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Russian Academy of Sciences
in January 1936
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IssuesArchive of Issues2013-2pp.235-244

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K.M. Zingerman and V.A. Levin, "Extension of the Lamé-Gadolin problem for large deformations and its analytical solution," J. Appl. Math. Mech. 77 (2), 235-244 (2013)
Year 2013 Volume 77 Issue 2 Pages 235-244
Title Extension of the Lamé-Gadolin problem for large deformations and its analytical solution
Author(s) K.M. Zingerman (Moscow, Russia,
V.A. Levin (Moscow, Russia)
Abstract The formulation and solution of the axisymmetric static problem of the stress-strain state of two hollow circular elastic cylinders, one of which is predeformed and inserted into the other cylinder, is considered in the case of large plane deformations (an extension of the Lamé-Gadolin problem to large deformations). Using the theory of the superposition of large deformations, an exact analytical solution of the static problem for cylinders made of incompressible Treloar and Bartenev-Khazanovich materials is obtained, including the case when the cylinders are made of dissimilar materials. An analytical solution is obtained in parametric form for a compressible Blatz-Ko material. Non-linear effects are investigated.
Received 23 May 2011
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