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Thank you. Now I remember using a CDC machine at a computer place in the early 1980's before we got PC's. I used to run ULARC and AXISHELL to design steel structures for coal mines. These programs came from Powell's group at UCB. Brings back memories, we had the programs on a tape that my boss bought at UCB when he was a grad student. It included TABS, but I had a a lot of trouble getting that to run and it was not really useful.
Back to Fortran, Harrison and a few others developed elastic and plastic structures programs in the late 1960's and early 1970s. His book and papers are really helpful to understand why they did what they did. Essentially without great data they designed elastically and the ventured into plastic using Fortran. It appears that the first inverter was written by Wang in the mid 1960's I am trying to get a copy of the paper.
But the current problem is we now have great longitudinal frequency data from steel and concrete bridges, and the results mirror the interesting points that Harrison and the others raised about the problems they saw with the analysis, but lacked the data to analyze. Plus they were just getting the programs accepted.
As an aside it is sad to see civil engineering depts teaching this stuff with MatLab, you cannot design a real structure with MatLab.
The question is can we amend a Fortran program based on plastic to include strain hardening, the need is the elastic/plastic analysis on old structures has a probability of failure approaching the lower limit, the frequency data leads to this refined result, but the structures are still "ok". It has to be the strain hardening, I think.
Can I use Newton Ralphson to amend the plastic program to follow the strain hardening increase? If I use Harrison's second order analysis I can get the worst case strain e and then look for the capacity, which is greater than the plastic capacity. Or is this a waste of time?
https://caeassistant.com/product/abaqus-kinematic-hardening-1/#1674478660080-7f8862a6-aa43
Yes, it is good software, as is the European Dlubal software and Strand 7, and I have used all of them, but they do not fit inside a Monte Carlo simulation to do 2,000,000 iterations in a night for a Structural Reliability Problem. And getting the answers out can be a pain, even with Fortran. At a constant thermal strain, EI and EA are not constant with time, but linearly decreasing. Consider the structural eigenvalue equation with EI dropping with time, then the frequency drops and we are now measuring that with t-Stats in the hundreds.
But, their outline provides a path forward for this type of modelling, thanks.
From Abaqus - this is one model, which is the alternative to a simple two element linear model.
Here is a paper I just got, the opening paragraphs show the problem.
You have one day to determine the structural reliability beta for a bridge, you are not going to get there with Abaqus, if you could there would be papers on this matter and the people I work with would be discussing it.
The main structural frequency is dropping at 1500 microHz per day with a t-Stat of say 50 on the linear regression elements, we are trying to pattern match these curves. The best solution is Fortran with a special purpose program.
Hello @witwald
Is there any chance you could put up a screen shot of the 11.9 problem with the crossed braces, complete. I am interested in the elastic and second order deflection arrays, I am sorry, I do not have time to load your program in for a week or so
Yes my convergence was about 7.
it is the -5.874 that is weirdly different to Harrison's result, but the final is much closer
If I have an error I would like to track it down. Thanks
John
When I entered the program I had an error in a do loop.
Witwald's code had corrected the error and he had the correct answer. So I went through the two codes and found that I had a 1 instead of an I. I corrected it and somewhere in here thanked Witwald.
So now my answer matches your results.
Harrison published his results with the code. All the answers were correct to about three places except I kept getting -5.74 instead of the -2.74 on the initial run, but it converged to the correct result. I knew I would find the mistake sooner or later.
I went through your code yesterday, your comments explained a few things I did not fully grasp. His inverter is interesting.
Harrison used a somewhat interesting convergence check method, I put in a slightly different way of getting his answer, by simply summing the difference between new defl and old defl. And comparing to ZZ. After six iterations you get an answer that is
Total Error :: 0.00014
Allowable Error :: 0.00100
Error Ratio :: 0.13802
Harrison's convergence method check was just a little bit convoluted, using ASAT with the last column of deflections. The use of displacement's and rotation's as a joint sum is interesting because they are orders of magnitude different in magnitude.
I had put the allowable error to 1/5th of Harrison's amount as you did, but the real error is 1/6th of the new allowable.
Playing with the allowable error causes some interesting output if you go below 0.00024.
Harrison's book has a number of typographical errors. Usually they are simple to see, sometimes not, it must have been hard for the typist to transcribe all of the output.
I put in the MKL solver, it is interesting as I have not used it before. I wanted to get rid of the deflections out of the last column of the stiffness, so the problem could be simply expanded using allocates.
So thanks for the help.
The ultimate use is to put a Monte Carlo routine around the system and then feed in a range of statistical variations of member properties and loads. Then you look for the probability of failure in the statistical mess of output. It works nicely with ULARC from UCB, which is a plastic analysis package.
This comes from wanting the correct answer to what is the actual impact of strain hardening on mild steel on safety. When you get a ULARC answer for an old bridge if it is close to the limits, you know the strain hardening is still there, so I want to quantify it. Telling a client, don't worry we still have strain hardening is not a real comfort.
If we have 100 yr old bridges this starts to become an important component of the safety factor.
I was too lazy to put in Pardiso, the map of where Pardiso is located in the world is
The ten in the yellow circle in the middle of Australia is Pine Gap a joint NASA- Aussie facility, there are not many people there. Compare it to the number in Houston which has a few million people. There is some heavy duty number crunching there. Ten to one they have some Fortran compilers.
I do not use three compilers, I have used the child of the Microsoft Fortran since the late 1980's.
