After several deliveries of graduate level courses in linear and nonlinear structural analysis, I have started to think that we over-emphasize the stiffness matrix in linear structural analysis. And this emphasis can lead to conceptual difficulties in nonlinear structural analysis.
The steps to a linear analysis are presented as:
- Form the stiffness matrix
- Form the load vector
- Solve for the nodal displacements
Done. You can traverse the stiffness matrix hyperplane at will and find the nodal displacements for any load vector.
When analyzing a linear model in a nonlinear framework, where the residual force vector is the main concept instead of the stiffness matrix, the steps are a little different.
- Form the resisting force vector
- Form the load vector (and residual force vector)
- Form the stiffness matrix
- Solve for the nodal displacements
If you put these steps in a loop, nonlinear analysis is simple.
This YouTube video shows what I mean.
Making videos is HARD! This video took (only) three tries. I typed up the PDF in the video after failing miserably with a blank screen on the first try and losing the point I was trying to make on the second try. I much prefer written content.
Check out Dr. Silvia Mazzoni’s channel for many informative OpenSees videos.
Portwood Digital 
Nice! I too like videos where I have some written scaffolding to start from, and just annotate in key ideas rather than drawing everything from scratch. It’s easier for my thinking, and I think easier for the students to see the key ideas.
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Agreed. Thanks, Jack!
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