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On Saint-Venant’s problem for an elastic strip. (English) Zbl 0657.73003
The author claims that the two-dimensional Saint-Venant problem for a nonlinear homogeneous isotropic hyperelastic semi-infinite strip with small strains can be formulated in terms of suitable periodic solutions of the nonlinear field equations for an infinite strip. He also shows that there is a one-to-one correspondence between these periodic solutions and those satisfying two-dimensional nonlinear rod equations. The claim is based on a centre manifold theorem due to the author [cf. Math. Methods Appl. Sci. 10, No.1, 51-66 (1988; Zbl 0647.35034)].
Reviewer: J.Ignaczak

MSC:
74G50 Saint-Venant’s principle
74B20 Nonlinear elasticity
58D25 Equations in function spaces; evolution equations
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