Saturday, April 29, 2006

1998 Timoshenko Medal Lecture by Olgierd C. Zienkiewicz


AS I REMEMBER
by O. C. Zienkiewicz, University of Wales, Swansea

The text of the Timoshenko Medal Acceptance Speech delivered at the Applied Mechanics Dinner of the 1998 IMECE in Anaheim, California.

1. Introduction
It is a great pleasure and honour to be included in the distinguished list of recipients of the Stephen Timoshenko Medal. I would like to take this opportunity to thank the American Society of Mechanical Engineers and the various friends I have in it who must have been responsible for my selection.

Because of my age and my long involvement in the field I know personally, or have known, more than half of the previous recipients of this award. Indeed, the very first recipient and namesake of the award, Stephen Timoshenko, was one of these. We met in 1960 at Northwestern University when he visited one of his early doctoral students, much distinguished in the field, Professor Nick Hetenyi. Both of these acquaintances are now gone, having worked long and contributed much to the subject of applied mechanics. In the long list of recipients, now departed, I find my own Ph.D. supervisor, Sir Richard Southwe1l, and an old adviser and friend, Professor William Prager. Amongst those no longer here is another friend, James Lighthill. Though he received his medal as early as 1963, he was still healthy and fit this year. But many may not know that it is only a few months ago that he met his end – trying to swim round the Island of Sark in the Channel islands, a feat much younger men would not attempt and which he, using his knowledge of the tides, previously accomplished more than once. I salute his courage and achievements.

2. Timoshenko: teaching and research
Though my first personal encounter with Stephen was in 1960, he was well known to me by that time. In my Ph.D. studies, which started in 1943, his book on Theory of Elasticity became my bible. At the outset of my study with Professors Pippard and Southwell I had to acquaint myself with the earlier numerical solutions produced in 1910 by J. F. Richardson. As that work used the Airy stress function to formulate the solution, some introduction to elasticity was clearly necessary. I had many gaps in my knowledge having just completed the very brief, two-year, wartime degree at Imperial College. Therefore, after some unsuccessful encounters with various texts I followed the recommendation of a senior colleague and invested in Timoshenko’s famous book, which today still holds a privileged place in my library. That text solved my problem completely. In the first two chapters I found all that was needed and it was only his excellent presentation which made me read further.

This episode - and indeed later contact with the works of Timoshenko - made two important impressions on me. First, I realised that even quite complex ideas could be presented in a lucid form. This was most helpful to me later when I was compiling my own first book on the finite element method. Of course this was some 20 years later, but I have always tried to follow the master by avoiding the alternative process, very popular among some scientific writers. They follow the maxim quite probably coined by a German philosopher, which simply said: “Warum einfach machen wenn man auch kompliziert sein kann.”

Second, which perhaps took me longer to realise, was the fact that good teaching cannot be practised properly without underlying research. Certainly the example of Timoshenko provided an example for me when I became a young teacher.

The conflict between the two directions of teaching and research, still much discussed in Academia, was originally the subject that I wanted to discuss in this talk - but, enough has been said on this matter. It was after reading Timoshenko’s autobiography that I changed my mind and in true “plagiaristic” spirit I adopted his title for the present talk – “As I Remember”. This will allow me (1) to reminisce a little on my own origins and (2) to discuss the development of my own research and how this led to my present involvement with the finite element method.

3. As I remember - the linking of life's strands
Timoshenko’s autobiography was written in Paris in 1963 and was translated into English with his help five years later when he reached the ripe old age of 90. Reading this book was a most interesting experience, especially when I realised that our own life’s strands were interlinked and even intersected on many occasions. Timoshenko was born in the Ukraine in 1878, five years after the birth of my father. The places of their birth, as far as I can trace from the available atlases, were about 100 miles apart and each a similar distance from Kiev. Both of them were citizens of Imperial Russia at the time of their birth, but their nationalities were different. Timoshenko was basically Ukrainian and my father was Polish - both facts quite well recognized at that time when nationalities and citizenships were separate entities.

Though my father was a lawyer and Timoshenko an engineer, it is interesting to speculate whether their paths at one time or another crossed. Certainly, for a limited period both of them lived in Kiev and it is also certain that during later years both were much involved with St. Petersburg where, after the Revolution, the first liberal, provisional government in Russia was formed under the premiership of Kerenski.

It was during that provisional government time that the divergence of their paths occurred. My father, perhaps because of his English wife and knowledge of the English language, was chosen to be the Consul in England of Kerenski’s provisional Russian government. However, my father was stranded and started a new life when the Bolshevik revolution erupted in Russia. It was in England that both my sister and I were born. Timoshenko, on the other hand, left Russia by a completely different route. This led him later, via Turkey and Serbia to Zagreb in Croatia where he became a professor at the Technical University for some time, before moving finally to the U.S.A. in 1922.

Those who read his autobiography will find full details of the adventures of his life at that time, and the story of his rise to fame in the American continent and indeed in Europe. He first established his position firmly as an engineer and teacher at Westinghouse, then became a professor at the University of Michigan in Ann Arbor in 1927. Finally, in 1936 he reached Stanford University. The Chair he held there became his last permanent employment although he finished his life in Switzerland - a country he had much loved in his younger days.

So how did our life strands interlink again? Well, I have already mentioned the importance of his text in producing my doctoral work under Professors Pippard and Southwell. It is through the work of the latter that the connection will arise again. Professor (later Sir) Richard Southwell was, at the time of my doctorate studies, leading a research team concerned with the solution of finite difference equations in elasticity for various problems of realistic application. Indeed many of these problems were concerned with the war effort and therefore confidential. Others were not - like my own analysis of a dam - though the methodology was not publishable during the war. Even the proceedings of the Royal Society were at that time “confidential”. It was then that I acquired a general interest, not only in elasticity, but also in fluid mechanics, which to Sir Richard presented just one more problem to be dealt with by a general numerical procedure.

It happened that Southwell was one of Timoshenko’s guests at the University of Michigan as early as 1935. This in turn led to a later encounter after the war in 1949 and again at Ann Arbor. At Timoshenko’s invitation both were involved in a summer course and this meeting was to be more important. Certainly Timoshenko was always the engineer, and being at that stage engaged in the quantitative solution of problems, he was much impressed by the generality which was established by using numerical, finite difference solutions. I believe this caused him to write an extensive appendix when the second edition of his book on Theory of Elasticity, now co-authored by J. N. Goodier, appeared in 1951. This appendix included a full description of Southwell’s procedures and solutions. He remained at all times a protagonist of numerical solutions, and it was here that our interests began to overlap.

4. The engineering beginnings of numerical analysis
The first finite difference solutions of equations of elasticity dated back to the work of Runge in 1908 and Richardson in 1910. The latter indeed solved the problem of stress distribution in a gravity dam, a subject of much interest at the time in view of the construction of the Aswan Dam in Egypt. Indeed, during the same period, inconsistencies and difficulties of using standard, “cantilever” approximations were realised and a true elastic solution was obviously needed to settle the controversy.

As Southwell’s relaxation methods were available, Professor Pippard - my doctoral Supervisor - set me the goal of providing a very accurate answer to the above question. I was eventually successful and in 1945 I duly handed in my thesis solving that problem, as well as others on meshes very much finer than those initially used by Richardson. The success was due to the use of relaxation methods, but why were they so successful and where-in lay their magic?

It is my belief that the ideas introduced by Southwell, which were of considerable importance, could be summarised as:

  1. The recognition that the finite difference equations could be made equivalent to an analogous discrete structural system, and
  2. The solution of the structural discrete system could be performed most efficiently by an iterative process.

As is well known, discrete structural systems, which provide the basic work for all civil, aeronautical and structural engineers, can be formulated using either the so-called “displacement” method or the “force” method. The first of these methods is obvious and direct, though it is well known that the second (the force method) is also useful in many simple cases of redundant structures for which it provides an economical and elegant solution. It is difficult to say who first formulated the direct displacement (or direct stiffness) approach. Certainly the method was well known at the beginning of this century and certainly it was included in the education of engineers in the 1930’s. In this approach stiffness coefficients were obtained for each element of the structure and the system equation was obtained by a simple addition of such coefficients. Matrix ideas were useful in this process and certainly provided a shorthand. They were not, however, essential to the understanding or indeed to the solution of the equations. Fraser, Duncan and Collar in the 1930’s appeared to be the first to use matrices for such problems in structural engineering in the aeronautical industry.

The procedures used in the direct stiffness approach were precisely the same for many other engineering systems, typically those that occurred in the solution of pipe network systems or electric networks. In each of these exactly the same formulation applied and in all cases the procedures were the same. It is therefore worthwhile to talk about a standard discrete system in this context and we observe in the literature a rapid diffusion of ideas from one area of application to another.

Southwell’s method of relaxation used for iterative solution of structures, or similar problems formulated in a discrete system, was a procedure he named “systematic relaxation of constraints” in 1934. In this process, each “nodal” displacement or similar system quantity was first assumed to be fixed in an arbitrary position by imaginary constraints (which he often described as “jacks”). On “relaxing” of such a constraint by removing the “jack”, the load was transferred to adjacent nodes and the node in question then was displaced by an amount which was easily calculable. Obviously, in the continuing process of constraint relaxation the load transfer in the structure would ultimately lead to correct solutions when all the load was thus transferred to the supports.

