Abstract
Consider a long elastic isotropic beam with a convex cross-section and a sufficiently smooth boundary. Suppose that a self-equilibrated load is applied at each end but the sides are stress-free and there are no internal body forces. It is proved in the context of three-dimensional, nonlinear elastostatics that if the first four derivatives of the displacement vector are a priori assumed to be everywhere sufficiently small with respect to the physical constants and the geometry of the cross-section, then the strains at any point decay exponentially with the distance of the point from the nearest end.
This result is an extension of known results on Saint-Venant's Principle in linear and two-dimensional nonlinear elasticity.
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Communicated by R.A. Toupin
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Breuer, S., Roseman, J.J. On Saint-Venant's Principle in three-dimensional nonlinear elasticity. Arch. Rational Mech. Anal. 63, 191–203 (1977). https://doi.org/10.1007/BF00280605
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DOI: https://doi.org/10.1007/BF00280605