, linear elastic material behavior, and thermal expansion for solid continuum elements; shell offsets; orientation angles on the layers of composite solid continuum elements; local coordinate systems on membrane elements; and membrane thickness on an element-by-element basis.

# Distributions

A distribution is a spatial analogy of an amplitude definition (see “Amplitude curves,” Section 34.1.2). Amplitude definitions are used to provide arbitrary time variations of loads, displacements, and other prescribed variables. Distributions are used to specify arbitrary spatial variations of selected element properties, material properties, local coordinate systems, boundary conditions, and spatial variations of initial contact clearances.

The two main components of a distribution are its location and field data. The location identifies where the distribution is defined, either on elements, nodes, or element faces. Field data are a specified number of floating point values defined for each element, node, or element face in the distribution.

To define a distribution, you must assign it a unique name. You must also specify the number and physical dimension of each data value in the distribution by referring to a distribution table.

Input File Usage: \*DISTRIBUTION, NAME=name, TABLE=distribution table name

Abaqus/CAE Usage: Abaqus/CAE supports distributions using discrete fields.

Property, Interaction, or Load module: Tools→Discrete Field→Create

# Specifying the location of a distribution

You can define a distribution on elements, nodes, or element faces. Distributions on nodes are supported only for defining initial contact clearances as described in “Controlling initial contact status for general contact in Abaqus/Explicit,” Section 36.4.4. Only Abaqus/CFD supports distributions on element faces. For a distribution used with pressure-volume fluid boundary definitions in Abaqus/CFD, you specify that no location is required. All other applications of distributions require distributions defined on elements.

There is no limit on the number of distributions to which a given element or node may belong. Elements, nodes, and element faces cannot be combined within the same distribution definition.

# Defining a distribution on elements

Defining a distribution on elements requires you to specify field data for each element or element set included in the distribution definition. All distributions on elements require that default data be defined. Default data are used for all elements that are not specifically assigned a value in the distribution.

Input File Usage: \*DISTRIBUTION, LOCATION=ELEMENT

blank space, field data

element set or element number, field data

Default data are defined by using a blank space instead of an element number or element set for the first data item on the first data line of a distribution definition.

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Only one set of default data can be defined for a distribution. If you specify only default data, all elements that reference that distribution use the default values.

If an element is specified more than once in a given distribution definition, the last specification given is used.

Abaqus/CAE Usage: Property, Interaction, or Load module: Tools→Discrete

Field→Create: Definition: Elements

# Defining a distribution on nodes

Defining a distribution on nodes requires you to specify field data for each node or node set included in the distribution definition.

Input File Usage: \*DISTRIBUTION, LOCATION=NODE

node set or node number, field data

If a node is specified more than once in a given distribution definition, the last specification given is used.

Abaqus/CAE Usage: Defining a distribution on nodes for initial contact clearances is not supported in Abaqus/CAE.

# Defining a distribution on element faces

Defining a distribution on element faces requires you to specify field data for each element or element set and element face identifier included in the distribution definition.

Input File Usage: \*DISTRIBUTION, LOCATION=FACE

element set or element number, element face identifier, field data

If an element and element face identifier are specified more than once in a given distribution definition, the last specification given is used.

Abaqus/CAE Usage: Defining a distribution on element faces is not supported in Abaqus/CAE.

# Defining a pressure-volume distribution used in Abaqus/CFD

For a distribution used to define fluid boundary conditions for pressure that varies with the total volume of fluid crossing a surface, you specify field data and that no location is required.

Input File Usage: \*DISTRIBUTION, LOCATION=NONE

field data, field data

Abaqus/CAE Usage: Defining a distribution used in Abaqus/CFD is not supported in Abaqus/CAE.

# Defining a distribution table

Every distribution definition must refer to a distribution table. A distribution table defines the number of field data items needed for each element or node in a distribution. The distribution table also defines the physical dimension of each data value in a distribution. A distribution table can be referred to as many times as needed by different distributions. The distribution table consists of a list of predefined labels

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shown in Table 2.8.1–1 and Table 2.8.1–2. The combination of labels needed for a given distribution is determined by how the distribution is applied.

Table 2.8.1–1 Distribution table labels—Abaqus/Standard and Abaqus/Explicit. 