Mathematically, of course, the procedure was carried out in a sequence similar to that of the Gauss-Seidel iteration, but in a manner guided by the user. However, the physical interpretation of the process made it very understandable and such methods as moving a whole group of nodes simultaneously etc. could be used effectually by an intelligent operator to accelerate convergence.

The “structural” relaxation procedure of the Southwell type was apparently used as early as 1922 in Zagreb by a man called Calisev, (viz. Timoshenko). However, much more important was the development of the so-called “method of moment distribution” by Hardy Cross in the U.S.A. in 1932. This preceded the Southwell process by only two years but the Hardy Cross Method gained fame internationally and became the standard process for solution of framed buildings, etc. in the 1930’s and 1940’s.

It is of interest to make a marginal remark that there is a good reason for the success of the Hardy Cross moment distribution method vis-à-vis the Southwell relaxation method then applied to tension bar structures. The “carry over” factor in bending computations was one half rather than unity in bar structures and this of course led to a very much more rapid convergence.

When Southwell entered the area of finite difference computations he generally endowed the discrete equations with a structural interpretation. Thus the Poisson equation, which was well known could represent the deformation of stretched membrane, became in the finite difference net the deformation of a string net with given tensions. The string net being a simple structure could of course be solved by precisely thesame procedures as Southwell applied earlier to actual discrete structures and thus the Systematic Relaxation Constraints of 1934 could be used again.

It is of interest to note that such a physical interpretation of finite difference equations, when used for elasticity, was simultaneously and independently derived in the U.S.A. The conditions of wartime secrecy and the resulting restrictions on exchange of documents prevented Southwell’s work with this being widely known there. However, two important developments were derived in the U.S.A. The first one was arrived at by Hrenikoff who in 1941 established a so-called framework analogy to the finite difference equations of elasticity, and the second was arrived at by McHenry who in 1943 presented the lattice analogy. Clearly engineers liked this physical manner of interpreting equations which also simplified boundary conditions which were now purely physical. These analogue procedures were the precursor of the concept of finite elements.

In the classic paper of 1956, Turner, Clough, Martin and Topp presented the idea of dividing the real continuum directly into elements of arbitrary shape and directly establishing their stiffness. This became known as the method of Finite Elements only in 1960, following a paper presented by Ray Clough. In the original work very explicit physical models were used, thus completely avoiding the writing down of either finite difference or differential equations.

Much later the finite element method was to become based on the use of variational or weighted residual procedures of Galerkin type applied directly to the differential equations used to model rationally the elements of a continuum. Though most engineers applied this initially to the elasticity equations, it must be remarked that Courant did this much earlier in 1943 - i.e. precisely when Southwell, Hrenikoff and McHenry were active. In his work he showed that such direct procedures could be used for the Poisson equation. Courant introduced what is essentially the same linear triangle as that derived in 1956. Being, however, a mathematician he did not see the need nor did he have the desire to seek a physical interpretation.This perhaps accounts for the fact that his work was only unearthed several years after the mainstream engineers had been happily using the finite element procedure for solving their structural problems.

5. Is F.E.M.'s success due to its intuitive appeal or its generality?
There is no doubt that it is the intuitive appeal of the finite element process which makes it so popular today. When in the late 1950s I met Ray Clough and for the first time encountered his idea of splitting a continuum into “physical lumps”, the procedure did not appeal to me. Surely it all could be done more precisely and conveniently with finite processes I learned from Southwell and used successfully over many years? We did, however, agree that one problem remained which needed solution. That problem was the analysis of shells of arbitrary shape as these were much encountered at the time in the design of arch dams and in architectural flights of fancy.

The twin difficulties of the finite difference approach that I had been using were: (a) deciding which set of governing equations to use. Here the choice was wide with many authors contributing different approximations, and (b) establishing analytically the co-ordinates of an arbitrary shell in which the governing equations were to be approximated.

Both Ray and I agreed that here the finite element approach could well be used, employing as elements flat facets of a triangular or rectangular shape with the former of course being needed for arbitrary shells. In such a manner both difficulties could be simultaneously avoided.

For such a finite element formulation the “inplane” stiffnesses were already well established and surely the corresponding bending stiffnesses based on the Kirchhoff thin plate theory could easily be added.

It was on these problems that Ray’s and my own research students spent much time during the early 1960’s. By 1965 both of the groups were successful and found suitable formulations for triangular plates. Two years later they established the possibility, and indeed were successful in solving arbitrarily shaped shells. The thin shell modelling by flat facets proved convergent despite a few variational crimes committed on the way, but both the problem and its solution were overtaken by events which occurred in parallel.

My colleague, Bruce Irons, and myself also developed in 1965 the first three-dimensional solution using higher order elements, which could be curved by an isoparametric mapping to fit almost any shape. Clearly, by making such elements thin, any curved shell or plate could be modelled without introducing the super-human efforts needed to establish Cl continuity or the necessity of introducing thin plate and shell theory assumptions.

This development resulted in the fact that by the end of the decade the thin plate and shell problem disappeared, being today largely of historical interest. But many difficulties still were encountered in establishing a robust formulation. I shall not dwell on them except to say that by the mid-1980s all of these were overcome.

Did intuition or mathematics drive the second development to success? Who knows? But without the proper and precise use of mathematics the present case of dealing with thin wall structures would not exist. Further, the developments of rational approaches to such new fields as those of fluid mechanics, electro-magnetism, etc. would not be possible. Which way should we direct our research now ?

6. Which way now?
It is recognised by many that the finite element process of today is but a particular form of the weighted residual approach. The latter was classified well by Stephen Crandall in his excellent book of 1955, though the fundamentals were established by Galerkin somewhat earlier in 1915. (This occurred I believe in St. Petersburg and must have coincided with the time Stephen Timoshenko was there!)

The difference between the various approximation procedures that are today still used is that of the specific trial or weighting functions that are employed. Much of the research done today centres on finding better, newer, and more efficient designs.

Von Karman said:

The Scientist studies what is, the engineer creates what has never been.

Surely this requires more efficient analysis procedures to design what “never has been”.

Charles H. Duell, commissioner of U.S. Office of Patents in 1899 mentioned at the time that

Everything that can be invented has been invented.

I do not share this pessimistic view and I think we shall see many exciting developments in the coming years. It is evident that both applied mechanicians and mathematicians will continue to contribute to the numerical analysis field.

However, I have reservations about making predictions for the future, especially since in public speeches these may lead to such mistakes as the famous one of Thomas Watson, Chairman of IBM in 1943. His prediction was that

I think there is a world market for maybe five computers.

. . . . probably more than a trivial miscalculation.

This could only be rivalled, however, by a statement by the famous British scientist, Lord Kelvin, who was the President of the Royal Society in 1895 and apparently said:

Heavier-than-air flying machines are impossible. ”

Perhaps silence on matters of predicting the future is golden – and here I shall rest.

Monday, April 24, 2006

Ranking of Mechanics Related Journals (2004)

Based on a survey from Journal Citation Report (JCR),
we listed below the 2004 Journal Impact Factors (IF) for some
mechanics and materials related scientific journals.
Our list and information are not complete. We welcome
readers' input, comments, and information.
We also caution readers that using IF as the sole criterion to rank scientific journals' academic reputation may not be objective nor true to a journal's actual scientific merits.

