On the nonlinear theory of elastic shells under the Kirchhoff hypothesis
Authors:
P. M. Naghdi and R. P. Nordgren
Journal:
Quart. Appl. Math. 21 (1963), 49-59
MSC:
Primary 73.53
DOI:
https://doi.org/10.1090/qam/145743
MathSciNet review:
145743
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Additional Information
- 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
W. Z. Chien, The intrinsic theory of thin shells and plates, Quart. Appl. Math. 1 (1944) 297; 2 (1944) 43 and 120
P. M. Naghdi, A survey of recent progress in the theory of elastic shells, Appl. Mech. Reviews 9 (1956) 365
- J. L. Ericksen and C. Truesdell, Exact theory of stress and strain in rods and shells, Arch. Rational Mech. Anal. 1 (1958), 295–323. MR 99135, DOI https://doi.org/10.1007/BF00298012
- V. V. Novozhilov, Foundations of the nonlinear theory of elasticity, Graylock Press, Rochester, N. Y., 1953. MR 0054465
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- Eric Reissner, On axisymmetrical deformations of thin shells of revolution, Proc. Symposia Appl. Math. v. 3, McGraw-Hill Book Co., New York, N. Y., 1950, pp. 27–52. MR 0039489
J. L. Sanders, Jr., Nonlinear theories of thin shells, Tech. Rept. No. 10, Contract Nonr 1866(02), Harvard University, 1961
R. W. Leonard, Nonlinear first approximation thin shell and membrane theory, NASA, 1961, to appear.
- P. M. Naghdi, Foundations of elastic shell theory, Progress in Solid Mechanics, Vol. IV, North-Holland, Amsterdam, 1963, pp. 1–90. MR 0163488
- A. E. Green and W. Zerna, Theoretical elasticity, Oxford, at the Clarendon Press, 1954. MR 0064598
- R. S. Rivlin and J. L. Ericksen, Stress-deformation relations for isotropic materials, J. Rational Mech. Anal. 4 (1955), 323–425. MR 68413, DOI https://doi.org/10.1512/iumj.1955.4.54011
- R. S. Rivlin, Further remarks on the stress-deformation relations for isotropic materials, J. Rational Mech. Anal. 4 (1955), 681–702. MR 71980, DOI https://doi.org/10.1512/iumj.1955.4.54025
- C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik, Bd. III/1, Springer, Berlin, 1960, pp. 226–793; appendix, pp. 794–858. With an appendix on tensor fields by J. L. Ericksen. MR 0118005
- A. E. Green and J. E. Adkins, Large elastic deformations, Clarendon Press, Oxford, 1970. Second edition, revised by A. E. Green. MR 0269158
J. L. Synge and W. Z. Chien, The intrinsic theory of elastic shells and plates, Th. v. Karman Anniv. Vol., 103, 1941
W. Z. Chien, The intrinsic theory of thin shells and plates, Quart. Appl. Math. 1 (1944) 297; 2 (1944) 43 and 120
P. M. Naghdi, A survey of recent progress in the theory of elastic shells, Appl. Mech. Reviews 9 (1956) 365
J. L. Ericksen and C. Truesdell, Exact theory of stress and strain in rods and shells, Arch. Ratl. Mech. Anal. 1 (1958) 295
V. V. Novozhilov, Foundations of the nonlinear theory of elasticity (translated from the first 1948 Russian edition), Graylock Press, 1953.
E. Reissner, On the theory of thin elastic shells, H. Reissner Anniversary Volume, J. W. Edwards, Ann Arbor, Mich., 231, 1949
E. Reissner, On axisymmetrical deformations of shells of revolution, Proc. Symposia Appl. Math. 3 (1950) 27
J. L. Sanders, Jr., Nonlinear theories of thin shells, Tech. Rept. No. 10, Contract Nonr 1866(02), Harvard University, 1961
R. W. Leonard, Nonlinear first approximation thin shell and membrane theory, NASA, 1961, to appear.
P. M. Naghdi, Foundations of elastic shell theory, Tech. Rept. No. 15, Contract Nonr 222(69), University of California, Berkeley, to appear
A. E. Green and W. Zerna, Theoretical elasticity, Oxford, Clarendon Press, 1954
R. S. Rivlin and J. L. Ericksen, Stress-deformation relations for isotropic materials, J. Ratl. Mech. Anal. 4 (1955) 323
R. S. Rivlin, Further remarks on the stress-deformation relations for isotropic materials, J. Ratl. Mech. Anal. 4 (1955) 681
C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik III/1, 226, 1960
A. E. Green and J. E. Adkins, Large elastic deformations, Oxford, Clarendon Press, 1960
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Article copyright:
© Copyright 1963
American Mathematical Society
