We proposed an analytic-numerical method for the solution of axisymmetric boundary-value problems of the theory of elasticity for two-layer cylindrical bodies with the help of homogeneous solutions. The components of the vector of displacements and the stress tensor are represented in the form of series whose coefficients are determined by the constructed eigenfunctions. A computer procedure is developed for the solution of boundary-value problems for a two-layer cylinder. We establish criteria such that the constructed solution coincides with the exact solution in the case where these criteria are satisfied. The qualitative and quantitative regularities of the behavior of the components of the stress-strain state of the analyzed two-layer cylinder under the action of local loads with clearly defined maximum are described.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.-Q. Tarn and Y.-M. Wang, “Laminated composite tubes under extension, torsion, bending, shearing, and pressuring: a state space approach,” Int. J. Solids Struct., 38, 9053–9075 (2001).
I. Tsukrov and B. Drach, “Elastic deformation of composite cylinders with cylindrically orthotropic layers,” Int. J. Solids Struct., 47, 25–33 (2010).
G. Chatzigeorgiou, N. Charalambakis, and F. Murat, “Homogenization problems of a hollow cylinder made of elastic materials with discontinuous properties,” Int. J. Solids Struct., 45, 5165–5180 (2008).
V. P. Revenko, “Determination of the three-dimensional stress-strain state of a thick-walled two-layer cylinder,” Fiz.-Khim. Mekh. Mater., 50, No. 3, 53–58 (2014); English translation: Mater. Sci., 50, No. 3, 369–376 (2014).
M. P. Savruk, L. I. Onyshko, and M. M. Senyuk, “A plane dynamic axisymmetric problem for a hollow cylinder,” Fiz.-Khim. Mekh. Mater., 44, No. 1, 7–14 (2008); English translation: Mater. Sci., 44, No. 1, 1–9 (2008).
X. C. Yin and Z. Q. Yue, “Transient plane-strain response of multilayered elastic cylinders to axisymmetric impulse,” J. Appl. Mech., 69, No. 6, 825–835 (2002).
V. P. Revenko, “On the solution of three-dimensional equations of the linear theory of elasticity,” Prikl. Mekh., 45, No. 7, 52–65 (2009).
А. I. Lur’e, Theory of Elasticity [in Russian], Nauka, Moscow (1970).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review, McGraw-Hill, New York (1968).
V. P. Revenko, “Investigation of the stressed state of a loaded finite cylinder with the use of eigenfunctions,” Prykl. Probl. Mekh. Mat., Issue 7, 183–190 (2009).
V. P. Revenko, “Investigation of the three-dimensional stressed state in elastic plates with circular holes,” Fiz.-Khim. Mekh. Mater., 45, No. 5, 71–76 (2009); English translation: Mater. Sci., 45, No. 5, 688–695 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 53, No. 5, pp. 48–53, September–October, 2017.
Rights and permissions
About this article
Cite this article
Revenko, V.P. Evaluation of the Axisymmetric Stress-Strain State of a Two-Layer Cylinder Under the Action of Local Loads. Mater Sci 53, 630–636 (2018). https://doi.org/10.1007/s11003-018-0117-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11003-018-0117-z