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.

**[1]**C. E. Pearson,*General theory of elastic stability*, Quart. Appl. Math.**14**, 133-144 (1956) MR**0079414****[2]**R. Hill,*On uniqueness and stability in the theory of finite elastic strain*, J. Mech. Phys. Solids**5**, 229-241 (1957) MR**0092379****[3]**J. T. Holden,*Estimate of critical loads in elastic stability theory*, Arch. Rational Mech. Anal.**17**, 171-183 (1964) MR**0170530****[4]**M. F. Beatty,*Some static and dynamic implications of the general theory of elastic stability*, Arch. Rational Mech. Anal.**19**, 167-188 (1965) MR**0176687****[5]**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) MR**0198772****[6]**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) MR**0145750****[7]**R. T. Shield,*On the stability of linear continuous systems*, Zeitschrift angew. Math. Phys.**16**, 649-686 (1965) MR**0190539****[8]**H. Ziegler,*Linear elastic stability*, Zeitschrift angew. Math. Phys.**4**, 89-121 and 168-185 (1953) MR**0056445****[9]**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 MR**0076568****[10]**V. V. Bolotin,*Nonconservative problems of the theory of elastic stability*, Pergamon Press, Inc., New York, 1963 (Moscow, 1961) MR**0189343****[11]**S. Nemat-Nasser and G. Herrmann,*On the stability of equilibrium of continuous systems*, Ing. Arch.**35**, 17-24 (1966)**[12]**J. L. Ericksen,*Thermoelastic stability, Proc. Fifth U. S. National Congress of Appl. Mech*., 187-193 (1966)**[13]**J. L. Ericksen,*A thermo-kinetic view of elastic stability theory*, Int'l. Jour. Solids and Structures**2**, 573-580 (1966)**[14]**W. Prager,*Introduction to mechanics of continua*, Ginn and Company, 1961 MR**0126974****[15]**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 MR**1766413****[16]**B. D. Coleman and W. Noll,*The thermodynamics of elastic materials with heat conduction and viscosity*, Arch. Rational Mech. Anal.**13**, 167-178 (1963) MR**0153153****[17]**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)**[18]**E. F. Masur,*On tensor rates in continuum mechanics*, Zeitschrift angew. Math. Phys.**16**, 191-201 (1965) MR**0184475**

Additional Information

DOI:
https://doi.org/10.1090/qam/99863

Article copyright:
© Copyright 1968
American Mathematical Society