МОДЕЛЮВАННЯ НЕЛІНІЙНОГО ДЕФОРМУВАННЯ ТА ВТРАТИ СТІЙКОСТІ ПРУЖНИХ НЕОДНОРІДНИХ ОБОЛОНОК

Заголовок (російською): 
МОДЕЛИРОВАНИЕ НЕЛИНЕЙНОГО ДЕФОРМИРОВАНИЯ И ПОТЕРИ УСТОЙЧИВОСТИ УПРУГИХ НЕОДНОРОДНЫХ ОБОЛОЧЕК
Заголовок (англійською): 
MODELING OF NONLINEAR DEFORMATION AND BUCKLING OF ELASTIC INHOMOGENEOUS SHELLS
Автор(и): 
В.А. Баженов, М.О. Соловей, О.П. Кривенко
Автор(и) (англ): 
V.A. Bazhenov, N.A. Solovei, O.P. Krivenko
Ключові слова (укр): 
геометрично нелінійне деформування, стійкість, тонка пружна неоднорідна оболонка, термосилове навантаження
Ключові слова (рус): 
геометрически нелинейное деформирование, устойчивость, тонкая упругая неоднородная оболочка, термосиловая нагрузка
Ключові слова (англ): 
geometrically nonlinear deformation, buckling, thin elastic inhomogeneous shell, thermomechanical load
Анотація (укр): 
Викладено основи метода розв'язування статичних задач геометрично нелінійного деформування, стійкості та закритичної поведінки тонких пружних неоднорідних оболонок, що мають складну форму серединної поверхні, геометричні особливості за товщиною, багатошарову структуру матеріалу та знаходяться в умовах складного термосилового навантаження. Підхід базується на геометрично нелінійних співвідношеннях тривимірної теорії термопружності та використанні моментної схеми скінченних елементів. Дано чисельне обґрунтування метода. Виконано порівняння розв'язків с розв'язками інших авторів і в програмних комплексах ЛІРА, SCAD
Анотація (рус): 
Изложены основы метода решения статических задач геометрически нелинейного деформирования, устойчивости и закритического поведения тонких упругих неоднородных оболочек, имеющих сложную форму срединной поверхности, геометрические особенности по толщине, многослойную структуру материала и находятся в условиях сложного термосилового нагружения. Подход основан на геометрически нелинейных соотношениях трехмерной теории термоупругости и использовании моментной схемы конечных элементов. Дано численное обоснование метода. Выполнено сравнение решений с решениями других авторов и в программных комплексах ЛИРА, SCAD.
Анотація (англ): 
The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped mid-surface, geometrical features throughout the thickness, and multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finiteelement scheme. The method is justified numerically. Comparing solutions with those obtained by other authors and by software LIRA and SCAD is conducted.
Публікатор: 
Київський національний університет будівництва і архітектури
Назва журналу, номер, рік випуску (укр): 
Опір матеріалів і теорія споруд. 2014. № 92
Мова статті: 
English
Формат документа: 
application/pdf
Документ: 
12.pdf
Дата публікації: 
01 Март 2015
Номер збірника: 
92
Університет автора: 
Київський національний університет будівництва і архітектури
References: 
1. Alfutov N.A. Fundamentals of Stability Analysis of Elastic Systems [in Russian],Mashinostroenie, Moscow (1978). 312 р.2. Babich D.V. “Stability of thermosensitive shells nonuniformly heated throughout thethickness,” Dokl. AN Ukrainy, No. 4, 41–45 (1993).3. Bazhenov V.A., Dekhtyaryuk E.S., Solovei N.A, Krivenko O.P. “Generating finite-elementmodels of complex shells,” in: Proc. Int. Sci. Conf. on Architecture of Shells and StrengthDesign of Thin-Walled and Engineering Structures of Complex Shape[in Russian], Izd.RUDN, Moscow (2001), pp. 30–34.4. Bazhenov V.A., Krivenko O.P., Solovei M.O. “Effect of thermomechanical loading conditionson the stability and postbuckling behavior of shells with constant and