Abstract
Axisymmetric contact problem about bending of a plate lying on inhomogeneous foundation with complicated structure is considered. The plate is bent under the action of distributed load and elastic response from a foundation. The foundation consists of elastic inhomogeneous soft interlayer and elastic homogeneous half-space. Lamé parameters of interlayer vary with depth by arbitrary law. Both continuously inhomogeneous and stratified interlayers are considered. Also case when layer is significantly softer than an underlying half-space is considered. Bilateral asymptotic method was used to construct an analytical solution of the problem. Analytical expressions for contact stresses and deflection of the plate are provided. The obtained solution is bilaterally asymptotically exact both for large and small ratio of layer thickness to plate radius. Both flexible and stiff plates can be modeled. Numerical results are given which shows that found approximations for kernel transform of integral equation of the problem allow us to construct analytical solution that is effective in the whole range of values of inhomogeneous layer thickness and plate stiffness.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S.M. Aizikovich, V.M. Aleksandrov, Mech. Solids 19(2), 73 (1984)
S.M. Aizikovich, J. Appl. Math. Mech. 54(5), 719 (1990)
S. Aizikovich, A. Vasiliev, I. Sevostianov, I. Trubchik, L. Evich, E. Ambalova, in Shell-like Structures: Non-classical Theories and Applcations, ed. by H. Altenbach, V.A. Eremeyev, vol. 15 (Springer, Heidelberg, 2011)
S.M. Aizikovich, A.S. Vasiliev, J. Appl. Math. Mech. 77(1), 91 (2013)
V.M. Aleksandrov, M.D. Solodovnik, Sov. Appl. Mech. 10(7), 749 (1974)
S.V. Bosakov, J. Appl. Math. Mech. 72(1), 59 (2008)
P. Dayal, N. Savvides, M. Hoffman, Thin Solid Films 517, 3698 (2009)
M.I. Gorbunov-Posadov, J. Appl. Math. Mech. 4(3), p. 61 (1940) (in Russian)
M. Kashtalyan, M. Menshykova, Compos. Struct. 89, 167 (2009)
G.N. Pavlik, in Mechanics of Contact Interactions, ed. by I.I. Vorovich, V.M. Aleksandrov, vol. 73 (Fizmatlit, Moscow, 2001) (in Russian)
R.D. Silva Andrea, A.M. Silveira Ricardo, B. Goncßalves Paulo, Int. J. Solids Struct. 38(10–13), p. 2083 (2001)
A.I. Tseitlin, Izvestiya AN USSR. Mech. Solids 1, 99 (1969). (in Russian)
A. Vasiliev, S. Volkov, S. Aizikovich, Y.-R. Jeng, ZAMM—Z. Angew. Math. Mech. (2013). doi:10.1002/zamm.201300067
S.S. Volkov, S.M. Aizikovich, Y.-S. Wang, I. Fedotov, Acta. Mech. Sin. 29(2), 196 (2013)
Acknowledgments
The authors acknowledge the support of the Ministry of Education and Science of Russia (State Contract No. 11.519.11.3028 and Agreement No. 14.B37.21.1131) and the Russian Foundation for Basic Research (Nos. 13-07-00954-a, 12-07-00639-a). Dr. Vasiliev A. S. thanks the Southern Federal University for financial support in fulfillment of this research.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Volkov, S.S., Vasiliev, A.S. (2014). Mathematical Modeling of Interaction of a Circular Plate with an Elastic Inhomogeneous Layer. In: Chang, SH., Parinov, I., Topolov, V. (eds) Advanced Materials. Springer Proceedings in Physics, vol 152. Springer, Cham. https://doi.org/10.1007/978-3-319-03749-3_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-03749-3_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03748-6
Online ISBN: 978-3-319-03749-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)