Modeling Is Always Nonlinear, but Not the Response

As a narrative device, an ellipsis omits events that are unimportant to a story and that an audience can easily understand and reconstruct if necessary.

For example, a movie montage is a narrative ellipsis. In Bull Durham, we don’t need to see every game in the Bulls’ road winning streak. We just need to see some scoreboards and the team bus, then Crash confronting Nuke over his cockiness and lack of respect for the game.

This blog is full of ellipses too. Many posts omit details of plotting and managing OpenSees results in order to stay focused on the modeling issue or verification at hand.

And if we drill down further, when stringing a few words together, ellipses help avoid redundancy where the reader can easily fill in the meaning. For example, the title of this post is an ellipsis because I expect you to fill in the gap on “Response”.

But sometimes, when striving for efficiency of words, an ellipsis can present a different meaning to the reader. Consider the following hypothetical title:

Nonlinear Modeling of Reinforced Concrete Moment Frames

Within our niche domain, this title is generally understood to mean “Modeling the Nonlinear Response of Reinforced Concrete Moment Frames”, which is explicit in “Nonlinear” referring to the “Response”. The ellipsis’s removal of “Response” from the title forces the reader to attach “Nonlinear” to “Modeling”, leading to a less precise meaning. Readers from outside our domain could be confused.

And if you want to double down on imprecise ellipses, add “Fiber Elements” to the title.

But anyway, maybe “Nonlinear Modeling …” is not an ellipsis at all. As a process, modeling the response of reinforced concrete moment frames–or any structural system–is never a straight path from start to finish, even if the model response is linear. It is impossible to make one pass through nodes, materials, sections, elements, loads, and analyses and arrive at reasonable results. You spend one hour building the model and ten hours debugging one small mistake.

So, yes, modeling is always nonlinear.