<table><tr><td>Label</td><td>Physical dimension</td><td>Number of data items per label</td></tr><tr><td>ANGLE</td><td>angle in degrees</td><td>1</td></tr><tr><td>COORD3D</td><td>(L, L, L)</td><td>3</td></tr><tr><td>DENSITY</td><td> $ML^{-3}$ </td><td>1</td></tr><tr><td>EXPANSION</td><td> $\theta^{-1}$ </td><td>1</td></tr><tr><td>LENGTH</td><td>L</td><td>1</td></tr><tr><td>MODULUS</td><td> $FL^{-2}$ </td><td>1</td></tr><tr><td>RATIO</td><td>dimensionless</td><td>1</td></tr><tr><td>SHELLSTIFF1</td><td> $FL^{-1}$ </td><td>1</td></tr><tr><td>SHELLSTIFF2</td><td>F</td><td>1</td></tr><tr><td>SHELLSTIFF3</td><td>FL</td><td>1</td></tr></table>

Table 2.8.1–2 Distribution table labels—Abaqus/CFD. 

<table><tr><td>Label</td><td>Physical dimension</td><td>Number of data items per label</td></tr><tr><td>PRESSURE</td><td> $FL^{-2}$ </td><td>1</td></tr><tr><td>VOLUME</td><td> $L^{3}$ </td><td>1</td></tr><tr><td>VELOCITY</td><td> $LT^{-1}$ </td><td>1</td></tr><tr><td>TEMPERATURE</td><td> $\theta$ </td><td>1</td></tr><tr><td>TURBKE</td><td> $L^{2}T^{-2}$ </td><td>1</td></tr><tr><td>TURBEPS</td><td> $L^{2}T^{-3}$ </td><td>1</td></tr><tr><td>TURBOMEGA</td><td> $T^{-1}$ </td><td>1</td></tr><tr><td>TURBNU</td><td> $L^{2}T^{-1}$ </td><td>1</td></tr><tr><td>LENGTH</td><td>L</td><td>1</td></tr><tr><td>RATIO</td><td>dimensionless</td><td>1</td></tr></table>

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<table><tr><td>Input File Usage:</td><td>Use the following option to define a distribution table:*DISTRIBUTION TABLE, NAME=distribution table namelist of labels</td></tr><tr><td>Abaqus/CAE Usage:</td><td>Abaqus/CAE creates a distribution table when you specify a distribution by selecting a discrete field.Defining a distribution table used in Abaqus/CFD is not supported in Abaqus/CAE.</td></tr></table>

# Applying distributions

The data defined in a distribution are not used in an Abaqus analysis unless the distribution is referred to by name by a feature that supports distributions, and the distribution is applied only to the elements, nodes, or element faces that are associated with the referenced feature. In addition, a distribution definition can be referenced more than one time in a given model. These points are illustrated in the examples below.

If an element in an Abaqus/Standard or Abaqus/Explicit analysis is declared rigid (see “Rigid body definition,” Section 2.4.1) any distributions used to define element properties, material properties (with the exception of density), or local coordinate systems are ignored.

# Examples

The simple examples below illustrate how distributions are defined. A large number of illustrative example problems using distributions can be found in “Spatially varying element properties,” Section 5.1.4 of the Abaqus Verification Guide.

# Example 1

A distribution for shell thickness is defined and applied to two different shell section definitions through the SHELL THICKNESS parameter—as noted above the distribution dist0 would not be used if it is not referred to by a feature that supports distributions. See “Using a shell section integrated during the analysis to define the section behavior,” Section 29.6.5, for more details. The distribution table defines both the number of data values (one) and the physical dimension (LENGTH) of the thickness data. The thicknesses defined in distribution dist0 are assigned only to shell elements that belong to the element set elset1 or elset2. The default thickness (t0) defined in the first data line of dist0 will be assigned to all elements in elset1 and elset2 that are not explicitly assigned a thickness in dist0.

```txt
* DISTRIBUTION TABLE, NAME=tab0
LENGTH
* DISTRIBUTION, NAME=dist0, LOCATION=element, TABLE=tab0
, t₀
element set or number, t₁
element set or number, t₂
... 
```

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```txt
*SHELL SECTION, ELSET=elset1, SHELL THICKNESS=dist0
*SHELL SECTION, ELSET=elset2, SHELL THICKNESS=dist0 
```

# Example 2

A distribution for spatially varying isotropic elastic material behavior is defined and applied to a material definition (“Linear elastic behavior,” Section 22.2.1). This material is then referred to by a solid section definition. This is important because like any material definition, a material defined by a distribution is not used unless it is referred to by a section definition, and then it is applied only to the elements associated with the section definition. The distribution table defines both the number of data values (two) and the physical dimensions (MODULUS and RATIO) of the isotropic elastic data. Other material behaviors (in this case plasticity) can also be included in the material definition. The default elastic constants $( \mathrm { E } _ { 0 } , \nu _ { 0 } )$ in distribution dist1 will be assigned to all elements in elset3 that are not explicitly assigned elastic constants in dist1.

