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The Approach to the Construction of Difference Schemes with a Consistent Approximation of the Stress-Strain State and the Energy Balance of the Medium in Cylindrical Geometry

  • Yury Poveshchenko
  • Vladimir Gasilov
  • Viktoriia PodrygaEmail author
  • Yulia Sharova
Conference paper
  • 74 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)

Abstract

In the paper, on unstructured metric grids of the theory of the support operator method, on the topological and geometric structure of which minimal reasonable restrictions are imposed, applicable to the symmetricized displacement tensor \(t_\mathbf {u}\), discrete analogs of self-adjoint and sign-definite operations \(\mathop {\mathrm {div}}(t_\mathbf {u})\) and \(\mathop {\mathrm {div}}(\mathop {\mathrm {tr}}(t_\mathbf {u})\delta )\) which are invariants to solid rotations, were obtained for modeling of force fields of elastic processes, as well as approximation of integrals of the form \(\int _{\varOmega }\mathrm{tr}\left( \mathrm{t}_{\mathbf {u}}^{2} \right) dV \) and \(\int _{\varOmega }\mathrm{tr}^{2} \left( \mathrm{t}_{\mathbf {u}} \right) dV \), sufficient to simulate elastic-dependent energy balances of the medium taking into account the curvature of space of the cylindrical geometry of the system.

Keywords

Difference schemes Support operator method Theory of elasticity Cylindrical geometry 

Notes

Acknowledgments

The work was funded by Russian Foundation for Basic Research, projects no. 16-29-15081-ofi_m, 18-37-20062-mol_a_ved, 18-07-00841-a.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Yury Poveshchenko
    • 1
  • Vladimir Gasilov
    • 1
  • Viktoriia Podryga
    • 1
    • 2
    Email author
  • Yulia Sharova
    • 1
  1. 1.Keldysh Institute of Applied MathematicsMoscowRussia
  2. 2.Moscow Automobile and Road Construction State Technical University (MADI)MoscowRussia

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