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Erschienen in: Acta Mechanica 11/2019

07.08.2019 | Original Paper

Stability of corrugated expansion bellows: shell and rod models

verfasst von: Tatiana V. Zinovieva, Kirill K. Smirnov, Alexander K. Belyaev

Erschienen in: Acta Mechanica | Ausgabe 11/2019

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Abstract

The problem of stability of corrugated thin-wall expansion bellows under hydrostatic internal load is considered. The bellows is modeled by an elastic rod with equivalent tensile, bending, and shear stiffness. Equations for calculating the critical value of fluid pressure at which the bellows loses stability are analytically derived, using an expression for hydrostatic follower load. The equivalent stiffness of the bellows is determined further from the solution of static problems for the elastic corrugated shell. The numerical solutions of the boundary value problems and the critical values of the pressure are obtained by the finite difference method. Additionally, a computer model of the expansion bellows was developed by ANSYS software, and the bellows stability was analyzed using shell finite elements. Calculations confirm the necessity of accounting for the axial displacement of expansion joint support when determining the critical pressure.
Literatur
3.
Zurück zum Zitat Eliseev, V.V.: Mechanics of Deformable Solids. Polytechnic University Press, St. Petersburg (2003). (in Russian) Eliseev, V.V.: Mechanics of Deformable Solids. Polytechnic University Press, St. Petersburg (2003). (in Russian)
4.
Zurück zum Zitat Eliseev, V.V., Zinovieva, T.V.: Mechanics of thin-wall structures: theory of rods. Polytechnic University Press, St. Petersburg (2008). (in Russian) Eliseev, V.V., Zinovieva, T.V.: Mechanics of thin-wall structures: theory of rods. Polytechnic University Press, St. Petersburg (2008). (in Russian)
5.
Zurück zum Zitat Simo, J.C.: A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Comput. Methods Appl. Mech. Eng. 49, 55–70 (1985)CrossRef Simo, J.C.: A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Comput. Methods Appl. Mech. Eng. 49, 55–70 (1985)CrossRef
6.
Zurück zum Zitat Crisfield, M.A., Jelenic, G.: Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 455(1983), 1125–1147 (1999)MathSciNetCrossRef Crisfield, M.A., Jelenic, G.: Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 455(1983), 1125–1147 (1999)MathSciNetCrossRef
7.
Zurück zum Zitat Romero, I.: The interpolation of rotations and its application to finite element models of geometrically exact rods. Comput. Mech. 34, 121–133 (2004)MathSciNetCrossRef Romero, I.: The interpolation of rotations and its application to finite element models of geometrically exact rods. Comput. Mech. 34, 121–133 (2004)MathSciNetCrossRef
8.
Zurück zum Zitat Meier, C., Popp, A., Wall, W.A.: Geometrically exact finite element formulations for slender beams: Kirchhoff–Love theory versus Simo–Reissner theory. Arch. Comput. Methods Eng. 26, 163–243 (2019)MathSciNetCrossRef Meier, C., Popp, A., Wall, W.A.: Geometrically exact finite element formulations for slender beams: Kirchhoff–Love theory versus Simo–Reissner theory. Arch. Comput. Methods Eng. 26, 163–243 (2019)MathSciNetCrossRef
9.
Zurück zum Zitat Humer, A.: Exact solutions for the buckling and postbuckling of shear-deformable beams. Acta Mech. 224(7), 1493–1525 (2013)MathSciNetCrossRef Humer, A.: Exact solutions for the buckling and postbuckling of shear-deformable beams. Acta Mech. 224(7), 1493–1525 (2013)MathSciNetCrossRef
10.
Zurück zum Zitat Kheisina, V.V., Eliseev, V.V., Sukhanov A.A.: Forces acting on a tube in a liquid. In: Proceedings of Scientific Conference XXVII Week of Science of SPbGTU 3. St. Petersburg, Polytechnic University Press, pp. 58–59 (1999). (in Russian) Kheisina, V.V., Eliseev, V.V., Sukhanov A.A.: Forces acting on a tube in a liquid. In: Proceedings of Scientific Conference XXVII Week of Science of SPbGTU 3. St. Petersburg, Polytechnic University Press, pp. 58–59 (1999). (in Russian)
11.
Zurück zum Zitat Yeliseyev, V.V., Zinovieva, T.V.: Nonlinear-elastic strain of underwater pipeline in laying process. Comput. Contin. Mech. 5(1), 70–78 (2012). (in Russian)CrossRef Yeliseyev, V.V., Zinovieva, T.V.: Nonlinear-elastic strain of underwater pipeline in laying process. Comput. Contin. Mech. 5(1), 70–78 (2012). (in Russian)CrossRef
12.