stepwise-varyingthickness” // Opir Mater. Teor. Sporud, 77, pp. 30–42 (2005).5. Bazhenov V.A., Krivenko O.P., Solovei M.O. “Stability of conical shells with linearly varyingthickness” // Opir Mater. Teor. Sporud, 78, pp. 46–51 (2006).6. Bazhenov V.A., Krivenko O.P., Solovei M.O. “Convergence and accuracy of solutions for aspatial finite element in problems of nonuniform heating of rods and beams” // Opir Mater.Teor. Sporud, 80, pp. 54–65 (2006).7. Bazhenov V.A., Krivenko O.P., Solovei N.A. “Assessment of the curvature effect on thestability and postbuckling behavior of ribbed panels” // Strength of Materials, 39, No. 6, pp.658–662 (2007).8. Bazhenov V.A., Sakharov A.S., Solovei N.A., Krivenko O.P., Ayat N. “Moment scheme of thefinite-element method in problems of the strength and stability of flexible shells subjected tothe action of forces and thermal factors” // Strength of Materials, 31, No. 5, pp. 499–504(1999).9. Bazhenov V. A., Solovei M. O., and Krivenko O. P., “Nonlinear equations of deformation ofribbed thin multilayer shells under thermomechanical loading” // Opir Mater. Teor. Sporud,64, pp. 116–127 (1998).10. Bazhenov V.A., Solovei M.O., Krivenko O.P., Ayat N. “Stability of flexible shells undercombined thermomechanical loading,”Opir Mater. Teor. Sporud, 65, pp. 75–90 (1999).11. Bazhenov V.A., Solovei M.O., Krivenko O.P. “Equations of the moment finite-element schemein buckling problems for inhomogeneous shells under thermomechanical loading” // OpirMater. Teor. Sporud, 66, pp. 22–25 (1999).12. Bazhenov V.A., Solovei N.A., Krivenko O.P. “Stability of shallow shells of revolution withlinearly varying thickness” // Aviats.-Kosmich. Tekh. Tekhnol., No. 2, pp. 18–25 (2004).13. Belostotskii A.M. “Finite-element models of spatial plates, shells, and solids: Creation,program implementation, and research” // Sb. Nauch. Trudov Gidroproekta, 100, pp. 24–35(1985).14. 14. Bolotin V.V. “Nonlinear theory of elasticity and stability in large” // Rasch. Prochn., 3, pp.310–354 (1958).15. 15. Bushnell D., Smith S. “Stress and buckling of nonuniformly heated cylindrical and conicalshells” // AIAA J., 9, No. 12, pp. 2314–2321 (1971).16. Vainberg D.V., Gotsulyak E.A., Gulyaev V.I. “Thermomechanical instability of a deformablemedium” // Sopr. Mater. Teor. Sooruzh., 16, pp. 153–156 (1972).17. Valishvili N.V. Methods for Computer Design of Shells of Revolution [in Russian],Mashinostroenie, Moscow (1976). – 278 p.18. Varvak P.M., Buzun I.M., Gorodetskii A.S., [et al.]. Finite-Element Method [in Russian],Vysshaya Shkola, Kyiv (1981). – 176 p.19. Vol’mir A.S. Stability of Deformable Systems [in Russian], Nauka, Moscow (1967). – 984 p.20. Golovanov A.I., Kornishin M.S. “Introduction to the finite-element method in statics of thinshells,”Kazan. Fiz.-Tekh. Inst. KF AN SSSR, Kazan (1990). – 269 p.21. Gondlyakh A.V. “Iterative analytical theory of deformation of multilayer shells” // Sopr. Mater.Teor. Sooruzh., 53, pp. 33–37 (1988).22. Grigolyuk É.I. and Kabanov V.V. Stability of Shells [in Russian], Nauka, Moscow (1978). –360 p.23. Grigolyuk É.I., Shalashilin V.I. Problems of Nonlinear Deformation: Parameter ContinuationMethod in Nonlinear Problems of Solid Mechanics, Nauka, Moscow (1988). – 232p.24. Grigorenko Ya.M. and Gulyaev V.I., “Nonlinear problems of shell theory and their solutionmethods (review)” // Int. Appl. Mech., 27, No. 10, pp. 929–947 (1991).25. Gulyaev V.I., Bazhenov V.A., Gotsulyak E.A. Stability of Nonlinear Mechanical Systems [inRussian], Vyshcha Shkola, Lviv (1982). – 255 p.26. Descloux J. Méthode