The general canonical functional of linear elastostatics is associated with the names of Hu and Washizu, who published it independently in 1955. This note discusses how that functional, in a generalized four-field form, had been derived by B. M. Fraeijs de Veubeke in a 1951 technical report. This report presents five of the seven canonical functionals of elasticity. In addition to the general functional, it exhibits what is likely the first derivation of the strain-displacement dual of the Hellinger-Reissner functional. The tour of five variational principles takes only a relatively small portion of the report: 8 pages out of 56. The bulk is devoted to the use of energy methods for analysis of wing structures. The title, technology focus, and limited dissemination may account for the subsequent neglect of this original contribution to variational mechanics. [S0021-8936(00)00401-3]

Issue Section:
Brief Notes
Keywords:
elasticity, variational techniques, statics, deformation
Topics:
Displacement, Elasticity, Variational principles, Construction, Variational techniques
1.
Hu
,
H.-C.
,
1955
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On Some Variational Methods on the Theory of Elasticity and the Theory of Plasticity
,”
Sci. Sin.
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4
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54
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2.
Washizu, K., 1955, “On the Variational Principles of Elasticity and Plasticity,” Aeroelastic and Structures Research Laboratory, Technical Report 25-18, MIT, Cambridge, MA.
3.
Fraeijs de Veubeke, B. M., 1965, “Displacement and Equilibrium Models,” Stress Analysis, O. C. Zienkiewicz and G. Hollister, eds., Wiley, London, pp. 145–197.
4.
Fraeijs de Veubeke, B. M., 1951, “Diffusion des Inconnues Hyperstatiques dans les Voilures a` Longeron Couple´s,” Bull. Serv. Technique de L’Ae´ronautique No. 24, Imprimerie Marcel Hayez, Bruxelles, 56 pp.
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7.
Gurtin, M. E., 1983, “The Linear Theory of Elasticity,” Mechanics of Solids Vol II, C. Truesdell, ed., Springer-Verlag, Berlin, pp. 1–296.
8.
Felippa
,
C. A.
,
1994
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A Survey of Parametrized Variational Principles and Applications to Computational Mechanics
,”
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9.
Oden, J. T., and Reddy, J. N., 1982, Variational Methods in Theoretical Mechanics, Springer-Verlag, Berlin.
10.
Oden
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Reddy
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,
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11.
Washizu, K., 1968, Variational Methods in Elasticity and Plasticity, Pergamon Press, New York.
12.
Geradin, M., ed., 1980, B. M. Fraeijs de Veubeke Memorial Volume of Selected Papers, Sitthoff & Noordhoff, Alphen aan den Rijn, The Netherlands.
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