• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2223-2233
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• 1996

The analytical solutions for the free vibration of cross-ply laminated composite cyllindrical shell with axial stiffeners(stringers) are presented usint the energy method. The stiffeners are taken to be smeared over the surface of shell with the smeared stffener theory. The effect of the parameters such as the stacking sequences, the shell thichness, the shell radius-to stringer depth ratio, the stringer depth-to width ratio, the shell length-to radius ratio are studied. By comparison with the previously published experimental results and the analytical results for the stiffened isotropic cylindrical shell and the unstiffened orthotropic composite laminated cylindrical shell, it is shown that natural frequencies can be determined with adequate accuracy.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.883-888
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• 2001

The theoretical method is developed to investigate the effects of ring stiffeners on free vibration characteristics and transient response for the ring stiffened composite cylindrical shells subjected to the impulse pressure loading. In the theoretical procedure, the Love's thin shell theory combined with the discrete stiffener theory to consider the ring stiffening effect is adopted to formulate the theoretical model. The concentric or eccentric ring stiffeners are laminated with composite and have the uniform rectangular cross section. The modal analysis technique is used to develop the analytical solutions of the transient problem. The analysis is based on an expansion of the loads, displacements in the double Fourier series that satisfy the boundary conditions. The effect of stiffener's eccentricity, number, size, and position on transient response of the shells is examined. The theoretical results are verified by comparison with FEM results.

• Journal of KSNVE
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• v.6 no.4
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• pp.457-467
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• 1996

The analytical solutions for the free vibration and buckling of cross -ply laminated composite cylindrical shell with the orthogonal stiffeners, i. e., axial stiffeners(stringers) and circumferential stiffeners(rings), are presented using the energy method. The stiffeners are assumed to be an integral part of the shell and have been directly included in analysis(it's called discrete stiffener theory). The effect of the parameters such as the stacking sequences, the shell thickness, the shell length-to-radius ratio are studied. By comparison with the previously published analytical results for the stiffened cylindrical shells, it is shown that natural frequencies can be determined with adequate accuracy.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.1
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• pp.42-50
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• 1987

The energy expressions are formulated for the axially stiffened shell treating the stiffeners as discrete elements. The principle of minimum potential energy is employed to formulate the buckling equations for a simply supported, axially stiffened shell under uniform axial compression. The displacement functions are expended into double trigonometric series. The mode assuming method employed in this paper makes it possible to reduce the matrix size of the eigenvalue problem considerably. Effects are made to investigate the transition from overall buckling to local buckling and to verify the existence of the minimum stiffness ratio of stiffener as in the case of stiffened plate. The results of the calculation show that the critical stiffener size increase linearly as the length of the shell increases. The results also show that the overall buckling load decreases and the local buckling load has a nearly constant value as the length of the shell increases. The results show very good agreements with other computational available.

• Steel and Composite Structures
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• v.19 no.1
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• pp.75-92
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• 2015

In this paper, optimization of cylindrical shells under external pressure to minimize its weight has been studied. Buckling equations are based on standard of ABS underwater vehicles. Dimension and type of circumferential stiffeners, and its distance from each other are assumed as variables of optimization problem. Considering the extent of these variables, genetic algorithms have been used for optimization. To study the effect of hydrostatic pressure on the shell and its fabrication according to the existing standards, geometrical and construction as well as stress and buckling constraints have been used in optimization algorithm and also penalty functions are applied to eliminate weak model. Finally, the best model which has the minimum weight considering the applied pressure has been presented.

• Steel and Composite Structures
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• v.51 no.5
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• pp.543-562
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• 2024

While the external axial compressive load is applied to only the shell edge of stringer-stiffened shell in the most of numerical and analytical previous studies (entitled as conventional approach), a part of external load is applied to the stringers in real conditions. It leads to decrease the accuracy of the axial buckling load calculated by the conventional eigenvalue analysis approach performed in the most of previous studies. In this study, the distribution of stress in the pre-buckling analysis was enhanced by applying the axial external compressive load to both shell and stringers to perform an accurate eigenvalue analysis of the stringer-stiffened composite shell. In this regard, a model was developed in FORTRAN environment to simulate the laminated stringer-stiffened shell under axial compressive load using finite strip method. The axial buckling load of the shell was obtained through eigenvalue analysis. A comparison was made between the results obtained from the model and those available in the previous studies to evaluate the validity of the results obtained from the model. Through a parametric study, the effects of different parameters such as stringer properties and composite layup on the buckling load of the shell under different loading patterns were investigated. The results indicated that in some cases, the axial buckling load obtained for the conventional approach used in the most of previous studies is significantly overestimated or underestimated due to neglecting the stringer in distribution of external load applied to the stringer-stiffened shell. According to the results obtained from the parametric study, some graphs were derived to show the accuracy of the axial buckling load obtained from the conventional approach utilized in the literature.

• Advances in nano research
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• v.16 no.6
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• pp.565-577
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• 2024

Vibration investigation of fluid-filled functionally graded cylindrical shells with ring supports is studied here. Shell motion equations are framed first order shell theory due to Sander. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Langrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is immersed in a fluid which is a non-viscous one. These shells are stiffened by rings in the tangential direction. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. After these, ring supports are located at various positions along the axial direction round the shell circumferential direction. The influence of the ring supports is investigated at various positions. Effect of ring supports with empty and fluid-filled shell is presented using the Rayleigh - Ritz method with simply supported condition. The frequency behavior is investigated with empty and fluid-filled cylindrical shell with ring supports versus circumferential wave number and axial wave number. Also the variations have been plotted against the locations of ring supports for length-to-radius and height-to-radius ratio. Moreover, frequency pattern is found for the various position of ring supports for empty and fluid-filled cylindrical shell. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. It is found that due to inducting the fluid term frequency result down than that of empty cylinder. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• Advances in concrete construction
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• v.9 no.6
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• pp.557-568
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• 2020

In this study, the impact of ring supports around the shell circumferential has been examined for their various positions along the shell axial length using Rayleigh-Ritz formulation. These shells are stiffened by rings in the tangential direction. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. The influence of the ring supports is investigated at various positions. These variations have been plotted against the locations of ring supports for three values of length-to-diameter ratios. Effect of ring supports with middle layer thickness is presented using the Rayleigh-Ritz procedure with three different conditions. The influence of the positions of ring supports for clamped-clamped is more visible than simply supported and clamped-free end conditions. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. The Lagrangian functional is created by adding the energy expressions for the shell and rings. The axial modal deformations are approximated by making use of the beam functions. The comparisons of frequencies have been made for efficiency and robustness for the present numerical procedure. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped, simply supported-simply supported frequency curves are higher than that of clamped-simply curves. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.