Instability pitfall 1

Instability is not always easy to recognize. In this section we try to describe the most common cases and, of course, how to solve or avoid the problems related to that computational instability.

The model below is unstable and gives large displacements (4901 mm) in y-direction. While calculating, XFEM4U also gives you a warning


rotatie.xfem (52.8 KB)

Why does this occur?
Plate elements can only handle bending moments and membrane forces but not rotational moments. It simply has to do with the type of element. In this case, a plate element. Because the rotational moment from the vertical column cannot be absorbed, the column is unstable about its axis. This can lead to strange outcomes such as here. Large node displacements in y-direction.

But how to solve that?
There are several ways. One is to constrain the rotation about the global z-axis of the top node.

rotatie1.xfem (52.8 KB)

Another way is to add an extra (dummy) beam in the plate at the base of the column. The rotation of the column is in that way prevented. The column is momentarily connected to the lower beam in the plate. And that beam redirects the forces to the nodes in the plate. So the membrane force gives that rotational rigidity to the column.

rotatie2.xfem (56.9 KB)

There are, of course, more solutions possible.

Kind regards
Rob Baaij

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