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1. Nature : 32.182
2. Science : 31.853
3. Solid State Phys. : 16.000
4. Nature Materials : 13.531
5. Nano Letters: 8.449
6. Physical Review Letters: 7.218
7. Advanced Materials: 6.801
8. ANNU REV FLUID MECH :6.694
9. Applied Physics Letters: 4.308
10. ADV APPL MECH : 4.000
11. INT J PLASTICITY: 3.819
12. Acta Materialia: 3.49
13. Physical Review B: 3.49
14. MRS Bulletin: 3.444
15. J MECH PHYS SOLIDS : 3.443
16. Physical Review A: 2.902
17. J RHEOL :2.525
18. Geophysical Research Letters: 2.378
19. Journal of Applied Physics: 2.255
20. J MICROMECH MICROENG : 2.048
21. Geophysical Journal International: 2.014
22. J. Biomechanics: 1.911
23. GRANUL MATTER : 1.897
24. J NON-NEWTON FLUID : 1.862
25. J FLUID MECH : 1.853
26. J NONLINEAR SCI : 1.850
27. ARCH RATION MECH AN : 1.769
28. PHYS FLUIDS : 1.761
29. Journal of Crystal Growth: 1.707
30. RHEOL ACTA : 1.558
31. MECH MATER : 1.512
32. Int. J. Numer. Meth. Eng. 1.501
33. J. Acoust. Soc. AM: 1.482
34. INT APPL MECH+ : 1.427
35. INT J MULTIPHAS FLOW : 1.383
36. INT J SOLIDS STRUCT: 1.378
37. PHILOS MAG B : 1.343
38. Proc. Royal Soc. London, A: 1.325
39. ENG FRACT MECH : 1.299
40. J. Biomech. Eng-T ASME: 1.290
41. COMPUT METHOD APPL M : 1.263
42. INT J HEAT MASS TRAN : 1.220
43. Archiv. Comput. Meth. Eng. :1.182
44. PHILOS MAG : 1.167
45. COMPUT FLUIDS : 1.164
46. Geophysics: 1.087
47. Int. J. Eng. Sci. :1.065
48. J TURBUL : 1.062
49. J APPL MECH-T ASME : 1.012
50. INT J NONLINEAR MECH : 1.004
51. INT J HEAT FLUID FL : 0.988
52. THEOR COMP FLUID DYN : 0.957
53. EXP MECH : 0.954
54. INT J FRACTURE : 0.950
55. J ADHES SCI TECHNOL : 0.937
56. EUR J MECH B-FLUID : 0.930
57. MECH TIME-DEPEND MAT : 0.926
58. INT J MECH SCI : 0.906
59. WAVE MOTION : 0.902
60. Int. J. Fatigue: 0.874
61. EUR J MECH A-SOLID : 0.862
62. Quarterly Applied Math.:0.852
63. EXP FLUIDS : 0.851
64. INT J THERMOPHYS :0.846
65. CONTINUUM MECH THERM : 0.838
66. GEOPHYS ASTRO FLUID : 0.829
67. J SOUND VIB : 0.828
68. J Eng. Mater-T ASME: 0.819
69. THEOR APPL FRACT MEC : 0.806
70. STRUCT MULTIDISCIP O : 0.803
71. ENERG CONVERS MANAGE : 0.794
72. NONLINEAR DYNAM : 0.774
73. COMPUT MECH : 0.764
74. INT J NUMER ANAL MET : 0.758
75. J ENG Mech-ASCE: 0.743
76. KOREA-AUST RHEOL J : 0.727
77. ACTA MECH SINICA : 0.719
78. J COMPOS CONSTR : 0.712
79. OPEN SYST INF DYN : 0.702
80. Q J MECH APPL MATH : 0.701
81. J VIB ACOUST : 0.694
82. J THERM STRESSES : 0.692
83. Fatigue & Frac. Eng. Mater. Stru.: 0.673
84. FINITE ELEM ANAL DES : 0.620
85. FLUID DYN RES : 0.620
86. J NON-EQUIL THERMODY : 0.619
87. APPL MATH MODEL : 0.617
88. MULTIBODY SYST DYN : 0.610
89. MATH MECH SOLIDS : 0.609
90. NUMER HEAT TR B-FUND : 0.598
91. APPL THERM ENG: 0.596
92. J FLUID STRUCT : 0.590
93. INT J IMPACT ENG: 0.588
94. PROBABILIST ENG MECH : 0.554
95. ACTA MECH : 0.546
96. Zeitsch. fur angew. Math. und Phy. (ZAMP):0.546
97. J STRAIN ANAL ENG : 0.545
98. NUMER HEAT TR A-APPL: 0.524
99. MECH RES COMMUN : 0.522
100. ARCH APPL MECH : 0.514
101. INT J DAMAGE MECH : 0.514
102. J VIB CONTROL : 0.508
103. J ADHESION : 0.505
104. J WIND ENG IND AEROD : 0.500
105. MECH STRUCT MACH : 0.500
106. INT J COMPUT FLUID D : 0.485
107. INT J NONLINEAR SCI : 0.483
108. INT J NUMER METH FL : 0.476
109. Comm. in Num. Meth. in Eng.:0.476
110. INT COMMUN HEAT MASS: 0.441
111. J. of Applied Biomechanics: 0.438
112. J ELASTICITY : 0.433
113. Z. Angew Math Mech (ZAMM): 0.433
114. Quarterly Journal of Mathematics 0.408
115. Journal of Ship Research 0.388
116. Meccanica: 0.371
117. Int. J. of Num. Meth. for Heat & Fluid Flow 0.358
118. Int. J. of Appl. Electromagne. Mech. 0.348
119. Acta Mechanica Solida Sinica 0.341
120. Mech. Compos. Mater.: 0.331
121. Shock Waves: 0.312
122. Engineering Computation 0.295
123. CR Mecanique: 2.93
124. Dokl. Phys. : 0.291
125. Appl. Math. Mech-Engl
126. JSME Int. J. A-Solid Mech. Mater. Engin. 0.205
127. Engineering Failure Analysis 0.202
128. PMM-J. Appl. Math. Mech. : 0.200
129. JSME Int. J. --B -Fluids and Therm. Engin. 0.141
130. Sound Vib. : 0.137

THE MOST CITED SCIENTIFIC PAPERS IN SOLID AND COMPUTATIONAL MECHANICS

Based on a survey of Web of Science, we compiled a list of papers that are
``THE MOST CITED SCIENTIFIC PAPERS IN SOLID AND COMPUTATIONAL MECHANICS PUBLISHED IN THE 20th CENTURY''.

The paper making the list must be: (1) in the areas of solid mechanics, mechanics of materials, or computational mechanics, and (2) it has at least 1000 citations.

First, since the citation is a dynamic process, both the entry and the order of this list may change from time to time. Second, this list may not be complete, if anyone finds a missing entry, please inform us, and we should include it immediately.
The survey is up to April 24, 2006, and we should keep it updated once every two months.

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(1) ESHELBY JD,
The determination of the elastic field of an ellipsoidal inclusion, and related problems,
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES 241 (1226): 376-396, 1957. Times Cited: 3781

(2) WILLIAMS ML
Mechanical properties of substances of high molecular weight .19. The temperature dependence of relaxation mechanism in amorphous polymers and other glass-forming liquids.
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 77(14), 3701-3707, 1955. Times Cited: 3103

(3) GRIFFITH AA
The phenomena of rupture and flow in solids,
Philosophical Transactions of the Royal Society of London, Sereis A, 221:163-198, 1921. Times Cited: 2646

(4) MATTHEWS JW and BLAKESLEE AE
Defects and epitaxial multilayers: 1. Misfit dislocations,
JOURNAL OF CRYSTAL GROWTH 27 (DEC): 118-125, 1974. Times Cited 2426

(5) TAYLOR GI
Dispersion of soluble matter in solvent flowing slowly through a tube.
PROCEEDINGS OF ROYAL SOCIETY OF LONDON, A. 219, 187-203, 1953. Times Cited: 2232

(6) RICE JR
A path independent integral and approximate analysis of strain
concentration by notches and cracks,
JOURNAL OF APPLIED MECHANICS 35 (2): 379-386, 1968. Times Cited: 2032

(7) Taylor GI
Plastic strain in metals
JOURNAL OF THE INSTITUTE OF METALS 62: 307-324, 1938. Times Cited: 1753

(8) DUGDALE DS
Yielding of steel sheets containing slits,
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 8 (2): 100-104, 1960. Times Cited: 1688

(9) BIOT MA ,
Theory of propagation of elastic waves in a fluid-saturated porous solid. 1. Low-frequency range, JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 28 (2): 168-178, 1956.
Times Cited: 1638

(10) MINDLIN RD,
Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates,
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME 18 (1): 31-38, 1951.
Times Cited: 1410

(11) Biot MA
General theory of three-dimensional consolidation
Source: JOURNAL OF APPLIED PHYSICS 12 (2): 155-164, FEB 1941. Times Cited: 1392

(12) ESHELBY JD,
The continuum theory of lattice defects,
SOLID STATE PHYSICS-ADVANCES IN RESEARCH AND APPLICATIONS 3: 79-144, 1956.
Times Cited: 1209

(13) RICE JR, ROSENGRE GF
Plane strain deformation near a crack tip in a power-law hardening material,
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 16 (1): 1-12, 1968. Times Cited: 1202

(14) HUTCHINSON JW,
Singular behavior at end of a tensile crack in a hardening material,
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 16 (1): 13-31, 1968. Times Cited: 1196

(15) MORI T, TANAKA K
Average stress in matrx and average elastic energy of materials with misfitting inclusions;
ACTA METALLURGICA 21 (5): 571-574, 1973. Times Cited: 1177

(16) Taylor GI
Th formation of emulsions in definable fields of flow
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES 146 (A858): 0501-0523, OCT 1934. Times Cited: 1174

(17) BROOKS AN, HUGHES TJR
Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations,
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 32 (1-3): 199-259, 1982. Times Cited: 1090

(18) GURSON AL,
Continuum theory of ductile rupture by void nucleation and growth,
1. Yield criteria and flow rules for porous ductile media,
JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY-TRANSACTIONS OF THE ASME 99 (1): 2-15, 1977. Times Cited: 1069

Saturday, April 22, 2006

1993 Timoshenko Medal Lecture by John L. Lumley

John L. Lumley

I am profoundly honored by the award of this medal. Awards like this are made, of course, not by faceless organizations, but by collections of individuals, voting in rooms which are no longer smoke-filled; it is particularly gratifying to find that so many of my colleagues think I am worthy of this honor. As Jan Achenbach remarked last year, we are of the sputnik generation, too young to have known Timoshenko, who, in fact, did have some connections with Cornell long before I came there. Although I have spent my life in fluid mechanics, I began by taking all the standard courses in solid mechanics: strength of materials, elasticity, plates and shells, buckling; in nearly every one there was a text by Timoshenko or a friend or relation, all admirably clear. I felt very grateful to him.

I would like to mention that the three ASME medal winners this year (Roger Arndt, David Crighton and I) were all together at Penn State in the Aerospace Engineering Department and the Garfield Thomas Water Tunnel, under the leadership of George Wislicenus about thirty years ago. Roger and I were on the faculty, and David came in the summers as a consultant. I think that says something about the vision and values that George used as he built his group.

