Gottfried Wilhelm Flügge

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18 March 1904
Greiz, Thuringia, now Germany
19 March 1990
Los Altos, California, USA

Gottfried Wilhelm Flügge was a German mathematician and engineer who wrote the standard work on the theory of shells.


Wilhelm Flügge's father, also named Wilhelm Flügge, was a minister in the Protestant church. Wilhelm had a younger brother Siegfried Flügge (1912-1997). Let us record at this point that Siegfried obtained a doctorate in theoretical physics from the University of Göttingen in 1933 where he was advised by Max Born. In 1910 the Flügges' father took the family to Dresden when he became a minister in a church there. Wilhelm attended a Gymnasium in Dresden, graduating in 1921. In the same year he entered the Technische Hochschule Dresden, renamed the Dresden University of Technology in 1961, graduating in 1925 with a Diploma in Civil Engineering. Then he was the appointed as an assistant to Kurt Beyer while he undertook research for his doctorate.

Kurt Beyer (1881-1952), who had been a student at the Technische Hochschule Dresden, was an expert on applying mathematics to reinforced concrete. He had been appointed as the Professor of the Statics of Structures and Applied Mechanics at the Technische Hochschule Dresden in 1919. During the years that Flügge was his student, Beyer was working on his most important work Die Statik im Eisenbetonbau (1927). Flügge graduated with his doctorate in 1927 and then worked in the construction industry for Dyckerhoff & Widmann. This firm, founded in 1865 by Wilhelm Gustav Dyckerhoff (1805-1894) in Karlsruhe, made concrete components. They were highly innovative and in the 1920s they developed a concrete shell construction system. It was on this system that Flügge worked during his three years with the company at their Leipzig and Wiesbaden factories. We note that the firm was later awarded the Edward Longstreth Medal by the Franklin Institute for this thin shell concrete structure.

Flügge left Dyckerhoff & Widmann in 1930 when he was appointed to a post-doctoral position at the University of Göttingen. At the Aerodynamics Research Institute in Göttingen he met Irmgard Lotz (Flügge-Lotz after her marriage) who had recently been appointed as a Junior Research Engineer in Ludwig Prandtl's research group. Flügge was soon made aware of the difficulties that Lotz had in a male dominated team:-
... the position of a female in the world of science and engineering was difficult. Wilhelm has told of the secretary who served tea to the group at the weekly conference, but refused to serve Irmgard: "She can make her own tea."
In 1932 Flügge submitted his habilitation thesis and became a privatdozent at the University of Göttingen. In the following year he was one of the founders of the important journal Zentralblatt für Mechanik. He published Statik und Dynamik der Schalen in 1934. A review of the German text states:-
... the book deals to a considerable extent with linear membrane theory of shells of revolution, with the linear theory of circular cylindrical shells and with linear bending theory for symmetrical deformations of shells of revolution. Some consideration is given to classical elastic stability theory of circular cylindrical shells and spherical shells and to vibrations of shells.
This classic book was translated into English and appeared under the title Stresses in shells in 1960. Eric Reissner (1913-1996) writes in a review of the English edition:-
About two hundred pages of this book are devoted to linear membrane theory (which is that aspect of shell theory where bending moments and transverse shear forces, as well as non-linear effects, are assumed negligible. For many problems this is a practically adequate assumption.) The treatment here is quite thorough and comprehensive, except concerning the nature of appropriate boundary conditions in problems where this represents a significant question (as for instance in the problem of unsymmetrical deformations of spherical shells). About one hundred pages are concerned with bending theory of circular cylindrical shells. Unsymmetrical deformations are analysed to a considerable extent by means of the author's own system of basic equations. Another one hundred pages cover the subject of linear-theory bending of shells of revolution. This includes the classical material on symmetrical bending and edge effects associated with the names of Hans Reissner [(1874-1967), Eric Reissner's father], E Meissner and J W Geckeler
The five years from 1933 to 1938 were difficult ones for both Flügge and Lotz in Göttingen as the Nazi policies had a major affect on the staff. Flügge was branded "politically unreliable" and realised that his chance of an academic career had vanished. Someone who was "politically unreliable" stood no chance of a professorship. However, as Flügge and Lotz prepared to marry, Lotz's career had progressed well for she had continued research at the Aerodynamics Research Institute making major advances in techniques to predict the aerodynamic pressure on various parts of a plane such as its body, wings, and turbine blades. By 1938 she had been appointed Head of the Department of Theoretical Aerodynamics. In 1938 Irmgard Lotz and Wilhelm Flügge were married, and in the following year they moved to Berlin where Flügge was appointed to the Deutschland Versuchsanstalt Luftfahrt. It seems that the benefits to the German air force of his expertise outweighed the fact that he was considered "politically unreliable". At the start of World War II in 1939, Berlin was a relatively safe place for the Deutschland Versuchsanstalt Luftfahrt to be sited but, as the war progressed, Berlin came under increasingly heavy bombing raids from the allies [2]:-
In the spring of 1944, the destruction of Berlin had progressed so far that Wilhelm and Irmgard moved with their departments to Saulgau, a little town in the hills of southern Germany. After the end of the war, Saulgau was in the French zone of occupation. The French aeronautical establishment was resurrected after the war on an enlarged scale and was eager to take in the German intelligentsia. In 1947 Wilhelm Flügge and Irmgard Flügge-Lotz moved with many of their co-workers to Paris, to become part of the Office National d'Études et de Recherches Aéronautiques.
Although Flügge and his wife were happy living in Paris, the positions both of them held there in the Office National d'Études et de Recherches Aéronautiques gave them little hope of progressing in their careers. They wrote to Stephen Timoshenko enquiring about the possibility of working in the United States and, in 1948, both received offers of posts at Stanford University which they quickly accepted [5]:-
Timoshenko deserves the credit for bringing mathematical analysis into engineering practice, certainly in the area of structures. He realized the advantage of bringing Wilhelm Flügge to strengthen the work in applied mechanics at Stanford.
However, Stanford University had a policy that a husband and wife could not both have a professorial role in the same Department. With Wilhelm Flügge being appointed as a professor, this meant that, despite Flügge-Lotz's eminence in research, she had to accept a lowly position of "lecturer".

