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Influence of the Reinforcement Structure and Boundary Conditions on the Stability of Quadrangular Composite Panels

  • RELIABILITY, STRENGTH, AND WEAR RESISTANCE OF MACHINES AND STRUCTURES
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Abstract

An analysis of the stability of quadrangular orthotropic composite panels under compression and shear is presented. The stability problem is solved by the Rayleigh–Ritz method in displacements with approximation of the deflection eigenmodes by Krylov functions. An assessment is made of the influence of fastening conditions and the laying pattern of layers of a composite structure on the parameters of the critical behavior of quadrangular panels. The accuracy of the numerical procedures is confirmed by comparison with the results of the exact solution of the main linearized equation of stability theory using the example of an isotropic plate.

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REFERENCES

  1. Ganiyev, R.F. and Glazunov, V.A., Actual problems of machines science and ways of their decision, Sprav. Inzh. Zh., 2015, no. 11, pp. 1–16. https://doi.org/10.14489/hb.supp.2015.011.pp.001-016

  2. Vasil’ev, V.V., Mekhanika konstruktsii iz kompozitsionnykh materialov (Mechanics of Structures of Composite Materials), Moscow: Mashinostroenie, 1988.

  3. Ganiev, R.F., Fundamental and applied problems of nonlinear wave mechanics and engineering: Groundbreaking wave technologies and wave engineering, J. Mach. Manuf. Reliab., 2019, vol. 48, no. 6, pp. 477–502. https://doi.org/10.3103/s1052618819060050

    Article  Google Scholar 

  4. Ganiev, R.F., Glazunov, V.A., and Filippov, G.S., Urgent problems of machine science and ways of solving them: Wave and additive technologies, the machine tool industry, and robot surgery, J. Mach. Manuf. Reliab., 2018, vol. 47, no. 5, pp. 399–406. https://doi.org/10.3103/S1052618818050059

    Article  Google Scholar 

  5. Irisarri, F.-X., Julien, C., Bettebghor, D., Lavelle, F., Guerin, Ya., and Mathis, K., A general optimization strategy for composite sandwich structures, Struct. Multidiscip. Optim., 2021, vol. 63, no. 6, pp. 3027–3044. https://doi.org/10.1007/s00158-021-02849-8

    Article  Google Scholar 

  6. Boitsov, B.V., Gavva, L.M., Endogur, A.I., and Firsanov, V.V., Stress-strain state and buckling problems of structurally-anisotropic aircraft panels made of composite materials in view of production technology, Russ. Aeronaut., 2018, vol. 61, no. 4, pp. 524–532. https://doi.org/10.3103/s1068799818040049

    Article  Google Scholar 

  7. Alhajahmad, A. and Mittelstedt, C., Buckling and postbuckling performance of composite fuselage panels with cutouts using continuous streamline fibres, Int. J. Mech. Sci., 2021, vol. 212, no. 4, p. 106841. https://doi.org/10.1016/j.ijmecsci.2021.106841

    Article  Google Scholar 

  8. Akishev, N.I., Zakirov, I.I., Ivanov, V.A., Paimushin, V.N., and Shishov, M.A., Approximate analytical solutions of stability problems for skew plates under combined loading, Russ. Aeronaut., 2011, vol. 54, no. 2, pp. 115–124. https://doi.org/10.3103/S1068799811020012

    Article  Google Scholar 

  9. Azikov, N.S., Zinin, A.V., Gairadzhi, Yu.V., and Saifullin, I.Sh., Strength under supercritical deformation of skew composite panels, J. Mach. Manuf. Reliab., 2021, vol. 50, no. 5, pp. 430–437. https://doi.org/10.3103/S1052618821050058

    Article  Google Scholar 

  10. Azikov, N.S. and Zinin, A.V., Analysis of free vibrations of a skew orthotropic composite panel, J. Mach. Manuf. Reliab., 2022, vol. 51, no. 5, pp. 406–418. https://doi.org/10.3103/s105261882205003x

    Article  Google Scholar 

  11. Azikov, N., Zinin, A., and Gaidarzhi, Yu., Buckling and free vibration analysis of skew shallow composite panel, AIP Conf. Proc., AIP Publishing, 2023, vol. 2507, no. 1, p. 40013. https://doi.org/10.1063/5.0109355

  12. Chen, Q. and Qiao, P., Buckling and postbuckling of rotationally-restrained laminated composite plates under shear, Thin-Walled Struct., 2021, vol. 161, p. 107435. https://doi.org/10.1016/j.tws.2021.107435

