Abstract
A thick rectangular plate of incompressible isotropic elastic material is subjected to a pure homogeneous deformation by tensile forces or thrusts applied to a pair of opposite faces. The theory of small deformations superposed on finite deformations is applied to determine the critical conditions under which bifurcation solutions (i.e. adjacent equilibrium positions) can exist. The adjacent equilibrium positions considered are those for which the superposed deformation is two-dimensional and is coplanar with the loading force and the thickness direction of the plate, the faces of the plate normal to its thickness being force-free. A number of theorems relating to the critical conditions for superposed deformations of the flexural and barreling types are derived under conditions on the strain-energy function more general than those employed in earlier work. It is also shown how these results can be applied to the determination of the bifurcation conditions corresponding to any specified strain-energy function.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A. E. Green, R. S. Rivlin and R. T. Shield, General theory of small elastic deformations superposed on large elastic deformations, Proc. R. Soc. A, 211, 128–154 (1952).
E. W. Wilkes, On the stability of a circular tube under end thrust, Q. J. Mech. appl. Math. 8, 88–100 (1955).
A. E. Green and A. J. M. Spencer, The stability of a circular cylinder under finite extension and torsion, J. Math. Phys. 37, 316–338 (1959).
R. L. Fosdick and R. T. Shield, Small bending of a circular bar superposed on finite extension or compression, Arch. Ration. Mech. Analysis 12, 223–248 (1963).
Guo Zhong-Heng, Vibration and stability of a cylinder subject to finite deformation, Arch. Mech. Stos. 14, 757–768 (1962).
K. N. Sawyers and R. S. Rivlin, Instability of an elastic material, Int. J. Solids Struct. 9, 607–613 (1973).
Z. Wesolowski, Stability in some cases of tension in the light of the theory of finite strain, Arch. Mech. Stos. 14, 875–900 (1962).
M. Levinson, Stability of a compressed neo-Hookean rectangular parallelopiped, J. Mech. Phys. Solids 16, 403–415 (1968).
J. L. Nowinski, On the elastic stability of thick columns, Acta Mechanica 7, 279–286 (1969).
C.-H. Wu and O.E. Widera, Stability of a thick rubber solid subject to pressure loads, Int. J. Solids Struct. 5, 1107–1117 (1969).
I. W. Burgess and M. Levinson, The instability of slightly compressible rectangular rubberlike solids under biaxial loadings, Int. J. Solids Struct. 8, 133–148 (1972).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Sawyers, K.N., Rivlin, R.S. (1997). Bifurcation Conditions for a Thick Elastic Plate Under Thrust. In: Barenblatt, G.I., Joseph, D.D. (eds) Collected Papers of R.S. Rivlin. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2416-7_48
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2416-7_48
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7530-5
Online ISBN: 978-1-4612-2416-7
eBook Packages: Springer Book Archive