While at Stanford, Flügge published a number of important books. We have already mentioned the English translation of his 1934 German text as Stresses in shells (1960). Before this, he published Four-place tables of transcendental functions in 1954. After the English translation of his German text, there followed Statique et dynamique des coques (1960), Viscoelasticity (1967), and Tensor analysis and continuum mechanics (1972). A review of this last mentioned book states:-
As is implied by the title, this is an account of tensor analysis written with continuum mechanics in mind. Indeed, the mathematics and mechanics are so intertwined that each new mathematical concept is immediately applied. The treatment is detailed but concise, so that in barely 200 pages the reader is taken from elementary vector analysis to the research level.
Flügge also edited Handbook of engineering mechanics (1962), an excellent reference book with many authors. The last of his books was published in 1975 after he had retired and one year after the death of his wife. However he continued to live as he had before [5]:-
... occasionally inviting guests for evening tea and on rarer occasions preparing an elaborate meal for guests. The spirit of Irmgard was always present. ... [Later] he devoted his attention to his hobbies of photography, bird watching, a cactus collection, and travelling. Many will remember the unique Christmas cards he would prepare, featuring an interesting angle photograph of his latest little creation, such as a quizzical owl from a pine cone.
His outstanding contributions led to him receiving a number of awards. He held a Fulbright Scholarship during the 1966-67 academic year and in 1970 was awarded the Theodore von Kármán Medal by the American Society of Civil Engineers. He also received the Worcester Reed Warner Medal from the American Society of Mechanical Engineers [5]:-
It seems to be no coincidence that he died on the day after his 86th birthday. On that day his driver's license expired and could not be renewed because of failing eyesight, as well as failing strength. He simply was not willing to yield the home he had shared with Irmgard nor his independence. His departure marks the end of an era.

References (show)

  1. K-E Kurrer, The History of the Theory of Structures: From Arch Analysis to Computational Mechanics (John Wiley & Sons, 2012).
  2. J Gere, G Hermann and C R Steele, Memorial Resolution: Wilhelm Flügge (1904-1990), Stanford University.
  3. Guide to the Wilhelm Flügge Papers, Department of Special Collections and University Archives, Stanford University Libraries.
  4. N Makris, Eminent Structural Engineer: Professor James Marshall Kelly, Structural Engineering International 2 (2013), 229-231.
  5. C R Steele, Obituary. Wilhelm Flügge (1904-1990), Int. J. Solids Structures 26 (12) (1990), 1303-1304.

Additional Resources (show)

Written by J J O'Connor and E F Robertson
Last Update April 2015