Zurück zum Zitat Feodosiev, V.I.: Advanced Stress and Stability Analysis: Worked Examples. Foundations of Engineering Mechanics. Springer, Berlin (2006) Feodosiev, V.I.: Advanced Stress and Stability Analysis: Worked Examples. Foundations of Engineering Mechanics. Springer, Berlin (2006)
13.
Zurück zum Zitat Panovko, Y.G., Gubanova, I.I.: Stability and Oscillations of Elastic Systems: Modern Concepts, Paradoxes and Errors. Moscow, Nauka (1987). (in Russian) Panovko, Y.G., Gubanova, I.I.: Stability and Oscillations of Elastic Systems: Modern Concepts, Paradoxes and Errors. Moscow, Nauka (1987). (in Russian)
14.
Zurück zum Zitat Tarnopolsky, YuM, Roze, A.V.: Features of the Calculation of Parts from Reinforced Plastics. Zinatne, Riga (1969). (in Russian) Tarnopolsky, YuM, Roze, A.V.: Features of the Calculation of Parts from Reinforced Plastics. Zinatne, Riga (1969). (in Russian)
15.
Zurück zum Zitat Smirnov, K.K.: On accounting of material plastic properties when calculating the stability of metal bellows expansion joints (in Russian). In: The Development of Fast Neutron Reactor Technology with Sodium Coolant, pp. 120–130. Nizhny-Novgorod, JSC “OKBM Afrikantov” (2016) Smirnov, K.K.: On accounting of material plastic properties when calculating the stability of metal bellows expansion joints (in Russian). In: The Development of Fast Neutron Reactor Technology with Sodium Coolant, pp. 120–130. Nizhny-Novgorod, JSC “OKBM Afrikantov” (2016)
16.
Zurück zum Zitat Panovko, Y.G.: Mechanics of Solid Deformable Body. Lenand, Moscow (2017). (in Russian) Panovko, Y.G.: Mechanics of Solid Deformable Body. Lenand, Moscow (2017). (in Russian)
18.
Zurück zum Zitat Eliseev, V.V., Vetyukov, YuM: Finite deformation of thin shells in the context of analytical mechanics of material surfaces. J. Acta Mech. 209(1), 43–57 (2010)CrossRef Eliseev, V.V., Vetyukov, YuM: Finite deformation of thin shells in the context of analytical mechanics of material surfaces. J. Acta Mech. 209(1), 43–57 (2010)CrossRef
19.
Zurück zum Zitat Eliseev, V.V., Vetyukov, Yu M.: Theory of shells as a product of analytical technologies in elastic body mechanics. In: Pietraszkiewicz, Gorski, (eds.) Shell Structures: Theory and applications, vol. 3. Balkema, London (2014) Eliseev, V.V., Vetyukov, Yu M.: Theory of shells as a product of analytical technologies in elastic body mechanics. In: Pietraszkiewicz, Gorski, (eds.) Shell Structures: Theory and applications, vol. 3. Balkema, London (2014)
20.
Zurück zum Zitat Eliseev, V.V., Zinovieva, T.V.: Lagrangian mechanics of classical shells: theory and calculation of shells of revolution. In: Pietraszkiewicz W and Witkowski W (eds) Shell Structures: Theory and Applications Volume 4. Proceedings of the 11\(^{th}\) International conference “Shell structures: theory and applications” (SSTA 2017). October 11–13, 2017, Gdansk, Poland, pp. 73–76. Taylor & Francis Group, London (2018) Eliseev, V.V., Zinovieva, T.V.: Lagrangian mechanics of classical shells: theory and calculation of shells of revolution. In: Pietraszkiewicz W and Witkowski W (eds) Shell Structures: Theory and Applications Volume 4. Proceedings of the 11\(^{th}\) International conference “Shell structures: theory and applications” (SSTA 2017). October 11–13, 2017, Gdansk, Poland, pp. 73–76. Taylor & Francis Group, London (2018)
22.
Zurück zum Zitat Bakhvalov, N.S., Zhidkov, N.P., Kobelkov, G.G.: Numerical Methods. Laboratory of Knowledges. Binom, Moscow (2011). (In Russian) Bakhvalov, N.S., Zhidkov, N.P., Kobelkov, G.G.: Numerical Methods. Laboratory of Knowledges. Binom, Moscow (2011). (In Russian)
23.
Zurück zum Zitat Chapra, S.C., Canale, R.P.: Numerical Methods for Engineers. McGraw-Hill Education, New York (2014) Chapra, S.C., Canale, R.P.: Numerical Methods for Engineers. McGraw-Hill Education, New York (2014)
24.
Zurück zum Zitat Borwein, J.M., Skerrit, M.B.: An Introduction to Modern Mathematical Computing: With Mathematica, vol. XVI. Springer, Berlin (2012)CrossRef Borwein, J.M., Skerrit, M.B.: An Introduction to Modern Mathematical Computing: With Mathematica, vol. XVI. Springer, Berlin (2012)CrossRef
25.
Zurück zum Zitat ANSYS Inc. PDF Documentation for Release 15.0 ANSYS Inc. PDF Documentation for Release 15.0
Metadaten
Titel
Stability of corrugated expansion bellows: shell and rod models
verfasst von
Tatiana V. Zinovieva
Kirill K. Smirnov
Alexander K. Belyaev
Publikationsdatum
07.08.2019
Verlag
Springer Vienna
Erschienen in
Acta Mechanica / Ausgabe 11/2019
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-019-02497-6

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