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Decay estimates for the constrained elastic cylinder of variable cross section. (English) Zbl 0706.73015

The main problem studied is the equilibrium of a cylinder of variable cross section and finite length, composed of a linearly elastic, isotropic material, acted upon by no body forces, and with Dirichlet boundary conditions: precisely, the displacement is everywhere null on the lateral surface, and equals two assigned vector fields over the ends. A typical result is a decay estimate for an \(L^ 2\)-norm of displacement over the cross section, holding under certain restrictions on the elastic moduli of the material. Other results obtained concern a semi-infinite cylinder, a decay estimate for a cross-sectional integral involving both the displacement and its gradient, and the case of an axisymmetric cylinder.
This is a well-written technical paper, of interest for students of the qualitative behavior of solutions of problems in classical elasticity.
Reviewer: P.Podio-Guidugli

MSC:

74G50 Saint-Venant’s principle
74B05 Classical linear elasticity

Citations:

Zbl 0453.73005
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