clough talk history of fem

7/28/2019 Clough Talk History of FEM

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERINGInt. J. Numer. Meth. Engng 2004; 60:283287 (DOI: 10.1002/nme.962)

SPEECH BY PROFESSOR R. W. CLOUGH

Early history of the finite element method from theview point of a pioneer

I am happy to take part in WCCM V because this meeting is making it possible for me to meet

again with a number of my European structural engineering friends with whom I have been

associated for more than 40 years. During my teaching career at Berkeley, which extended from

1949 to 1987, I observed the development and growth of the field of computational mechanics

from the earliest days when the name Computational Mechanics did not yet exist, to the

present when the scope of the field is almost unlimited.

The subject of my talk, as you know, is the Early History of the Finite Element Method

(FEM). In any comprehensive discussion of this subject, four names should be mentioned, asfollows:

John H. Argyris (John) [1]

Ray W. Clough (Ray) [2]

M. J. Turner (Jon) [3]

O. C. Zienkeiwicz (Olek) [4]

They are shown here in alphabetical order to avoid establishing any sense of priority among

them. With each name, I also show a number from the reference list at the end of this paper.

For present purposes, that reference best characterizes the contribution each man has made to

FEM history, in my opinion.

At the start of this talk, I must point out that I have presented several papers on this subjectbefore, as is evident from the reference list. However, before I get into the details of the

FEM history, I think it will be useful for me to say a few words about my personal history

during that period, because it was that history which got me pointed in the direction of this

new approach to structural analysis. When I was in my final year of Civil Engineering at the

University of Washington, my structural engineering professor, Prof. C. C. More, suggested

that I should go on to Graduate School after I finished my B.S. C.E. degree. This certainly

was a new idea to me because in those days very few students went on to do graduate studies.

But Professor More made a strong case for my going to M.I.T., and he helped me prepare my

application for the M.I.T. Graduate School. Professor More had graduated from Cornell, but

for some reason he was pushing M.I.T. strongly at that time.

Within a couple of months after I had submitted my application, I was surprised and pleased

to receive notice that I had been awarded a tuition fellowship from M.I.T. for the term startingin September 1942. To have such a fellowship was very important because the tuition at M.I.T.

Correspondence to: R. W. Clough, Earthquake Engineering Research Center, University of California, 1306 South46th street, Richmond, CA 94804, U.S.A.

Received 10 May 2003

Copyright 2004 John Wiley & Sons, Ltd. Accepted 25 July 2003


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284 R. W. CLOUGH

was many times greater than the residents fee I had been paying at Washington. However, the

most important aspect of the situation at that time was that the U.S. was at war, so I had to

go to my Draft Board to request a deferment that would permit me to continue my studies

at M.I.T. I was shocked and very disappointed when the Draft Board told me they could not

defer my military service any longer just so I could go to Graduate School. In fact they saidI was lucky that already I had been deferred long enough to complete my Bachelors Degree.

After the disappointment of not being able to go to Graduate School, I took a job in the

Stress analysis unit at the Boeing Airplane Companyworking on the design of the B-47

airplane. This was a position that I was sure would keep me out of military service for the

duration of the war, and it had the additional advantage that I could continue living in my

parents home in Seattle. However, in spite of this very favourable situation, I soon began to

explore the possibilities that might be open to me in military service because I was bored

with the stress analysis job at Boeing. My first military job choice at that time was to join

the Navy Civil Engineer Corps as a Sea Bee Officer, but I was rejected from that possibility

because I could not pass the Navy eye exam. They required 20/20 vision in those days, and

I had been wearing glasses for several years. So I had to consider some other possibility, and

when I learned that the Air Force was accepting candidates for their Aviation Cadet program

in Meteorology, which did not require 20/20 vision, I decided to apply for that program. The

idea was that in about 9 months I would receive a commission as a Weather Officer, and then

would be sent to an Air Force base to predict weather for the pilots.

I was accepted as a Weather Aviation Cadet in December 1942 and was assigned to the

Weather School at the California Institute of Technology. Then in September 1943 I received

my Commission as a Weather Officer, as well as a Masters Degree in Meteorology from Cal

Tech. Rather than sending me into the field to practice the art of weather forecasting, the Air

Force decided that the best plan for me was to stay at Cal Tech to be an instructor for the next

class of weather cadets. That class was graduated in September 1944, but by that time (with five

different weather schools producing weather officers) the Air Force realized that they had far

more weather officers than they could use. So at that point they went through their personnelrecords and decided that any weather officer who already had an engineering degree could

apply for a position in the Air Force that would take advantage of that previous education. I

had never liked being a Weather Officer because I liked to do work in which I could expect

to get the right answer somewhat more than half of the time. Parenthetically, I may remark

that while I was serving as a Weather Officer, I was disappointed to note that the best forecast

