Famous First Words is a recurring LabKitty feature in which we take a look at the opening line of an historic scientific article.
Finite Element Analysis (FEA) is one of the genuine Rosetta stones of engineering. Imagine drawing a thingy on your computer, then having that thingy respond as if it existed -- no mere pretty picture, but real virtual reality in space and time. You might say FEA was the lighting that rose Frankenstein CAD off the slab. With the arrival of finite elements, computer models didn't just look cool, they also behaved right -- in theory, at least -- when pulled, pushed, squished, stretched, accelerated, crushed, fractured, heated, magnetized, electrified, flowed, impacted, exploded, or gronkulated.
FEA crawled from the primordial computing ooze around the time NASA started putting meat into orbit. The punchcard era, old-timers call it and shake their heads, back when computers were as big as bread trucks and you submitted jobs to them in great stacks of meticulously formatted FORTRAN-IV like a pilgrim offering a swaddling babe to the Shrike (often with similar results). And yet, this primitive wonder of nerdcraft ate the world. Heutzutage, there's almost nothing you live in, ride on, drive over, or talk at that did not have some essential ingredient shaped by finite elements. It's an active research area in universities everywhere, not to mention a billion dollar industry employing thousands around the globe. Consider: ANSYS and ABAQUS -- both household names, in households where that sort of thing is -- and we haven't even gotten out of the As yet. These days, there's even finite element packages that run, badly, on your phone.
I know what you're thinking: It's time the Prometheus of this great fire is given his or her due!
Here we encounter trouble.
Gushing about FEA is easy; identifying an "inventor" is not. The rise of finite elements was more a job of weaving various yarns into a coherent whole rather than harvesting them de novo from the verdant soil in which yarn is grown. (Is that were yarn comes from? I have no idea. If civilization ever devolves to the point where I can't order clothes off the Internet, I will go naked.) And there was no shortage of FEA giants back in the salad days, the days of salad. Indeed, once mathematicians got hold of the method, they started retconning discovery to their elder gods. Galerkin and Feng. Hrennikoff and Courant. Rayleigh, and Ritz. Before them Euler; some even go so far as to credit Archimedes!
It is a crowded field of worthies. Yet, we seek the spark. The jumpstart. One of those saltatory leaps Thomas Kuhn goes on about. Or so I'm told. (I tried to read his book, I really did. But like James' Varieties of Religious Experience and Aurelius' Meditations I simply could not penetrate The Structure of Scientific Revolutions. If any of you liberal arts majors attempt to shame me for this tender admission, I will show you pictures of eigenvectors and make you cry.)
Galerkin and Rayleigh (and Archimedes) did not have computers to compute on, and it is that compliment that complements FEA. The Kerrigan to its Raynor, the alien to its Ripley, the peanut butter to its chocolate. A dividing of the way into that which went before from that which goes after. Yes, there were adding machines before computers, and hand solutions before those. But the arrival of programmable digital computers is what really transformed FEA from curio to Curia.
Who worked the cusp? Here, too, we find a profligate of famous names. Honorable mentions include Ciarlet, Fix, Gallager, Hinton, Irons, Melosh, Strang, and Wilson (all of whom wrote very nice FEA textbooks, IIRC). But, in keeping with my whole "weaving" analogy, three names loom large above all others: J.H. Argyris, R.W. Clough, and O.C. Zienkiewicz.
Argyris the Greek polymath. Clough the legendary Berkeley engineer. Zienkiewicz the prolific Swansea professor. They collaborated, they competed. They lived and loved, worked and played together. It would be unfair to single one out for glory. But I picked the middle guy.
Clough coined the term "finite element" (it first appeared in the title of a paper he presented at a 1960 ASCE conference). More decisively, Clough arrived at a decisive crossroads. In 1952, he participates in the Boeing Summer Faculty program as a young assistant professor. It is the height of the Red Scare, and the US Department of Defense is dumping dumptrucks full of money into advanced aircraft design. Boeing had the vision and the motivation, and now the dough, to buy a computer (back then something like $20E06 in today's dollars). Clough had a burning interest in computational mechanics, as the field would come to be called, arriving at the aerospace giant equipped with a knowledge of matrix algebra and the stiffness method. Destiny had her hand on Clough's back, and she was pushing.
The watershed publication that resulted from this perfect storm inaugurated FEA as a computational sensation ("computational" being generous -- we're talking hardware like a PDP-1). In an 11th-hour plot twist, first author on the paper is not Clough, but rather Boeing colleague M.J. Turner, then head of the structural dynamics division. Here is how they worded the arrival of a thunderclap:
The rest, as they say, is history. In the decades that follow, finite element will be deployed in the design of nuclear bombers and gravity dams and all things in between. Argyris will develop applications in fluid mechanics and elsewhere. Zienkiewicz, too, will make countless contributions, and also write the first FEA textbook (still in use today). The technique will be extended to solve problems in electromagnetics, hydrodynamics, and heat transfer. Others will absorb FEA as nothing more than a solver of partial differential equations, reconnecting these engineers' boorish FORTRAN to the method's roots in variational calculus (although we tend to think of finite element as modeling something that exists -- an airframe, a bridge, a snowglobe -- FEA is also a general numerical method for solving PDEs which need not have any real world presence, which always makes mathozoids happy.)
The fact that Turner remained in industry might explain why he never achieved the name recognition of Clough and other FEA pioneers working in academics. Esse quam videre. In a 1990 retrospective, Clough gave full-throated credit to Turner for shepherding the method through its early critical years. Thus a Rosetta stone of engineering was born.