I have heard a story about L. M. Milne-Thomson, whom we all know for his work on theoretical hydro- and aerodynamics. Many years ago he was asked to speak after dinner at a grand banquet in the Washington area. He may have been given an award; I am not sure. The banquet was attended by wives in elegant dresses, and there were naval officers of flag rank in class A uniforms. To everyone's surprise, he said that he wanted to give a technical lecture. After a short delay they found a tiny portable blackboard, and as he covered it with equations, he had two full admirals erasing for him in relays, tossing the eraser back and forth to each other over his head. I won't do that this evening.

Instead, I want to talk about becoming a scientist and being one, during the latter part of the twentieth century, in the United States. I realize that, when people reach my age, they think that anything they have to say is golden. I am reminded of Eric Walker, former president of Penn State. When he retired, he started writing a column in the local newspaper called "Now it's my turn". Many of us thought it had already been his turn for entirely too long, and his column was not too popular. I will try to spare you that syndrome as much as possible, but some of it is unavoidable. If the Medal Committee had any decency, they would not require a speech, and we would all be spared.

My father was an architectural engineer, and a do-it-yourself craftsman, car buff and spare-time artist. My earliest recollections are of being allowed to wash the spokes of the artillery wheels on our Hudson, while Dad polished the car with the chamois. We always had a car that was a little bit special, a little different. As we drove around Detroit, Dad would point out buildings that he had had a hand in designing or building. On Saturday mornings I remember being taken to completed buildings and building sites, and having the various flaws pointed out to me. Dad was a very demanding man; everything had to be just so. Ann Landers recently had a letter describing engineers as uncompromising, inflexible and perfectionist. That was certainly Dad. One of his friends said that Charlie was a wonderful guy, but he would hate like Hell to work for him. For years my mother talked about the dog house Dad built. It was large enough for a child to play in, with insulation and a shingled roof, and a baffle at the door to keep the cold wind out. It was a lot better built than many houses for people - certainly than the ones in Dade county in Florida. Dad never did manage to teach me how to do lettering and make arrowheads on drawings in a thoroughly professional manner, though God knows he tried. He also tried to get me always to make a complete set of drawings before I fabricated something; it never took - I always preferred to plan the project in my head, and make modifications as I went along; very unprofessional. Dad had ambiguous feelings about engineering, and from time to time thought he might have been happier as an architect. He once asked me if I was prepared to spend my life among these gray, inarticulate people. That's not entirely unfair, though I have grown rather fond of many of these people, who are only gray if you don't look beneath the surface. And there are not many, but enough poets and artists among us, so I am happy.

This is really how I got into engineering. I have always loved machinery, making things, building things. But I have spent my life as a research scientist, which is not quite the same thing. It seems that when I work on a problem, even a practical problem, I turn it into a research project; I chop it up finer and finer until there is nothing left but the fundamentals. In fact, half the theses I have supervised were experimental - a good experiment is a little closer to engineering; you usually have an opportunity to design some piece of equipment, and see it come into being. That, of course, is not quite the same as making it yourself. Evenings and weekends I restore old cars out in the barn - that satisfies the urge to make things. It also satisfies the craftsman-like desire to design in your head, with the materials and tools at hand, and modify as you go along. I get tired of too much calculation, too much precision, which I get enough of professionally. In addition, what I do professionally has a very delayed payoff - something of the order of twenty years or more. It is nice to do something that provides shorter-term gratification. It is also peaceful out in the barn.

There is less dichotomy than you might think, however, between what I do professionally and what I do evenings and weekends. I believe it was von Karman who said "There is nothing so practical as a good theory". I have always felt when constructing a very mathematical theory, that I was constructing something real and practical, to explain something physical, to make design possible. I have always been deeply offended by the attitude we meet so often, "it's just a theory", although I am certainly used to it.

More important, perhaps, I have always wanted to be involved with real things. That is, I have never wanted to abstract what I do too much, remove it too far from the real world, from the application. When I was in graduate school, it was rather nice to work on clean, neat problems that were somewhat removed from the real world. When I got my first job with George Wislicenus at Penn State, I was connected with the Garfield Thomas Water Tunnel, as well as with the Aerospace Engineering Department. The water tunnel is the world's largest high speed water tunnel, and is a part of the Applied Research Laboratory, that Penn State operates for the Naval Sea Systems Command. The Laboratory is responsible for various aspects of undersea warfare. At the Water Tunnel I was quickly immersed in the very practical problems arising from torpedoes and submarines: primarily various schemes for reduction of turbulent skin friction drag, and the many problems connected with testing in the water tunnel. At first I was a little appalled by the complex interdisciplinary problems. I had been unconsciously trained to be a bit disdainful of real problems; somehow, if you were concerned with real problems, it suggested that you didn't have the wit to find the fundamental problem underlying the real problem. It seemed that, to be socially acceptable in my circles, you never mentioned the real problem, but only the fundamental problem that you had abstracted from it. I discovered fairly fast that this was not such a straightforward matter, and that the business of reducing a real problem to a series of connected fundamental problems, all simple enough to resolve, without throwing out the baby with the bath water, was very challenging. Of course, in this reduction process you have to clip away everything that seems extraneous, hoping to be left with something that, while only a skeleton, still shares enough with the real problem to shed light on it. I think my colleagues often thought that I had pruned a bit too much, leaving a stunted stub that could not survive. However, even if they could no longer see the connection, I always saw the theoretical result as still directly connected to the real world. I also quickly came to see what a tremendously rich environment this was, how stimulating, how many problems there were to solve. I think it is a great mistake to get too far away from the applications; you dry up, you starve.

In the last few years I have managed to combine my hobby and my profession. When I was a relatively junior faculty member, I taught undergraduates. As I became more senior, however, I taught only graduate students, and for many years this was true. When I went to Cornell, I was told that I would have to teach undergraduates, but in fact I was never asked, and I never volunteered. Three years ago, however, I was made an offer I could not refuse, and I am now responsible for the undergraduate course in automotive engineering, with between fifty and one hundred students. This is one of our capstone design courses, and is a nice synthesis of much of what the kids have learned in their other courses. It is fun to teach, and I enjoy the undergraduates, although they still frighten me a bit. The young can be very judgmental and demanding. I think it helps to have raised some children. The first year I taught the course, my teaching evaluations were appalling - I hope the dean never sees them. I must say they were richly deserved. Now, however, the evaluations have substantially improved, and they no longer give me nightmares.

As I have gotten older, I have found that more and more I am a research administrator. I am sure I am not unique - this happens to all of us, but it is a bit sad. That is, I have less and less opportunity to do things myself. I am supervising others who are having all the fun. The world of science in which I live and work is structured differently now from the way it was when I was young. The world itself is changing, but of course it is also changing for me because I am getting older. The changes are also not uniform from country to country. In any event, at present, at my age, in this country, a successful scientist must have a large operation, which means a hand-full of contracts, students, post-docs, colleagues, visitors. This is a nice environment for the people working in it - I try to make it that way, recalling my earlier years. I certainly was very grateful for the environment that my thesis advisor created around us. Mostly that is simply a matter of collecting an interesting group of people, and letting them interact. I was an only child, and when I was little I became accustomed to playing by myself. Probably because of that, what attracted me to science was the pleasure of working alone at a problem uninterruptedly, following thoughts to their conclusions, trying various possibilities. I now recognize that that is not always an efficient way to work - it sometimes makes more sense to break off, and sleep on a problem, or do something unrelated, or go to the library and read something that someone else has said on the subject. That was something I never wanted to do when I was young - I didn't care what someone else had said - I wanted to do it myself. In any event, this lovely environment for everybody else is not really a nice environment for me. Whether it is desirable or not, uninterrupted work is rarely possible for me. I function in the interrupt mode, which I understand is the norm for managers. In addition, I do virtually nothing myself, but must act collaboratively with others, and at second hand. This makes me feel somewhat like a child who is forced to share his toys.

Gertrude Stein compared politicians to garbage collectors; they do necessary, but not very exciting, things that keep the place running, and are not really noticed until the system breaks down and the garbage is not collected. Administration is a lot like that, even research administration. A lot of what I do these days is the moral equivalent of garbage collection.

When I came to Cornell, of course I no longer had a connection with the water tunnel and its sophisticated but practical problems. At Cornell, I have found a certain satisfaction in being an expert witness and consultant. The problems that I solve in this capacity are reminiscent of the problems that I enjoyed resolving when I was younger. They are practical problems, usually complex and interdisciplinary, which must be broken up and abstracted to be resolved. This process involves some technology transfer, since I am often applying fundamental things that my research has taught me over the years to industrial or environmental problems.

