Model stability analysis

Model stability analysis can be helpful in detecting the causes of ill conditioning in GSA models. As mentioned in model stability analysis theory, if a model is reported as being ill-conditioned in a static analysis, a model stability task can be setup and run. It is best to start with the default values of low and high stiffness modes requested. The task returns two sets of results.

• Element virtual energies that can be contoured or viewed as an output table.
• Eigenvalues of the stiffness matrix, which can be viewed from Global Results > Model stability summary in the Output explorer.

Assuming the number of low stiffness modes requested was w and high stiffness modes was h, then virtual energies for modes 1 to w represent element virtual kinetic energies whereas modes (N-h) to N represent element virtual strain energies. Here N stands for the number of degrees of freedom in the model.

Once the contours are generated, it can be seen that a handful of elements have relatively large energies (compared with other elements) in either low stiffness or high stiffness modes. These are to be viewed in conjunction with the eigenvalues reported in the Model stability summary output. The eigenvalues corresponding to low stiffness modes (the first w eigenvalues) will often have a ‘gap’ in their magnitude i.e. there is an $i < w$ such that

$$\frac{\lambda_i}{\lambda_{i+1}} \gg \frac{\lambda_{i-1}}{\lambda_i}$$

If such a gap is not found in the w smallest eigenvalues computed, the task must be modified by increasing w (say by doubling it) and executed again.

Elements with large relative virtual kinetic energies (low stiffness modes) are badly connected with the rest of the model. This can happen, for example, when beam elements are free to spin about their X axis due to insufficient restraints when moments are released or when they are connected to bars. Another common reason is when a beam is normal to the plane of a connected QUAD8 element, it does not have restraint against rotation about its axis.

Elements with large relative virtual strain energies (high stiffness modes) are ones that have disproportionately large stiffnesses compared with other elements in the model. The most common reason for this are beams with very short lengths but a large section size, which can result when a model is imported from CAD.

In both cases, the model definition in the vicinity of the elements identified needs to be examined for the presence of modelling errors. Once such errors are found and fixed, the task must be run again to ensure the condition number is below the warning threshold. Thus the analysis is an iterative procedure.

Running model stability analysis

You can run a model stability analysis by adding a new Analysis task and selecting Model stability (or Model stability P-delta).