des Éléments Finis, Suisse, Lausanne (1973). – 95 p.27. Johnson M.W. Jr., McLay R.W. “Convergence of the finite element method in the theory ofelasticity” // ASME, J. Appl. Mech., 35, No. 2, pp. 274–278 (1968).28. Zienkiewicz O.C. The Finite-Element Method in Engineering Science, McGraw-Hill, NewYork (1971).29. Zienkiewicz O.C., Irons B.M., Scott F.C., Campbell J.S. “Three-dimensional stress analysis,”in: B.F. de Veubeke (ed.), High Speed Computing of Elastic Structures, Universite de Liege(1971).30. Il’in V.P., Karpov V.V. Stability of Ribbed Shells against Large Displacements [in Russian],Stroiizdat, Leningrad (1986). – 168 p.31. Kantor B.Ya. Nonlinear Problems in the Theory of Inhomogeneous Shallow Shells [inRussian], Naukova Dumka (Kyiv) (1974). – 136 p.32. Kislookii V.N., Sakharov A.S., Solovei N.A. “Moment scheme of the finite-element method ingeometrically nonlinear problems regarding the strength and stability of shells” // Strength ofMaterials, 9, No. 7, pp. 808–817 (1977).33. Koldunov V. A., Kudinov A. N., and Cherepanov O. I., “Three-dimensional stability analysis ofshells,” in: Proc. 6th Int. Sci. Symp. on Modern Problems of Plasticity and Stability in SolidMechanics (Tver, March 1–3, 2006) [in Russian], TGTU, Tver (2006), pp. 31–39.34. Koldunov V.A., Cherepanov O.I. “Numerical model for design of shells and shell structuresusing three-dimensional nonlinear theory of elasticity,” in: Complex Systems: DataProcessing, Modeling, and Optimization [in Russian], TvGU, Tver (2002), pp. 48–59.35. Kucheryuk V.I., Dorogin A.D., Bochagov V.P. “Design of multilayer plates by anexperimental-theoretical method” // Sroit. Mekh. Rasch. Sooruzh., No. 2, pp. 72–74 (1983).36. Liao C.-L., Reddy J.N. “Analysis of anisotropic stiffened, composite laminates using acontinuum-based shell element” // Comput. Struct., 34, No. 6, pp. 805–815 (1989).37. Sakharov A.S., Kislookii V.N., Kirichevskii V.V. [et al.]. Finite-Element Method in SolidMechanics [in Russian], Vyshcha Shkola, Kyiv (1982). – 480 p.38. Nikolaev A.P., Kiselev A.P. “Using the three-dimensional theory to design shells,” in: Proc.Int. Sci. Conf. on Architecture of Shells and Strength Analysis of Thin-Walled Building andEngineering Structures of Complex Shape [in Russian], Izd. RUDN, Moscow (2001), pp. 29–30.39. Nikolaev A.P., Kiselev A.P. “Design of shells based on three-dimensional finite elements in theform of a triangular prism and octagon,” in: Proc. Int. Sci. Conf. on Architecture of Shells andStrength Analysis of Thin-Walled Building and Engineering Structures of Complex Shape [inRussian], Izd. RUDN, Moscow (2001), pp. 319–323.40. Nowacki W. Theory of Elasticity[in Polish], PWN, Warsaw (1970). – 872 p.41. Novozhilov V.V. Theory of Thin Shells[in Russian], Sudpromgiz, Leningrad (1962). – 431 p.42. Ogibalov P.M., Gribanov V.F. Thermal Stability of Plates and Shells [in Russian], Izd. MGU,Moscow (1968). – 520 p.43. Oden J.T. Finite Elements of Nonlinear Continua, McGraw-Hill, New York (1971).44. Perel’muter A.V., Slivker V.I. Design Models of Structures and Possibility to Analyze Them[in Russian], Izd. DMK Press, Moscow (2007). –600 p.45. Piskunov V.G., Verizhenko V.E. Linear and Nonlinear Problems for Layered Structures [inRussian], Budivel’nyk, Kyiv (1986). – 176 p.46. Podstrigach Ya.S., Shvets R.N. Thermoelasticity of Thin Shells [in Russian], Naukova Dumka,Kyiv (1983). – 343 p.47. Rasskazov A.O., Sokolovskaya I.I., Shul’ga N.A. Theory and Design of Layered OrthotropicPlates and Shells [in Russian], Naukova Dumka, Kyiv (1986). – 