La ricerca della forma di un corpo solido sufficientemente resistente ai carichi che deve trasmettere, ma nello stesso tempo, il più possibile leggero, è un problema che ha impegnato gli artigiani di tutte le più antiche società civili. Molte di queste soluzioni empiriche si possono ora giustificare mediante il Calcolo delle Variazioni. Ma il fatto più stupefacente che anche in natura, la disposizione dei rami delle piante, delle fibre lignee, delle ossa dei vertebrati, sembrano aver anticipato le soluzioni variazionali attraverso un lentissimo processo evolutivo.
The research of the shape of a solid body, sufficiently strong with respect to the loads that it must transmit, but, at the same time, the lightest as possible, is a problem that has engaged kraftmen of oldest civil societies. Many of these empirical solutions can be now justified through Calculus of Variations. But the must surprising fact is that even in nature the arrangement of branches of plants, of wooder fibres, of bones of vertebrates, seem to have anticipated variational solutions through a slow evolutionary process.
@article{BUMI_2004_8_7A_1_49_0,
author = {Piero Villaggio},
title = {Calcolo delle variazioni e teoria delle strutture},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {7-A},
year = {2004},
pages = {49-76},
zbl = {1192.49001},
language = {it},
url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7A_1_49_0}
}
Villaggio, Piero. Calcolo delle variazioni e teoria delle strutture. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 49-76. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7A_1_49_0/
[1] , Optimal shape design as a material distribution problem, Struct. Optim., Vol. 1 (1989), 193-202 (cf. anche : Optimization of Structural Topology, Shape, and Material, Springer (1995)). | MR 1439157
[2] - , Harmonics holes for nonconstant fields, J. Appl. Mech., Vol. 46 (3) (1979), 573-576. | MR 1350791 | Zbl 0406.73026
[3] , Thin insulating layers: the optimization point of view. In Proc. of Mat. Inst. in Cont. Mech. and Rel. Math. Problems (Ed. ), 1119. Oxford: Un. Press (1988). | Zbl 0645.73015
[4] , Variational Methods for Structural Optimization, New York: Springer (2000). | MR 970514
[5] COLLIER’S ENCYCL., Birds, ed. , New York: Crowell-Collier (1962). | MR 1763123
[6] , On Growth and Form, Cambridge: Un. Press (1961).
[7] - , Topology optimization of continuum structures: A review, Appl. Mech. Rev., Vol. 54, n. 4 (2001), 331-390. | MR 128562
[8] , Structures or Why Things Do Not Fall Down, London: Penguin (1978). | Zbl 0431.73001
[9] - , Contact Problems in the Theory of Plates and Shells, Moskow: Mir (1987).
[10] - , Hanging rope of minimum elongation, SIAM Rev., Vol. 26 (1984), 569-571. | Zbl 0548.73081
[11] , The shape of the strongest column, Arch. Rat. Mech. Anal., Vol. 5 (1968), 275-285 (cf. anche : The Rational Mechanics of Flexible or Elastic Bodies 1638-1788, Orell Füssli (1960)). | MR 765673
[12] , Variational Principles of Mechanics, Toronto: Un. Press (1966). | MR 128160
[13] , Design in Nature. Learning from Trees, Berlin-Heidelberg: Springer (1998).
[14] , The Limits of Economy of Material, Phil. Mag. Serie 6, Vol. 8 (1904), 589-597 (cf. anche : Introduction to Optimization of Structures, Springer (1990)). | Zbl 35.0828.01
[15] , Recenti progressi nel Calcolo delle Variazioni, Boll. U.M.I. (5), Vol. 17-A (1980), 209-225. | MR 1101808
[16] , Kerbspannungslehre, Berlin-Heidelberg: Springer (1985).
[17] , Einführung in die Technische Mechanik, Berlin-Göttinger-Heidelberg: Springer (1963).
[18] , Geschichte der mechanischen Prinzipien, Basel: Birkhäuser (1979). | MR 153138
[19] , Stealing ideas from nature, R.S.A. Journal, August/Sept. (1997), 36-43.