On local stability of a finitely deformed solid subjected to follower type loads
Author:
S. Nemat-Nasser
Journal:
Quart. Appl. Math. 26 (1968), 119-129
DOI:
https://doi.org/10.1090/qam/99863
MathSciNet review:
QAM99863
Full-text PDF Free Access
Abstract |
References |
Additional Information
Abstract: In this study the problem of the local stability (stability in the small) of a finitely deformed solid subjected to a set of follower type surface loads is analyzed, and a necessary, and a sufficient condition for asymptotic stability is established. Certain implications of the commonly used modal analysis are also investigated, and necessary and sufficient conditions for stability are formulated.
- Carl E. Pearson, General theory of elastic stability, Quart. Appl. Math. 14 (1956), 133–144. MR 79414, DOI https://doi.org/10.1090/S0033-569X-1956-79414-4
- R. Hill, On uniqueness and stability in the theory of finite elastic strain, J. Mech. Phys. Solids 5 (1957), 229–241. MR 92379, DOI https://doi.org/10.1016/0022-5096%2857%2990016-9
- J. T. Holden, Estimation of critical loads in elastic stability theory, Arch. Rational Mech. Anal. 17 (1964), 171–183. MR 170530, DOI https://doi.org/10.1007/BF00282436
- Millard F. Beatty, Some static and dynamic implications of the general theory of elastic stability, Arch. Rational Mech. Anal. 19 (1965), 167–188. MR 176687, DOI https://doi.org/10.1007/BF00277007
- W. T. Koiter, The energy criterion of stability for continuous elastic bodies. I, II, Nederl. Akad. Wetensch. Proc. Ser. B 68 (1965), 178–189, 190–202. MR 0198772
- R. T. Shield and A. E. Green, On certain methods in the stability theory of continuous systems, Arch. Rational Mech. Anal. 12 (1963), 354–360. MR 145750, DOI https://doi.org/10.1007/BF00281232
- Richard Thorpe Shield, On the stability of linear continuous systems, Z. Angew. Math. Phys. 16 (1965), 649–686 (English, with German summary). MR 190539, DOI https://doi.org/10.1007/BF01590967
- Hans Ziegler, Linear elastic stability. A critical analysis of methods, Z. Angew. Math. Phys. 4 (1953), 89–121, 167–185. MR 56445, DOI https://doi.org/10.1007/bf02067575
- Hans Ziegler, On the concept of elastic stability, Advances in applied mechanics, vol. IV, Academic Press Inc., New York, N. Y., 1956, pp. 351–403. MR 0076568
- V. V. Bolotin, Nonconservative problems of the theory of elastic stability, Corrected and authorized edition, A Pergamon Press Book. The Macmillan Co., New York, 1963. Translated from the Russian by T. K. Lusher; English translation edited by G. Herrmann. MR 0189343
S. Nemat-Nasser and G. Herrmann, On the stability of equilibrium of continuous systems, Ing. Arch. 35, 17–24 (1966)
J. L. Ericksen, Thermoelastic stability, Proc. Fifth U. S. National Congress of Appl. Mech., 187–193 (1966)
J. L. Ericksen, A thermo-kinetic view of elastic stability theory, Int’l. Jour. Solids and Structures 2, 573–580 (1966)
- William Prager, Introduction to mechanics of continua, Introductions to Higher Mathematics. Ginn and Co., Boston, Mass.-Toronto-London, 1961. MR 0126974
- Sia Nemat-Nasser, A micromechanically-based constitutive model for frictional deformation of granular materials, J. Mech. Phys. Solids 48 (2000), no. 6-7, 1541–1563. The J. R. Willis 60th anniversary volume. MR 1766413, DOI https://doi.org/10.1016/S0022-5096%2899%2900089-7
- Bernard D. Coleman and Walter Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13 (1963), 167–178. MR 153153, DOI https://doi.org/10.1007/BF01262690
R. T. Knops and E. W. Wilkes, On Monchan’s theorems for stability of continuous systems, Int’l. Jour. Engr. Sci. 4, 303–329 (1966)
- E. F. Masur, On tensor rates in continuum mechanics, Z. Angew. Math. Phys. 16 (1965), 191–201 (English, with German summary). MR 184475, DOI https://doi.org/10.1007/BF01587645
C. E. Pearson, General theory of elastic stability, Quart. Appl. Math. 14, 133–144 (1956)
R. Hill, On uniqueness and stability in the theory of finite elastic strain, J. Mech. Phys. Solids 5, 229–241 (1957)
J. T. Holden, Estimate of critical loads in elastic stability theory, Arch. Rational Mech. Anal. 17, 171–183 (1964)
M. F. Beatty, Some static and dynamic implications of the general theory of elastic stability, Arch. Rational Mech. Anal. 19, 167–188 (1965)
W. T. Koiter, The energy criterion of stability for continuous elastic bodies, Proc. Kon. Ned. Ak. Wet., Series B, 68, 178–189 and 190–202 (1965)
R. T. Shield and A. E. Green, On certain methods in the stability theory of continuous systems, Arch. Rational Mech. Anal. 12, 354–360 (1963)
R. T. Shield, On the stability of linear continuous systems, Zeitschrift angew. Math. Phys. 16, 649–686 (1965)
H. Ziegler, Linear elastic stability, Zeitschrift angew. Math. Phys. 4, 89–121 and 168–185 (1953)
H. Ziegler, On the concept of elastic stability, Advances in Applied Mechanics, edited by H. L. Dryden and T. von Kärmän, vol. 4, Academic Press, Inc., New York, 1956, pp. 351–403
V. V. Bolotin, Nonconservative problems of the theory of elastic stability, Pergamon Press, Inc., New York, 1963 (Moscow, 1961)
S. Nemat-Nasser and G. Herrmann, On the stability of equilibrium of continuous systems, Ing. Arch. 35, 17–24 (1966)
J. L. Ericksen, Thermoelastic stability, Proc. Fifth U. S. National Congress of Appl. Mech., 187–193 (1966)
J. L. Ericksen, A thermo-kinetic view of elastic stability theory, Int’l. Jour. Solids and Structures 2, 573–580 (1966)
W. Prager, Introduction to mechanics of continua, Ginn and Company, 1961
S. Nemat-Nasser and J. Roorda, On the energy concepts in the theory of elastic stability, ONR Report No. 3, University of California, San Diego, November 1966; to appear in Acta Mechanica
B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178 (1963)
R. T. Knops and E. W. Wilkes, On Monchan’s theorems for stability of continuous systems, Int’l. Jour. Engr. Sci. 4, 303–329 (1966)
E. F. Masur, On tensor rates in continuum mechanics, Zeitschrift angew. Math. Phys. 16, 191–201 (1965)
Additional Information
Article copyright:
© Copyright 1968
American Mathematical Society