History of FEA analysis

[iainuts]

I'm working on a paper which I hope to publish and could use some help on some background information. Part of the paper concerns the history of the control volume concept as used in thermodynamics and fluid mechanics. Similarly, some history of the finite element analysis used for analyzing stress or EM fields would apply. Also, history on the development of any similar method, regardless of what it is called might also be applicable such as "free body diagrams" used for statics and dynamics or "nodal analysis" sometimes used for heat transfer.

I'd like to give credit where credit is due. I'm looking for any papers, published in peer reviewed journals, which have shown how to apply either the control volume concept, the finite element analysis concept, or similar reductionist concepts to a physical simulation. Any information on the use of these concepts is applicable, regardless of whether the paper published uses the concept to analyze stress, fluid flow, EM fields, or any other phenomenon. The important part is that the paper should show how to apply the basic concept to a computer analysis.

Thanks for your help.

 

[GregLocock]

Check out the Wiki entry for FEA and/or FEM, it has a reasonable history of the early days.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[iainuts]

Thanks for the lead, Greg.

 

[jheidt2543]

You might take a look at the extensive list of references in the book "Concepts and Applications of Finite Element Analysis" by Robert D. Cook, John Wiley & Sons, 1974. The book deals primarily with the analysis of displacement, strain and stress in structures using FEA, but the references are many and go back to the late '50s and '60s.

 

[iainuts]

Thanks jheidt.

 

[ssx]

Here is an inventor of finite element methods, Feng Kang. Most of the people here probably do not know his works in FEM.

http://en.wikipedia.org/wiki/Feng_Kang

"In the later 1950s and early 1960s, based on the computations of dam constructions, Professor Feng proposed a systematic numerical method for solving partial differential equations. The method was called Finite difference method based on variation principle. This method was also independently invented in the West, called there the finite element method. It is now considered that the invention of trhe finite element method is a milestone of computational mathematics. In 70s Professor Feng gave embedding theories in the discontinuous finite element space, and generalized classical theory on elliptic equations to various dimensional combination, which provided a mathematical foundation for elastic composite structures."

 

[iainuts]

Thanks for the info ssx. I wonder if the control volume concept or finite element/finite difference concept came first. I thought I'd read the control volume concept had begun in the 1940's. Perhaps the only difference is that control volumes typically only consider a single element whereas fea generally considers many elements - otherwise the concepts are very similar in that they are both reductionist approaches to an analysis.

 

[GregLocock]

control volumes were used in thermo from some time in the 19th century.

I don't really see why you keep mentioning them in the same breath as FE, I certainly don't see any useful parallels.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[JStephen]

I was wondering that myself, Greg- didn't know if there was some terminology I wasn't familiar with.

 

[JStephen]

Some early references from my old textbook:

D. McHenry, A lattice analogy for the solution of plane stress problems, J. Inst. Civ. Eng., 21, 59-82, 1943

A. Hrenikoff, Solution of problems in elasticity by the framework method, J. Appl. Mech., A8, 169-75, 1941

N. M. Newmark, Numerical methods of analysis in bars, plates, and elastic bodies, in Numerical Methods in Analysis in Enginering, Macmillan, 1949

J. H. Argyris, Enerty Theorems and Structural Analysis, Butterworth, 1960, reprinted from Aircraft Eng., 1954-55

 

[iainuts]

Re: why CV's and FE's in same breath, the point of the paper is more along the lines of a philisophical treatment of cause and effect or causal relationships, ie: reductionism.

One purpose of a CV is to help isolate some specific volume of space in order to apply only those causal relationships to it which affect what is inside. Similarly an FE isolates some specific volume of space in order to apply only those causal relationships which affect it.

I'd quickly agree that CV's were used initially for thermo and/or perhaps fluid dynamics whereas FE are the more modern equivalent which are applied to those phenomena and many more including EM fields, stress analysis and others. But the basic philosophy of how you can reduce some mechanism to it's bits and pieces is the same when it comes to the various methods employed, be they CV's, FE's, "free bodys", or other concepts.

I'm not really interested in what specific numeric methods are used for any given analysis or any of the actual math involved at all. Rather I'm looking for how the original idea of reducing some mechanism to it's constituent parts was started and how it was described originally such that the mathematical treatment could be applied to some volume of space. Hope that makes a bit more sense.

Thanks again for the feedback.

 

[GregLocock]

Oh, OK. Abstracting mechanisms for mathematical analysis goes back at least as far as Galileo, who, admittedly, couldn't figure out exactly how a cantilevered beam worked. I guess if he had seen a truss he would have figured it out. I'm sure there are earlier examples.







Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.