2-7: Nonlinear Finite Elements in 1-D (Solution Methods - Explicit Central Difference)

Develops the procedure to solve the nonlinear time-dependent discretized equations of motion using a central difference explicit approach.

[bobbrowning]

Really great explanation here. I did want to offer two comments worth unpacking a little more.

1) The critical time step is frequently variable within the problem. This just means there should be an extra step in the loop over the elements where the time increment is computed for each element and then the minimum is used for the next step. This is necessary because nonlinearities often change the critical time increment.

2) The critical time increment is actually based on the eigenvalue of the GLOBAL mesh. The method shown here of using the shortest distance and the wave speed is well established and frequently used in many commercial codes, but it is not always conservative when compared to the theoretical value obtained from an eigenvalue analysis. Thus, the shortest distance method typically requires the time increment to be reduced by a scale factor. Common values can range from 0.5-0.9 depending on the type of problem.

Hopefully this helps anyone studying the CDM and explicit methods. Again, this was a very good introduction.

[audacityofimagineering]

Sir, @ 8:58 how do we compute the internal resistance at n = 0