539.3:621.01 Numerical simulation of nonlinear deformation of thin elastic shells

Gavryushin S. S. (Bauman Moscow State Technical University)

FLEXIBLE SHELL, NONLINEAR DEFORMATION, STABILITY, SUPERCRITICAL BEHAVIOR, NUMER-ICAL ALGORITHM.


doi: 10.18698/2309-3684-2014-1-115130


The article shows theoretical bases of the methods and algorithms developed to analyze the stability and supercritical behavior of thin elastic shells. The author deals with the problem of numerical analysis of nonlinear deformation of the spherical dome loaded with uniform external pressure. An algorithm for the numerical analysis method based on the parameter continuation method combined with the method of the subspace change of control parameters. The author illustrates the effectiveness of the proposed algorithm by sample calculations.


[1] Zienkiewicz O.C. The Finite Element Method. 3rd ed. New York, McGraw-Hill, 1977, 787 p.
[2] Grigolyuk E.I., Lopanitsyn E.A. Konechnye progiby, ustoichivost' i zakriticheskoe povedenie tonkikh pologikh obolochek [Finite deflections, stability and supercritical behavior of thin shallow shells]. Moscow, Moscow State University of Mechanical Engineering Publ., 2004, 162 p.
[3] Marguerre K. Proc. 5th Intern. Congr. Appl. Mech. Cambridge, Massachusetts, 1938, New York, Wiley, 1939, pp. 93–101.
[4] Reissner E. Proc. 3rd Symp. Appl. Math., New York, McGrow-Hill, 1950, vol. 3, pp. 27–52.
[5] Timoshenko S.P., Voinovsky-Kriger S. Plastinki i obolochki [Plates and shells], Moscow, Fizmatgiz Publ., 1963, 635 p.
[6] Vol'mir A.S. Ustoichivost' deformiruemykh system [Stability of Deformable Systems]. Moscow, Fizmatgiz Publ., 1967, 984 p.
[7] Grigolyuk E.I., Kabanov V.V. Ustoichivost' obolochek [Stability of shells]. Moscow, Nauka Publ., 1978, 359 p.
[8] Grigoliuk E.I., Mamai V.I. Nelineinoe deformirovanie tonkostennykh konstruktsii [Nonlinear deformation of thin-walled structures]. Moscow, Fizmatgiz Publ., 1997, 272 p.
[9] Kornishin M.S. Nelineinye zadachi teorii plastin i pologikh obolochek i metody ikh resheniya [Nonlinear problems of the theory of plates and shallow shells and solution methods]. Moscow, Nauka Publ., 1964, 192 p.
[10] Filin A.P. Elementy teorii obolochek [Elements of the theory of shells]. Leningrad, Stroyizdat Publ., 1987, 384 p.
[11] Vorovich I.I., Minakova N.I. Itogi nauki i tekhniki. Mekhanika tverdykh deform. tel. — Results in Science and Technology. Mechanics of deformable solids, vol. 7, VINITI Publ., 1973, pp. 5–86.
[12] Grigorenko Ya.M., Gulyaev V.I. Prikladnaya mekhanika — Applied mechan-ics, 1991, vol. 27, no. 10, pp. 3–23.
[13] Mescall J. AIAA J, 1966, vol. 4, no. 11, pp. 2041–2043.
[14] Valishvili N.V. PMM — J. Appl. Math. Mech., 1968, vol. 32, iss. 6, pp. 1089–1096.
[15] Shapovalov L.D. Mekhanika tverdogo tela — Mechanics of solids, 1969, no. 1, pp. 56–63.
[16] Valishvili N.V. Metody rascheta obolochek vrashcheniia na ETsVM [Methods for calculating the shells of revolution on a computer]. Moscow, Mashinostroenie Publ., 1976, 278 p.
[17] Riks E. J. Appl. Mech., 1972, vol. 39, pp. 1060–1065.
[18] Crisfield M.A. Cоmput. and Structures, 1981, vol. 13, no. 1, pp. 55–62.
[19] Grigolyuk E.I., Shalashilin V.I. Problemy nelineinogo deformirovaniya: Metod prodolzheniya resheniya po parametru v nelineinykh zadachakh mekhaniki tverdogo deformiruemogo tela [Nonlinear deformation problems: The method of the parameter continuation in nonlinear problems of mechanics of deforma-ble bodies]. Moscow, Nauka Publ., 1988, 232 p.
[20] Gavryushin S.S. Izv. AN SSSR. MTT — Proc. Acad. Sci. USSR. Mechanics of solids, 1994, no. 1, pp. 109–119.
[21] Arnol'd V.I. Teoriya katastrof [Catastrophe theory]. Moscow, Nauka Publ., 1990, 128 p.
[22] Vainberg M. M., Trenogin V. A. Teoriya vetvleniya resheniy nelineinykh uravneniy [The theory of branching of nonlinear equations solutions]. Moscow, Nauka Publ., 1969, 527 p.
[23] Gavriushin S.S., Baryshnikova O.O. Izvestiia Vuzov. Mashinostroenie — Univ. Proceed. Mechanic engineering, 2000, no. 1, pp. 29–37
[24] Gavryushin S.S. Mekhatronika — Mechatronics, 2000, no. 5, pp. 16–18.
[25] Ali Abdul Karim, Gavryushin S.S. Izvestiya vuzov. Mashinostroenie — Univ. Proc. Mechanic engineering, 2005, no. 8, pp. 17–23.
[26] Gavryushin S.S. Chislennyi analiz i sintez gibkikh elementov konstruktsii s upravliaemoi uprugoi deformatsiei. Problemy prikladnoi mekhaniki, dinamiki i prochnosti mashin. [Numerical analysis and synthesis of flexible structural el-ements with controlled elastic deformation. Problems of applied mechanics, dynamics and strength of machines]. Coll. art. V.A. Svetlitsky, O.S. Naraikin, eds. Moscow, Bauman MSTU Publ., 2005, pp. 114–129.
[27] Gavryushin S.S., Baryshnikova O.O., Boriskin O.F. Chislennye metody v dinamike i prochnosti mashin [Numerical methods in dynamics and strength of machines]. Moscow, Bauman MSTU Publ., 2012, 492 p.


Gavryushin S. Numerical simulation of nonlinear deformation of thin elastic shells. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 115-130



Download article

Колличество скачиваний: 331