191 p.48. Rikards R.B. Finite-Element Method in the Theory of Shells and Plates [in Russian], Zinatne,Riga (1988). – 284 p.49. Sakharov A.S. “A moment finite-element scheme (MFES) that allows for rigid-bodydisplacements” // Sopr. Mater. Teor. Sooruzh., 24, pp. 147–156 (1974).50. Sakharov A.S., Solovei N.A. “Convergence analysis of the finite-element method in problemsof plates and shells,” // in: Spatial Structures of Buildings and Installations [in Russian], Issue3, Stroiizdat, Moscow (1977), pp. 10–15.51. Solovei M.O. “Modeling the thermoelastic properties of multilayer materials in bucklingproblems for inhomogeneous shells” // Opir. Mater. Teor. Sporud, 73, pp. 17–30 (2003).52. Solovei M.O. “A modified three-dimensional finite element for modeling thin inhomogeneousshells” // Opir. Mater. Teor. Sporud, 80, pp. 96–113 (2006).53. Solovei N.A., Krivenko O.P. “Comparative analysis of solutions to buckling problems forflexible shells subject to different laws of nonuniform heating” // Opir. Mater. Teor. Sporud,70, pp. 104–109 (2002).54. Solovei N.A., Krivenko O.P. “Influence of heating on the stability of smooth shallow sphericalshells with linearly varying thickness” // Opir. Mater. Teor. Sporud, 74, pp. 60–73 (2004).55. Solovei N.A., Krivenko O.P. “Influence of heating on the stability of faceted shallow sphericalshells” // Opir. Mater. Teor. Sporud, 75, pp. 80–86 (2004).56. Strang G., Fix G.J. An Analysis of the Finite-Element Method, Prentice-Hall, EnglewoodCliffs (1973).57. Timoshenko S.P., Woinowsky-Krieger S. Theory of Plates and Shells, McGraw-Hill, New York(1959).58. ANSYS User’s Manual for revision 5.6. Vol. I. Procedure; Vol. II. Command; Vol. III.Elements; Vol. IV. Theory.59. Solovei N.A. “Geometrical modelling of shells with complex form by finite element system forstrength analysis” // Prikl. Geometr. Inzhen. Grafika, 69, pp. 245–251 (2001).60. Bazhenov V.A., Solovei N.A. Nonlinear Deformation and Buckling of Elastic InhomogeneousShells under Thermomechanical Loads // International Applied Mechanics, 2009 [in Russian].– Vol. 45. – № 9. – Pp. 3-40.61. Bazhenov V.A., Solovei N.A. Nonlinear Deformation and Buckling of Elastic InhomogeneousShells under Thermomechanical Loads // International Applied Mechanics, 2009. – Vol. 45. –№ 9. – Pp. 923-953.62. Bazhenov V.A., Krivenko O.P., Solovei N.A. Nonlinear Deformation and Buckling of ElasticShells with Inhomogeneous Structure [in Ukraine] – ZAT «Vipol», (Kyiv), 2010. – 316 p.63. Bazhenov V.A., Solovei N.A. Nonlinear Deformation and Buckling of Elastic InhomogeneousShells under Thermomechanical Loads // Mechanics successes in 6 volumes. Vol. 6(book 2). – Litera LTD (Kyiv), 2012. – Pp. 609-645.64. Bazhenov V.A., Krivenko O.P., Solovei N.A. Nonlinear Deformation and Buckling of ElasticShells with Inhomogeneous Structure: Models, Methods, Algorithms, Poorly Studied and NewProblems [in Russian]. – Book House "LIBRIKOM" (Moscow), 2013. – 336 p.65. LIRA 9.4 User Guide. Basics. Textbook. / Strelets- Streletsky E.B., Bogovis V.E., GenzerskyY.V., Geraymovich Y.D., [et al.]. – Izd. "Fact" (Kyiv), 2008. – 164 p.66. SCAD Office. Software SCAD. / Karpilovsky V.S., Kriksunov E.Z., Perel'muter A.V.,Perel'muter M.A. – Izd. "SCAD SOFT" (Moscow), 2009 [in Russian]. – 656 p.67. GOST 82-70 (ST SEV 2884-81). Steel mill universal broadband. Assortment. – Instead ofGOST 82-57; introduced. 1.1.72. – Publishing House of Standards, " (Moscow), 1983. – 6 p.68. Gorodetski A.S., Evzerov I.D. Computer models of structures. – Izd. "Fact" (Kyiv), 2007. –394 p.