Sometimes it is like detective work. Let me tell you about something I worked on last year, that will illustrate how a complex, interdisciplinary practical problem can lead to fundamental problems. This is in the area of atmospheric turbulence, in which I worked for some years at Penn State. Some of the material may be unfamiliar, but I think you will find the logical chain interesting. My client was a sheep farmer whose sheep seemed to be dying as a result of emissions of sulfur dioxide and hydrogen sulfide from a heavy water plant. Both sulfur dioxide and hydrogen sulfide are toxic in sufficiently high concentrations. The farmer was just a kilometer and a half from the plant, which is very close, but any normal calculations suggested that his sheep were receiving concentrations at a level considered completely safe. In addition, monitoring stations placed near his farm indicated low concentrations. I must explain how Hydrogen sulfide and sulfur dioxide happened to be emitted. Hydrogen sulfide is used in the process of making heavy water, and once a year the towers in which the heavy water is made have to be cleaned. After as much hydrogen sulfide as possible has been removed from the towers, the majority of the remainder is burned on a flare stack and converted to sulfur dioxide. The plant was right on the edge of one of the great lakes, and the stack was close to the water. After several false starts, we finally realized that the on-shore breeze from the lake, during the spring and summer, was stably stratified, and thus not turbulent, from traveling over the cooler lake water for hundreds of kilometers. The top of the stack was in this stably stratified air. Thus, the stack plume did not disperse. The cool, stable air, when it started over the warmer land, began to grow an internal turbulent boundary layer, and when this reached the height of the stack plume, the plume was sucked into the first downgoing eddy, and taken to the surface. The distances were about right so that the place where this happened was right over my client's farm, and the first descending eddy was probably caused by his cool, insulated farm buildings. His sheep were thus getting the stack plume at nearly full strength. The plume, of course, did not descend on the monitoring station. The matter was complicated by the fact that the sulfur dioxide was considerably heavier than air, and could lie on the ground in hollows among the vegetation, where the sheep would be immersed in it.

This general situation is called shoreline fumigation, and is well-known to meteorologists. However, they are only familiar with the average effects. The phenomenon of the descent of the instantaneous plume to ground level, with its associated high instantaneous concentrations, has not been measured. One of my colleagues has now submitted a proposal for laboratory measurements of instantaneous concentrations in this situation. In addition, the pooling of the sulfur dioxide at ground level, and the probability of its remaining for various periods, was a nice little fundamental problem that was fun to solve.

Everything has its down side, and I must admit I don't much like being questioned in hearings. In addition, this was all part of an environmental impact hearing in connection with a request for license renewal for the heavy water plant. When it became evident that my client had a case that would stand up, the request for license renewal was withdrawn. As a result, the outcome is moot. Also, although I work hard at communicating my results, I sometimes suspect that my clients find my name and credentials more useful to them than my findings. That's all right - at least I had fun.

Well, I hope I have kept you awake. Let me thank you again for this wonderful honor you have bestowed on me.

Tuesday, April 18, 2006

A Virtual Tour of the 1906 Great Earthquake in Google Earth

The California earthquake of April 18, 1906 (one century ago today) ranks as one of the most significant earthquakes of all time. Today, its importance comes more from the wealth of scientific knowledge derived from it than from its sheer size --it marked the dawn of modern science of earthquakes.

U.S. Geological Survey (USGS) recently provides a virtual tour utilizing the geographic interactive software Google Earth to explain the scientific, engineering, and human dimensions of this earthquake. This virtual tour can help you visualize and understand the causes and effects of this and future earthquakes.

Enjoy this virtual tour to explore how Google Earth (and other new softwares...) can facilitate and improve the way we teach and conduct research.

Monday, April 17, 2006

Organic LED could replace light bulb?


Lighting accounts for about 22% of the electricity consumed in buildings in the United States, and 40% of that amount is eaten up by inefficient incandescent light bulbs. The search for economical light sources has been a hot topic.

Recently, scientists have made important progress towards making white organic light-emitting diodes (OLEDs) commercially viable as light source. As reported in a latest Nature article, even at an early stage of development this new source is up to 75% more fficient than today's incandescent sources at similar brightnesses. The traditional light bulb's days could be numbered.

Read media report here.

Sunday, April 16, 2006

A new wiki is set up to solve the Millennium Problems in Mathematics

This entry in Slashdot links to the new wiki, from which one can at least learn what these problems are, as well as their prize tags. The 139 comments in Slashdot once again show the issues concerning any wikiscience project.

Saturday, April 15, 2006

2001 Timoshenko Medal Lecture by Ted Belytschko

Ted Belytschko, November 13, 2001, New York


Well I have been sitting in the audience of Applied Mechanics dinners for more than 30 years now, never even dreaming that I would get the Timoshenko medal. I have enjoyed many of the talks, and heard many nuggets of wisdom to guide me in research and life. I still vividly remember one of the first talks I heard by Den Hartog- in those days every Timoshenko lecturer could still start with a reminiscence of their contact with Timoshenko. Den Hartog had worked for Timoshenko one summer, and when he wrote his study up as a report, Timoshenko told him to submit it for publication. Den Hartog responded that he did not think that this work was something the world was waiting for. Timoshenko replied-"How many publications that have appeared in the literature do you think the world was waiting for?" One outcome was that I proceeded to publish too many papers, but it is interesting that many of the papers I did not think much of had some impact, whereas many that I liked had no impact .

In preparing this talk, I noticed that many of the talks were autobiographical. But I quickly decided not to make mine autobiographical because I still remember that when I was program chairman, a very witty and brilliant Timoshenko medallist chose his autobiography as the topic. He was only eighteen by 10 PM, and I was at the edge of my chair because I was Program Chairman and the union crew that was waiting at the doors of the banquet hall to clean up.

So I will not give an autobiography, but I would like to say a few words about my teachers. The most important teacher in any research career is the Ph.D. advisor. My advisor was Phil Hodge, who many of you know and who was also advisor of Carl Herakovich, a former member of the Executive Committee who is sitting at the center table. Phil came from Brown, trained by William Prager, and he taught us many things: the importance of clarity and conciseness, personal integrity, and the joys of a career in research and teaching.

Phil also gave us some maxims that you might find useful. One was: "Any research worth doing is worth doing well." The other, which I have found even more useful, went something like this: "Academic paperwork has to be done, but it is usually not worth doing well."

My other mentor was Ernie Masur, who was Chair in my first position at the University of Illinois at Chicago. Ernie was quite different from Phil-whereas Phil trudged to the computer center every day with a box of cards for his daily run- in those days you were a computer jock if your computer cards filled one box, a superjock if it required two or more boxes -Ernie disdained to even type, saying that gentlemen did not type. But Ernie had impeccable taste and a terrific nose for what he called "substance", and he taught me to recognize the substance from the chaff. He also had a great sense of humor, though wit, like principles, can’t be taught

A Timoshenko talk I really enjoyed was Roshko's talk "Think Small." There were many precepts in his talk that I found very appealing, so I have decided to take a similar vein but call it "Think Big Persistently." Now you might think I am contradicting him, but some of the things I will say echo what he said.

I will address only two facets of thinking big persistently-what it means for young people, and what it means for our society, the Applied Mechanics Division.

First let me address the Applied Mechanics Division. Over the thirty years that I have been associated with this Division, the research of this group has continued to flower: the impact of this Division on the applied and theoretical issues of engineering and science has been simply amazing. Fracture mechanics, the theory of plasticity (which really underlies almost all rational nonlinear material models), micromechanics, composites, the finite element method have either originated here or owe a large part of their development to this Division. Yet, during this time, funding from NSF, which is still the best place for research support and supports many pure and applied fields very generously, has almost shrunk to zero.

This is astounding when one considers the impact of this Division on basic knowledge, basic knowledge that is not only intellectually beautiful, but has had tremendous impact on our society. This one of the most talented groups in analytic thinking in the world and the closed form solutions that have been produced by this group have provided the basic understanding of a host of important phenomena. I might add that although I am a computational mechanician, I often say that: “A good closed form solution is worth a thousand of computations."

Now it is difficult to ascertain to what to exactly ascribe this decline, but I have long felt that it is not strictly due to external forces. I believe it stems from our lack of self knowledge, our lack of identity and our reluctance to sell ourselves. Many disciplines, like computer science, have actually hired lobbyists to plead their cause, but as a Division, we almost never talk to the upper echelons of NSF or Congressional staffers. There have been a few attempts at this, but they always seem to wane, and that is why I have added that we must think big persistently-the benefits of interactions do not come overnight

Another source of our difficulties is our fuzzy self-identity. For many years, this Division has attempted to represent fields that were no longer a part of it- the fluid mechanicians have departed for the American Physical Society, but we still included fluids, and most dynamicists are in other places, but we still pretend that it is part of our Division. Perhaps even the name of our division is no longer appropriate. For one thing, the name is not appealing to younger people-most young people starting careers in research and teaching want a more attractive name, they don't want to be confused with those who fix their cars. Furthermore, most of us are not really engineers-much of our work is indistinguishable from physics or from materials science. I daresay the contributions of some members of the Applied Mechanics Division, such as Jim Rice and John Hutchinson, rank with the most important in materials science. So maybe we should look at another name-it was very beneficial for soils engineers, who changed their name to geotechnical engineering, and have much improved their image with the public.

What should such a name be? I have asked a number of people. Some would not even give it an attempt, because they consider it sacrilegious. Lalit Anand, a former member of the Executive Committee, proposed “Solid and Mechanical Engineering and Sciences.” He suggested we would then go by the acronym SMEC. My preference is "Science and Engineering of Solids" -SES. I think it is high time we recognize that we are scientist as well as engineers, and that we get a name that accurately reflects what we do and what we have done!

