Buckling and postbuckling of anisotropic laminated cylindrical shells under combined axial compression and torsion (original) (raw)
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Mechanics of Advanced Materials and Structures, 2009
A postbuckling analysis is presented for a shear deformable anisotropic laminated cylindrical shell of finite length subjected to torsion. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on a higher order shear deformation shell theory with von Kármán-Donnell-type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The results confirm that there exists a shear stress along with an associate compressive stress when the shell is subjected to torsion. The postbuckling equilibrium path is stable for a moderately thick laminated cylindrical shell under torsion and the shell structure is virtually imperfection-insensitive.
POSTBUCKLING OF SHEAR-DEFORMABLE ANISOTROPIC LAMINATED CYLINDRICAL SHELLS UNDER AXIAL COMPRESSION
International Journal of Structural Stability and Dynamics, 2008
A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to axial compression. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on a higher order shear-deformable shell theory with the von Kármán-Donnell type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The results confirm that there exists a compressive stress along with an associate shear stress and twisting when the anisotropic shell is subjected to axial compression. The postbuckling equilibrium path is unstable for the moderately thick cylindrical shell under axial compression and the shell structure is imperfection-sensitive.
Composite Structures, 2008
A boundary layer theory for the buckling and postbuckling of anisotropic laminated thin shells is extended to the loading case of torsion. A singular perturbation technique is employed to determine the buckling load and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of twist, perfect and imperfect, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The new finding is that there exists a shear stress along with an associate compressive stress when the anisotropic shell is subjected to torsion, and all the results published previously need to be reexamined. The results confirm that the effect of the boundary layer on the solution of a twist shell is of the order e 5/4. The postbuckling equilibrium path is unstable for the moderately long shell subjected to torsion and the shell structure is less sensitive to initial imperfections than in the case of axial compression.
Approximate Solution for the Compression Buckling of Fully-Anisotropic Cylindrical Shells
AIAA Journal, 2005
The circular cylindrical thin-walled shell is a fundamental building block of many structures, such as aircraft fuselages. When used with laminated composites, highly efficient structures can be designed. As a result, the analytical treatment of cylindrical shells has received significant attention over recent decades. However, most of the works carried out in this area concern isotropic materials or orthotropic laminates, that is, those with no couplings. The present analysis develops a closed-form, yet simple solution for the linear buckling of laminated circular cylindrical shell, from the Donnell's model, including all available couplings. Although the usefulness of a linear solution for predicting buckling loads is questionable, its worth is in initial sizing and layup selection during the early stages of design. The resulting model could be used to examine the usefulness of different couplings that are not yet well understood. It is found that extension/shear coupling results in torsional movement of the cylinder, which, when restricted, induces a secondary torsional loading on the cylinder, thus reducing its overall buckling load by up to 50%. When not restricted, extension/shear couplings generally increase buckling loads.
International Journal of Mechanical Sciences, 1998
A postbuckling analysis is presented for a stiffened laminated cylindrical shell of finite length subjected to combined loading of external pressure and a uniform temperature rise. The formulation is based on a boundary layer theory of shell buckling which includes the effects of nonlinear prebuckling deformations, nonlinear large deflections in the postbuckling range and initial geometrical imperfections of the shell. The "smeared stiffener" approach is adopted for the stiffeners. The analysis uses a singular perturbation technique to determine the interactive buckling loads and the postbuckling equilibrium paths. Numerical examples are presented that relate to the performance of perfect and imperfect, stiffened and unstiffened cross-ply laminated cylindrical shells. Typical results are presented in dimensionless graphical form for different parameters and loading conditions. ~2
In present work, post-buckling behavior of imperfect (of eigen form) laminated composite cylindrical shells with different L/D and R/t ratios subjected to axial, bending and torsion loads has been investigated by using an equilibrium path approach in the finite element analysis. The New-ton-Raphson approach as well as the arc-length approach is used to ensure the correctness of the equilibrium paths up to the limit point load. Post-buckling behavior of imperfect cylindrical shells with different L/D and R/t ratios of interest is obtained and the theoretical knock-down factors are reported for the considered cylindrical shells.
Thin-Walled Structures, 1993
A new approach is extended to investigate the buckling and postbuckling behaviour of perfect and imperfect, stringer and ring stiffened cylindrical shells of finite length subject to combined loading of external pressure and axial compression. The formulations are based on a boundary layer theory which includes the edge effect in the postbuckling analysis of a thin shell. The analysis uses a singular perturbation technique to determine the buckling loads and the postbuckling equilibrium paths. Some interaction curves for perfect and imperfect stiffened cylindrical shells are given and compared well with experimental data. The effects of initial imperfection on the interactive buckling load and postbuckling behaviour of stiffened cylindrical shells have also been discussed.
Rigorous buckling of laminated cylindrical shells
Thin-walled Structures, 2009
The effect of pre-buckled nonlinearity on the bifurcation point of laminated cylindrical shells is examined on the basis of Donnell's shell theory. The eigenvalue problem is solved iteratively about the nonlinear equilibrium state up to the bifurcation point. An algorithm is presented for the real buckling behavior, dispensing with the need to cover the entire nonlinear pattern. This algorithm is very important for structures characterized by a softening process in which the pre-buckled nonlinearity depresses the buckling level relative to the classical one.
Thin-Walled Structures, 1991
Buckling and postbuckling behaviour of perfect and imperfect cylindrical shells of finite length subject to combined loading of external pressure and axial compression are considered. Based on the boundary layer theory which includes the edge effect in the buckling of shells, a theoretical analysis for the buckling and postbuckling of circular cylindrical shells under combined loading is presented using a singular perturbation technique. Some interaction curves for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, and it is shown that both agree well. The effects of initial imperfection on the interactive buckrng load and postbuckling behaviour of cylindrical shells have also been discussed NOTATION
Nonlinear Engineering, 2013
Imperfection sensitivity of cylindrical shells subjected to axial compressive load is investigated by means of non-linear buckling analysis and post-buckling analysis. Non-linear buckling analysis involves the determination of the equilibrium path (or load-deflection curve) upto the limit point load by using the Newton-Raphson approach, whereas post-buckling analysis involves the determination of the equilibrium path beyond the limit point load and up to the collapse load by using the arc-length approach. Limit point loads evaluated from these two approaches for various imperfection magnitudes show an excellent agreement which clearly confirms the numerical results obtained.