Comparative Analysis of Nonlinear Deformation and Buckling of Thin Elastic Shells of Step-Variable Thickness
DOI:
https://doi.org/10.32347/2410-2547.2022.108.107-118Keywords:
flexible shell, step-variable thickness, thin inhomogeneous shell, universal spatial finite element, finite element moment scheme, geometrically nonlinear deformation, buckling, post-buckling behavior, thermo-mechanical loadAbstract
A comparative analysis of finite element models and methods for solving complex problems of geometrically nonlinear deformation, buckling and post-buckling behavior of thin shells of stepwise variable thickness is carried out. An approach based on the use of the moment scheme of finite elements is considered. The features of using the software suite LIRA and integrated software system SCAD for solving the assigned problems are also provided. Thin and medium thickness shells are considered. They can have different geometric features in thickness and be under the action of static thermomechanical loads. A technique for solving these problems with the help of an efficient refined approach is presented. The technique is based on the general methodological positions of the three-dimensional theory of thermoelasticity and the use of the finite element moment scheme. With this approach, the approximation through the shell thickness is carried out by a single universal spatial finite element. The element can be modified in different portions of the shell with a step-variable thickness. It can be located eccentrically relative to the middle surface of the casing and can change its dimensions in the direction of the shell thickness. Such a unified approach made it possible to create a unified designed finite element model of a shell of an inhomogeneous geometric structure under the combined action of a thermomechanical load. A comparative analysis of the application of three finite element approaches for problems of geometrically nonlinear deformation and buckling of shells of stepwise variable thickness is carried out.
References
Bazhenov V.A., Krivenko O.P., Solovei M.O. Nonlinear deformation and buckling of elastic shells with inhomogeneous structure (Neliniine deformuvannia ta stiikist pruzhnykh obolonok neodnoridnoi struktury). – Kyiv: ZAT Vipol, 2010. – 316 p. ISBN: 978-966-646-097-7 (in Ukrainian).
Bazhenov V.A., Krivenko O.P., Solovey N.A. Nonlinear deformation and stability of elastic shells of an inhomogeneous structure: Models, methods, algorithms, poorly-studied and new problems (Nelineynoe deformirovanie i ustoychivost uprugih obolochek neodnorodnoy strukturyi: Modeli, metodyi, algoritmyi, maloizuchennyie i novyie zadachi). – M.: Knizhnyiy dom LIBROKOM, 2013. – 336 s. ISBN: 978-5-397-03500-2 (in Russian).
Bazhenov V.A., Solovei N.A., Krivenko O.P. Modeling of Nonlinear Deformation and Buckling of Elastic Inhomogeneous Shells // Strength of Materials and Theory of Structures: Scientific-and-technical collected. K.: KNUBA, 2014. – Issue 92. – Р.121-147. DOI: 10.5862/MCE.53.6.
Solovei N.A., Krivenko O.P., Malygina O. Finite element models for the analysis of nonlinear deformation of shells stepwise-variable thickness with holes, channels and cavities // Magazine of Civil Engineering, 2015. – No. 1. – P 56-69. DOI: 10.5862/MCE.53.6 (in Russian).
Bazhenov V.A., Krivenko O.P. Buckling and Natural Vibrations of Thin Elastic Inhomogeneous Shells. Saarbruken, Deutscland: LAP LAMBERT Academic Publishing, 2018. – 97 p. ISBN: 978-613-9-85790-6.
Bazhenov V.A., Krivenko O.P. Buckling and vibrations of elastic inhomogeneous shells under thermo-mechanical loads (Stiikist i kolyvannia pruzhnykh neodnoridnykh obolonok pry termosylovykh navantazhenniakh). – Kyiv: Karavella, 2020. – 187 p. ISBN: 978-966-8019-85-2 (in Ukrainian).
Bazhenov V.A., Krivenko O.P., Vorona Yu.V. Effect of heating on the natural vibrations of thin parabolic shells // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles. – K.: KNUBA, 2019. – Issue 103. – P. 3-16. DOI: 10.32347/2410-2547.2019.103.3-16
Bazhenov V.A., Krivenko O.P. Buckling and vibrations of the shell with the hole under the action of thermomechanical loads // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles – Kyiv: KNUBA, 2020. – Issue 104. – P. 136-146. DOI: 10.32347/2410-2547.2020.104.136-146
Krivenko O.P., Vorona Yu.V. Finite element analysis of nonlinear deformation, stability and vibrations of elastic thin-walled structures // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles. – K.: KNUBA, 2021. – Issue 107. – P. 20-34.