But more important, the Executive Committee and its past members should be in constant contact with people at Congressional staffers, NSF and other funding agencies. There are 10,000 of us in ASME and more in ASCE, and I think we should have a strong voice. We have to let them know what we do, why it is important, and what we can do for the country. This can not be a one-shot effort, it needs to be done persistently. (for example, Mathematics has just won a commitment for a fourfold increase in funding through such long-term efforts)

My second theme pertains to young people, to whom I would like to give some advice based on my past successes and mistakes. To think big is to look for important problems at the cutting edge. Too many young researchers choose their topics by reading a paper and seeing how they can extend it- that is not how the important problems are found. You have to talk with many people, read both the literature of your disciplines and other fields, and identify the emerging fields and important problems. I fortunately stumbled into nonlinear finite elements through my consulting work early in my career-I wrote a crash code in 1971 when a visionary in DOT initiated a research program by selling the idea that crash testing could be replaced by computer simulation. Well at that time, computers were so slow that even a 500 element simulation (500,000 are customarily used today) cost more than a test, so the program was quickly shelved. But it gave me the opportunity to do some work in a new area that had considerable impact.

To highlight the importance of working on new problems, I quote Arno Penzien, the Noble Prize winner who discovered the background radiation that underpins the big bang theory: “ there are two types of scientists: 2% discover new things and blaze new frontiers, the other 98% fix up their mistakes; the accolades go to the former.”

It is also crucial for the success of this Division that we nurture our young researchers- our future obviously lies with them. In this, I think that we must de-emphasize the role of money in our promotion criteria. We have now reached the point where in many schools, the volume of money supersedes all other factors in a professor’s promotions and recognition. This is really quite absurd, since a university does not exist to make money- our purpose is to teach and do research, and money is only a means to that end. But in many places, right at the top of your annual report is your dollars spent. Everyone seems to have become obsessed with the U.S. New and World Report ratings, in which money plays a dominant role. If this trend continues, I can see two young assistant professor talking one day and wondering: "What is the fuss over Einstein all about?- I hear he never brought in 100k per year.”

So I think we ought to persistently remind our administrators that our goals are not to bring in money. Administrators have incorporated indirect funds into operating budgets, so they are becoming addicted to large research fund flows. It will be a big job to bring this to an end, but if we can think big and persistently, we can at least moderate this.

There are tremendous opportunities for us in emerging fields such as micromechanics, nanomechanics, cellular mechanics, biomechanics, computer simulation, and many that are only barely visible on the horizon today. But to enjoy these, we must do the things that need to be done persistently.

To conclude, I would like to thank my family, my wife Gail and my children Peter, Nicole, and Justine; my colleagues at Northwestern in the field of mechanics, Wing Kam Liu, Brian Moran, Jan Achenbach, Cate Brinson, Zdenek Bazant, Jian Cao, Isaac Daniel, and John Rudnicki (we have the best group in the world, and their collaboration, collegiality and competitiveness have helped me immensely), my students and post-docs, and my professional colleagues, particularly Tom Hughes and Tinsley Oden, who were so instrumental in my winning this award.

Thursday, April 13, 2006

Nanogenerators created by a team led by Zhonglin Wang

Saturday, April 08, 2006

1989 Timoshenko Medal Lecture by Bernard Budiansky

Professor Bernard Budiansky delivered this lecture at the Applied Mechanics Dinner of the 1989 Winter Annual Meeting of ASME, in San Francisco, California. He died in 1999, and his colleagues at Harvard University have published a memorial minute.

Reflections
Bernard Budiansky

Many thanks for honoring me with the Timoshenko Medal. Forty-five years ago, fresh out of college with a bachelor’s degree in civil engineering, I started my first job at Langley Field, Virginia, with the National Advisory Committee for Aeronautics, and my very first assignment was to learn about buckling of plates from Timoshenko’s famous book on the theory of elastic stability. Timoshenko’s extraordinary influence on research and education in applied mechanics all over the world, and his central role in this country, needs no reiteration. Like so many others, I was seduced by his book into a life-long infatuation with buckling problems, and so to receive this award bearing his name from my fellow applied mechanikers is very heart-warming, and I am very grateful.

On occasions like this, it is traditional for the speaker to grapple with cosmic issues of research, educations, scholarship and the like, even though he would feel much more comfortable giving a technical lecture. One distinguished colleague managed to rattle me thoroughly by saying – I think mischievously – that he looked forward to my “words of inspiration”; on the other hand, John Hutchinson simply suggested that I keep it short.

Not only will I follow John’s advice, I will also avoid major matters of science and technology, because I neither have any profundities to peddle, not do I wish to contribute any new cliché’s or buzzwords to these subjects. The present supply is quite adequate. I have to admit that I was really impressed the first time I heard the phrase “the cutting edge of technology” (even though the imagery did no quite match that of Tom Lehrer’s immortal line about “sliding down the razor blade of life”) but after several hundred repetitions, the effect has grown dull. Words and phrases invented inside the Beltway do spread like wildfire. One popular Washington proverb I can do without is: “If it ain’t broke, don’t fix it.” This is a perfect prescription for the technological stagnation that is often deplored in the next breath. In the last few years, we have been deluged with “initiatives” – Strategic Defense Initiative (SDI), Universities Research Initiative (URI), Accelerated Research Initiative (ARI), and so on. My current favorite is the recently announced BNI – Bold New Initiative – which sounds exciting, but I have forgotten what it’s for. Heavy phrases like technological innovation, manufacturing productivity, international competitiveness, and environmental disaster are on everybody’s lips. I certainly do not wish to demean either the importance of the issues they represent, or the seriousness with which the problems are being confronted. However, I am sure you will be relieved to learn that these topics are beyond the scope of the present talk.

What I will do is reflect a bit about applied mechanics and applied mechanikers. At the same time, I will try to avoid excessive introspection, which I consider to be a dangerous practice that can lead to a morbid preoccupation with the meaning of life. Fortunately, it seems to me that most of us in applied mechanics do enjoy a fairly un-self-conscious approach to our work, relatively free of subjective inner contemplation. To varying degrees, we simply love to do research in our fields, we accept the frustrations, false starts, and dead ends that go with the territory, and do not make a habit of either melancholy self-doubt or manic self-adulation. And so, to those who assert that the unexamined life is not worth living, I say, speak for yourselves, and let me get back to work!

But if research in applied mechanics is such a happy enterprise, why are we occasionally afflicted with the Rodney Dangerfield syndrome, namely: “We don’t get any respect!”? We share a monumental intellectual legacy of knowledge and achievement, and our contributions to many branches of engineering and applied sciences are central, vital, and growing. And yet, the visibility and recognition of applied mechanics as a coherent discipline has been diminishing, not only in the eyes of the general public, where it has always been negligible, but within the scientific and technical establishments as well. Starting at the top, applied mechanics as a field of learning and research is surely terra incognita to the President of the United States, his cabinet, most members of Congress, the CEO’s of the Fortune 500, all but a handful of university presidents, and about a quarter of a billion other Americans, including even the Vice-President. University departments or division tagged with the applied mechanics name seem to be in a process of extinction. With some exceptions, governmental funding agencies tend not to assign the applied mechanics label to the research they support. Neither the National Academy of Engineering nor the National Academy of Sciences nor the American Association for the Advancement of Science contains a section in applied mechanics. I have yet to see the words “applied mechanics” in the science pages of any newspaper or newsmagazine, and I suspect that they have rarely, if ever, appeared in general science publications like Science or Nature or Scientific American. But we do exist! We are like members of a closely knit secret society, with clandestine cells in mechanical, civil, chemical, and aerospace engineering, in geophysics, in materials science, in biotechnology – but we’re quite ready and willing to have our cover blown!

There are two obvious reasons for this lack of visibility, one sublime and one ridiculous. Our very success in promulgating the role of applied mechanics within such a large number and variety of fields has led to the seamless integration of substantial parts of applied mechanics into the various fields I mentioned. This, of course, is very welcome. But as a natural consequence, subsequent research in such an incorporated segment of applied mechanics tends to assume the identity of its host. The absurd reason for our lack of status is that we still don’t know what to call ourselves! Can it be that this is the crux of the problem? We are not the only group whose activity cuts broadly across traditional disciplinary boundaries, but mathematicians, engineers, physicists, biologists, and computer scientists proudly retain their identities, no matter how scattered and diverse their working environments, and, of course, their titles provoke instant recognition. But what are we? In informal conversation, “applied mechaniker” is all right, but is clearly too whimsical and slang-ey for general acceptance. Some years ago, Norman Goodier urged the adoption of the appellation “applied mechanicist” but this never really took hold, and “applied mechanician” doesn’t seem to make it either.

