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The Path Towards Energetical Principles

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An Introduction to the History of Structural Mechanics

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Abstract

If Paoli’s judgment at the end of the eighteenth century is a little abrupt, so is the suddenness with which the enigma vanishes from the great treatises of statics which inaugurate the new century. For example, Poinsot, in his Élémens de statique (1803) interprets the static indeterminacy of the problem of supports as a necessary consequence of his concept of rigid bodies: “We should then guard ourselves from the conclusion that the theory known up to now is insufficient to resolve the problem in question; for we will see that this problem is indeterminate by the hypothesis itself which we have made, and that the theory gives all we could ask without contradiction.”1

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References

  1. L. Poinsot, Élémens de statique (Paris, 1803). p. 151.

    Google Scholar 

  2. S.D. Poisson, Traité de mécanique (Paris, 1811), book 3, part 2, ch. 1, pp. 523–525.

    Google Scholar 

  3. J.B. Labey, Traité de statique (Paris, 1812), pp. 94–98.

    Google Scholar 

  4. C. Bonnycastle, “On the Pressures Which Sustain a Heavy Body in Equilibrium when the Points of Support Are More than Three,” Annals of Philosophy, Vol. 13 (1819). p. 307.

    Google Scholar 

  5. “Note sur un paradoxe de statique. Par un abboné,” in J.D. Gergonne, Annales de mathématiques pures et appliquées, Vol. 17 (1826–1827), pp. 75-

    Google Scholar 

  6. P. Barilari, Intorno un problema del Dottore Ambrogio Fusinieri, sul modo di determinare le pression che esercita un grave sopra pizG appoggi (Pesaro, 1833).

    Google Scholar 

  7. F. Bertelli, “Ricerche sperimentali circa la pressione de’ corpi solidi ne’ casi in cui la misura di essa, secondo le analoghe teorie meccaniche, si manifesta indeterminata…,” Memorie della Accademia delle Scienze dell’ Istituto di Bologna, Vol. 1 (1850) pp. 433–461

    Google Scholar 

  8. G. Fagnoli, “Riflessioni intorno la teorica delle pressioni che un corpo o sistema di forma invariabile esercita contro gli appoggi rigidi ed irremovibili dai quali è sostenuto in equilibrio,” Memorie della Accademia delle Scienze dell’ Istituto di Bologna, Vol.4 (1853) pp. 109–138. Bertelli’s memoir was presented in two parts in 1843 and 1844; Fagnoli’s was given in 1852.

    Google Scholar 

  9. G. Piola, Sull’applicazione de’ principj della meccanica del Lagrange ai principali problemi. Prize-winning memoir presented for the competition of the Imperial Regio Istituto di Scienze, Milan, October 4, 1824 (Milan, 1825), pp. 77–78.

    Google Scholar 

  10. Cf. R. Dugas, Histoire de la mécanique (Neuchâtel, 1950), p. 421.

    Google Scholar 

  11. L. Navier, “Sur des questions de statique dans lesquelles on considère un corps supporté par un nombre de points d’appui surpassant trois,” Bulletin des sciences par la Société Philomatique de Paris (1825), p. 35.

    Google Scholar 

  12. G. Green, “On the Laws of the Reflexion and Refraction of Light at the common Surface of two non-crystallized Media,” Transactions of the Cambridge Philosophical Society, Vol. 7 (1839), pp. 1–24

    Google Scholar 

  13. also published in G. Green, Mathematical Papers of the Late George Green (London, 1871) (hereafter Green, Mathematical Papers), pp. 243–269.

    Google Scholar 

  14. Cf. A. Castigliano, “Nuova teoria intorno all’equilibrio dei sistemi elastici,” Atti della Reale Accademia delle Scienze di Torino, Vol. 11 (1875) p. 132.

