Stability Optimization of Functionally Graded Pipes Conveying Fluid
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:51776", author = "Karam Y. Maalawi and Hanan E.M EL-Sayed", title = "Stability Optimization of Functionally Graded Pipes Conveying Fluid", abstract = "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 = "Functionally graded materials, pipe flow, optimumdesign, fluid- structure interaction", volume = "5", number = "7", pages = "1231-6", }