Flavin, J. N.; Knops, R. J.; Payne, L. E. Decay estimates for the constrained elastic cylinder of variable cross section. (English) Zbl 0706.73015 Q. Appl. Math. 47, No. 2, 325-350 (1989). 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 Cited in 1 ReviewCited in 59 Documents MSC: 74G50 Saint-Venant’s principle 74B05 Classical linear elasticity Keywords:second-order differential inequality; mean-square cross-sectional integral of the displacement; first-order differential inequality; linearly elastic, isotropic material; Dirichlet boundary conditions Citations:Zbl 0453.73005 PDFBibTeX XMLCite \textit{J. N. Flavin} et al., Q. Appl. Math. 47, No. 2, 325--350 (1989; Zbl 0706.73015) Full Text: DOI