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On Bending of Rod Under Strong Longitudinal Compression

  • A. A. Ershov
  • A. A. Ershova
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

In this paper, we consider typical processes of rod bending under strong longitudinal compression. The corresponding dynamic equation of bending is considered as a perturbation of the two-dimensional Laplace equation. It is established that, for these processes, expanding of domains of rapid increase of bending begins in small neighborhoods of singularity points of solutions of the limiting Laplace equation. The initial stages of these increases are described using the Hardy integral. Several typical examples of the development of buckling of a rod under the action of strong compression are simulated in the work.

Keywords

Asymptotics Laplace equation Singularities Rod Bending Compression Hardy integral 

Notes

Acknowledgements

For the information, we found very useful when writing this article and we express our gratitude to B. I. Suleimanov, N. F. Valeev, A. R. Danilin, M. A. Il’gamov, and I. V. Mel’nikova. This work was supported by the Russian Foundation for Basic Research, project no. 18-31-00018-mol_a.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.N.N. Krasovskii Institute of Mathematics and MechanicsYekaterinburgRussia
  2. 2.South Ural State UniversityChelyabinskRussia

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