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ProductsAbaqus/StandardAbaqus/ExplicitAbaqus/CAE
Distributions
A distribution is a spatial analogy of an amplitude definition (see Amplitude Curves). 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: 
Specifying the location of a distribution
You can define a distribution on elements or nodes. Distributions on nodes are supported only for defining initial contact clearances as described in Controlling initial contact status for general contact in Abaqus/Explicit. 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 and nodes 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. 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: : 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 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 shown in Table 1. The combination of labels needed for a given distribution is determined by how the distribution is applied.
| Label | Physical dimension | Number of data items per label |
|---|---|---|
| ANGLE | angle in degrees | 1 |
| COORD3D | (L, L, L) | 3 |
| DENSITY | ML−3 | 1 |
| EXPANSION | θ−1 | 1 |
| LENGTH | L | 1 |
| MODULUS | FL−2 | 1 |
| RATIO | dimensionless | 1 |
| SHELLSTIFF1 | FL-1 | 1 |
| SHELLSTIFF2 | F | 1 |
| SHELLSTIFF3 | FL | 1 |
| ORIENTS | dimensionless | 6 |
Input File Usage
Use the following option to define a distribution table:
DISTRIBUTION TABLE, NAME=distribution table name list of labels
Abaqus/CAE Usage
Abaqus/CAE creates a distribution table when you specify a distribution by selecting a discrete field.
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) 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.
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 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.
DISTRIBUTION TABLE, NAME=tab0 LENGTH DISTRIBUTION, NAME=dist0, LOCATION=element, TABLE=tab0 , t0 element set or number, t1 element set or number, t2 … 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). 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 (E0, ν0) in distribution dist1 will be assigned to all elements in elset3 that are not explicitly assigned elastic constants in dist1.
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) 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 three-dimensional coordinates points must be specified for each element in the distribution.
DISTRIBUTION TABLE, NAME=tab2 COORD3D, COORD3D DISTRIBUTION, NAME=dist2, LOCATION=element, TABLE=tab2 , aX0,aY0,aZ0,bX0,bY0,bZ0 element set or number, aX1,aY1,aZ1,bX1,bY1,bZ1 element set or number, aX2,aY2,aZ2,bX2,bY2,bZ2 … DISTRIBUTION TABLE, NAME=tab3 ANGLE DISTRIBUTION, NAME=dist3, LOCATION=element, TABLE=tab3 , θ0 element set or number, θ1 element set or number, θ2 … 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.
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 , ϕ0 element set or number, ϕ1 element set or number, ϕ2 … SHELL SECTION, ELSET=elset1, COMPOSITE thickPly1, 3, mat1, 0. 1., 3, mat2, oriAnglePly2 thickPly3, 3, mat3, oriAnglePly3
Example 5
A distribution for a spatially varying volume fraction is defined in distribution distVF. A distribution for a spatially varying aspect ratio is defined in distribution distAR, and a distribution for the second-order orientation tensor is defined in distribution distOriTens. These distributions are then applied to the definition of a constituent, which is then used in the material definition of a multiscale material with mean-field homogenization (Mean-field homogenization). The distribution table for the volume fraction and aspect ratio specifies RATIO, and the distribution table for the orientation tensor specifies ORITENS.
DISTRIBUTION TABLE, NAME=vfTable RATIO DISTRIBUTION TABLE, NAME=arTable RATIO DISTRIBUTION TABLE, NAME=oriTable ORITENS DISTRIBUTION, NAME=distVF, LOCATION=element, TABLE=vfTable element set or number, vf DISTRIBUTION, NAME=distAR, LOCATION=element, TABLE=arTable element set or number, ar DISTRIBUTION, NAME=distOriTens, LOCATION=element, TABLE=oriTable element set or number, a11,a22,a33,a12,a13,a23 … MATERIAL, NAME=MAT MEAN FIELD HOMOGENIZATION CONSTITUENT distVF, distAR, distOriTens