Finite Element Analysis (FEA) is one of the genuine Rosetta stones of engineering. Imagine drawing a thingy on your computer, then having that thingy respond as if it existed -- no mere pretty picture, but real virtual reality in space and time. You might say FEA was the lighting that rose Frankenstein CAD off the slab. With the arrival of finite elements, computer models didn't just look cool, they also behaved right -- in theory, at least -- when pulled, pushed, squished, stretched, accelerated, crushed, fractured, heated, magnetized, electrified, flowed, impacted, exploded, or gronkulated.
FEA crawled from the primordial computing ooze around the time NASA started putting meat into orbit. The punchcard era, old-timers call it and shake their heads, back when computers were as big as bread trucks and you submitted jobs to them in great stacks of meticulously formatted FORTRAN-IV like a pilgrim offering a swaddling babe to the Shrike (often with similar results). And yet, this primitive wonder of nerdcraft ate the world. Heutzutage, there's almost nothing you live in, ride on, drive over, or talk at that did not have some essential ingredient shaped by finite elements. It's an active research area in universities everywhere, not to mention a billion dollar industry employing thousands around the globe. Consider: ANSYS and ABAQUS -- both household names, in households where that sort of thing is -- and we haven't even gotten out of the As yet. These days, there's even finite element packages that run, badly, on your phone.
I know what you're thinking: It's time the Prometheus of this great fire is given his or her due!
Here we encounter trouble.
Gushing about FEA is easy; identifying an "inventor" is not. The rise of finite elements was more a job of weaving various yarns into a coherent whole rather than harvesting them de novo from the verdant soil in which yarn is grown. (Is that were yarn comes from? I have no idea. If civilization ever devolves to the point where I can't order clothes off the Internet, I will go naked.) And there was no shortage of FEA giants back in the salad days, the days of salad. Indeed, once mathematicians got hold of the method, they started retconning discovery to their elder gods. Galerkin and Feng. Hrennikoff and Courant. Rayleigh, and Ritz. Before them Euler; some even go so far as to credit Archimedes!
It is a crowded field of worthies. Yet, we seek the spark. The jumpstart. One of those saltatory leaps Thomas Kuhn goes on about. Or so I'm told. (I tried to read his book, I really did. But like James' Varieties of Religious Experience and Aurelius' Meditations I simply could not penetrate The Structure of Scientific Revolutions. If any of you liberal arts majors attempt to shame me for this tender admission, I will show you pictures of eigenvectors and make you cry.)
Galerkin and Rayleigh (and Archimedes) did not have computers to compute on, and it is that compliment that complements FEA. The Kerrigan to its Raynor, the alien to its Ripley, the peanut butter to its chocolate. A dividing of the way into that which went before from that which goes after. Yes, there were adding machines before computers, and hand solutions before those. But the arrival of programmable digital computers is what really transformed FEA from curio to Curia.
Who worked the cusp? Here, too, we find a profligate of famous names. Honorable mentions include Ciarlet, Fix, Gallager, Hinton, Irons, Melosh, Strang, and Wilson (all of whom wrote very nice FEA textbooks, IIRC). But, in keeping with my whole "weaving" analogy, three names loom large above all others: J.H. Argyris, R.W. Clough, and O.C. Zienkiewicz.
Argyris the Greek polymath. Clough the legendary Berkeley engineer. Zienkiewicz the prolific Swansea professor. They collaborated, they competed. They lived and loved, worked and played together. It would be unfair to single one out for glory. But I picked the middle guy.
Clough coined the term "finite element" (it first appeared in the title of a paper he presented at a 1960 ASCE conference). More decisively, Clough arrived at a decisive crossroads. In 1952, he participates in the Boeing Summer Faculty program as a young assistant professor. It is the height of the Red Scare, and the US Department of Defense is dumping dumptrucks full of money into advanced aircraft design. Boeing had the vision and the motivation, and now the dough, to buy a computer (back then something like $20E06 in today's dollars). Clough had a burning interest in computational mechanics, as the field would come to be called, arriving at the aerospace giant equipped with a knowledge of matrix algebra and the stiffness method. Destiny had her hand on Clough's back, and she was pushing.
The watershed publication that resulted from this perfect storm inaugurated FEA as a computational sensation ("computational" being generous -- we're talking hardware like a PDP-1). In an 11th-hour plot twist, first author on the paper is not Clough, but rather Boeing colleague M.J. Turner, then head of the structural dynamics division. Here is how they worded the arrival of a thunderclap:
Present configuration trends in the design of high-speed aircraft have created a number of difficult, fundamental structural problems for the worker in aeroelasticity and structural dynamics.
Stiffness and Deflection Analysis of Complex Structures
M.J. Turner, R.W. Clough, H.C. Martin, and L.J. Topp
Journal of the Aeronautical Sciences, 23:805-823 (1956)
The rest, as they say, is history. In the decades that follow, finite element will be deployed in the design of nuclear bombers and gravity dams and all things in between. Argyris will develop applications in fluid mechanics and elsewhere. Zienkiewicz, too, will make countless contributions, and also write the first FEA textbook (still in use today). The technique will be extended to solve problems in electromagnetics, hydrodynamics, and heat transfer. Others will absorb FEA as nothing more than a solver of partial differential equations, reconnecting these engineers' boorish FORTRAN to the method's roots in variational calculus (although we tend to think of finite element as modeling something that exists -- an airframe, a bridge, a snowglobe -- FEA is also a general numerical method for solving PDEs which need not have any real world presence, which always makes mathozoids happy.)
The fact that Turner remained in industry might explain why he never achieved the name recognition of Clough and other FEA pioneers working in academics. Esse quam videre. In a 1990 retrospective, Clough gave full-throated credit to Turner for shepherding the method through its early critical years. Thus a Rosetta stone of engineering was born.
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