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Etudiant de Maurice Anthony Biot;
Professeur à l'université de Liège ;
Professeur à l'université de Louvain ;
Membre de l'Académie royale de Belgique.
From:
http://www.colorado.edu/engineering/CAS/Felippa.d/FelippaHome.d/Publications.d/FdVNeglect.html
Fraeijs de Veubeke: Neglected Discoverer of the "Hu-Washizu Functional" by Carlos A. Felippa
This note was motivated by a "Classical Reprint Series" appearance of Fraeijs de Veubeke's Displacement and Equilibrium Models chapter in the International Journal for Numerical Methods in Engineering [4]. In the reprint preface Olek Zienkiewicz reminds readers of several neglected aspects of de Veubeke's seminal contributions to finite element methods. This note calls attention to an ignored fundamental contribution to variational mechanics [3]. For technical details, including a step by step review of de Veubeke's derivations, interested readers are referred to a recent Technical Note in the Journal of Applied Mechanics [2].
The Canonical Functional
The three-field canonical functional of linear elastostatics, herein abbreviated to C3FLE, is identified as the "Hu-Washizu functional" in the mechanics literature. In this functional the three interior fields: displacements, stresses and strains, are independently varied. This attribution is supported by two independent publications, which, by strange coincidence, appeared simultaneouly on March 1955 [10,14]. A four-field generalization, in which surface tractions are independently varied, will be called C4FLE.
The reprinted chapter [4] is still cited as one of the early classics in the finite element literature. That article contains the first enunciation of the limitation principle, which has since served as guide in the construction of mixed models. De Veubeke's exposition of variational methods starts from the C4FLE functional, which he calls "the general variational principle." However, it does not reference Hu and Washizu as its source but an earlier technical report, written in French [3]. This appears as the third reference in that chapter.
A subsequent journal paper [5] on variational principles and the patch test is slightly more explicit. It begins: "There is a functional that generates all the equations of linear elasticity theory in the form of variational derivatives and natural boundary conditions. Its original construction [here he refers to the 1951 report] followed the method proposed by Friedrichs ..."
These references motivated me to investigate whether de Veubeke had indeed constructed that functional in the 1951 report. That would confer him priority over Hu and Washizu, although of course these two contributions were more influential in subsequent work. I was able to procure an archived copy of [3] thanks to Professors Beckers and Geradin of the University of Liege, where de Veubeke was a Professor of Aeronautical Engineering from the early 1950s until his untimely death on September 1976.
For more see the link:
Prof. Baudouin M. Fraeijes de Veubeke (1917 - 1976)
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