Eigenvalues of the Stiffness Matrix

Students are exposed to eigenvalues and eigenvectors a few times through their structural engineering education. After the math department's obligatory treatment to sophomores with definitions, characteristic polynomials, and toy matrices, two to three years pass before students see eigenanalysis again as first year graduate students: Structural dynamics - find natural modes of vibration of a … Continue reading Eigenvalues of the Stiffness Matrix

Another Way to Get Bad Eigenvalues

With daily posts during NaBloPoMo, LBUs are highly coveted. And I'm not afraid to partake in incremental blogging. Heck, LPUs and incremental publishing seem to be de rigueur. Anyway, with zero shame, here's an insidious variation of a recent post on how to get bad eigenvalues from your OpenSees model. If negative mass can lead … Continue reading Another Way to Get Bad Eigenvalues

More Than You or Eigen Chew

Software does exactly what you tell it to do. But problems arise when you don't know--or assume you know--what instructions you're giving. For example, many people like to use the 'fullGenLapack' eigenvalue solver in OpenSees because it will compute all N eigenpairs (eigenvalue with corresponding eigenvector) for a model whereas the default eigenvalue solver will … Continue reading More Than You or Eigen Chew

Eigenvalues During an Analysis

How to compute the eigenvalues (natural periods) of a structural model during an analysis, as the stiffness changes due to yielding, unloading, reloading, large displacement, etc., is a common question. In general, periods elongate during yielding events, then shorten again upon unloading. The extent and duration of period change depends on the constitutive models and … Continue reading Eigenvalues During an Analysis

Ordinary Eigenvalues

There are three applications of eigenvalue analysis in structural engineering. Vibration analysis and buckling analysis involve generalized eigenvalue analysis. OpenSees does vibration eigenvalue analysis pretty well, but does not perform buckling eigenvalue analysis--although you might be able to fake the geometric stiffness matrix for simple frame models. The third application of eigenvalue analysis is ordinary … Continue reading Ordinary Eigenvalues

Modal Participation Factors

Computing modal participation factors (yes, I know it's a misnomer) from an OpenSees model is straightforward if you define only nodal mass with no element mass. Examples are available online showing how to compute the factors in OpenSees using Tcl, but let's go over how to do it with OpenSeesPy. After you define your model … Continue reading Modal Participation Factors