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# Rigid Rims, Coupling with Concentrated Masses, and Superelements

# 2.5. Rigid Rims, Coupling with Concentrated Masses, and Superelements

Extra steps are needed in both the Sierra/SM and the Sierra/SD analysis to treat parts of the mesh as rigid bodies during the Sierra/SD analysis. This section reviews those steps in the case of a Rigidset. The missing mass is accounted for by adding a concentrated mass. A similar approach for a Superelement is also described.

Suppose for example that a model has sidesets with ids \(901\) and \(902\). If sidesets \(901\) and \(902\) surround two pieces of the mesh, then the following command block will make the surfaces rigid. Although these parts are free to deform, the resulting modes are very high frequency and thus out of range of the low frequency range of interest.

    RIGIDSET set1
      sideset 901
      sideset 902
    END

It is also often effective to add the mass properties of a rigid body onto its centroid. This can be accomplished by coupling to a concentrated mass. For this, a sphere element needs to be added to the mesh file. This can be done with a tool to manipulate the mesh such as Cubit or Patran (with gjoin). The sphere can be added to the Sierra/SM input file, and it will be inactive for the first stage analysis. For the Sierra/SD portion, the following blocks would connect the concentrated mass to the rigid body.

    RIGIDSET set1
      sideset 901
      sideset 902
      centernode tiedto node 28539 block 20
    END

    BLOCK 20
      coordinate 1
      Joint2G
      kx=elastic 1.0e+10
      ky=elastic 1.0e+10
      kz=elastic 1.0e+10
      krx=elastic 1.0e+10
      kry=elastic 1.0e+10
      krz=elastic 1.0e+10
    END

    BEGIN RECTANGULAR COORDINATE SYSTEM 1
      origin 0 0 0
      z point 0 0 1
      xz point 1 0 1
    END

    BLOCK 17
      conMass
      mass 1.0e1
      Ixx 1.0e1
      Iyy 1.0e1
      Izz 1.0e1
      Ixy 0.0
      Ixz 0.0
      Iyz 0.0
      offset 0 0 0
    END

In this example, block 17 is the concentrated mass, and contains both the mass and inertial properties of the rigid body. Thus, the actual rigid body would be given zero density. Block 17 is also node 28539, and is connected to the reference node of the Rigidset through block 20 via the statement `centernode tiedto node 28539 block 20`. The reference node of the Rigidset is chosen to be the node in the Rigidset that is closest to its geometric centroid (which is computed by averaging the coordinates of the nodes in the Rigidset). Since that node will most likely not be at the same location as the concentrated mass node, block 20 will usually have a non-zero length.

We also note that in the statement `centernode tiedto node 28539 block 20`, Node 28539 must be connected to a virtual Joint2G block, in this case block 20. That is, block 20 is not part of the mesh file in Exodus, but instead is created internally in Sierra/SD during execution of the code. It is necessary that block 20 be a virtual Joint2G block, otherwise the code will die with a fatal error message. This element provides \(6\) components of elastic resistance (\(3\) translations and \(3\) rotations) between the concentrated mass and the reference node of the rigid body. As these elastic stiffnesses increase, the effect converges to a rigid bar between the pair of nodes.

This same approach can be used to couple to a Superelement in the case where the Superelement has a single interface node. In that case, the Superelement is also represented in the mesh with a sphere element, and the coupling between the Superelement and the reference node of the rigid body is specified in exactly the same manner. In this case, however, block 17 is defined to be a Superelement rather than a concentrated mass, and is given a corresponding Netcdf file that contains the reduced mass and stiffness matrices of the Superelement.

    RIGIDSET set1
      sideset 901
      sideset 902
      centernode tiedto node 28539 block 20
    END

    BLOCK 20
      coordinate 1
      Joint2G
      kx=elastic 1.0e+10
      ky=elastic 1.0e+10
      kz=elastic 1.0e+10
      krx=elastic 1.0e+10
      kry=elastic 1.0e+10
      krz=elastic 1.0e+10
    END
    BEGIN RECTANGULAR COORDINATE SYSTEM 1
       origin 0 0 0
       z point 0 0 1
       xz point 1 0 1
    END

    BLOCK 17
       Superelement
       file='superelement.ncf'
       map
         // local grid id   cid
            1            1
            1            2
            1            3
            1            4
            1            5
            1            6
            0  0
            0  0
            0  0
            0  0
            0  0
            0  0
            0  0
            0  0
            0  0
    END