Time-history analysis investigation

[madil4]

The goal is to define a mechanism where we can input signals (earthquake signals) and assign them to supports to simulate, for example, time-history analysis (dynamic analysis) for a building frame.

Here is what I imagine the app to look like:

It is exactly like the double-pendulum app but with an additional bar where the signal is graphed.

There are two challenges we want to investigate here:

1. How to compute the forces and moments for a beam element in order to use them in our explicit solver.
2. How to render the signal (probably we will use an existing library like (https://developers.google.com/chart/interactive/docs/gallery/linechart).

This issue is just an investigation, so the code can be ugly or unstructured. After we know exactly how we can do it, then we will create another issue for the actual implementation.

[madil4]

Chapter 4 of this book (A First Course in the Finite Element Method - Daryl L. Logan - 2022) explains how to compute the forces and moments for a beam. To keep it simple let's do the 2D case first without shear deformation, then we can extend the solver in other projects.