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.
References
Belyaev, A.K., Zinovieva, T.V., Smirnov, K.K.: Theoretical and experimental studies of the stress–strain state of expansion bellows as elastic shells. St. Petersburg Polytech. Univ. J. Phys. Math. 3, 7–14 (2017). https://doi.org/10.1016/j.spjpm.2017.03.003
Yeliseyev, V.V., Zinovieva, T.V.: Nonlinear-elastic strain of underwater pipeline in laying process. Comput. Contin. Mech. 5(1), 70–78 (2012). https://doi.org/10.7242/1999-6691/2012.5.1.9. (in Russian)
Eliseev, V.V.: Mechanics of Deformable Solids. Polytechnic University Press, St. Petersburg (2003). (in Russian)
Eliseev, V.V., Zinovieva, T.V.: Mechanics of thin-wall structures: theory of rods. Polytechnic University Press, St. Petersburg (2008). (in Russian)
Simo, J.C.: A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Comput. Methods Appl. Mech. Eng. 49, 55–70 (1985)
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)
Romero, I.: The interpolation of rotations and its application to finite element models of geometrically exact rods. Comput. Mech. 34, 121–133 (2004)
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)
Humer, A.: Exact solutions for the buckling and postbuckling of shear-deformable beams. Acta Mech. 224(7), 1493–1525 (2013)
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)
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)
Feodosiev, V.I.: Advanced Stress and Stability Analysis: Worked Examples. Foundations of Engineering Mechanics. Springer, Berlin (2006)
Panovko, Y.G., Gubanova, I.I.: Stability and Oscillations of Elastic Systems: Modern Concepts, Paradoxes and Errors. Moscow, Nauka (1987). (in Russian)
Tarnopolsky, YuM, Roze, A.V.: Features of the Calculation of Parts from Reinforced Plastics. Zinatne, Riga (1969). (in Russian)
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)
Panovko, Y.G.: Mechanics of Solid Deformable Body. Lenand, Moscow (2017). (in Russian)
Zinovieva, T.V.: Calculation of equivalent stiffness of corrugated thin-walled tube. In: Evgrafov, A. (ed.) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering, pp. 211–220. Springer, Switzerland (2019). https://doi.org/10.1007/978-3-030-11981-2
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)
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., 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)
Zinovieva, T.V.: Calculation of shells of revolution with arbitrary meridian oscillations. In: Evgrafov, A. (ed.) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering, pp. 165–176. Springer, Switzerland (2017). https://doi.org/10.1007/978-3-319-53363-6_17
Bakhvalov, N.S., Zhidkov, N.P., Kobelkov, G.G.: Numerical Methods. Laboratory of Knowledges. Binom, Moscow (2011). (In Russian)
Chapra, S.C., Canale, R.P.: Numerical Methods for Engineers. McGraw-Hill Education, New York (2014)
Borwein, J.M., Skerrit, M.B.: An Introduction to Modern Mathematical Computing: With Mathematica, vol. XVI. Springer, Berlin (2012)
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Zinovieva, T.V., Smirnov, K.K. & Belyaev, A.K. Stability of corrugated expansion bellows: shell and rod models. Acta Mech 230, 4125–4135 (2019). https://doi.org/10.1007/s00707-019-02497-6
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DOI: https://doi.org/10.1007/s00707-019-02497-6