Date July 7, 2002 Memo Number STI:02/07Subject ANSYS.NET Tips and TricksANSYS.NET Tips and TricksANSYS.NET Tips and TricksANSYS.NET Tips and Tricks: : : : CERIG vs RBE3, RIGID184CERIG vs RBE3, RIGID184CERIG vs RBE3, RIGID184CERIG vs RBE3, RIGID184Keywords CERIG, RBE3, RIGID184

1.1.1.1. Introduction:Introduction:Introduction:Introduction:Constraint equations provide many useful features in ANSYS, such as tying together dissimilar

meshes, representing parts of the system not explicitly modeled, or distributing loads. Twoautomated methods of generating constraint equations are the CERIG and RBE3 commands. Becausethere is often confusion over their use, this memo hopes to provide some information on differencesbetween the two methods.

Constraint equations in ANSYS are linear, so they are not valid for large-rotation analyses.RIGID184 is a beta element in version 6.1 which provides rigid link/beam capabilities, valid for large-rotation problems. The latter part of this memo will cover some details of this undocumentedfeature, available in 6.1.

2.2.2.2. Background on CERIG vs. RBE3:Background on CERIG vs. RBE3:Background on CERIG vs. RBE3:Background on CERIG vs. RBE3:Constraint equations (CE) are linear equations which relate various DOF to each other, as shown

in the following:

�=

⋅=N

iii DOFCA

1where “A” is a constant and “Ci” is a coefficient for a particular DOFi. CE are of a more general formthan nodal coupling (CP), which relate DOF to each other directly (e.g., DOF1 = DOF2). In bothcases, however, one often speaks of ‘independent’ and ‘dependent’ DOF because the former are theDOF actually solved for in the matrix equation [K]{u}={F}, then the latter are derived from theindependent DOF via the constraint equations. In ANSYS, the constraint equations are written suchthat the first term is always a dependent DOF.

CERIG and RBE3 are two of several commands in ANSYS to create complex constraint equationsautomatically for specific situations. CERIG is typically used to generate a rigid region, whereasRBE3 is often used to provide a weighed distribution of forces/moments/mass. Both are created in asimilar fashion with one ‘master’ node and several ‘slave’ nodes.

The CERIG command1 creates a ‘CE-based RIGid region’. The user selects one master node,several slave nodes, and the DOF affected. The ‘master node’ in this case means that this is the node(and DOF) which control the behavior of the rigid region. Generally speaking, any rigid body has6 DOF in 3D and 3 DOF in 2D – hence, the master node should have the appropriate number ofDOF to control how this rigid region moves. The slave nodes can have translational DOF only orrotational DOF as well, and this is specified via the “Ldof” argument of the CERIG command. Whilethe CERIG command can be used to tie specific DOF only, the following discussion will assume useof one of two options (“Ldof = ALL” or “Ldof = UXYZ”) used to construct a typical rigid region.

The first point of confusion commonly encountered is that users expect to have a master nodeby itself (unattached to any element) when using CERIG. In ANSYS, the actual DOF used by thenode is determined by the attached element, such as TEMP, UX, WARP, or ROTZ. Since CERIG is aconstraint equation, not an element, it does not provide information about active DOF. Hence, if themaster node is unattached to any other element, a user should create a MASS21 element at themaster node to provide that node with information on what the active DOF are. The actual mass ofthe MASS21 element usually doesn’t matter unless inertial loads are present or dynamic analyses areinvolved, although the user can specify a very small mass value in these situations.

Another point of confusion is that even when users create a MASS21 at the master node,KEYOPT(3)=2 (“3-D mass without rotary inertia”) is sometimes invoked by the user. Because of this,the active DOF at the master node of CERIG has translational DOF only. As noted above, generallyspeaking, any rigid body has 6 DOF in 3D (and 3 DOF in 2D), so rotational DOF are important to

1 Users more familiar with the GUI can access the CERIG command via the menu item: “Main Menu > Preprocessor >Coupling / Ceqn > Rigid Region”

specify the behavior of the rigid region. (Even if no rotation is expected, the user can subsequentlyconstrain the rotational DOF of the master node.)

In the case of CERIG, it is important to note that the ‘master’ node contains the independentDOF, and the ‘slave’ nodes contain the dependent DOF. Hence, the user can specify boundaryconditions on the ‘master’ node only – boundary conditions conflicting with the ‘slave’ DOF used inCERIG should not be applied to the ‘slave’ nodes. This should be a reasonable requirement because,as a rigid region, a user should not be able to specify movement on a local area of the rigid region –otherwise, the region is no longer ‘rigid.’

