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[LitusSaxonicum]

Nearly 50 years ago, I shared an office with a structural engineer*, who saw the following paper and asked me if I would program up the method for him. At the time, I was using the then current Swansea solver, and dealing with serendipity type numerically-integrated isoparametric elements.

The paper is:
E HINTON, JD DAVIES, A RAZZAQUE, OC ZIENKIEWICZ (1975). A Simple Finite Element Solution For Plates Of Homogenous, Sandwich And Cellular Construction. Proceedings of the Institution of Civil Engineers Volume 59 Issue 1, March 1975, pp. 43-65.

A few years ago, I dug out that old code, and bolted on some routines from a general purpose finite element graphics program of the same vintage, but with the addition of ClearWin+ graphics. At the same time I enlarged the array sizes enormously, because the original was capable of being run on a 32k word ICL 1900 series computer!

If there is anyone out there who would like a copy of the source code, including the data preparation instructions and a couple of typical datafiles, then send me a PM.

I found the solutions of some interest, as the element deals properly with shear, and thus demonstrates anticlastic bending due to the Poisson Ratio effect. Run times with very large meshes are quite quick even on a modest PC, in contrast to the dreadfully slow 1900 run times.

Eddie

*The blighter never used it, despite my considerable efforts on his behalf!

[JohnCampbell]

Hi Eddie,

I would be interested to look at the code and also a copy of the paper, if you have a scan or link.

I worked on Isoparametric 8 or 9 node shell elements at that time. This involved both deflection and rotation freedoms. They had a problem with "shear locking" as the deflection field was quadratic, but the shear field was only linear.
This was mitigated by under-integrating to release the shear field, but problems remained, especially when using these elements in dynamic analysis.

The work to prove the superiority of these elements was inconclusive, especially for non-uniform meshes that can occur in practical problems.
The appearence of unnecessary eigen modes in the element was also an annoying distraction.

The use of under-integration and extra internal deflection modes was much more effective for 3D solid elements using only deflection freedoms as the interaction of bending and shear results was not a problem in this case.

I gave up on this and went back to a 3/4-node shell, developed by Felippa from 1968, which although less accurate was more reliable for general use when used in a slightly more intense mesh.

I wonder how these problems were resolved in later element approaches, especially when using higher order field polynomials ?
A lot of these higher order elements were developed in commercial packages, where the reliability information was not as openly discussed as in 1970's.

[arctica]

Hello

I would be interested to see the structure of your plate flexure code as it will have applications within geology too! As a structural geologist we often apply plate flexure studies to crustal-scale modelling.

Thanks
Lester

[LitusSaxonicum]

Hi Lester,

If you send me a PM (private message) then I'll send you the whole shebang via WeTransfer. I used Dropbox for a long time, but they changed the way it was used and I couldn't get on with the new approach. I'd never contemplated its use in plate tectonics.

Eddie

[LitusSaxonicum]

John,

The reference is in my original post. I have a copy somewhere, but can't find it. I'll look again. I'll send you the files via WeTransfer.

Best regards

Eddie