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Buckling Optimization of Radially-Graded, Thin-Walled, Long Cylinders under External Pressure

Authors: Karam Y. Maalawi


This paper presents a generalized formulation for the problem of buckling optimization of anisotropic, radially graded, thin-walled, long cylinders subject to external hydrostatic pressure. The main structure to be analyzed is built of multi-angle fibrous laminated composite lay-ups having different volume fractions of the constituent materials within the individual plies. This yield to a piecewise grading of the material in the radial direction; that is the physical and mechanical properties of the composite material are allowed to vary radially. The objective function is measured by maximizing the critical buckling pressure while preserving the total structural mass at a constant value equals to that of a baseline reference design. In the selection of the significant optimization variables, the fiber volume fractions adjoin the standard design variables including fiber orientation angles and ply thicknesses. The mathematical formulation employs the classical lamination theory, where an analytical solution that accounts for the effective axial and flexural stiffness separately as well as the inclusion of the coupling stiffness terms is presented. The proposed model deals with dimensionless quantities in order to be valid for thin shells having arbitrary thickness-to-radius ratios. The critical buckling pressure level curves augmented with the mass equality constraint are given for several types of cylinders showing the functional dependence of the constrained objective function on the selected design variables. It was shown that material grading can have significant contribution to the whole optimization process in achieving the required structural designs with enhanced stability limits.

Keywords: Structural Optimization, functionally graded material, Buckling instability, laminated cylindrical shells, externalhydrostatic pressure

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[1] I. M. Daniel and O. Ishai, Engineering Mechanics of Composite Materials, 2nd ed., New York: Oxford, University Press, 2006.
[2] J. S. Anastasiadis and G. J. Simitses, "Buckling of pressure-loaded, long, shear deformable cylindrical laminated shells," Computers and Structures, vol. 23, pp. 221-231, 1993.
[3] H. A. Rasheed and O. H. Yousif, "Buckling of thin laminated orthotropic composite rings/long cylinders under external pressure," International Journal of Structural Stability and Dynamics, vol. 1, no.4, pp. 485-507, 2001.
[4] H. A. Rasheed and O. H. Yousif, "Stability of anisotropic laminated rings and long cylinders subjected to external hydrostatic pressure," Journal of Aerospace Engineering, vol. 18, no. 3, pp. 129-138, 2005.
[5] D. H. Hodges, "Non-linear inplane deformation and buckling of rings and high arches," International Journal of Non-Linear Mechanics, vol.34, no.4, pp. 723-737, 1999.
[6] L. Librescu and K.Y. Maalawi, "Material grading for improved aeroelastic stability in composite wings," Journal of Mechanics of Materials and Structures, vol. 2, no. 7, pp. 1381-1394, 2007.
[7] S. Suresh and A. Mortensen, Fundamentals of Functionally Graded Materials, Cambridge University Press, 1998.
[8] W. H. Chen and R.F. Gibson, "Property distribution determination of non-uniform composite beams from vibration response measurements and Galerkin-s method," Journal of Applied Mechanics, vol. 65, pp. 127-133, 1998.
[9] S. H. Chi and Y.L. Chung, "Mechanical behavior of functionally graded material plates under transverse load- part I: Analysis," International Journal of Solids and Structures, vol. 43, pp. 3657-3674, 2006.
[10] Li Shi-Rong and R. C. Batra, "Buckling of axially compressed thin cylindrical shells with functionally graded middle layer," Thin-Walled Structures, vol. 44, pp. 1039-1047, 2006.
[11] R. C. Batra RC. and G. L. Iaccarino, "Exact solutions for radial deformations of a functionally graded isotropic and incompressible second-order elastic cylinder," International Journal of Non-Linear Mechanics, 2008.
[12] K. Y. Maalawi, "Buckling optimization of flexible columns," International Journal of Solids and Structures, vol. 39, pp. 5865-5876, 2002.
[13] K. Y. Maalawi and N. M. El-Chazly, "Global optimization of multielement beam-type structures," presented at the 2nd International Conference on Advances in Structural Engineering and Mechanics, ASEM02, Busan, South Korea, August 21-23, 2002.
[14] A. Chattopadhyay A. and J. Ferreira, " Design sensitivity and optimization of composite cylinders," Journal of Composites Engineering, vol.3, pp. 169-179, 1993.
[15] K. Y. Maalawi, "Optimal stability design of anisotropic rings/long cylinders under external pressure," Journal of Mechanics of Materials and Structures, vol. 3, no. 4, pp. 775-793, 2008.
[16] J. C. Halpin and S.W. Tsai, "Effects of environmental factors on composite materials," technical report AFML-TR-67-423, Dayton, OH, 1967.
[17] J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed. N.W.: CRC Press LLC, 2004.
[18] G. J. Simitses, An Introduction to the Elastic Stability of Structures, NJ: Prentice Hall, Inc., Englewood Cliffs, 1976.
[19] G. N. Vanderplaats, Numerical Optimization Techniques for Engineering Design with Applications, New York: McGraw-Hill, 1994.
[20] P. Venkataraman, Applied Optimization with MATLAB Programming, New York: John Wiley, 2002.