Semiаnalytical finite elements method efficiency in the geometrically nonlinear elastic-plastic problems
Keywords:dynamics, geometric nonlinearity, plastic deformations, bodies of revolution, axisymmetric constructions, semi-analytical finite element method
Particular interest, among the variety of objects considered using analytical and numerical methods, are bodies of revolution with complex shape and cross-sectional structure. The selected geometric class is used as natural structure components in the construction and various fields of mechanical engineering. The sufficiently high prevalence of these forms in the construction and machine-building sectors on the one hand, and the possibility of a significant simplification math equestions by taking into account their geometric features on the other, is attracting increasing attention of researchers.
It is known that today the finite element method (FEM) is the most powerful tool for analyzing the problems of building mechanics and deformable solid mechanics. Over the past few years, the dimension of FEM models has grown dramatically, driven by increased demands for accuracy and reliability of results. In addition, the difficulties of studying the behavior of structures in the presence of dynamic loads are many times increased in comparison with static analysis. To overcome these problems, in many cases, it introduce additional hypotheses, which, as a rule, narrow the class of objects and processes under study, but can significantly improve efficiency and significantly reduce the duration of the calculation. Semi-analytical finite element method (SAFEM) is one of such approaches that is widely used for solving problems whose objects are prismatic and rotational bodies. High efficiency of SAFEM for a certain range of objects was demonstrated in the field of static analysis, continuous mechanics of fracture under creep conditions, processes of nonlinear deformation of reinforced concrete structures. The analysis of the results obtained by domestic and foreign scientists on this issue shows that most analytical and numerical methods of scientific research are usually oriented to geometrically nonlinear problems at static load. The veracity and effectiveness of the semi-analytical finite element method in the problems of geometrically nonlinear elastoplastic deformation of axisymmetric structures under dynamic loads is considered. The capabilities of methodology are demonstrated by examples of numerical modeling of the stress-strain state of building structures with large linear strains and analysis of technological processes of pulsed metal processing.
Bazhenov V.A. Napivanalitychnyy metod skinchenykh elementiv v zadachakh ruynuvannya prostovykh til (Semi-analytic method of finite elements in problems of destruction of ordinary solids) / [Bazhenov V.A., Hulyar O.I., Pyskunov S.O., Sakharov O.S.] – K., KNUBA, 2005. – 298 p.
Bazhenov V.A. Napivanalitychnyy metod skinchennykh elementiv v zadachakh dynamiky prostorovykh til (Semi-analytic method of finite elements in problems of dynamics of spatial solids)/ [Bazhenov V.A., Hulyar O.I., Sakharov O.S., Solodey I.I.] – K., KNUBA, 2012. - 248 p.
Bazhenov V.A. Chislennoye modelirovaniye razrusheniya zhelezobetonnykh konstruktsiy po metodu konechnykh elementov (Numerical modeling of the destruction of reinforced concrete structures using the finite element method) / [Bazhenov V.A., Gulyar A.I., Kozak A.L., Rutkovskiy V.A., Sakharov A.S.] – K., Naukova dumka, 1996. – 360 p.
Bazhenov V.A. Postanovka evolyutsiynoyi heometrychno-neliniynoyi zadachi mekhaniky ruynuvannya dlya prostorovykh til obertannya ta pryzmatychnykh til (Formulation of an evolutionary geometric-nonlinear problem of fracture mechanics for spatial rotational bodies and prismatic solids ) / [Bazhenov V.A., Solodey I.I., Vabishchevych M.O., Stryhun R.L.] // Opir materialiv i teoriya sporud. (Strength of Materials and Theory of Structures) – K.: KNUBA, Vip.101, 2018, pp. 3-13
Galishin A.Z. Opredeleniye osesimmetrichnogo geometricheski nelineynogo termovyazkouprugoplasticheskogo sostoyaniya tonkikh sloistykh obolochek s uchetom povrezhdayemosti materiala (Determination of the axisymmetric geometrically nonlinear thermoviscoelastic state of thin layered shells taking into account damage to the material) / [Galishin A.Z., Shevchenko YU.M.] // Matematichní metodi ta fíziko-mekhaníchní polya (Mathematical methods and physical-mechanical fields). – 2016. – t.51, No. 2. - S. 175−187.
Hlushchenkov V.A. Chyselʹne doslidzhennya protsesiv vysokoshvydkisnoho deformuvannya na osnovi metodu skinchennykh elementiv (Numerical study of high-speed deformation processes based on finite element method) / [Hlushchenkov V.A. etc.] // Mashynovedenye. 1986. №4. P.146-151.
Kachanov L.M. Osnovy mekhaniky ruynuvannya (Fundamentals of fracture mechanics) / [Kachanov L.M.] – M. Nauka. 1974.-312p.
Kolmogorov V.L. Mekhanika obrabotki metallov davleniyem (The mechanics of metal processing) / [Kolmogorov V.L.] – M.: Metallurgiya, 1986. – 688 p.
Li/Lee E.H. Analiz osesimetrichnoy osadki i poperechnoy osadki v usloviyakh ploskoy deformatsii sploshnykh tsilindricheskikh zagotovok metodom konechnykh elementov (Analysis of axisymmetric upsetting and transverse upsetting under conditions of plane deformation of continuous cylindrical billets by the finite element method) / [E.H. Lee, S. Kobayashi] // ASME, ser. B, - 1971. No. 2 - c. 73-84.
Maksym’yuk YU.V. Vykhidni spivvidnoshennya neliniynoho dynamichnoho formozminennya visesymetrychnykh ta ploskodeformivnykh til (Initial relations of nonlinear dynamic shape change of axisymmetric and plane-deformable solids) / [Maksym’yuk YU.V., Solodey I.I., Stryhun R.L.] // Opir materialiv i teoriya sporud.(Strength of Materials and Theory of Structures) – K.: KNUBA, Vip. 102, 2019, pp. 252-262.
Solodey I.I. Skinchennoelementni modeli prostorovykh til v zadachakh dynamiky z urakhuvannyam velykykh plastychnykh deformatsiy (Finite element models of spatial solids in dynamics problems with consideration of large plastic deformations)/ [Solodey I.I., Vabishchevych M.O., Stryhun R.L.] // Upravlinnya rozvytkom skladnykh system (Management of development of complex systems). –K .: KNUBA, Vol.39, 2019.-p.151-156.
Chernyshenko I.S. Fizicheski i geometricheski nelineynoye deformirovaniye konicheskikh obolochek ellipticheskim otverstiyem (Physically and geometrically nonlinear deformation of conical shells by an elliptical hole) / [Chernyshenko I.S., Storozhuk Ye.A., Kharenko S.B.] // Prikl. mekhanika. – 2008. – t.44, № 2. – S. 68−85.
Galishin A.Z. Axisymmetric physically nonlinear state of orthotropic shells / [Galishin A.Z., Shevchenko Yu.N.] // International Applied Mechanics, 2013.
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