Shariff, M. H. B. M. A general approach to axial deformation of bonded elastic mounts of various cross-sectional shapes. (English) Zbl 0786.73092 Appl. Math. Modelling 17, No. 8, 430-436 (1993). An approximate explicit three-dimensional solution is obtained that is reasonable, easy to use, and compares well with experimental data. The method developed makes use of a variational principle that is equivalent to the general equations of elasticity expressed in terms of the displacement and a scalar function associated with the mean pressure. The analysis developed here unifies previous analyses and allows scope for better approximations. Upper and lower bounds on the axial nominal stress, energy, and apparent Young’s modulus are given. Cited in 1 Document MSC: 74S30 Other numerical methods in solid mechanics (MSC2010) 74P10 Optimization of other properties in solid mechanics 74B05 Classical linear elasticity Keywords:three-dimensional solution; variational principle; displacement; mean pressure; upper and lower bounds PDF BibTeX XML Cite \textit{M. H. B. M. Shariff}, Appl. Math. Modelling 17, No. 8, 430--436 (1993; Zbl 0786.73092) Full Text: DOI References: [1] Gent, A.N.; Meinecke, E.A., Compression, bending and shear of bonded rubber blocks, Polymer eng. sci., 10, 1, 48-53, (1970) [2] Lindley, P.B., Effect of Poisson’s ratio on compression modulus, J. strain anal., 3, 142-145, (1968) [3] Gent, A.N.; Lindley, P.B., Compression of bonded rubber blocks, Proc. inst. mech. eng., 173, 111-117, (1959) [4] Shariff, M.H.B.M., An approximate analysis of infinitesimal deformations of bonded elastic mounts, J. strain anal., 23, 115-120, (1988) [5] Herrmann, L.R., Elasticity equations for incompressible and nearly incompressible materials by a variational theorem, Aiaa j., 3, 1896-1900, (1965) [6] Shariff, M.H.B.M., An analysis of non-linear deformation of bonded rubber mounts, Proc. inst. mech. eng., 203, 113-119, (1989) [7] Klingbeil, W.N.; Sheild, R.T., Large deformation analyses of bonded elastic mounts, Zamp, 17, 281-305, (1966) [8] Haddow, J.B.; Ogden, R.W., Compression of bonded elastic bodies, J. mech. phys. solids, 36, 551-579, (1988) · Zbl 0655.73024 [9] Gent, A.N.; Lindley, P.B., Internal rupture of bonded rubber cylinders in tension, Proc. R. soc. London A, A249, 195-205, (1958) [10] Flavin, J.N., Asymptotic bounds for extension of bonded elastic cylinders, Int. J. solids struct., 21, 267-272, (1985) · Zbl 0564.73061 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.