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The Stressed State of a Stiffened Conical Shell with Thermal Protective Coating with Temperature-Dependent Properties

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The equations of the mathematical model are solved in terms of special functions. The results for the design scheme of the aircraft forebody are obtained with a guaranteed accuracy by the stable method of functional normalization.

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  1. Bakulin, V.N., Borzykh, S.V., and Voronin, V.V., Space Vehicle Landing Dynamics at Failure of Landing Gear, Izv.Vuz. Av. Tekhnika, 2016, vol. 59, no. 1, pp. 22–26 [Russian Aeronautics (Engl. Transl.), vol. 59, no. 1, pp. 23–28].

    Google Scholar 

  2. Novozhilov, V.V., Teoriya tonkikh obolochrk (Theory of Thin Shells), Leningrad: Sudpromgiz, 1962.

    Google Scholar 

  3. Matveenko, A.M. and Nerubailo, B.V., Voprosy prochnosti, ustoichivosti i nadezhnosti konstruktsii (The Issues of Strength, Stability and Reliability of Constructions), Moscow: MAI, 2013.

    Google Scholar 

  4. Bakulin V.N. and Potopakhin V.A., Use of the Equations of the Three-Dimensional Elasticity Theory to Solve the Multilayer Shell Dynamics Problems, Izv.Vuz. Av. Tekhnika, 1985, vol. 28, no. 3, pp. 7–12 [Soviet Aeronautics (Engl.Transl.), vol. 28, no. 3, pp. 6–11].

    Google Scholar 

  5. Vinogradov, Yu.I. and Bakulin, V.N., Experimental and Analytical Investigation of the Stressed Strained State of a Cylindrical Shell under the Action of Concentrated Radial Forces, Materials Physics and Mechanics, 2016, vol. 26, no. 1, pp. 49–52.

    Google Scholar 

  6. Materialy i pokrytiya v ekstremal’nykh usloviyakh. Vzglyad v budushcheee (Materials and Coatings in Extreme Conditions. Prospection), Reznik, S.V., Ed., Moscow: MGTU im. N.E. Baumana, 2002, vol. 1, Prediction and Analysis of Extreme Conditions, 224 p.

  7. Strakhov, V.L., Kuz’min, I,A., and Bakulin, V.N., Model of High-Temperature Thermal Properties of Rubber-Like Heat-Shielding Materials, Materialy 11-oi mezhdunarodnoi konferentsii po neravnovesnym protsessam v soplakh i struyakh (Proc. 11th Int. Conf. on Nonequilibrium Processes in Nozzles and Jets Moscow: MAI, 2016, p. 531–534.

    Google Scholar 

  8. Strakhov, V. L., Atamanov, Yu. M., Kuzmin, I. A., and Bakulin, V. N., Mathematical Modeling of High-Temperature Thermophysical Characteristics of Rubber-Like Thermal Protection Materials, High Temperature, 2017, vol. 55, no. 4, pp. 515–523.

    Article  Google Scholar 

  9. Bakulin, V.N., Kaledin, V.O., and Rassokha, A.A., Analysis of Thermoelastic Stresses in Layered Shells of Twofold Curvature, Mechanics of Composite Materials, 1988, vol. 23, no. 6, pp. 732–737.

    Article  Google Scholar 

  10. Bakulin, V.N. and Ostrik, A.V., The Combined Thermal and Mechanical Effect of Radiation and Shock Waves on a Multilayer Orthotropic Shell with a Heterogeneous Coating, Journal of Applied Mathematics and Mechanics, 2014, vol. 78, issue 2, pp. 225–235.

    MathSciNet  MATH  Google Scholar 

  11. Bakulin, V.N. and Potopakhin, V.A., Analysis of Multilayer Shells under the Action of Dynamic Loads and Heat Fluxes, Izv. AN SSSR. Mekhanika Tverdogo Tela, 1991, no. 5, pp. 156–169.