Well, so what? Is this a true identity crisis, or just an annoying pinprick to our collective ego? After all, we do respond with acceptable answers when our neighbors ask us what we do for a living, or when we have to fill in the blanks labeled “occupation” on our income-tax forms or passport application. I suppose most of us say “engineers”, some say “mathematician”, others (like Irwin Corey) simply say “professor”, or “educator”, or “geophysicist”, or something else as respectable. The fact is, we all do have at least one profession we can honestly claim besides our beloved applied mechanics. I am reminded of Josephine Baker’s song “J’ai deux amours, mon pays et Paris”, but the analogy is not apt, because everybody’s heard of Paris! Furthermore, most of us certainly do not want to sever our professional allegiances to the traditional fields. The engineering profession, in particular, has its own serious problems that may be worthy of our attention. And since applied mechanics should be truly interdisciplinary, might not intellectual isolation and sterility be an unhappy consequence of the greater autonomy that would inevitably flow from increased visibility for applied mechanics? And therefore, shouldn’t we leave well-enough alone? Finally, we obviously do enjoy substantial communal ties. Here we are in the Applied Mechanics Division of the ASME, there is a parallel Engineering Mechanics Division of ASCE, we have a National Congress of Applied Mechanics and an International Congress every four years, and we have umpteen journals as outlets for our research publications. So why worry?

I have almost persuaded myself to adopt the Panglossian view that everything has happened for the best – but not quite. First, and maybe foremost, greater visibility would obviously attract more talented young people to applied mechanics, and I know that most of you share my belief that this is very much needed. Next, greater autonomy for groups in applied mechanics could enhance interfield communication, and spark the effective spread of applied mechanics into new areas. (The models for this are the spectacular rise of biomechanics in the last few decades, and the vigorous growth of mechanics in materials science and geophysics.) There’s more: applied mechanics and applied mathematics have gone hand in hand for a long time, with applied mechanics people taking major responsibility for university instruction in applied math. Weaken applied mechanics and you weaken applied mathematics, and this has been happening. In connection with applied math, let me say a word about computing; our applied mechanics community has led, and continues to lead, the exploitation of computers in scientific and technological research. As a long-time addict, I am enthusiastically pro-computer, and I never used to take very seriously the gloomy prediction of some of my uncontaminated colleagues, who deplored the inanities of massive, mindless computations as substitutes for elegant classical analysis, and foresaw the loss of analytical skills that would be induced by excessive reliance on computers. But now I believe that the balance has finally tipped, that applied mathematics in the classical sense, needs rescuing and that strengthening applied mechanics may be the best way to do it. Finally, we need the extra power and freedom that would flow from greater visibility and prestige in order to secure the right to do what I would call pure applied mechanics. Such research is intended to nourish the heart and soul of applied mechanics, and is not particularly meant to be “useful” in any prosaic sense. Its virtues – something funding agencies would, of course, have to judge – would be measured on the basis of depth, beauty, and truth, the same graces that characterize and justify good pure mathematics. Incidentally, I have no patience with the widespread myth that pure math, done without applications in mind inevitably turns out to be “useful”; sometimes it does, but more often, it doesn’t. However, the phony promise of ultimate utility is not necessary to justify support of pure math, and I demand equal treatment for a certain amount of pure applied mechanics!

So if we agree that we should burst the bonds of anonymity, perhaps we should begin by coming to grips with the question of our job description. I could live with either “applied mechanicist” or “applied mechanician”. Why not boldly start using one or the other at every opportunity, and let the better one survive! Then – let’s lobby scientific and technical societies, honorary or otherwise, that have not yet seen the light, to establish applied mechanics divisions! In universities, reverse the slide into oblivion and recommend that establishment of applied mechanics committees across standard departmental lines, maybe empowered to grant degrees as well as give courses! Preach to funding agencies about the merits of interdisciplinary sections of applied mechanics! Give interview, or write popular articles, about applied mechanics and its practitioners! Run for Congress!

Well, enough agitation, which does not fall within my area of expertise, anyhow. To conclude these reflections, I would like to flip quickly though some verbal snapshots of a few of the people who have enriched my professional life. I had a remarkable trio of bosses in my first job at the Structures Research Division of NACA in 1944; Pai-Chuan Hu, a fresh Ph.D. in Engineering Mechanics from the University of Michigan, whose knowledge and intellect were awesome; Sam Batdorf, a renegade physicist, whose insightful way of thinking about problems in applied mechanics has been an enduring inspiration; and the big boss, the Chief of Structures Gene Lundquist, a great pioneer of structures research, whose legacy as a research leader has been enduring. It was an exciting time at NACA, in those pre-space days of aeronautical research, and my experience there has left me fiercely supportive of scientific civil servants, who are at least as smart and hard-working as those in the private sector, but often are slandered by invidious comparisons. I was lucky to meet and even interact with some famous people at NACA outside my field of structures, like Ed Garrick, Carl Kaplan, and the great aerodynamicists Robert T. Jones and Adolph Busemann, who had independently conceived of swept wings for high-speed flight – Jones in America, Busemann in Germany. Jones told me how to calculate the lift on a swept wing, so that I could go on to study its aeroelasticity. Busemann got sufficiently interested in plasticity to join Lyell Sanders, John Hedgepeth and me in many happy hours of exploration of 6-dimensional stress space. Busemann had a marvelous, infectious technical vocabulary in English; an eavesdropper would have heard us earnestly discussing Humpty-Dumpties, meaning hyperspheres; stalactites, meaning hypervectors; and stalagmites, vectors pointing the other way! When I went to Brown University for graduate study in applied math, what an extraordinary group of professors I had: Prager, Drucker, Carrier, Lee, Handelman, Greenberg, Diaz – all of whom taught me much more than simply the material in their courses. During those early post-war years, Brown attracted a fantastic international brigade of graduate students: among my special buddies were Frithiof Niordsen, Carl Pearson, Jean Kestens, Pei-ping Chen, and Hirsch Cohen – respectively, from Stockholm, Vancouver, Brussels, Peking and Milwaukee. (As you see, I am name-dropping shamelessly.) It has become a cliché that one learns as much from fellow students in graduate school as from faculty – and was this ever true in my case! As I look back over my life in applied mechanics during the decades that followed, I realize that I always think first of people rather than problems. (If this be introspection, make the most of it.) I suppose I love applied mechanikers as well as applied mechanics, and I had better start rationing my sentimental recollections. But I particularly want to mention Eli Sternberg, sadly gone now, our pre-eminent elastician, whose extraordinary charm, wit, and intelligence brightened and blessed us all, and whose friendship I cherished for over forty years; and the incomparable Max Krook, astrophysicist, applied mathematician, and certainly applied mechaniker, who actually knew everything. I have been enormously influenced, instructed and encouraged by Warner Koiter, the sage of Delft; and now, for over a decade, by Tony Evans, the ceramics guru of the western world. A little more introspection, despite by vow: there are many styles of research, none intrinsically superior, but I have to be able to exchange ideas freely, and talk things out, face-to-face with others. Recently, I was stopped by a camera crew doing snap interviews on campus, and was asked what I liked best about Harvard. Without any chance to reflect, I popped out the answer: colleagues. And so it is, even after reflection. How very fortunate I have been to enjoy the company of such a splendid group of kindred spirits in applied mechanics. I owe them more than they would be willing to believe, and here’s who they are: George Carrier and Howard Emmons, recently inducted into the ranks of the emeritus professors; and the remaining hardy band of applied mechanikers Fred Abernathy, John Hutchinson, Dick Kronauer, Tom McMahon, Jim Rice, Lyell Sanders, and Howard Stone. We will do our best to keep and promulgate the faith, and I hope you will too! Thank you.

Wednesday, April 05, 2006

USNC/TAM Report on Research Fluid Dynamics

Carl Herakovich, the secretary of the US National Committee on Theoretical and Applied Mechanics (USNC/TAM), has posted the following entry in the Applied Mechanics Google Group today:

The USNC/TAM has just released a report by a Subcommittee on Research Directions in Mechanics, entitled Research in Fluid Dynamics: Meeting National Needs.

Saturday, April 01, 2006

1985 Timoshenko Medal Lecture by Eli Sternberg

Rumination of a Reclusive Elastician

By Eli Sternberg

Delivered at the Applied Mechanics Dinner of the 1985 Annual ASME Meeting in Miami Beach, Florida

Ladies and Gentlemen: As you know, medals - much like arthritis - are a common symptom of advancing years. Be this as it may, I am grateful for the recognition implied by this award.

Every medal has a proverbial reverse side. The reverse side of the Timoshenko Medal is the requirement that the recipient must make a speech. In view of my lifelong allergy to after-dinner speeches, the thought of having to give one has been rather unsettling. To make matters worse, I was asked over two months ago to submit a title for my talk.

Since a technical topic seemed inappropriate for the occasion, I tried hard to think of a suitably broad and vacuous subject: something with a sexy title, like "Applied Mechanics - Past, Present, and Future." I abandoned this idea, first, because I always feel a little uneasy in making pronouncements about the future of anything and, second, because I am not sure I know what is meant by "Applied Mechanics".

I had been in a similar quandary as to the meaning of "Applied Mathematics" until a good many years ago, when Lester Ford, who was then chairman of the mathematics department at the Illinois Institute of Technology, called me into his office to show me a letter he had just received from an inmate of Alcatraz Prison. It read: "Dear Professor Ford, I am serving a life sentence at Alcatraz and am studying calculus on my own. I don't know how to solve Problem No. 3 on p. 275 of the calculus book by Granville, Smith, and Longley. Can you help me?" I allowed that this was an amusing letter, at which point Professor Ford handed me a copy of the book. Problem No. 3 on p. 275 started with the sentence: "A tunnel is to be drilled." If this isn't Applied Mathematics, what is?

