Elected in 1977
“Contributions to solid mechanics, stability theory, aircraft safety, and aeronautics.”
WARNER TJARDUS KOITER, the world’s leading expert on elastic stability theory and shell theory, died at the age of 83 on September 2, 1997.
He was born in Amsterdam on June 16, 1914, and grew up in the eastern region of the Netherlands in the town of Zutphen. His academic career, from his BSc and MSc (1931–1936) to his PhD (completed in 1945), was spent at the Technological University of Delft. Before becoming chair of Applied Mechanics there in 1949 he worked in several government research positions mainly related to aircraft development, including the National Aeronautical Research Institute (1936–1938) and the Department of Civil Aviation (1939–1949), where he became head of the Engineering Division.
During his career he made fundamental contributions to some of the most important areas of aeronautical structures and solid mechanics more broadly. His PhD thesis on elastic stability is regarded by many in the field of solid mechanics as perhaps the most important thesis of the past century. He applied his stability theory to plate and shell buckling problems arising in aeronautics, and was the lead researcher in the continuing development of shell theory during this period. He made seminal contributions to plasticity theory, crack
mechanics, and understanding of the interplay between buckling and imperfection sensitivity in structural optimization.
In addition to his research, he was one of the most effective and visible leaders in the international mechanics community, serving for many years on the executive council of the International Union of Theoretical and Applied Mechanics (IUTAM). He was also active in the Netherlands on national committees devoted to aircraft development and safety.
The story of Koiter’s thesis, Over de stabiliteit van het elastisch evenwicht (On the Stability of Elastic Equilibrium; Uitgeverij H.J. Paris, 1945), deserves telling.1 A strong tradition existed in structures and mechanics at Delft, personified by Koiter’s thesis supervisor, Cornelis Benjamin Biezeno. In the first half of the 20th century, it had become clear that there was a major discrepancy between experimentally measured buckling loads for the elastic buckling of many shell structures and theoretical buckling predictions derived from shell theory. The behavior was in stark contrast with the well-established behavior of columns and plates, for which the elastic buckling predictions of idealized geometries were generally in good agreement with buckling experiments. Some attributed the discrepancy to the inadequacy of existing shell theories.
Koiter instead explored the nature of the solution that bifurcates from the state of fundamental compression using perturbation techniques in a completely general framework applicable to any conservative elastic solid or structural system. In addition, he took into account the influence of small imperfections in the geometry of the structure, which for shells are slight undulations of the middle surface or small thickness variations.
Although most column and plate structures have stable postbuckling behavior and are relatively insensitive to imperfections, Koiter found that many shell structures have unstable postbuckling behavior and, concomitantly, are highly sensitive
1 Parts of this story and other information in this tribute were informed by the 1999 memoir of W.T. Koiter by a colleague from the Netherlands, D.H. van Campen, published in Biographical Memoirs of Fellows of the Royal Society London 45:269–273.
to imperfections because they drastically lower the maximum load the structure can carry. The cylindrical shell under axial compression and the spherical shell under external pressure are the most imperfection-sensitive, with experientially measured loads that are typically as low as one fifth of the prediction for the perfect shell.
Koiter carried out his thesis work in the dark period of World War II when the occupiers of the Netherlands did not permit publication in the country’s native language. Although his thesis was completed in 1942 he delayed publication until 1945 when it could be published in Dutch, and then it was almost two decades before the rest of the world began to appreciate his thesis. More than any other individual, Bernard Budiansky at Harvard University, with the aid of an Afrikaans colleague who translated the Dutch, accelerated the dissemination by publishing papers applying Koiter’s theory to a series of important shell problems. Budiansky was assisted in this task by the writer of this memoir who made the mistake of asking Koiter, when they first met, why he had not published his thesis. Looking down his long nose at the neophyte researcher, Koiter replied that he had published it, in Dutch!
Nearly all of his subsequent papers were published in English—and with a command of the language matched by few technical authors. He claimed that he polished his English writing skills by reading Winston Churchill’s history of the Second World War. Although he resisted all attempts to republish his thesis, we are fortunate that a former student and colleague, Arnold van der Heijden, published a book that comprehensively presents Koiter’s course lectures on elastic stability.2
Koiter was also a dominant figure in the development of shell theory in the two decades beginning in the mid-1950s. His major new contributions were to nonlinear shell theory, but he also performed an enormous service to the field by helping to settle the fractious dispute about which of the
2 van der Heijden, A.M.A., ed. 2009. W.T. Koiter’s Lectures on the Elastic Stability of Solids and Structures. Cambridge University Press.
many competing systems of linear shell theory equations was the correct one. He showed that certain differences between one theory and another were allowable, and indeed inevitable, owing to the errors inherent in the construction of two-dimensional equations for a shell as an approximation to the three-dimensional body. He established that several (but not all) of the competing theories were equivalent within these inherent errors. In fact, the linear shell equations in the classic elasticity treatise of A.E.H. Love, first published in 1911, were shown to be among those acceptable (when the Beatles became popular, Koiter even delivered a talk entitled “All You Need Is Love”).
The state of affairs for nonlinear shell theory was far from satisfactory in 1960. Buckling phenomena are inherently nonlinear and in his thesis Koiter had addressed some of the unresolved issues of nonlinear shell theory. Because no single set of equations is capable of characterizing all nonlinear shell phenomena, a specific set of equations must be identified for a given class of problems (e.g., large strain membrane behavior versus finite amplitude bending and stretching). His subsequent contributions, which expanded on those of J. Lyell Sanders published in 1962, systematically laid out various nonlinear shell theory approximations and identified the class of problems for which each would be accurate.
Koiter’s enormous stature in the mechanics community was also reflected by his leadership role in IUTAM, for which he served on the executive committee for 16 years, including as president (1968–1972). His service coincided with the period in which outstanding mechanicians from the Soviet Union had increasing, but complicated, interactions with counterparts from the west. Such difficulties, and Koiter’s strength of character, were illustrated by the 1976 IUTAM International Congress held in Delft and chaired by Koiter. As was not uncommon during this period, authorities in the Soviet Union manipulated the list of attendees such that a number of the most prominent Soviet invitees did not appear but were replaced by others with the idea that these individuals would fill the open lecture slots. This was unacceptable to Koiter and
his colleagues and they decided against reassigning these slots as a silent, but effective, protest.
Koiter’s contributions were internationally recognized by medals, honorary degrees, and academy memberships. He was elected to the Royal Netherlands Academy of Sciences in 1959, the US National Academy of Engineering in 1977 (as a foreign member), the French Academy of Sciences in 1981, and the Royal Society of London in 1982. In 1965 he was awarded the Theodore von Kármán Medal of the American Society of Civil Engineers. In 1968 he received the Timoshenko Medal of the American Society of Mechanical Engineers (ASME) and in 1980 he became an honorary member of the society. In 1996 ASME created the Warner T. Koiter Medal to be awarded every year to a solid mechanician distinguished in both research and international leadership, reflecting the career of its namesake. The writer of this memoir had the honor of presenting on behalf of ASME the first Koiter Medal to Koiter himself at a festive gathering of his former students, colleagues, and family at Delft in January 1997.
Koiter was a devoted family man, married in 1939 to Louise Clara, known affectionately by all as Lous. They raised two boys and two girls.