I could make usually was a persistence forecastthat is to predict that tomorrows weather

will be just like todays. Of course, that was decades before weather satellites were giving

beautiful images of cloud cover over most of the surface of the earth, and I might not have

made the same decision if the tools of today were available then. In any case, I seized on the

opportunity to apply for transfer to the Air Force Aviation Engineers; and shortly thereafter I

was assigned to the 1870th Engineer Aviation Battalion and was sent to MacDill Field, Florida

for unit training.In about 4 months our unit was put on a troop ship and sent to Okinawa. Fortunately, we

had the good luck to be landing on Okinawa about the time that the Japanese surrendered.

Because of this I have always been an enthusiastic supporter of President Trumans decision to

use the atomic bombs at Hiroshima and Nagasaki. My return from Okinawa was delayed by

several months because I had not yet accumulated enough points to be eligible for discharge

from the Air Force, but finally I was shipped back to the States. Then I was able to make use

Copyright 2004 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2004; 60:283287


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EARLY HISTORY OF THE FINITE ELEMENT METHOD 285

of my tuition fellowship at M.I.T., starting in September 1946 and completing my doctorate in

June 1949. At that time I accepted a position as Assistant Professor with the Civil Engineering

Department at U.C. Berkeley.

All of this is a preamble to the subject of my talk this evening on the Early History of the

Finite Element Method. My studies at M.I.T. had included a course in Dynamics of AircraftStructures, and this fitted well with the interest of the Berkeley Civil Engineering Department

that my teaching should emphasize the dynamic response of structures to earthquake excitation.

So Earthquake Engineering became my chosen field at Berkeley. As a matter of fact, there

were no programs on that subject at any school in the United States at that time, so I had

to develop my lectures from the ground up. Also, the National Science Foundation had no

experience with providing research support in this field. In these circumstances, the closest

I could get to academic support for my work was the Boeing Summer Faculty Program, in

which Boeing would provide the equivalent of an academic salary for work that was of interest

to Boeing.

When I applied for the Boeing Summer Faculty job in June 1952, I was assigned to the

Structural Dynamics Unit under the supervision of Mr M. J. Turner. He was a very competent

engineer with a background in applied mathematics, and several years of experience with

Boeing. The job that Jon Turner had for me was the analysis of the vibration properties of a

fairly large model of a delta wing structure that had been fabricated in the Boeing shop. This

problem was quite different from the analysis of a typical wing structure which could be done

using standard beam theory, and I spent the summer of 1942 trying to formulate a mathematical

model of the delta wing representing it as an assemblage of typical 1D beam components. The

results I was able to obtain by the end of the summer were very disappointing, and I was

quite discouraged when I went to say goodbye to my boss, Jon Turner. But he suggested that

I come back in Summer 1953. In this new effort to evaluate the vibration properties of a delta

wing model, he suggested I should formulate the mathematical model as an assemblage of 2D

plate elements interconnected at their corners. With this suggestion, Jon had essentially defined

the concept of the finite element method.So I began my work in Summer 1953 developing in-plane stiffness matrices for 2D plates

with corner connections. I derived these both for rectangular and for triangular plates, but

the assembly of triangular plates had great advantages in modeling a delta wing. Moreover,

the derivation of the in-plane stiffness of a triangular plate was far simpler than that for a

rectangular plate, so very soon I shifted the emphasis of my work to the study of assemblages

of triangular plate elements, as I called them. With an assemblage of such triangular elements,

I was able to get rather good agreement between the results of a mathematical model vibration

analysis and those measured with the physical model in the laboratory. Of special interest was

the fact that the calculated results converged toward those of the physical model as the mesh

of the triangular elements in the mathematical model was refined.

It should be emphasized now that the work I was doing for Jon Turner had as its objective

the analysis of vibrations, and that objective is reflected in the title of Reference [3], whichpaper often is taken as the first paper in the history of FEM. It is of interest to note that Jon

Turner presented that paper at the annual meeting of the Institute of Aeronautical Sciences in

January 1954 but, for reasons I have never understood, it was not immediately submitted for

publication. So the 1956 publication date of the paper is nearly 3 years after the work was

done at Boeing. That work was described in the report I submitted to Jon Turner at the end

of my 1953 Summer Faculty Employment.



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286 R. W. CLOUGH

Although my Boeing summer work was never directed toward the analysis of stresses, it

was apparent that the Boeing Direct Stiffness Method could be used for stress analysis as well

as for calculating vibrations, and I decided I would investigate the stress analysis application

as soon as possible. However, because of my other research interests at Berkeley, I did not

begin to look into the stress analysis question until I went on my first sabbatical leave. Thiswas when I went to Norges Tekniske Hogskole in Trondheim, Norway in September 1956.

