Rigid-body Element for Stress Analysis

1. Introduction

The "rigid-body" element couples the displacement and the rotational degrees-of-freedom of one or several slave nodes with the displacement and rotational degrees-of-freedom of the master node in such a way that this corresponds to a rigid-body motion.

2. MDL Syntax

Because the number of connected nodes is not fixed, the element connectivity has to be enclosed by square brackets "[" and "]". The master node is specified first, followed by the slave nodes. For mesh-independent definitions, the slave nodes can be specified by means of nodesets.

elements
  ...
  type RBE element-id "[" master-node-id
    [dof slave-dofsnodeset nodeset-id
    [dof slave-dofsepatch epatch-id e1-e12|f1-f7|b
    [dof slave-dofsslave-node-id
    ...
  "]"
  ...
end

The degrees-of-freedom of the slave nodes to be coupled can be specified optionally, by means of the dof option. It takes an integer number which contains the digits 1-6, corresponding to the UX, UY, UZ, RX, RY, RZ degrees-of-freedom. For example, 123 means all displacement degrees-of-freedom, and 123456 means all displacement and rotation degrees-of-freedom. The default (123456) will be applied, unless dof is specified. Once set, the specified dof will be applied to any subsequent slave nodes until a new dof option is given.

3. Example

In this example, the use of the dof and of nodesets is illustrated on a cylindrical shell made of aluminium with a radius of 2 m , a length of 10 m and a thickness of 2.5 mm. The axis of the cylinder coincides with the z-direction. Both ends are connected to an RBE element. One end is fixed, while an axial force is applied to the other end.

Cylinder mesh and one of the two RBE elements.

Figure 39. Cylinder mesh and one of the two RBE elements.


The MDL input file is the following:

epatch 1
  geometry cylinder
  radius 2.0 thickness 0.0025 phi1 0.0 phi2 360.0 length 10.0
  local all
  ne1 72
  ne2 50
  eltype Q9.S.MITC
  mid 1
end

material 1 type isotropic
  # Aluminium 2024-T3
  e 72.4e9
  nu 0.33
  density 2800.
  alpha 22.8e-6 # [1/K]
  failure von_mises
    r 138e6
    filter max_of_element
  end
end

nodes
  100000 0. 0.  0.
  100001 0. 0. 10.
end

elements
  type RBE
  100000 [100000  dof 23456  epatch 1 e1]
  100001 [100001  dof 23456  epatch 1 e3]
end

ebc 1
  dof [UX UY UZ RX RY RZ] value 0. node 100000
end

nbc 1
  dof FZ value -1e6 node 100001
end

case 1
  analysis  linear
  ebc       1
  nbc       1
  gradients 1
end

adir
  cases 1
end

The epatch command is used to generate a cylindrical mesh, here with Q9.S.MITC shell elements. The option local all generates local reference frames for all nodes, with the first direction aligned with the radial direction.

When defined like this, the nodes move freely in the radial direction. Alternatively, the RBE elements can be specified such that the radial displacements of the slaves are fixed:

elements
  type RBE
  100000 [100000  dof 123456  epatch 1 e1]
  100001 [100001  dof 123456  epatch 1 e3]
end

The displacement field is compared for the two models in the following figure.

Axially-compressed cylinder (linear analysis, deformations are amplified). Left: The radial displacement dof's are not coupled. Right: All slave dof's are coupled.

Figure 40. Axially-compressed cylinder (linear analysis, deformations are amplified). Left: The radial displacement dof's are not coupled. Right: All slave dof's are coupled.