```txt
* DISTRIBUTION TABLE, NAME=tab1
MODULUS, RATIO
* DISTRIBUTION, NAME=dist1, LOCATION=element, TABLE=tab1
, E₀, ν₀
element set or number, E₁, ν₁
element set or number, E₂, ν₂
...
*MATERIAL, NAME=MAT
*ELASTIC
dist1
*PLASTIC
...
*SOLID SECTION, ELSET=elset3, MATERIAL=MAT 
```

# Example 3

A spatially varying local coordinate system ( “Orientations,” Section 2.2.5) is defined by specifying both spatially varying coordinates for points a and b as well as a spatially varying additional rotation angle. This orientation is then referred to by a general shell section definition. This is important because like any orientation definition, an orientation defined by a distribution is not used unless it is referred to by a section definition, and then it is applied only to the elements associated with the section definition. The distribution table for the coordinates specifies COORD3D twice to indicate that data for two threedimensional coordinates points must be specified for each element in the distribution.

* DISTRIBUTION TABLE, NAME=tab2
COORD3D, COORD3D
* DISTRIBUTION, NAME=dist2, LOCATION=element, TABLE=tab2
, $aX_{0}, aY_{0}, aZ_{0}, bX_{0}, bY_{0}, bZ_{0}$ element set or number, $aX_{1}, aY_{1}, aZ_{1}, bX_{1}, bY_{1}, bZ_{1}$

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element set or number, $aX_{2}$ , $aY_{2}$ , $aZ_{2}$ , $bX_{2}$ , $bY_{2}$ , $bZ_{2}$ ...
*DISTRIBUTION TABLE, NAME=tab3
ANGLE
*DISTRIBUTION, NAME=dist3, LOCATION=element, TABLE=tab3
, $\theta_{0}$ element set or number, $\theta_{1}$ element set or number, $\theta_{2}$ ...
*ORIENTATION, NAME=ORI, DEFINITION=COORDINATES
dist2
3, dist3
*SHELL GENERAL SECTION, ELSET=elset4, ORIENTATION=ORI

# Example 4

Spatially varying thicknesses and orientation angles are defined on the layers of a composite shell element. The distribution table for the thicknesses specifies LENGTH, and the distribution table for the orientation angles specifies ANGLE. A distribution of thicknesses is used on layers 1 and 3, while a distribution of angles is used on layers 2 and 3.

```txt
* DISTRIBUTION TABLE, NAME=tableThick
LENGTH
* DISTRIBUTION, NAME=thickPly1, LOCATION=element, TABLE=tableThick
, t₀
element set or number, t₁
element set or number, t₂
...
* DISTRIBUTION, NAME=thickPly3, LOCATION=element, TABLE=tableThick
, t₀
element set or number, t₁
element set or number, t₂
...
* DISTRIBUTION TABLE, NAME=tableOriAngle
ANGLE
* DISTRIBUTION, NAME=oriAnglePly2, LOCATION=element,
TABLE=tableOriAngle
, φ₀
element set or number, φ₁
element set or number, φ₂
...
* DISTRIBUTION, NAME=oriAnglePly3, LOCATION=element,
TABLE=tableOriAngle 
```

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, $\phi_{0}$ element set or number, $\phi_{1}$ element set or number, $\phi_{2}$ ...
*SHELL SECTION, ELSET=elset1, COMPOSITE
thickPly1, 3, mat1, 0.
1., 3, mat2, oriAnglePly2
thickPly3, 3, mat3, oriAnglePly3

# Example 5

Spatially varying velocities are specified on a fluid inlet condition. The distribution table for the velocity specifies VELOCITY.

```txt
* DISTRIBUTION TABLE, NAME=velocityTable
VELOCITY
* DISTRIBUTION, NAME=xvelocity, LOCATION=face, TABLE=velocityTable
element set or number, element face identifier, v₁
element set or number, element face identifier, v₂
...
*FLUID BOUNDARY, VELOCITY INLET, SURFACE=inletSurface
VELX, xvelocity
VELY, 0.0
VELZ, 0.0 
```

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# 2.9 Display body definition

• “Display body definition,” Section 2.9.1

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