While I was in Norway on this leave, I became aware of the very important work that

had been done by Dr John Argyris in the field of airplane structural analysis. This work was

presented in a series of articles published in Aircraft Engineering between October 1954

and May 1955. It was published later by Butterworths of London as a single volume entitled

Energy Theorems and Structural Analysis. In my opinion, this monograph (listed here as

Reference [1]) certainly is the most important work ever written on the theory of structural

analysis, and when I read those articles during my sabbatical leave I immediately concluded

that there was no need for me to deal with the subject of Structural Analysis Theory during

my stay in Trondheim.

From my point of view, the next important event in the finite element history was my

coining the name Finite Element Method. I never thought that the name used by Boeing for

their procedure, the Direct Stiffness Method, was at all descriptive of the concept involved

in the method. So when I later wrote the stress analysis paper that is listed as Reference [2],

I had to choose a new name for the procedure. On the basis that a deflection analysis done

with these new pieces (or elements) of the structure is equivalent to the formal integration

procedure of integral calculus, I decided to call the procedure the FEM because it deals with

finite components rather than differential slices.

A red letter event that occurred during this very early history of FEM was my visiting

Northwestern University to give a seminar lecture on finite elements. When I received this

invitation from Olek Zienkiewicz, who was teaching at Northwestern at that time, I expected we

would have some arguments about the relative merits of finite elements versus finite differences

because Olek had been brought up in the tradition of Professor Southwell. It is true that wedid have some such discussions, but Olek recognized very quickly the advantages of the finite

element approach. In fact I would say that my visit to Northwestern yielded a tremendous

dividend in the conversion of Olek from finite differences to finite elements.

It should be noted that the finite element name had been established by the paper I gave at

the ASCE Conference on Electronic Computation in Pittsburgh in 1960. On the other hand, it

will be observed that the name Computational Mechanics had not yet been adopted at that

time. That first FEM paper (Reference [2]) attracted very little attention, but Reference [5],

(to which my colleague of many years at Berkeley, Professor E. L. Wilson, made a significant

contribution) did attract some attention. We presented that paper at a Symposium in Lisbon,

Portugal, and in a relatively short time the name FEM came to be in common usage. I must

emphasize here the pivotal role that Ed Wilson played in the development of FEM. When he

was working as my doctoral student in 1962, I realized that I no longer had to worry aboutthe details of computer program developmentEd was so much more effective in that part

of the work than I ever could be. So from that time on, I used the method continually to

gain understanding of the behaviour to be expected in a given structural system, but there was

no need for me to try to improve on the program development work that was being done

by Ed Wilson. His recollections of that early work are well described in his paper cited here

as Reference [6].



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EARLY HISTORY OF THE FINITE ELEMENT METHOD 287

REFERENCES

1. Argyris JH. Energy Theorems and Structural Analysis. Butterworths: Washington, DC.

2. Clough RW. The finite element method in plane stress analysis. Proceedings of the Second ASCE Conference

on Electronic Computation, Pittsburgh, PA, 1960.

3. Turner MJ, Clough RW, Martin HC, Topp L. Stiffness and deflection analysis of complex structures. Journalof Aeronautical Sciences 1956; 23.

4. Zienkiewicz OC. The Finite Element Method (3rd edn). McGraw-Hill: New York, 1977.

5. Clough RW. Stress analysis of a gravity dam by the finite element method. Proceedings of the Symposium

on the Use of Computers in Civil Engineering, Laboratorio Nacional de Engenharia Civil, Lisbon, Portugal,

1962 (see also RILEM Bull. No. 19; June 1963).

6. Wilson EL. Automation of the finite element method, a personal historical view. Finite Elements in Analysis

and Design, vol. 13. Elsevier: Amsterdam, 1993; 91104.

7. Clough RW. The finite element method in structural mechanics. Stress Analysis, Chapter 7. Wiley:

New York, 1965.

8. Clough RW. The finite element method after 25 years. In Engineering Applications of the Finite Element

Method, A. S. Computas, Det Norske Veritas, Hovik, Norway, 1979.

9. Clough RW. Original formulation of the finite element method. ASCE Structure Congress, San Francisco,

CA, May 1989 (also published in Finite Elements in Analysis and Design, vol. 10, 1990).

10. Clough RW. FEMa personal view of its original formulation (in the special volume published to celebratethe 70th Birthday of Ivar Holand, see also Proceedings of the U.S. Conference on Computational Mechanics,

Boulder, CO, 1993).

11. Clough RW. Thoughts about the original formulation of the FEMa personal view. Proceedings of the

European Conference on Computational Mechanics, Munich, 1999.


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