Even for the cases of rotated nodes, ANSYS will generate the correct constraint equations withCERIG, as long as the nodes are rotated prior to issuing the CERIG command.

The RBE3 command, 2 on the other hand, behaves differently than CERIG. The user specifiesoptions similar to the CERIG command with one ‘master’ and several ‘slave’ nodes, although thereare some differences between the two commands.

The first difference is that the ‘master’ node in RBE3 is really a dependent node. As noted above,the ‘master’ node in CERIG defines the behavior of the rigid region, so it has the independent DOF.In RBE3, however, the ‘master’ node is actually a dependent node, and the ‘slave’ nodes define theindependent DOF. This means that RBE3 does not define a rigid region but, instead, it is a way inwhich forces/moments/mass on the ‘master’ (dependent) DOF can be distributed to the ‘slave’(independent) DOF.3

Secondly, the user has the option of inputting two array parameters listing the ‘slave’ nodes andthe weighting factors for each ‘slave’ node used for the interpolation of the forces/moments (bydefault, the weighting factor is 1.0). A force applied on the ‘master’ node is distributed to the ‘slave’nodes proportional to the weighting factors. A moment applied on the ‘master’ node is distributed asforces to the ‘slave’ nodes which are proportional to the distance from the ‘slave’ nodes times theweighting factors.

Lastly, while any DOF can be considered for the ‘master’ node (usually, all 6 DOF for the masterare used to transmit forces and moments), only translational DOF are used for the ‘slave’ nodes. Thisis because of the fact that the ‘master’ node is the dependent node – its rotation can be fullydescribed by the translation of the ‘slave’ (independent) nodes. The RBE3 ‘master’ node being adependent node also has the implication that a load can be applied on it, but a constraint cannot.

To compare the differences between CERIG and RBE3, a summary is provided below:

Table Table Table Table 1111

CERIG Command RBE3 CommandIndependent DOF Dependent DOFCan apply loads or constrain master node

Can only apply loads on master node

Slave Nodes ('n' nodes)

Dependent DOF Independent DOF

Number of CEs Generated

CE ≥ 1 (Depends on Ldof argument and 'n')

1 ≤ CE ≤ 6 (Depends on DOF argument)

Optional weight factors

N/A Supplied by array parameter in Wtfact

Example use Describe a rigid region in model

Distribute forces, moments, or mass

Master Node (1 node)

2 Users more familiar with the GUI can access the RBE3 command via the menu item: “Main Menu > Preprocessor >Coupling / Ceqn > Dist F/M at Mstr”3 For example, the RBE3 command constructs CEs for rotational DOF based on the location of the ‘slave’ nodes to the‘master’ node because of the fact that, for an applied moment, the distance from the ‘slave’ node to the ‘master’ nodeneeds to be considered.

3.3.3.3. Difference with Difference with Difference with Difference with Nastran:Nastran:Nastran:Nastran:For users who are familiar with Nastran, ANSYS’s CERIG command is similar to Nastran’s RBE2

element, and the ANSYS RBE3 command is similar to Nastran’s RBE3 element with Ci set to 123.ANSYS’s requirement that the ‘master’ node needs to be attached to an element often causes

confusion, but this is due to the difference in the definition of ‘active DOF’ in ANSYS and Nastran.In Nastran, each grid point (node) has 6 DOF. Hence, the DOF associated with a node are

predefined, so Nastran does not require the ‘master’ node to be attached to any elements when usingRBE2 or RBE3. However, the user must constrain unused DOF (such as via PARAM,AUTOSPC,YES),as in the case with solid-only elements (HEXA, TETRA) or 2D analyses. By not appropriatelyconstraining unused DOF, the matrix is singular and cannot be solved for.

In ANSYS, the element type defines the active DOF. Hence, there is a distinction between activeDOF for solid and shell/beam elements as well as a difference between 2D vs. 3D elements. A nodecan have any number of active DOF, depending on what elements are connected to it (such as forcoupled-field problems). Hence, for CERIG and RBE3, an element with 6 DOF should be connectedto the master node, and a common method is to use MASS21 if no other elements are connected tothe master node. Conversely, the user does not need to worry about any ‘unused’ DOF, as in thecase with Nastran.

This is not to say one method is better than the other, but this section was merely added inhopes of explaining the reasoning of the different modeling methods with both programs whenusing CERIG (RBE2) and RBE3.

4.4.4.4. Example of use of CERIG and RBE3:Example of use of CERIG and RBE3:Example of use of CERIG and RBE3:Example of use of CERIG and RBE3:The attached input files “plate_cerig.inp” and “plate_rbe3.inp” run the

models shown here. A shell plate with a hole is constrained at both ends.Both CERIG and RBE3 are used to model a region in the hole, and a load isapplied to the ‘master’ node in the center. A linear static analysis is run.

