Instability pitfall 3

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 combination 2.ULS Live Load shows large displacements. While calculating, XFEM4U also gives you a warning. Note also the instable nodes are drawn in red.

This is a classical example though. Almost all beams are purely hinged connected.

gehele constructie.xfem (321.4 KB)

What is going on here?
Because you connected everything hinged, it is not stable in the x direction. Mathematically this means: The global stiffness matrix becomes singular, or approaches singularity and therefore cannot be solved. (The determinant of the matrix becomes zero or approaches zero.)

Ok - but how to solve it?
You can solve this by replacing the pendulum columns with moment-fixed columns. But several solutions are possible. See below and the appendix gehele constructie reply.xfem.

gehele constructie reply.xfem (321.4 KB)

Kind regards
Rob Baaij