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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The membrane theory of shells of revolution
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by C. Truesdell
Trans. Amer. Math. Soc. 58 (1945), 96-166
DOI: https://doi.org/10.1090/S0002-9947-1945-0014024-0
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References
    E. H. Love, The mathematical theory of elasticity, 4th ed., Cambridge, 1927. Trefftz, Mathematische Elastizitätstheorie, Handbuch der Physik, vol. 6, 1928, Berlin. S. Sokolnikoff, Mathematical theory of elasticity (notes), Brown University, 1941. Lamé, Memoire sur l’équilibre d’élasticité des enveloppes spheriques, Journal des Mathématiques vol. 19 (1854) pp. 51-87. Neuber, Ein neuer Ansatz zur Lösung räumlicher Probleme der Elastizitätstheorie, Zeitschrift für Angewandte Mathematik und Mechanik vol. 14 (1934) pp. 203-212. Odqvist, Équations de compatibilité pour une système de coordonnés triples orthogonaux quelconques, C. R. Acad. Sci. Paris vol. 205 (1937) pp. 202-204. W. Geckeler, Elastostatik, Handbuch der Physik, vol. 6, 1928, Berlin. Flügge, Statik und Dynamik der Schalen, Berlin, 1934. Timoshenko, Theory of plates and shells, New York and London, 1940. Aron, Das Gleichgewicht und die Bewegung einer unendlich dünnen, beliebig gekrümmten elastischen Schale, Math. Ann. vol. 78 (1874) pp. 136-174. Reissner, Spannungen in Kugelschalen (Kuppeln), Müller-Breslau Festschrift, Leipzig, 1912. Schwerin, Über die Spannungen in symmetrisch und unsymmetrisch belasteten Kugeln (Kuppeln) usw., Dissertation (1917), Berlin, 1918. Dischinger, Schalen und Rippenkuppeln, Handbuch für Eisenbetonbau, vol. 6, 1928, Berlin. Nemenyi, Beiträge zur Berechnung der Schalen unter unsymmetrischer und unstetiger Belastung, Bygningsstatiske Meddelelser (Denmark), 1936. Pucher, Über die Spannungsfunktion beliebig gekrümmter dünner Schalen, Proceedings of the Fifth International Congress of Applied Mechanics, New York, 1939.
  • Eric Reissner, A new derivation of the equations for the deformation of elastic shells, Amer. J. Math. 63 (1941), 177–184. MR 3790, DOI 10.2307/2371288
  • J. L. Synge and W. Z. Chien, The intrinsic theory of elastic shells and plates, Theodore von Kármán Anniversary Volume, University of California Press, Berkeley, Calif., 1941, pp. 103–120. MR 0004596
  • P. Nemenyi and C. Truesdell, A stress function for the membrane theory of shells of revolution, Proc. Nat. Acad. Sci. U.S.A. 29 (1943), 159–162. MR 8985, DOI 10.1073/pnas.29.5.159
    • Truesdell, The membrane theory of shells of revolution, Dissertation (1943), MS in Princeton Library. T. Whittaker and G. N. Watson, A course of modern analysis, 4th ed., Cambridge, 1927. Bateman, Partial differential equations of mathematical physics, Cambridge, 1932.
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Bibliographic Information
  • © Copyright 1945 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 58 (1945), 96-166
  • MSC: Primary 73.2X
  • DOI: https://doi.org/10.1090/S0002-9947-1945-0014024-0
  • MathSciNet review: 0014024