539.3 Numerical solution of inverse three-dimensional problems of recovering the loads acting upon composite structural elements

Dimitrienko Y. I. (Bauman Moscow State Technical University), Yurin Y. V. (Bauman Moscow State Technical University), Yegoleva E. S. (Bauman Moscow State Technical University)

NUMERICAL MODELING, THE INVERSE PROBLEMS OF RESTORING LOADS, COMPOSITE STRUCTURES, FINITE ELEMENTS METHOD


doi: 10.18698/2309-3684-2017-4-4859


The article proposes a numerical method for solving the inverse three-dimensional problems of recovering the fields of loads acting upon composite structural elements based on the results of the experimental diagnostics of structural displacements on a certain surface. The problems of this type arise when creating the systems of the built-in diagnostics of structural movements and intelligent composite structures. The restored field of loads acting upon the parts of the outer surface of the composite structure is used to calculate the stress-strain state and forecast the structural life. The proposed method uses an alternating algorithm for solving the inverse problems of restoring loads in the problem of elasticity theory, in combination with the finite element method for solving the direct problems in the theory of elasticity. We consider an example of solving the inverse problem of restoring loads acting on the structural elements made from layered fibrous composite materials.


[1] Yakhno V.G. Obratnye koeffitsientnye zadachi dlya differentsialnykh uravneniy teorii uprugosti [Inverse coefficient problems for differential equations of the elasticity theory]. Novosibirsk, Nauka Publ., 1990, 304 p.
[2] Golushko S.K., Nemirovskiy Yu.V. Pryamye i obratnye zadachi mekhaniki uprugikh kompozitnykh plastin i obolochek vrashcheniya [Direct and inverse problems of the mechanics of elastic composite plates and revolution shells]. Moscow, Fizmatlit Publ., 2008, 432 p.
[3] Kabanikhin S.I. Obratnye i nekorrektnye zadachi [Inverse and ill-posed tasks]. Novosibirsk, Siberian Scientific Publ., 2009, 457 p.
[4] Vatulyan A.O. Obratnye zadachi v mekhanike deformiruemogo tverdogo tela [Inverse problems in the mechanics of a deformable solid]. Moscow, Fizmatlit Publ., 2007, 224 p.
[5] Sellier M. Journal of Fluids and Structures, 2011, vol. 27, iss. 8, pp. 1461–1470.
[6] Ellabib A., Nachaoui A. Mathematics and Computers in Simulation, 2008, vol. 77, iss. 2–3, pp. 189–201.
[7] Chock J.M.K., Kapania R.K. AIAA Journal, 2003, vol. 41, no. 9, pp. 1667–1673.
[8] Law S.S., Fang Y.L. Journal of Sound and Vibration, 2001, vol. 239, no. 2, pp. 233–254.
[9] Li J., Kapania R. Load updating for finite element models using reduced number of unknown load coefficients. Paper IAA-2004-4559, 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, August 30 — September 1, 2004, Albany, New York, pp. 1–16.
[10] Li Jing. Inverse problems in structural mechanics. The Ph.D. in Aerospace Engineering dissertation. Virginia Polytechnic Institute and State University, 2005. Available at: https://theses.lib.vt.edu/theses/available/etd-12132005-163943/ unrestricted/phddissertation_jing.pdf (accessed December 20, 2017).
[11] Vatulyan A.O., Kozarenko A.I. Izvestiya vysshikh uchebnykh zavedeniy. SeveroKavkazskiy region. Ser. Estestvennye nauki — University News, NorthCaucasian Region, Natural Sciences Series, 2004, no. 3, pp. 34–38.
[12] Fachinotti V.D., Albanesi A.E., Martínez J.M., José M. Computers & Structures, September 2015, vol. 157. DOI 10.1016/j.compstruc.2015.05.013
[13] Pacheco C.C., Dulikravich G.S., Vesenjak M., Borovinsĕk M., Duarte I.M.A., Jha R., Reddy S.R., Orlande H.R.B., Colaço M.J. Technische mechanik, 2016, vol. 36, no. 1–2, pp. 120–131.
[14] Dimitrienko Yu.I., Dimitrienko I.P. Voprosy oboronnoy tekhniki — Military Enginery, 2002, no. 1/2. pp. 21–25.
[15] Dimitrienko Yu.I., Gubareva E.A., Sborschikov S.V. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2016, no. 2 (10), pp. 3–23.
[16] Kozlov V.A., Mazya V.G., Fomin A.V. Zhurnal vychislitelnoy matematiki i matematicheskoy fiziki — Computational Mathematics and Mathematical Physics, 1991, vol. 31, no. 1, pp. 64–74.
[17] Postnov V.I., Pletin I.I., Veshkin E.A., Starostina I.V., Strelnikov S.V. Izvestiya Samarskogo nauchnogo tsentra Rossiyskoy akademii nauk — Izvestia of Samara Scientific Center of the Russian Academy of Sciences, 2016, vol. 18, no. 3–4, pp. 619–627.
[18] Dimitrienko Yu.I., Fedonyuk N.N., Gubareva E.A., Sborshchikov S.V., Prozorovskiy A.A., Erasov V.S., Yakovlev N.O. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2014, no. 5, pp. 66–82.
[19] Dimitrienko Yu.I. Mekhanika sploshnoi sredy. V 4 tomakh. Tom 4. Osnovy mekhaniki tverdykh sred [Continuum mechanics. In 4 vols. Vol. 4. Fundamentals of solid mechanics]. Moscow, BMSTU Publ., 2013, 624 p.
[20] Dimitrienko Yu.I. Composite science and technologies, 1999, vol. 59, no. 7, pp. 1041–1053.
[21] Dimitrienko Yu.I. Applied Composite Materials, 1997, vol. 4, no. 4, pp. 219–237.
[22] Dimitrienko Yu.I., Yakovlev D.O. Mekhanika kompozitsionnykh materialov i konstruktsiy — Mechanics of composite materials and structures, 2014, vol. 20, no. 2, pp. 259–282.
[23] Dimitrienko Yu.I., Dimitrienko I.D. Inzhenernyy zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2014, no. 5 (29). DOI 10.18698/2308-6033-2014-5-1236
[24] Dimitrienko Yu.I., Dimitrienko I.D., Sborschikov S.V. Inzhenernyy zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2016, no. 11 (59), pp. 68–77. DOI 10.18698/2308-6033-2016-11-1555


Dimitrienko Yu.I., Yurin Yu.V., Egoleva E.S. Numerical solution of inverse three-dimensional problems of recovering the loads acting upon composite structural elements. Mathematical Modeling and Computational Methods, 2017, №4 (16), pp. 48-59



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