    Google Scholar 

  12. Kovalenko, A.D., Grigorenko, Ya.M., and Iliin, L.A., Teoriya tonkikh konicheskikh obolochek i ee prilozhrnie v mashinostroenii (The Theory of Thin Conical Shells and its Application in Engineering), Kiev: AN USSR, 1963.

    Google Scholar 

  13. Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shells, New York: McGraw-Hill, 1959.

    MATH  Google Scholar 

  14. Hui-Shen Shen, Thermal Postbuckling Behavior of Anisotropic Laminated Cylindrical Shells with Temperature-Dependent Properties, AIAA Journal, 2008, vol. 46, no. 1, pp. 185–193.

    Article  Google Scholar 

  15. Oterkus, E., Madenci, E., Smeltzer, S., and Ambur, D., Thermo-Mechanical Analysis of Bonded Cylindrically Curved Composite Shell Structures, Proc. of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2006, Newport, Rhode Island, AIAA 2006–1963.

    Google Scholar 

  16. Gracheva, L.I., Thermal Stress State of a Cylindrical Thermal Protective Shell Depending on the Winding Angle of Carbon Reinforcement, International Applied Mechanics, 2014, no. 3, pp. 281–285.

    Article  Google Scholar 

  17. Bakulin, V.N. and Vinogradov, Yu.I., Analytical and Asymptotic Solution of Boundary Value Problems in the Mechanics of Deformed Shells under Concentrated Loading. Izv. Vuz. Av. Tekhnika, 2017, vol. 60, no. 1, pp. 14–20 [Russian Aeronautics (Engl. Transl.), vol. 60, no. 1, pp. 13–20].

    Google Scholar 

  18. Nerubailo, B.V., Analysis of Stresses in a Cylindrical Shell under Transverse Local Loading, Izv. Vuz. Av. Tekhnika, 2014, vol. 57, no 2, pp. 14–18 [Russian Aeronautics (Engl. Transl.), vol. 57, no. 2, pp. 127–133].

    Google Scholar 

  19. Kurennov, S.S., Koshevoi, A.G., and Polyakov, A.G., Through-Thickness Stress Distribution in the Adhesive Joint for the Multilayer Composite Material, Izv. Vuz. Av. Tekhnika, 2015, vol. 58, no. 2, pp. 10–15 [Russian Aeronautics (Engl. Transl.), vol. 58, no. 2, pp. 145–151].

    Google Scholar 

  20. Vinogradov, Yu.I. and Men’kov, G.B., Method of Functional Normalization of Solutions to Stiff Linear Ordinary Differential Equations for Boundary Value Problems, Doklady Physics, 1998, vol. 43, no. 2, pp. 122–123.

    MathSciNet  MATH  Google Scholar 

  21. Bakulin, V. N., Obraztsov, I. F., and Potopakhin, V. A., Dinamicheskie zadachi nelineinoî teorii mnogosloînykh obolochek. Deistvie intensivnykh termosilovykh nagruzok kontsentrirovannykh potokov energii (Dynamic Problems of the Nonlinear Theory of Multilayer Shells. The Action of Intense Thermopower Loading of Concentrated Energy Fluxes), Moscow: Fizmatlit, 1998.

    Google Scholar 

  22. Vasil’ev, Mekhanika konstruktsii iz kompozitsionnykh mayrtialov (Mechanics of Constructions from Composite Materials), Moscow: Mashinostroenie, 1988.

  23. Birger, I.A., Shorr, B.F., and Iosilevich, G.B., Raschet na prochnost’ detalei mashin (Strength Analysis of Machine Parts), Moscow: Mashinostroenie, 1993.

    Google Scholar 

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Correspondence to V. N. Bakulin.

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Original Russian Text © V.N. Bakulin, Yu.I. Vinogradov, G.B. Men’kov, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Aviatsionnaya Tekhnika, 2018, No. 2, pp. 10–17.

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Bakulin, V.N., Vinogradov, Y.I. & Men’kov, G.B. The Stressed State of a Stiffened Conical Shell with Thermal Protective Coating with Temperature-Dependent Properties. Russ. Aeronaut. 61, 156–164 (2018).

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