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Control of Surface Waviness

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Abstract

The elastic material loses the bulk stability at sufficiently large compression when the Hadamard condition is not satisfied. An elastic half-space could lose at compression the surface stability with the buckling waves localized near a free plane and exponentially decreased away from it. The compressed elastic plate lying on an elastic foundation also could lose stability. The problems of the critical loads and buckling modes determination are discussed.

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References

  1. Ciarlet, P.S.: Mathematical Elasticity. North-Holland, Amsterdam etc (1988)

    MATH  Google Scholar 

  2. Morozov, N.F., Tovstik, P.E.: On the modes of the surface stability loss. Problems of nonlinear mechanics of a deformable rigid body, conference 2, pp. 270–273, Kazan (2009)

    Google Scholar 

  3. Tovstik, P.E.: The volume and the surface stability of a transversely isotropic material under compression. Vestnik St.Petersburg University Series 1, N 1 (2010)

    Google Scholar 

  4. Morozov, N.F., Paukshto, M.V., Tovstik, P.E.: Stability of the surface layer under thermal loading. Izv. Russ. Akad. Nauk. MTT. (1), 130–139 (1998)

    Google Scholar 

  5. Tovstik, P.E.: Local stability of plates and shallow shells on an elastic foundation. Izv. Russ. Akad. Nauk. MTT. (1), 147–160 (2005)

    Google Scholar 

  6. Tovstik, P.E.: Vibrations and stability of a pre-stressed plate on an elastic foundation. Prikl. Math. Mekh. 73(1), 106–120 (2009)

    MathSciNet  MATH  Google Scholar 

  7. Morozov, N.F., Tovstik, P.E.: On the buckling modes of plate on an elastic foundation. Izv. Russ. Akad. Nauk. MTT. (4), 30–42 (2010)

    Google Scholar 

  8. Panin, L.E., Panin, V.E.: Effect of the “chessboard” and mass transfer in interfacial media of organic and inorganic nature. Phys. Nanomech. 10(6), 5–20 (2007)

    Article  Google Scholar 

  9. Tovstik, P.E., Smirnov, A.L.: Asymptotic Methods in the Buckling Theory of Elastic Shells, p. 347. World Scientific, Singapore, New Jersey, London, Hong Kong (2007)

    Google Scholar 

  10. Il’gamov, M.A., Ivanov, V.A., Gulin, B.V.: Strength, Stability and Dynamics of Shells with an Elastic Filler. Nauka, Moscow (1977)

    Google Scholar 

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Acknowledgements

The paper is written with the financial support of Russian Foundation of Basic Investigations, grants 09.01.92002, 09.01.00642 and 10.01.00244.

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Correspondence to N. F. Morozov .

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© 2012 Springer-Verlag/Wien

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Morozov, N.F., Tovstik, P.E. (2012). Control of Surface Waviness. In: Irschik, H., Krommer, M., Belyaev, A. (eds) Advanced Dynamics and Model-Based Control of Structures and Machines. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0797-3_19

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  • DOI: https://doi.org/10.1007/978-3-7091-0797-3_19

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  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-0796-6

  • Online ISBN: 978-3-7091-0797-3

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