Abstract
The mathematical theory of elastic vibrating plates originated in 1811, when Sophie Germain first developed the first valid hypothesis. This led to the first fourth-order partial differential equation now known as the Germain-Lagrange equation. Much more work had yet to be done, of course. The governing equation for the equilibrium of thin elastic plates was derived from that basic formulation.
…je me suis occupée, à diverses reprises, delà théorie des surfaces élastiques. J’ai multiplié les expériences, les calculs et les réflexions. J’avouerai que j’ai toujours cru voir de nouveaux motifs pour tenir à mon opinion.
—SOPHIE GERMAIN
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Todhunter (1886), p. 133.
- 2.
On 4 September 1820, de Prony, Fourier, and Girar gave an extensive verbal report on Navier’s work and adopted his conclusions, Procès-verbaux. Tome VII, pp. 84–88.
- 3.
Ventsel and Krauthammer (2001).
- 4.
Navier (1823).
- 5.
Cauchy (1823), pp. 9–13.
- 6.
Cauchy (1828), p. 328.
- 7.
The Princeton Companion to Mathematics (2008), p. 758.
- 8.
Greaves (2012).
- 9.
Bucciarelli and Dworsky (1980), pp. 106–107.
- 10.
Todhunter (1886), p. 356.
- 11.
André-Marie Ampère (1775–1836), physicist and mathematician, a professor of mathematics at the École Polytechnique since 1809. In 1824, he was elected chair in experimental physics at the Collège de France.
- 12.
Bucciarelli and Dworsky (1980), p. 106.
- 13.
Todhunter (1886).
- 14.
Ibid., Chapter V, pp. 319–376.
- 15.
Poisson (1811).
- 16.
Poisson (1827), pp. 384–387.
- 17.
Greaves (2012).
- 18.
Poisson (1829), p. 357.
- 19.
Institut de France. Procès-verbaux. Tome IX, p. 55.
- 20.
Germain (1828).
- 21.
Ibid., pp. 304–314. Note relative à d’article intitulé: Mémoire sur l’équilibre et le mouvement des Corps élastiques, page 337 du tome précédent.
- 22.
Ibid., p. 309.
- 23.
Truesdell (1953), p. 456.
- 24.
Poisson (1829).
- 25.
Institut de France. Procès-verbaux. Tome IX, p. 328.
- 26.
Ventsel and Krauthammer (2001).
- 27.
Kirchhoff (1850), pp. 51–88.
- 28.
Kurrer and Ramm (2012), p. 533.
- 29.
Translation by Karl-Eugen Kurrer (2012) from Kirchhoff’s paper, p. 54.
- 30.
Kurrer and Ramm (2012), p. 534.
- 31.
The first boundary condition of a Dirichlet boundary condition, named after Johann Peter Gustav Lejeune Dirichlet ; the normal derivative is known as the Neumann boundary condition after Carl Gottfried Neumann (1832–1925).
- 32.
Thomson and Tait (1883).
- 33.
Gander and Wanner (2011).
- 34.
Levy (1899), p. 219.
- 35.
Forman (1975).
- 36.
Gander and Wanner (2011), p. 18.
- 37.
Ritz (1909), pp. 737–786.
- 38.
Gander and Wanner (2011), p. 19.
- 39.
Ibid.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Musielak, D. (2020). Elasticity Theory After Germain. In: Sophie Germain. Springer Biographies. Springer, Cham. https://doi.org/10.1007/978-3-030-38375-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-38375-6_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-38374-9
Online ISBN: 978-3-030-38375-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)