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Stability Optimization of Functionally Graded Pipes Conveying Fluid

Authors: Karam Y. Maalawi, Hanan E.M EL-Sayed


This paper presents an exact analytical model for optimizing stability of thin-walled, composite, functionally graded pipes conveying fluid. The critical flow velocity at which divergence occurs is maximized for a specified total structural mass in order to ensure the economic feasibility of the attained optimum designs. The composition of the material of construction is optimized by defining the spatial distribution of volume fractions of the material constituents using piecewise variations along the pipe length. The major aim is to tailor the material distribution in the axial direction so as to avoid the occurrence of divergence instability without the penalty of increasing structural mass. Three types of boundary conditions have been examined; namely, Hinged-Hinged, Clamped- Hinged and Clamped-Clamped pipelines. The resulting optimization problem has been formulated as a nonlinear mathematical programming problem solved by invoking the MatLab optimization toolbox routines, which implement constrained function minimization routine named “fmincon" interacting with the associated eigenvalue problem routines. In fact, the proposed mathematical models have succeeded in maximizing the critical flow velocity without mass penalty and producing efficient and economic designs having enhanced stability characteristics as compared with the baseline designs.

Keywords: Pipe Flow, functionally graded materials, optimumdesign, fluid- structure interaction

Digital Object Identifier (DOI):

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[1] S. Suresh and A. Mortensen, Fundamentals of functionally graded materials. Cambridge University Press, 1998.
[2] M.P. Paidoussis and N.T. Issid, "Dynamic stability of pipes conveying fluid", Journal of Sound and Vibration, vol. 33, no. 3, 1974, pp. 267- 294.
[3] B.K. Mishra and P.C. Upadhyay, "On the dynamic response of fluidfilled buried pipelines", Journal of Sound and Vibration, vol. 117, no. 1, 1987, pp. 59-67.
[4] G.P. Zou, N. Cheraghi and F. Taheri, "Fluid-induced vibration of composite material gas pipelines", International Journal of Solids and Structures, vol. 42, Issue 3-4, 2005, pp. 1253-1268.
[5] E. Rabeih, M. El-Maddah, R. Gadelrab and A. Atwa, "Effect of composite material parameters on variational behavior of pipes conveying fluid", International Journal of Acoustics and Vibration, vol.10, no.2, 2005, pp. 93-97.
[6] G.G. Sheng and X. Wang, "Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads", Composite Structures, vol.93, issue 1, 2010, pp. 162-170.
[7] Tanaka, M., Tanaka, S., and Seguchi, Y., "Optimal and robust shapes of a pipe conveying fluid", Asia-Pacific Vibration conference 93, Kïtakyushu, pp. 1757-1762, November 1993.
[8] S├ñllström, J.H., "Stability optimization of beams conveying fluid or carrying other axially moving materials", Journal of Structural Optimization, Vol. 7, pp. 219-226, 1994.
[9] Borglund, D., "On the optimal design of pipes conveying luid", Journal of Fluids and Structures", Vol. 12, No. 3, 1998, pp. 353-365.
[10] Maalawi, K.Y., and Ziada, M.A., "On the static instability of flexible pipes conveying fluid", Journal of Fluids and Structures, Vol. 16, No. 5, 2002, pp. 685-690.
[11] Bendsoe, M.P., Olhoff, N., and Taylor, J.E., "A variational formulation for multicriteria structural optimization", Journal of Structural Mechanics, Vol. 11, 1983, pp. 523-544.
[12] Czyz, J.A., and Lukasiewicz, S.A., "Multimodal optimization of structures with frequency constraints", AIAA Journal, Vol.33, No. 8, pp. 1496-1502, August 1995.
[13] Haftka R.T., Gurdal Z., and Kamat M.P., "Elements of Structural Optimization", 2nd edition, Dordrecht; Kluwer Academic Publishers, 1990.
[14] Maalawi, K.Y., "Buckling optimization of flexible columns", International Journal of Solids and Structures, Vol. 39, No.23, 2002, pp. 5865-5876.
[15] L. Librescu and K. Maalawi, "Material grading for improved aeroelastic stability in composite wings", Journal of Mechanics of Structures, vol. 2, no.7, 2007, pp.1381-1394.
[16] Karam Y. Maalawi, "Optimization of elastic columns using axial grading concept," Engineering Structures, Vol. 31, 2009, pp.2922-2929.
[17] Karam Y. Maalawi, "Use of material grading for enhanced buckling design of thin-walled composite rings/long cylinders under external pressure," Composite Structures, 93(2), 2011, pp-351-359.
[18] C.H. Edwards and D.E. Penney, Differential equations and boundary value problems: computing and modeling, Prentice Hall, Englewood Cliffs, NJ, 2004.
[19] P. Venkataraman, Applied Optimization with MATLAB Programming, John Wiley & Sons, Inc., 2002.
[20] I.M. Daniel and O. Ishai, Engineering mechanics of composite materials, 2nd ed., Oxford Univ. Press, New York, 2006.