A 25-year retrospective on the finite element method

Ray Clough, emeritus professor at UC Berkeley, is credited with coining the term “finite elements” and is considered by some the father of the finite element method. At a minimum, he played a significant role in formalizing it.

In 1980, Clough published a 25-year retrospective on the finite element method, recounting his personal perspective during its early development. I consider this a classic paper and would recommend it to anyone, including non-FEM-practitioners, simply for his prescient insights into the challenges faced by numerical analysts.

Consider the following quote—every bit as relevant today as when it was published 32 years ago:

At present it probably is fair to say that the state-of-the-art has advanced to the point where solution of any structural engineering problem can be contemplated, but there may be a wide variation in the quality of the result obtained. Depending on the validity of the assumptions made in reducing the physical problem to a numerical algorithm, the computer output may provide a detailed picture of the true physical behavior or it may not even remotely resemble it. A controlling influence on where the final result lies along this scale is the skill of the engineer who prepares the mathematical idealization; when dealing with complex and unusual structures, this phase of the analysis is an art and the program cannot be treated merely as a “black box”. Because of the significant possibility that the analysis may have totally overlooked or misjudged some important aspects of the mechanical behaviour, experimental verification should be incorporated into the analytical process whenever it steps beyond the borders of experience and established practice.

This quote was a major inspiration for the name of this blog (Only A Model). It encapsulates much of what I observe to be a dramatic problem with modern engineers—an over-reliance on computers and trust of numerical results.

Check out the rest of this paper here:

Clough, Ray W., The finite element method after twenty-five years: A personal view, Computers & Structures, Volume 12, Issue 4, October 1980, Pages 361-370

(If you have trouble accessing that article, Clough wrote another article together with Ed Wilson—Early Finite Element Research at Berkeley—that covers a lot of similar history.)

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