Abstract
Plane deformations of a rectangular strip, composed of an homogeneous fully anisotropic linearly elastic material, are considered. The strip is in equilibrium under the action of end loads, with the lateral sides traction-free. Two conservation properties for certain cross-sectional stress measures are established, generalizing previously known results for the isotropic case. It is noteworthy that in the first of these conservation laws only one of the off-axis elastic constants appears explicitly while in the second only the opposite off-axis constant appears explicitly. Such conservation properties are useful in assessing the influence of material anisotropy on Saint-Venant's principle, as well as in establishing convexity properties for cross-sectional stress measures. In particular, it is anticipated that the results should be useful in determining the extent of edge effects in the off-axis testing of anisotropic and composite materials.
Similar content being viewed by others
References
J.N. Flavin and R.J. Knops, Some convexity considerations for a two-dimensional traction problem. Zeit. ang. Math. Phys. (ZAMP) 39 (1988) 166–176.
C.O. Horgan, Decay estimates for the biharmonic equation with applications to Saint-Venant principles in plane elasticity and Stokes flows. Quart. Appl. Math. 47 (1989) 147–157.
C.O. Horgan, On Saint-Venant's principle in plane anisotropic elasticity. J. Elasticity 2 (1972) 169–180.
C.O. Horgan, Some remarks on Saint-Venant's principle for transversely isotropic composites. J. Elasticity 2 (1972) 335–339.
I. Choi and C.O. Horgan, Saint-Venant's principle and end effects in anisotropic elasticity. J. Appl. Mech. 44 (1977) 424–430.
C.O. Horgan, Saint-Venant end effects in composites. J. Composite Materials 16 (1982) 411–422.
C.O. Horgan and J.K. Knowles, Recent developments concerning Saint-Venant's principle. In T.Y. Wu and J.W. Hutchinson (eds.), Advances in Applied Mechanics. Vol. 23. New York: Academic Press (1983) pp. 179–269.
C.O. Horgan, Recent developments concerning Saint-Venant's principle: an update. Applied Mechanics Reviews 42 (1989) 295–303.
J.K. Knowles and E. Sternberg, On a class of conservation laws in linearized and finite elastostatics. Arch. Rat. Mech. Anal. 44 (1972) 187–211.
P.J. Olver, Conservation laws in elasticity 1. General results. Arch. Rat. Mech. Anal. 85 (1984) 111–129.
P. J. Olver, Applications of Lie Groups to Differential Equations. New York: Springer-Verlag (1986).
S.G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body. Moscow: MIR Publishers (1981).
J.K. Knowles, Remarks on a question of Ericksen concerning elastostatic fields of Saint-Venant type. Arch. Rat. Mech. Anal. 90 (1985) 249–261.
C.O. Horgan and J.G. Simmonds, Saint-Venant end effects in composite structures. Composites Engineering (in press).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Miller, K.L., Horgan, C.O. Conservation properties for plane deformations of isotropic and anisotropic linearly elastic strips. J Elasticity 33, 311–318 (1993). https://doi.org/10.1007/BF00043253
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00043253