Abstract
Plane deformations of a curved strip, composed of an homogeneous cylindrically 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 case of a rectangular strip. 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 testing of anisotropic and composite curved strips.
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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.
K.L. Miller and C.O. Horgan, Conservation properties for plane deformations of isotropic and anisotropic linearly elastic strips.J. Elasticity 33 (1993) 311–318.
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.
C.O. Horgan and J.G. Simmonds, Saint-Venant end effects in composite structures.Composites Engineering 3 (1994) 279–286.
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.
J.N. Flavin, Convexity considerations for the biharmonic equation in plane polars with applications to elasticity.Quart. J. Mech. Appl. Math. 45 (1992) 555–566.