Some general results in the kinematics of axisymmetrical deformation of shells of revolution
Authors:
P. M. Naghdi and L. Vongsarnpigoon
Journal:
Quart. Appl. Math. 43 (1985), 23-36
MSC:
Primary 73L05; Secondary 73G99
DOI:
https://doi.org/10.1090/qam/782254
MathSciNet review:
782254
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: This paper deals with some kinematical aspects of shells of revolution whose torsionless axisymmetrical deformation may be finite or one with small strain accompanied by large or moderately large rotation. The results are summarized in the form of three theorems.
P. M. Naghdi, The theory of shells and plates, in S. Flügge’s Handbuch der Physik, Vol. VIa/2 (edited by C. Truesdell), Springer-Verlag, Berlin, 1972, 425–640
P. M. Naghdi, Finite deformation of elastic rods and shells. Proc. IUTAM Symp. on Finite Elasticity (Bethlehem, PA, 1980, edited by D. E. Carlson and R. T. Shield), Martinus Nijhoff Publishers, Hague, Netherlands, 1982, 47–103
- J. Casey and P. M. Naghdi, An invariant infinitesimal theory of motions superposed on a given motion, Arch. Rational Mech. Anal. 76 (1981), no. 4, 355–391. MR 628174, DOI https://doi.org/10.1007/BF00249971
- P. M. Naghdi and L. Vongsarnpigoon, Small strain accompanied by moderate rotation, Arch. Rational Mech. Anal. 80 (1982), no. 3, 263–294. MR 674547, DOI https://doi.org/10.1007/BF00251489
- P. M. Naghdi and L. Vongsarnpigoon, A theory of shells with small strain accompanied by moderate rotation, Arch. Rational Mech. Anal. 83 (1983), no. 3, 245–283. MR 701905, DOI https://doi.org/10.1007/BF00251511
- Luthur Pfahler Eisenhart, An Introduction to Differential Geometry, Princeton Mathematical Series, vol. 3, Princeton University Press, Princeton, N. J., 1940. MR 0003048
- Barrett O’Neill, Elementary differential geometry, Academic Press, New York-London, 1966. MR 0203595
- P. M. Naghdi and R. P. Nordgren, On the nonlinear theory of elastic shells under the Kirchhoff hypothesis, Quart. Appl. Math. 21 (1963), 49–59. MR 145743, DOI https://doi.org/10.1090/S0033-569X-1963-0145743-4
- 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
P. M. Naghdi, The theory of shells and plates, in S. Flügge’s Handbuch der Physik, Vol. VIa/2 (edited by C. Truesdell), Springer-Verlag, Berlin, 1972, 425–640
P. M. Naghdi, Finite deformation of elastic rods and shells. Proc. IUTAM Symp. on Finite Elasticity (Bethlehem, PA, 1980, edited by D. E. Carlson and R. T. Shield), Martinus Nijhoff Publishers, Hague, Netherlands, 1982, 47–103
J. Casey and P. M. Naghdi, An invariant infinitesimal theory of motion superposed on a given motion, Arch. Rational Mech. Anal. 76, 355–390 (1981)
P. M. Naghdi and L. Vongsarnpigoon, Small strain accompanied by moderate rotation, Arch. Rational Mech. Anal. 80, 263–294 (1982)
P. M. Naghdi and L. Vongsarnpigoon, A theory of shells with small strain accompanied by moderate rotation, Arch. Rational Mech. Anal. 83, 245–283 (1983)
L. P. Eisenhart, An introduction to differential geometry. Princeton University Press, Princeton, 1947
B. O’Neill, Elementary differential geometry, Academic Press, New York, 1966
P. M. Naghdi and R. P. Nordgren, On the nonlinear theory of elastic shells under the Kirchhoff hypothesis, Quart. Appl. Math. 21, 49–59, (1963)
E. Reissner, On axisymmetrical deformation of thin shells of revolution, Prov. Symp. Appl. Math. 3, 27–52 (1950)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73L05,
73G99
Retrieve articles in all journals
with MSC:
73L05,
73G99
Additional Information
Article copyright:
© Copyright 1985
American Mathematical Society
