Literature Cited
L. I. Balabukh and L. A. Shapovalov, “Variational equations of thermoelasticity,” Prikl. Mat. Mekh.,24, No. 4, 703–707 (1960).
V. I. Klimov, “Integral principle of the minimum of the total additional energy of a thermoelastic system,” in: Questions of Strength of Elements of Aviation Structures. Proceedings of the Kuibyshevsk. Aeronautics Institute [in Russian], No. 60 (1973), pp. 17–27.
V. M. Maizel' Temperature Problem of Elasticity Theory [in Russian], Izd. Akad. Nauk UkrSSR, Kiev (1951).
E. Betti, “Teoria della elastica,” Il Nuove Cimento, Ser. 2,7–8, 5–21, 69–97, 158–180, 357–367 (1872).
A. Castigliano, “Intorno ai sistemi elastici,” Dissertazione, Vincenzo Bona, Turin (1873).
A. Castigliano, “Intorno all'equilibrio dei sistemi elastici,” Atti Reall Accad. Sci. Torino,10, 380–423 (1875).
A. Castigliano, “Nuovo teoria intorno all'equilibrio dei sistemi elastici,” Atti Reall Accad. Sci. Torino,11, 127–286 (1876).
A. Castigliano, Theorie de l'Equilibre des Systèmes Élastiques et ses Applications, A. F. Negro (1879). English translation: The Theory of Equilibrium of Elastic Systems and Its Applications, Dover, New York (1966). See also E. S. Andrews, Elastic Stresses in Structures, Scott Greenwood and Son, London (1919).
F. Crotti, La Teoria dell Elasticita Nesuoi Principi Fondamentali e nelle sue Applicazioni Pratiche alle Construzione, Vol. 8, Ulrico Heopli, Milan (1888).
F. Engesser, “Uber statische unbestimmte Träger bei beliegigem Formänderungs-gesetze und über den Satz von der kleinsten Ergänzungsarbeit,” Z. Archit. Ing.-Vereins Hannover,35, 733–744 (1889).
J. C. Maxwell, “On the calculation of equilibrium and stiffness of frames,” Philos. Mag., Ser. 4,27, 294–299 (1864); reprinting: J. C. Maxwell, Scientific Papers, Vol. 1, Combridge University Press (1890), pp. 598–604.
L. F. Menabrea, “Nouveau principe sur la distribution des tensions dans les systèmés elastiques,” Comptes Rendus,46, 1056–1060 (1858).
L. F. Menabrea, “Sulla determinazione delle tensioni e delle pressioni ne sistemi elastici,” Atti Reall Accad. Lincei, Ser. 2,2, 201–220 (1875).
O. Mohr, “Beitrag zur Theorie der Bogenfach-Werksträger,” Z. Archit. Ing.-Vereins Hannover,20, No. 2, 223–238 (1874).
Lord Rayleigh (J. W. Strutt), “A statical theorem,” Philos Mag., Ser. 4,48, 452–456 (1874); reprinting J. W. Strutt, Scientific Papers, Vol. 1, Cambridge University Press (1899), pp. 223–229.
Lord Rayleigh (J. W. Strutt), “Some general theorems relating to vibrations,” Proc. London Math. Soc.,4, 357–368 (1873) reprinting: J. W. Strutt, Scientific Papers, Vol. 1, Cambridge University Press (1899), pp. 170–181.
Lord Rayleigh (J. W. Strutt), The Theory of Sound, Vol. 1 (1877); Vol. 2 (1878). Russian translation: The Theory of Sound, Gostekhizdat, Moscow, Vols. 1 and 2 (1955).
Additional information
Moscow Aeronautics Institute. Translated from Prikladnaya Mekhanika, Vol. 12, No. 1, pp. 25–31, January, 1976.
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Grigolyuk, É.I., Popovich, V.E. Formulation of Castigliano's second theorem for a nonuniformly heated elastic body. Soviet Applied Mechanics 12, 17–23 (1976). https://doi.org/10.1007/BF01073876
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DOI: https://doi.org/10.1007/BF01073876