    Google Scholar 

  15. William Thomson (Lord Kelvin), “On the Thermo-elastic and Thermo-magnetic Properties of Matter,” The Quarterly Journal of Pure and Applied Mathematics, Vol. 1 (1857), pp. 57–77

    Google Scholar 

  16. J. Second, Cournot et la psychologie vitaliste (Paris, 1910)

    Google Scholar 

  17. J. Rostand, “Cournot et la biologie,” Revue d’histoire des sciences (1953)

    Google Scholar 

  18. E. Callot, La philosophie biologique de Cournot (Paris, 1959)

    Google Scholar 

  19. F. Mentré, Cournot et la renaissance du probabilisme au XIX siècle (Paris, 1908)

    Google Scholar 

  20. A. Darbon, Le concept du hasard dans la philosophie de Cournot (Paris, 1911)

    Google Scholar 

  21. G. Milhaud, “La définition du hasard de Cournot,” Revue philosophique (1911)

    Google Scholar 

  22. R. Fedi, “Il probabilismo filosofico di A. Cournot,” Archivio di storia della filosofia italiana (1934)

    Google Scholar 

  23. J. De la Harpe, De l’ordre et du hasard: Le réalisme critique de A.A. Cournot (Paris, 1936)

    Google Scholar 

  24. E. Rocchi, “A.A. Cournot e gli odierni concetti di probabilità,” De Homine (1967)

    Google Scholar 

  25. R. Ruyer, L’humanité de l’avenir d’après Cournot (Paris, 1930)

    Google Scholar 

  26. F. Born-paire, Du principe de la liberté économique dans l’ouvre de Cournot et dans celle de l’École de Lausanne (Sirey, 1931)

    Google Scholar 

  27. P. Taviani, “Cournot e il positivismo,” Rivista internazionale di scienze sociali (1940).

    Google Scholar 

  28. B. Caizzi, La filosofia di A. Cournot (Bari, 1942).

    Google Scholar 

  29. A. Cournot, “Sur les percussions entre deux corps durs, qui se choquent en plusieurs points,” Bulletin des Sciences mathématiques,astronomiques, physiques et chimiques du Baron de Férussac (hereafter Bulletin de Férussac) (1827) (hereafter Cournot, “Percussions entre deux corps”), pp. 4–11.

    Google Scholar 

  30. See for example Castigliano’s first memoir of 1875, pp. 32–33.

    Google Scholar 

  31. G. Grioli, “On the Stress in Rigid Bodies,” Meccanica,Vol. 18 (1983), pp. 3–7

    Article  MATH  Google Scholar 

  32. S. Marzano, P. Podio Guidugli, “Materiali elastici approssimativamente vincolati,” Rendiconti del Seminario Matematico di Padova Vol. 73 (1985), pp. 1–19

    Google Scholar 

  33. “Formulazioni alternative del vincolo di rigidità sulle deformazioni di materiali elastici,” Atti del Settimo Congresso AIMETA, Vol. 2 (Trieste, 1984), pp. 131–141

    Google Scholar 

  34. in this context see also: G. Capriz, P. Podio Guidugli, “A generalization of Signorini’s perturbation method suggested by two problems of Grioli,” Rendiconti del Seminario Matematico di Padova, Vol. 68 (1982), pp. 149–162.

    Google Scholar 

  35. “Mémoire sur les pressions, par M. Vène,” Bulletin de Férussac (1828), p. 10.

    Google Scholar 

  36. A. Cournot, “Sur la théorie des pressions,” Bulletin de Férussac (1828) (hereafter cited as Cournot, “Sur la théorie des pressions”) pp. 10–22.

    Google Scholar 

  37. A. Castigliano, “Intorno all’equilibrio dei sistemi elastici,” Atti della Reale Accademia di Torino, Vol. 10 (1875) p. 5.

    Google Scholar 

  38. H. Moseley, “On a New Principle in Statics, called the Principle of least pressure,” Philosophical Magazine, 3rd series, Vol. 3, No. 16 (1833) (hereafter Moseley, “New Principle”), pp. 285–288

    Google Scholar 

  39. H. Moseley, “On the Theory of Resistances in Statics,” Philosophical Magazine, 3rd series, Vol. 3, No. 18 (1833) (hereafter Moseley, “Theory of Resistances”) pp. 431–436.

