Sommario
Questo lavoro studia la diffusione degli sforzi in un corpo elastico, lineare, isotropo rivestito da un guscio elastico sottile denominato la «crosta».
Sono considerati due problemi elastostatici. Il primo è quello di un semispazio coperto da una piastra sottile soggetta and un carico concentrato nell'origine. Nel secondo problema si studia una sfera solida elastica avvolta da un guscio sottile elastico con due carichi concentrati opposti nei poli. Nei due problemi le soluzioni in termini di spostamenti entro la crosta si ottengono rispettivamente mediante la trasformata di Hankel e i polinomi di Legendre.
Summary
This paper studies the diffusion of stresses in a linear isotropic elastic body coated with a thin elastic shell called the «crust».
Two static problems are considered. The first is that of the semi-infinite half-space covered by a thin plate subject to a point load at the origin. In the second problem a solid elastic sphere enveloped by a thin spherical elastic shell with two opposite point loads at the poles is investigated. Solutions for the displacement within the thin crust are obtained in the two problems by means of the Hankel transform and the Legendre polynomial respectively.
References
Gurtin M.E. andMurdoch A.I., Arch Rabron. Mech. Analysis,57 (1975), 291–323.
Gurtin M.E. andMurdoch A.I., J. Appl. Phys.47 (1976), 4414–4421.
Gurtin M.E. andMurdoch A.I., Int. J. Solids Structures,14 (1978), 431–440.
Sneddon I.N.,Fourier Transforms, McGraw-Hill Book Company (1951).
Love E.H.,The Mathematical Theory of Elasticity, Cambridge University Press, Fourth Edition (1927).
Gradshieyn I.S. andRyzhik I.M.,Tables of Integrals, Series and Products, Academic Press (1965).
See original manuscript, Handbuch der Physik.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Beevers, C.E. Some static problems for elastic bodies with a crust. Meccanica 20, 38–42 (1985). https://doi.org/10.1007/BF02337060
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02337060