Anyway, under duress to supply a title for this talk well in advance, I attempted to concoct one sufficiently noncommittal to permit me to hold forth on just about anything that might eventually come to my mind. I think you will agree that I succeeded admirably in choosing such a title.

Having spent all of my professional life in mechanics at academia, I finally decided to take advantage of a predominantly academic, captive audience and dwell on certain developments that have detracted from my favorite environment. Although some of what I intend to say applies to the contemporary academic scene in general, a more communicative heading for my remarks this evening might be: "Mechanics - an Apprehensive View from the Ivory Tower."

To begin with, there is the undeniable observation that mechanics, as an independent academic discipline, has suffered worrisome setbacks during the past twenty years or so. This fact is reflected in the demise of several mechanics departments at major American universities, the erosion of existing mechanics faculties, and the decline of the student population in mechanics. There are various and diverse reasons for this trend. Among them is the not uncommon perception of mechanics as an essentially stagnant field. After all, some of my physicist friends still regard the discovery of Hooke's law in the seventeenth century as the last noteworthy event in the history of the theory of elasticity.

Another, related circumstance is the need to cultivate important emerging disciplines. Given the financial limitations on university budget, as well as the inevitable time constraints on academic curricula, engineering schools are apt to look for compensatory cutbacks in traditional activities and at times see in mechanics a natural victim of such efforts toward modernization.

As far as the furtherance of computer science is concerned - and here I speak out of the richest store of ignorance conceivable - no one would earnestly question the enormous value of computing to applied mechanics and indeed to all of applied science. Yet computing without a proper theoretical background can be hazardous to the public health. Thus there are grounds to worry about the rising traffic in finite element codes for stress analysis, which are often secret codes (in the sense that their theoretical basis remains a closely guarded secret) and the authors of which are occasionally uninhibited by a more than cursory acquaintance with the theory governing the problems they purport to solve.

For this reason alone a serious background in mechanics is hardly a luxury safely to be done away with. But mechanics need not rely on such a tenuous defense. Not only has it provided unparalleled inspiration for far-reaching scientific achievements in the past, it has made impressive strides in more recent times that have illuminated its foundations, enlarged its scope, and encompassed new technological applications.

Even elasticity theory, which (to my unbiased mind) is the very model of a mathematically sound and physically successful theory – though declared dead in some premature obituaries, has not stood idle. Nor is it likely to become obsolete in the future. I am rather confident that the theory of elasticity will be around and useful long after some of the more glamorous additions to engineering curricula have joined the company of fading fads and discarded fashions.

By and large teaching has been one of my favorite preoccupations over the years. In fact, trying to make things clear, whether in lecturing or in writing, is an ultimately rewarding, if often painful, obsession of mine. And, incidentally, whenever I have particular trouble in explaining something to others, I usually find that it is not clear to me either.

My enthusiasm for teaching has been somewhat dampened by a no longer novel phenomenon that has, in my view, contaminated the academic teaching atmosphere. I am alluding to the teaching-quality surveys conducted by students, which are firmly entrenched at most universities and enjoy a blissful immunity from criticism: any faculty member venturing to question the merits of this ritual can count on having his own motives questioned in turn. Now this is hardly an issue to become exercised about, but it is cause for some legitimate concern. Let me start with a few truisms.

First, these surveys evidently serve a useful purpose: for example, in making teachers aware of distracting mannerism and bad habits, like speaking too fast, writing illegibly on the blackboard, or standing in front of what has been written.

Next, as the husband of a psychologist, I know that polls of this kind are conducive to the mental health of students in enabling them to vent their resentment against a teacher by taking anonymous potshots at him or her. I still remember from my own undergraduate days being handed a questionnaire at the end of an explosively dull course. It called for the usual ratings of the instructor for "mastery of subject," "clarity of presentation," "fairness," and so on. In addition, it asked for an overall grade for his performance: A, B, C, etc. In a fit of mischievous inspiration, I gave the man an "Incomplete." I doubt if he enjoyed the joke nearly as much as I did at the time.

Lastly, nobody can prevent students from carrying out and publicizing the results of such surveys.

My misgivings pertain to the official sanctioning of this sort of enterprise by university administrations and the weight assigned to its outcome in connection with faculty promotions. At my own university the annual teaching-quality evaluation is undertaken with the cooperation of the Registrar and reported on in a publication funded by the Office of the Vice-President for Student Affairs.

Why misgivings? Because such evaluations tend to inflate the importance of the most superficial aspects of teaching; because they invite a popularity contest among the faculty that may favor glib and facile efforts over more demanding expositions in depth. Further, it seems to me that students - even graduate students -may not be in a position to assess the true competence of an instructor or the permanent value of the material presented. Perhaps the most memorable teacher I ever had was a notoriously poor lecturer, and I failed to appreciate fully the influence of my exposure to him until later in life.

I might add my surmise that there is little of substance that can be taught about teaching at the university level and - Schools of Education notwithstanding - even less on a level of generality that divorces teaching from the subject to be taught.

Along with teaching, most universities place considerable emphasis on scholarly accomplishments of their faculty. I am glad to say that the old chestnut about an inherent antagonism between teaching and research has largely been put to rest nowadays.

But the dangers arising from an indiscriminate reliance on the number of publications as a criterion for academic advancement are too self-evident to be belabored. One way of coping with the perennial academic dilemma of "Publish or Perish!" is to publish perishables. There is a natural temptation, especially among younger people, to pad one's list of publications with minor spin-offs of earlier work, and an understandable reluctance to invest the time needed to learn something new.

Such pressures are in part responsible for the current avalanche of papers on mechanics, the number of authors of which threatens to exceed the number of their readers. Moreover, this state of affairs has led to a proliferation of ever more specialized journals catering to mechanics of one kind or another: any day now I expect to receive notice of a new International Journal of Shear Stresses.

Let me move on to some troubling trends in the role played by sponsored research at our universities. It is a fact - a regrettable fact, but a fact of life just the same - that American universities depend on sponsored research for their survival. As a consequence professors are expected to cover a substantial portion of their salaries through outside support. This, in turn, compels them to spend an appreciable portion of their time on entrepreneurial chores, such as the composition of seductive proposals - hardly the most appealing genre of creative writing.

More disturbing is the spreading practice of making new academic appointments explicitly contingent upon the faculty member's ability to attract a specified percentage of outside support. This practice is particularly burdensome for younger faculty, and especially so in a field such as mechanics, where funding is increasingly difficult to come by. It seems to be easier to obtain a multi-million dollar grant for an accelerator or a giant telescope then to secure relatively modest support for a study of, say, the foundations of the theory of elastic instability.

A major share of the support for the university-based research has come from various federal agencies and from the different branches of the Department of Defense. The policies governing such federal funding have on the whole been enlightened in recognizing the specific nature of academic, as distinct from industrial research. One of the most significant functions of government research grants and contracts has been to sustain the advanced education of scientists and engineers, which is of equally crucial and obvious benefit to the country as a whole.

I personally owe a large and lasting debt to the Office of Naval Research, which for a period of over thirty years allowed me to pursue my research interests and to contribute to the training of graduate students, with essentially no interference and with a minimum of bureaucratic harassment.

Of late, however, federal support for academic research in engineering has taken a rather ominous turn. Apparently, while physicists or chemists remain free to do their own thing, engineers are to be held to delivering the goods. In particular, I gather that according to some recent edicts, research in applied mechanics is "to be made relevant to national defense" and is "to impact the competitive vitality of the economy" - if I may use some in-language. Since the National Science Foundation is presumably a guardian of fundamental research, I was all the more taken aback by a list of ten recommended research areas, which was distributed at an NSF conference on "Future Directions in Solid Mechanics Research", about a year ago.

My first qualms concerning this manifesto were aroused on noting that it comprised exactly ten items, "ten" being a conspicuously round number. I always suspected that the committee charged with drafting the Ten Commandments initially arrived at only nine and then added "Thou shalt not commit adultery" for good measure. I will not bore you by quoting the complete list of suggested research areas to which I am referring. Suffice it to mention that one of the categories listed is the "Mechanics of Modern Manufacturing", while another is headed "Mechanics in Strategic and Conventional Military Systems"; here "missile systems", "tube-launch systems", and "warhead design" are cited as representative examples.

I realize of course that this document originated in response to new government directives and that it is intended to make research in solid mechanics more attractive to those in control of funds. Yet if this is a vision of the future role of such research, I cannot help feeling that it is at best a vision impaired by a well-intentioned myopia.

There is a general consensus that research conducted at universities ought to be basic research. Admittedly, everyone has his own definition of "basic research", tailored to include his own work. But I cannot conceive of any acceptable definition that would accommodate the design of warheads.

Nor am I making a plea for the license to do irrelevant work. Bent on platitudes, I ought to remind you, however, that "relevance" is a slippery notion and that what is irrelevant or even frivolous work to some, may be regarded to be of fundamental worth by others. Finally, it is well to keep in mind that many of the most enduring and consequential contributions to applied science and engineering stem from research that was prompted by sheer intellectual curiosity and unencumbered by an insistence on its immediate applicability.

I must not test your patience by prolonging these opinionated and rambling ruminations. Otherwise I might suffer the fate of the speaker who apologized for having carried on interminably on the grounds that there was no clock within his view, only to provoke a member of his audience into pointing out a calendar on a wall of the lecture room.