[★★★★☆] Bending of A Cantilever Beam
In this example, we show the application of 3D beam elements B31
and F31
with corotational
transformation B3DC
.
The model can be downloaded.
The Model
A simple cantilever beam is bent at the free end. Since the load and displacements are normalised, geometry does not
affect results. Here we simply choose the following parameters: beam length
Here five elements are used. Consequently, six nodes shall be defined.
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The Rectangle3D
section can be used.
Assuming the beam is in the
Now define the elements. Replacing F31
with B31
to use displacement based elements.
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It is known from the beam theory that a perfect circle would be formed if the free end is applied with an out-of-plane
moment of magnitude
Next, we apply boundary condition and load, define recorders to record free end displacements.
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It shall be noted since nonlinear geometry is adopted, the stiffness may not be symmetric anymore, it is necessary to switch off symmetric matrix storage to ensure correct results are computed. Since not all nonlinear geometry problems are asymmetric, the program itself has no mechanism to check if it is appropriate to use symmetric/asymmetric storage.
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Results
Normalised displacement components are shown in the following figure.
Since VTK does not have a proper cell type for beams, linear lines are used to represent beams. Here is the animation of deformation.