The exaggerated deformed shape clearly shows that in the case withCERIG on the left, the hole retains its shape since the region is assumed tobe rigid. On the other hand, the hole changes shape in the case with RBE3since the ‘slave’ nodes contain the independent DOF. Hence, both casestransmit the load, but the two situations can be thought of as representingextreme conditions (rigid region/infinite stiffness vs. no stiffness).

Figure 1 (CERIG)Figure 1 (CERIG)Figure 1 (CERIG)Figure 1 (CERIG) Figure 2 (RBE)Figure 2 (RBE)Figure 2 (RBE)Figure 2 (RBE)

The choice of using CERIG or RBE3 depends upon the application and the FE model. These twocommands provide the user with powerful tools in not only applying loads but connectingmeshes/regions and other functions without having to use ‘stiff’ beams or generating the constraintequations manually.

5.5.5.5. RIGID184:RIGID184:RIGID184:RIGID184:As noted earlier, constraint equations are linear relationships between DOF, so they are valid for

small-deflection analyses. However, constraint equations are not valid for large-rotation problems. In6.1, a beta feature is available which provides the user with rigid link/beam elements for use in large-rotation problems. These elements can be used to represent rigid regions or rigid connections, evenin nonlinear applications. Because this is an undocumented feature, the user is warned to use thisat his/her own risk. The element is tentatively planned to be released as a documented, fullysupported feature in ANSYS 7.0, which is currently scheduled to be released in October 2002.

The RIGID184 element is not supported in the GUI, so the user must use commands ingenerating these elements. RIGID184 assumes a unit area cross-section. It requires no real constantsand has optional material properties of ALPX and DENS for thermal expansion and density,respectively. KEYOPT(1) controls element behavior (active DOF) where KEYOPT(1)=0 represents arigid link (UX, UY, UZ only) and KEYOPT(1)=1 mimics a rigid beam (6 DOF). This element can alsobe used for birth and death applications.

The rigid behavior is internally satisfied with Lagrange multipliers. This means that RIGID184requires use of direct solvers, either sparse (EQSLV,SPARSE – preferred) or frontal (EQSLV,FRONT).Also, because this is an element whose active DOF are determined by KEYOPT(1), unlike CERIG orRBE3, the use of MASS21 is unnecessary when modeling rigid regions.

6.6.6.6. Example of use of RIGID184:Example of use of RIGID184:Example of use of RIGID184:Example of use of RIGID184:A simple example of a loop meshed with BEAM188 with L-shaped cross-

section was used to verify the large-rotation capability of RIGID184. Twomodels were created, one with RIGID184, the other with CERIG (and aMASS21 element in the center of the second model), as shown on the right.These are supplied as input files “cylin184.inp” and “cylince.inp,” respectively.

The only constraint in the model is applied to the center node. A rotationabout the x-axis (in plane of page) is applied, and the resulting deformationshould be stress-free (rigid-body rotation). The results for the two cases areshown below.

As expected, the case with RIGID184 produces no stress on the BEAM188 elements (stressreported between 1e-8 and 1e-11). On the other hand, the CERIG model shows artifically highstresses up to 1e+6. The resulting deformation is also incorrect for the CERIG case. This can beexplained by the fact that constraint equations are linear relationships of rotation and translationwhich are no longer valid in the large-rotation case.

Figure 3 (RIGID184)Figure 3 (RIGID184)Figure 3 (RIGID184)Figure 3 (RIGID184) Figure 4 (CERIG)Figure 4 (CERIG)Figure 4 (CERIG)Figure 4 (CERIG)

An additional input file, “plate_rigid184.inp,” is similar to the example shown in Section 4 butusing RIGID184 instead. As the reader may find, the results are the same as with CERIG for thislinear, small-deflection situation, so this helps to validate the use of RIGID184 in modeling rigidregions.

7.7.7.7. Conclusion:Conclusion:Conclusion:Conclusion:CERIG and RBE3 provide useful tools in automatically generating complex constraint equations

for a variety of purposes. As with all features in ANSYS, however, it is important to understand someof the basic behavior, such that one can use the modeling methods correctly.

Since CEs are linear, they are valid for small-rotation problems only. Hence, the use of the 6.1beta element, RIGID184, is useful for generating rigid connections/regions in nonlinear problems.

__________________________Sheldon ImaokaANSYS, Inc.

This document is not being provided in my capacity as an ANSYS employee. I am solelyresponsible for the content.

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