    Google Scholar 

  40. G.M. Pagani, “Note sur l’équilibre d’un système dont une partie est supposée inflexible et dont l’autre partie, est flexible et extensible,” Mémoires de l’Académie de Bruxelles, Vol. 8 (1834) (hereafter Pagani, “Note”), pp. 1–14

    Google Scholar 

  41. G.M. Pagani, “Mémoire sur l’équilibre des colonnes,” Memorie della Regia Accademia delle Scienze di Torino, 2d ser., Vol. 1 (1839) (hereafter Pagani, “Memoir”), pp. 316–371.

    Google Scholar 

  42. L.F. Menabrea, “Sul principio di elasticità, delucidazioni di L.F.M.,” Atti della Reale Accademia delle Scienze di Torino,Vol. 5 (1869–1870) (hereafter cited as Menabrea, “Principio”) p. 687.

    Google Scholar 

  43. A. Dorna, “Memoria sulle pressioni sopportate dai punti di appoggio di un sistema equilibrato ed in istato prossimo al moto,” Memorie della Reale Ac-cademia delle Scienze di Torino, Vol. 18 (1857), pp. 4–40.

    Google Scholar 

  44. B.P.E. Clapeyron, “ Calcul d’une poutre élastique reposant librement sur des appuis inégalement espacés,” Comptes rendus, Vol. 45 (1857) (hereafter cited as Clapeyron, “Calcul d’une poutre,”) pp. 1076–1080.

    Google Scholar 

  45. B.P.E. Clapeyron, “Calcul d’une poutre,” p. 1077.

    Google Scholar 

  46. See J.A.O Bresse, “Rectification de priorité,” Annales des Ponts et Chaussées, 3d ser., Vol. 20 (2d semester, 1860), pp. 405–406.

    Google Scholar 

  47. B.P.E. Clapeyron, “Calcul d’une poutre,” p. 1078.

    Google Scholar 

  48. G. Lamé, Leçons sur la théorie mathématique de l’elasticité des corps solides (Paris, 1852), lesson 7.

    Google Scholar 

  49. B.P.E. Clapeyron, “Mémoire sur le travail des forces élastiques dans un corps solide élastique déformé par l’action des forces extérieures,” Comptes rendus, Vol. 46 (1858), pp. 208–212.

    Google Scholar 

  50. L.F. Menabrea, “Nouveau principe sur la distribution des tensions dans les systèmes élastiques,” Comptes rendus, Vol. 46 (1858) (hereafter cited as Menabrea, “Nouveau principe”), pp. 1056–1060. A first memoir on this subject was presented by Menabrea to the Academy of Turin in 1857.

    Google Scholar 

  51. E. Sabbia, Errore del principio di elasticità formulato da L. Federico Menabrea. Cenno critico di E.S (Turin, 1869).

    Google Scholar 

  52. L.F. Menabrea, “Sulla determinazione delle tensioni e delle pressioni ne’ sistemi elastici,” Atti della Regia Accademia dei Lincei, 2d ser., Vol. 2 (1875), pp. 201–220.

    Google Scholar 

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Authors and Affiliations

  1. Ordinario di Scienza delle Costruzioni Facoltà di Architettura di Genova, Università di Genova, Genova, Italy

    Edoardo Benvenuto (Ordinario di Scienza delle Costruzioni)

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  1. Edoardo Benvenuto
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© 1991 Springer-Verlag New York Inc.

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Benvenuto, E. (1991). The Path Towards Energetical Principles. In: An Introduction to the History of Structural Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2994-0_6

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  • DOI: https://doi.org/10.1007/978-1-4612-2994-0_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7751-4

  • Online ISBN: 978-1-4612-2994-0

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