#### Vol. 3, No. 4, 2008

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Optimal buckling design of anisotropic rings/long cylinders under external pressure

### Karam Y. Maalawi

Vol. 3 (2008), No. 4, 775–793
##### Abstract

Structural buckling failure due to high external hydrostatic pressure is a major consideration in designing rings and long cylindrical shell-type structures. This paper presents a direct approach for enhancing buckling stability limits of thin-walled rings/long cylinders that are fabricated from multiangle fibrous laminated composite lay-ups. The mathematical formulation employs the classical lamination theory for calculating the critical buckling pressure, 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 associated design optimization problem of maximizing the critical buckling pressure has been formulated in a standard nonlinear mathematical programming problem with the design variables encompassing the fiber orientation angles and the ply thicknesses as well. The physical and mechanical properties of the composite material are taken as preassigned parameters. The proposed model deals with dimensionless quantities in order to be valid for thin shells having different thickness-to-radius ratios. Useful design charts are given for several types of anisotropic rings/long cylinders showing the functional dependence of the buckling pressure on the selected design variables. Excellent results have been obtained for cases of filament wound rings/long cylinders fabricated from three different types of materials: $E$-glass/vinyl-ester, graphite/epoxy and $S$-glass/epoxy. It was shown that significant improvement in the overall stability level can be attained as compared with a baseline shell design. In fact, the developed methodology has been proved to be a useful design tool for selecting an optimal stacking sequence of a thin-walled anisotropic ring/long cylinder having arbitrary thickness-to-radius ratio.

##### Keywords
buckling instability, structural optimization, fibrous composite, laminated ring/cylindrical shell, external hydrostatic pressure