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90°-Bending of an Elastic Strip

Tested with CGX 2.13 / CCX 2.13

This example demonstrates the application of prescribed rotations to node sets. The structure is an elastic flat strip of dimensions 100x10x1 mm³. One end is fixed and one end is rotated by 90°. The strip thus is bent into a quarter circle. We investigate the following cases:

  • Beam model
  • Shell model
  • Solid model with mean rotation constraint,
  • Solid model with rigid body constraint,
  • Solid model with coupling/distributing constraint,
  • Solid model with coupling/kinematic constraint,
Model CGX input CCX input
Beam b.fbd b.inp
Shell sh.fbd sh.inp
Solid, mean rotation MPC sm.fbd sm.inp
Solid, rigid body MPC sr.fbd sr.inp
Solid, Coupl./Distrib. scd.fbd scd.inp
Solid, Coupl./Kinem. sck.fbd sck.inp
Other files Contents
def-plot.fbd CGX input for deformation plot
view.fbd CGX input for view settings
test.py Python script to run all simulations

Reference solution

Click the image below to open a life SMath worksheet

Streifen

Beam Model

In CGX, b3 elements are specified. This results in B23R elements in the CCX input. These are internally expanded into C3D20R.

The rotation is applied as constraint to dof 5 of the node at the free end of the beam. With the default convergence control settings, only 12% of the specified rotation are reached.

> cgx -b b.fbd

The script contains the pre-processing, solution and post-processing.

Shell Model

In CGX, qu8 elements are specified. This results in S8R elements in the CCX input. These are internally expanded into C3D20R.

The rotation is applied as constraint to dof 5 of the nodes at the free end of the strip. The solution converges very well. Due to the large rotations, only invariant stress measures like v. Mises or principal stresses are useful.

> cgx -b sh.fbd

Solid Model

In CGX, he20r elements are specified. This results in C3D20R elements in the CCX input.

Mean Rotation MPC

The rotation is applied using the mean rotation multipoint constraint (MPC). This couples the mean rotation of a cloud of nodes to the first dof of a reference node. The initial position of that node indicates the axis of rotation.

In CGX, the required input for a rotation of 90° about the y-axis can be generated using the command

send rot abq mpc 90 0 1 0

This generates the files

  • rot.mpc with the ref node definition and the *mpc block (model data)
  • rot.bou with the *boundary block (step data)

Run the analysis:

> cgx -b sm.fbd

At 28% of the specified deformation, the incremental time becomes too small and the solution is stppped.

Rigid Body Constraint

The rotation is applied using a rigid body constraint. The right end is rigidly coupled to a rotation control node. In the pre-processing, it is useful to create the control node with a fixed number before meshing.

Run the analysis:

> cgx -b sr.fbd

At 74% of the specified deformation, the incremental time becomes too small and the solution is stppped.

Coupling/Distributing

The rotation is applied using surface based distributed coupling

*coupling,refnode=1,surface=Srot,constraint name=rot
*distributing
5

and

*boundary
Nrefnode,5,5,1.57

Run the analysis:

> cgx -b scd.fbd

The simulation doesn't complete a single increment.

Coupling/Kinematic

The rotation is applied using surface based kinematic coupling (with the y-displacement not coupled)

*coupling,refnode=1,surface=Srot,constraint name=rot
*kinematic
1
3

and

*boundary
Nrefnode,5,5,1.57

Run the analysis:

> cgx -b sck.fbd

At 78% of the specified deformation, the incremental time becomes too small and the solution is stopped.