Nonlinear theories for thin shells
Author:
J. Lyell Sanders Jr.
Journal:
Quart. Appl. Math. 21 (1963), 21-36
MSC:
Primary 73.99
DOI:
https://doi.org/10.1090/qam/147023
MathSciNet review:
147023
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Abstract: Strain-displacement relations for thin shells valid for large displacements are derived. With these as a starting point approximate strain-displacement relations and equilibrium equations are derived by making certain simplifying assumptions. In particular the middle surface strains are assumed small and the rotations are assumed moderately small. The resulting equations are suitable as a basis for stability investigations or other problems in which the effects of deformation on equilibrium cannot be ignored, but in which the rotations are not too large.
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K. Marguerre, Zur Theorie der gekrümmten Platte grosser Formänderung, Proc. of Fifth International Congress of Appl. Mech., Wiley and Sons, 1938, pp. 93–101
L. H. Donnell, Stability of thin-walled tubes under torsion, N. A. C. A. TR 479, 1934
Kh. M. Mushtari and K. Z. Galimov, Non-linear theory of thin elastic shells, Israel Program for Scientific Translations, 1961
E. Reissner, On axisymmetrical deformations of thin shells of revolution, Proc. of Symposia in Appl. Math., vol. 3, McGraw-Hill, 1950, pp. 27–52
J. L. Synge and W. Z. Chien, The intrinsic theory of elastic shells and plates, Th. von Kármán Anniversary Volume, Cal. Inst, of Tech., 1941, p. 103
W. Z. Chien, The intrinsic theory of thin shells and plates, Part I—General theory, Q. Appl. Math. 1, 297–327(1944)
W. Z. Chien, The intrinsic theory of thin shells and plates. Part III—Application to thin shells, Q. Appl. Math. 2, 120–135 (1944)
J. L. Ericksen and C. Truesdell, Exact theory of stress and strain in rods and shells, Archive for Rational Mech. and Anal. 1, 295–323 (1959)
A. E. Green and W. Zerna, The equilibrium of thin elastic shells, Q. Jour, of Mech. and Appl. Math. 3, 9–22 (1950)
F. B. Hildebrand, E. Reissner and G. B. Thomas, Notes on the foundations of the theory of small displacements of orthotropic shells, N. A. C. A. TN 1833, Mar. 1949
A. E. Green and W. Zerna, Theoretical elasticity, Oxford Press, 1954, pp. 375–394
V. V. Novozhilov, Foundations of the nonlinear theory of elasticity, Graylock Press, 1953, pp. 186–198
R. W. Leonard, Nonlinear first approximation thin shell and membrane theory, Thesis, Virginia Polytechnic Inst., June 1961
W. T. Koiter, A consistent first approximation in the general theory of thin elastic shells, Proc. of I. U. T. A. M. Symposium on the Theory of Thin Elastic Shells, North-Holland Pub. Co., 1959, pp. 12–33
A. E. H. Love, The mathematical theory of elasticity, Dover, Fourth edition, 1944, pp. 528–531
V. V. Novozhilov, The theory of thin shells, P. Noordhoff Ltd., 1959
J. L. Sanders, An improved first approximation theory for thin shells, N. A. S. A. Report 24, June 1959
P. M. Naghdi and J. F. Berry, On the equations of motion of cylindrical shells, Jour, of Appl. Mech. 21, 160–166 (June 1954)
J. K. Knowles and E. Reissner, Note on the stress-strain relations for thin elastic shells, Jour. Math, and Phys. 37, 269–282 (Oct. 1958)
J. W. Cohen, The inadequacy of the classical stress-strain relations for the right helicoidal shell, Proc. of the I. U. T. A. M. Symposium on the Theory of Thin Elastic Shells, North-Holland Pub. Co., 1959, pp. 415–433
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© Copyright 1963
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