    Article  Google Scholar 

  13. Shufrin, I., Rabinovitch, O., and Eisenberger, M., A semi-analytical approach for the geometrically nonlinear analysis of trapezoidal plates, Int. J. Mech. Sci., 2010, vol. 52, no. 12, pp. 1588–1596. https://doi.org/10.1016/j.ijmecsci.2010.07.008

    Article  Google Scholar 

  14. Cen, S. and Shang, Ya., Developments of Mindlin-Reissner plate elements, Math. Probl. Eng., 2015, vol. 2015, p. 456740. https://doi.org/10.1155/2015/456740

    Article  MathSciNet  Google Scholar 

  15. Kumar, A., Singha, M.K., and Tiwari, V., Stability analysis of shear deformable trapezoidal composite plates, Int. J. Struct. Stab. Dyn., 2019, vol. 19, no. 8, p. 1971004. https://doi.org/10.1142/s0219455419710044

    Article  MathSciNet  Google Scholar 

  16. Kumari, E. and Lal, S., Nonlinear bending analysis of trapezoidal panels under thermo-mechanical load, Forces Mech., 2022, vol. 8, no. 8, p. 100097. https://doi.org/10.1016/j.finmec.2022.100097

    Article  Google Scholar 

  17. Gürses, M., Civalek, Ö., Ersoy, H., and Kiracioglu, O., Analysis of shear deformable laminated composite trapezoidal plates, Mater. Des., 2009, vol. 30, no. 8, pp. 3030–3035. https://doi.org/10.1016/j.matdes.2008.12.016

    Article  Google Scholar 

  18. Yas, M.H., Bayat, A., Kamarian, S., Malekshahi, A., and Song, J.I., Buckling analysis and design optimization of trapezoidal composite plates under hygrothermal environments, Compos. Struct., 2023, vol. 315, no. 3, p. 116935. https://doi.org/10.1016/j.compstruct.2023.116935

    Article  Google Scholar 

  19. Watts, G., Kumar, R., Patel, S.N., and Singh, S., Dynamic instability of trapezoidal composite plates under non-uniform compression using moving kriging based meshfree method, Thin-Walled Struct., 2021, vol. 164, p. 107766. https://doi.org/10.1016/j.tws.2021.107766

    Article  Google Scholar 

  20. Alfutov, N.A., Osnovy rascheta na ustoichivost’ uprugikh sistem (Foundations of Stability Analysis of Elastic Systems), Moscow: Mashinostroenie, 1991.

  21. Prochnost’, ustoichivost’, kolebaniya: Spravochnik v 3-kh t (Strength, Stability, Oscillations: Reference Book in Three Volumes), Birger, I.A. and Panovko, Ya.I., Eds., Moscow: Mashinostroenie, 1968, vol. 3.

  22. Madelung, E., Die Mathematischen Hilfsmittel des Physikers, Grundlehren der Mathematischen Wissenschaften, vol. 4, Berlin: Springer, 1964.

  23. Nallim, L.G., Martinez, S.O., and Grossi, R.O., Statical and dynamical behaviour of thin fibre reinforced composite laminates with different shapes, Comput. Methods Appl. Mech. Eng., 2005, vol. 194, no. 17, pp. 1797–1822. https://doi.org/10.1016/j.cma.2004.06.009

    Article  ADS  Google Scholar 

  24. Liew, K.M. and Wang, C.M., pb-2 Rayleigh-Ritz method for general plate analysis, Eng. Struct., 1993, vol. 15, no. 1, pp. 55–60. https://doi.org/10.1016/0141-0296(93)90017-x

    Article  Google Scholar 

  25. Krylov, A.N., O raschete balok, lezhashchikh na uprugom osnovanii (On Analysis of Beams Lying on Elastic Foundation), Leningrad: Akad. Nauk SSSR, 1931.

  26. Kalitkin, N.N. and Al’shina, E.A., Chislennye metody (Numerical Methods), vol. 1: Chislennyi analiz (Numerical Analysis), Moscow: Akademiya, 2013.

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), Moscow, Russia

    N. S. Azikov

  2. Moscow Aviation Institute (National Research University), Moscow, Russia

    A. V. Zinin

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  1. N. S. Azikov
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  2. A. V. Zinin
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Correspondence to A. V. Zinin.

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Translated by K. Gumerov

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Azikov, N.S., Zinin, A.V. Influence of the Reinforcement Structure and Boundary Conditions on the Stability of Quadrangular Composite Panels. J. Mach. Manuf. Reliab. 52, 542–550 (2023). https://doi.org/10.1134/S1052618823060055

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