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Static and Dynamic Analysis of Hyperboloidal Helix Having Thin Walled Open and Close Sections

Authors: Merve Ermis, Murat Yılmaz, Nihal Eratlı, Mehmet H. Omurtag

Abstract:

The static and dynamic analyses of hyperboloidal helix having the closed and the open square box sections are investigated via the mixed finite element formulation based on Timoshenko beam theory. Frenet triad is considered as local coordinate systems for helix geometry. Helix domain is discretized with a two-noded curved element and linear shape functions are used. Each node of the curved element has 12 degrees of freedom, namely, three translations, three rotations, two shear forces, one axial force, two bending moments and one torque. Finite element matrices are derived by using exact nodal values of curvatures and arc length and it is interpolated linearly throughout the element axial length. The torsional moments of inertia for close and open square box sections are obtained by finite element solution of St. Venant torsion formulation. With the proposed method, the torsional rigidity of simply and multiply connected cross-sections can be also calculated in same manner. The influence of the close and the open square box cross-sections on the static and dynamic analyses of hyperboloidal helix is investigated. The benchmark problems are represented for the literature.

Keywords: Hyperboloidal helix, squared cross section, thin walled cross section, torsional rigidity.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1126391

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References:


[1] M.H. Omurtag and A.Y. Aköz, “The mixed finite element solution of helical beams with variable cross-section under arbitrary loading”, Comput. Struct., vol. 43, pp. 325–331, 1992.
[2] V. Haktanır and E. Kıral, “Statical analysis of elastically and continuously supported helicoidal structures by the transfer and stiffness matrix methods”, Comput. Struct., vol. 49, pp. 663–677, 1993.
[3] W. Busool and M. Eisenberger, “Exact static analysis of helicoidal structures of arbitrary shape and variable cross section”, J. Struct. Eng., vol. 127, pp. 1266–1275, 2001.
[4] V. Yıldırım, “Investigation of parameters affecting free vibration frequency of helical springs”, Int. J. Numer. Methods Eng., vol. 39, pp. 99–114, 1996.
[5] J.E. Mottershead, “Finite elements for dynamical analysis of helical rods”, Int. J. Mech. Sci., vol.22, pp. 267–283, 1980.
[6] J. Lee, “Free vibration analysis of cylindrical helical springs by the pseudospectral method”, J. Sound Vib., vol. 302, pp. 185–196, 2007.
[7] A.M. Yu, C.J. Yang and G.H. Nie, “Analytical formulation and evaluation for free vibration of naturally curved and twisted beams”, J. Sound Vib., vol. 329, pp. 1376–1389, 2010.
[8] N. Eratlı, M. Ermis and M.H. Omurtag, “Free vibration analysis of helicoidal bars with thin-walled circular tube cross-section via mixed finite element method”, Sigma Journal of Engineering and Natural Sciences, vol. 33(2), pp. 200-218, 2015.
[9] S.A. Alghamdi, M.A. Mohiuddin and H.N. Al-Ghamedy, “Analysis of free vibrations of helicoidal beams”, Eng. Comput., vol. 15, pp. 89–102, 1998.
[10] S. Timoshenko and J.N. Goodier, Theory of elasticity, McGraw-Hill, New York, 1951.
[11] R.J. Roark, Formulas for Stress and Strain, McGraw-Hill, New York, 1954.
[12] N.X. Arutunan and B.L. Abraman, Torsion of Elastic Bodies (in Russian), State Publisher, Fizmatgiz, Moscow, 1963.
[13] C.T. Wang, Applied Elasticity, McGraw-Hill, New York, 1953.
[14] J.F. Elyand and O.C. Zienkiewicz, “Torsion of compound bars-A relaxation solution”, Int. J. Mech. Sci., vol. 1, pp. 356-365, 1960.
[15] L.R. Hermann, “Elastic torsional analysis of irregular shapes”, J. Engng. Mech., ASCE, vol. 91(6), pp. 11-19, 1965.
[16] J.L. Krahula and G.F. Lauterbach, “A finite element solution for Saint-Venant torsion”, AIAA Journal, vol. 7(12), pp. 2200-2203, 1969.
[17] K. Darılmaz, E. Orakdogen, K. Girgin and S. Küçükarslan, “Torsional rigidity of arbitrarily shaped composite sections by hybrid finite element approach”, Steel and Composite Structures, vol. 7(3), pp. 241-251, 2007.
[18] Z. Li, J.M. Ko and Y.Q. Ni, “Torsional rigidity of reinforced concrete bars with arbitrary sectional shape”, Finite Elements in Analysis and Design, vol. 35, pp. 349-361, 2000.
[19] J.S. Lamancusa and D.A. Saravanos, “The torsional analysis of bars with hollow square cross-sections”, Finite Element in Analysis and Design, vol. 6, pp. 71-79, 1989.
[20] N. Eratlı, M. Yılmaz, K. Darılmaz and M.H. Omurtag, “Dynamic analysis of helicoidal bars with non-circular cross-sections via mixed FEM”, Struct. Eng. Mech., vol. 57(2), pp. 221-238, 2016.
[21] E.J. Sapountzakis, “Nonuniform torsion of multi-material composite bars by the boundary element method”, Computers and Structures, vol. 79, pp. 2805-2816, 2001.
[22] E.J. Sapountzakis and V.G. Mokos, “Nonuniform torsion of bars variable cross section”, Computers and Structures, vol. 82, pp. 03-715, 2004.
[23] J.T. Oden and J.N. Reddy, Variational Method in Theoretical Mechanics, Springer-Verlag, Berlin, 1976.