Saint-Venant's problem consists in finding elastic deformations of an infinite prismatic body taking given values for the cross-sectional resultants of force and moment. Using the center manifold approach we show that all deformations having sufficiently small bounded strains lie on a finite-dimensional manifold. In particular, the flow on this manifold is described by a set of equations having exactly the form of the classical rod equations. Moreover, the set of semi-inverse solutions can be analyzed locally.
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Communicated by J. M. Ball
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Mielke, A. Saint-Venant's problem and semi-inverse solutions in nonlinear elasticity. Arch. Rational Mech. Anal. 102, 205–229 (1988). https://doi.org/10.1007/BF00281347
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