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ON QUASI-STATIC DEFORMATION OF AN ELASTIC SUPPORTED STRIP UNDER COMPRESSION

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Abstract

On the basis of the formulated definition and the corresponding theorem, the conditions for the existence of quasi-static behavior of the studied object of continuum mechanics are obtained. The process of quasi-static deformation is characterized by the solution of a system of differential equations. The boundary of the quasi-static behavior of an elastically supported strip under compression is determined.

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REFERENCES

  1. S. C. Sorensen, Selected Works, Vol. 3: Quasi-Static and Fatigue Failure of Materials and Construction Elements (Nauk. Dumka, Kiev, 1985) [in Russian].

  2. I. G. Teregulov and R. H. Murtazin, “Quasi-static bending and stable-stability of shells under creep (theory of heredity),” in Research on the Theory of Plates and Shells, Ed. by K. Z. Galimov (Kazan. Uni., Kazan, 1964), pp. 145–158.

    Google Scholar 

  3. B. P. Russell, T. Liu, N. A. Fleck, and V. S. Deshpande, “Quasi-static three-point bending of carbon fiber sandwich beams with square honeycomb cores,” J. Appl. Mech. 78 (3), 031008 (2011). https://doi.org/10.1115/1.4003221

  4. Y. Imai, K. Nishitani, G. Fortin, et al., “Relationship between the initial fracture stress and fatigue limit-simple prediction method of tensile fatigue limit of composite,” Open J. Compos. Mater. 9 (4), 338–354 (2019). https://doi.org/10.4236/ojcm.2019.94021

    Article  Google Scholar 

  5. F. M. Mitenkov, N. G. Kodochigov, S. V. Lebedev, and A.V. Hodykin, “Comparing the quality of a controlling rotor with active magnetic bearings for linear and non-linear system structures,” J. Machin. Manufact. Reliab. 40 (6), 561–564 (2011). https://doi.org/10.3103/S1052618811060136

    Article  Google Scholar 

  6. V. V. Bolotin, Nonconservative Problems of the Theory of Elastic Stability (Fizmatlit, Moscow, 1961; Pergamon Press, London, 1963).

  7. Ya. G. Panovko, Stability and Vibrations of Elastic Systems (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  8. V. I. Van’ko, Essays about the Stability of Structural Members, 3d ed. (MGTU im. Baumana, Moscow, 2015) [in Russian].

  9. V. I. Van’ko and E. C. Perelygina, “Axial bending of elasticplastic rod: discussion of classical results,” Vestn. MGTU im. Baumana, No. 4(4), 9–15 (2012). https://doi.org/10.18698/2308-6033-2012-4-156

  10. J. A. C. Martins, N. V. Rebrova, and V. A. Sobolev, “On the (in)stability of quasi-static paths of smooth systems: Definitions and sufficient conditions,” Math. Meth. Appl. Sci. 29 (6), 741–750 (2006). https://doi.org/10.1002/mma.707

    Article  MathSciNet  MATH  Google Scholar 

  11. J. A. C. Martins, M. D. P. M. Marques, A. Petrov, et al., “(In)stability of quasi-static paths of some finite dimensional smooth or elastic-plastic systems,” J. Phys.: Conf. Ser. 22 (1), 124–138 (2005). https://doi.org/10.1088/1742-6596/22/1/008

    Article  ADS  Google Scholar 

  12. V. R. Zachepa and Y. I. Sapronov, Local Analysis of Fredholm Equations (Voronezh Gos. Univ., Voronezh, 2002) [in Russian].

    MATH  Google Scholar 

  13. B. M. Darinsky, Y. I. Sapronov, and S. L. Tsarev, “Bifurcations of extremals of Fredholm functionals,” J. Math. Sci. 145 (6), 5311–5453 (2007). https://doi.org/10.1007/s10958-007-0356-2

    Article  MathSciNet  Google Scholar 

  14. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Nauka, Moscow, 1981; Dover, New York, 1999).

  15. N. V. Minaeva, The Adequacy of Mathematical Models of Deformable Bodies (Nauchnaya Kniga, Moscow, 2006) [in Russian].

    Google Scholar 

  16. L. V. Ershov and D. D. Ivlev, “On stability of a strip in compression,” Dokl. Akad. Nauk SSSR 138 (5), 1047–1049 (1961).

    Google Scholar 

  17. N. V. Minaeva, “Strain state of the elastic strip with nearly rectangular cross section,” J. Phys.: Conf. Ser. 973, 012012 (2018). https://doi.org/10.1088/1742-6596/973/1/012012

  18. N. V. Minaeva and A. I. Shashkin, “Analysis and study of the problem of existence of a quasi-static process,” Vestn. ChGPU im. Yakovleva Ser.: Mekh. Pred. Sost., No. 4 (22), 124–128 (2014).

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Correspondence to N. V. Minaeva or A. I. Shashkin.

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Translated by M. K. Katuev

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Minaeva, N.V., Shashkin, A.I. & Aleksandrova, E.E. ON QUASI-STATIC DEFORMATION OF AN ELASTIC SUPPORTED STRIP UNDER COMPRESSION. Mech. Solids 57, 286–291 (2022). https://doi.org/10.3103/S0025654422020091

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