We are getting some really interesting results from bridge monitoring for vibration - particularly at higher frequencies. We are starting to look at second order effects to explain some of the scatter in the results.
The standard structural analysis uses a first order analysis and does not allow for sway etc.. I found a neat little program in the 1973 Harrison book that does a second oder analysis. A version of the program running on VS 2017 and latest Intel Fortran is attached.
I have not seen this solution method for matrix inversion before, maybe I am missing something, but has anyone seen this solution technique before. Harrison published the book whilst he was at Sydney University in Australia, but he appears to have done the bulk of the work in the USA at Lehigh Uni - a big steel place in the late 1960s. I include the program notes. He does not explain the technique and it is different to his other programs that appear more traditional linear algebra.
My program is effectively the Harrison code with minimal changes to make it run, but the arithmetic ifs etc have not yet been cleaned out.
I would aim to pull out Harrison's solver, make it 3D and then use Pardiso and then Feast.