The Stiffness Matrix Isn’t Everything

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:

  1. Form the stiffness matrix
  2. Form the load vector
  3. 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.

  1. Form the resisting force vector
  2. Form the load vector (and residual force vector)
  3. Form the stiffness matrix
  4. 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.

2 thoughts on “The Stiffness Matrix Isn’t Everything

  1. 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.

    Liked by 1 person

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