Reddy J. N. Theory and Analysis of Elastic Plates and Shells. Second Edition. CRC Press. 2006. 568 p.
Golovanov A.I., Tyuleneva O.N., Shigabutdinov A.F. Finite element method in statics and dynamics of thin-walled structures (Metod konechnyih elementov v statike i dinamike tonkostennyih konstruktsiy). – M.: FIZMATLIT, 2006. – 392 p. (in Russian).
Karpov V.V. Strength and buckling of reinforced shells of rotation. Part 2. Computational experiment with static mechanical action (Prochnost i ustoychivost podkreplennyih obolochek vrascheniya. Ch. 2. Vyichislitelnyiy eksperiment pri staticheskom mehanicheskom vozdeystvii). – M.: FIZMATLIT, 2011. – 248 p. (in Russian).
Chapelle D., Bathe K.J. The finite element analysis of shells – Fundamentals. Series: Computational fluid and solid mechanics. Berlin; Heidelberg: Springer, 2011. – 410 p.
Hutchinson J.W., Thompson J.M.T. Nonlinear Buckling Interaction for Spherical Shells Subject to Pressure and Probing Forces. J. Appl. Mech., 2017. 84(6). 061001.
Podvornyi A.V., Semenyuk N.P., Trach V.M. Stability of Inhomogeneous Cylindrical Shells Under Distributed External Pressure in a Three-Dimensional Statement. Int. Appl. Mech. 2017. 53. Р.623–638.
Karpov V.V., Semenov A.A. Mathematical models and algorithms for studying the strength and buckling of shell structures (Matematicheskie modeli i algoritmyi issledovaniya prochnosti i ustoychivosti obolochechnyih konstruktsiy) // Siberian J. of Industrial Mathematics, 2017. - V.20, No. 1. – P. 53–65. (in Russian).
Cinefra M. Formulation of 3D finite elements using curvilinear coordinates. Mechanics of Advanced Materials and Structures, 2020. P.1-10.
Gureeva N.A., Klochkov Yu.V., Nikolaev A.P., Yushkin V.N. Stress-strain state of shell of revolution analysis by using various formulations of three-dimensional finite elements. Structural Mechanics of Engineering Constructions and Buildings. 2020. 16(5). P. 361–379.
Okhten I.O., Lukianchenko O.O. Some aspects of consideration of initial imperfections in the calculations of stability of thin-walled elements of open profile // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles. – K.: KNUBA, 2021. – Issue 106. – P. 122-128.
Yakupov N. M., Kiyamov H. G. & Mukhamedova I. Z. Calculation of the Fragments Toroidal Shell with Local Internal Deepening // Lobachevskii J. Math. 42, 2257–2262 (2021). https://doi.org/10.1134/S1995080221090304
Sakharov A.S., Solovey N.A. Investigation of the convergence of the finite element method in the problems of plates and shells. (Issledovanie shodimosti metoda konechnyih elementov v zadachah plastin i obolochek) – In the book: Spatial designs of buildings and structures, vol. 3. – M.: Stroyizdat, 1977. – P. 10-15. (in Russian).
Novozhilov V.V. Theory of thin shells (Teoriya tonkih obolochek). – L.: Sudpromgiz, 1962. – 431 p. (in Russian).
Strelets-Streletskiy E.B., Bogovis V.E., Genzersky Y.V., Geraymovich Y.D. [et al.]. LIRA 9.4. User Guide. Basics. Textbook (LIRA 9.4. Rukovodstvo polzovatelya. Osnovy. Uchebnoe posobie). – Kyiv: Fact, 2008. 164 p. (in Russian).
Gorodeckiy, A.S., Evzerov, I.D. Computer models of Structures (Kompyuternyie modeli konstruktsiy). – Кyiv: Fact, 2007. – 394 p. (in Russian)
Karpilovsky V.S., Kriksunov E.Z., Perel'muter A.V., Perel'muter M.A. Software SCAD (Vyichislitelnyiy kompleks SCAD). – Moscow: SCAD SOFT, 2009. – 656 p. (in Russian).
Perel’muter A.V., Slivker V.I. Design models of structures and possibility of their analysis (Raschetnyie modeli sooruzheniy i vozmozhnost ih analiza). – Moscow: DMK Press, 2007. – 600 p. (in Russian).
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