Stability Analysis Of Composite Cylindrical Shells And New Algorithms Research

The stability of composite cylindrical shells is a basic research task in solid mechanics all the time and is also one of the difficult problems which need to be urgently solved in aerospace industry now. In this thesis, a theoretical analysis of the stability of composite cylindrical shells under axial compression is presented in detail. At the same time, some attempts about the algorithms are carried out.Firstly, the stability of perfect filament-wound composite cylindrical shells under axial compression is discussed on the ecumenical filament-wound condition. The buckling governing equations of the shells are established by means of post-buckling analysis. The eigenvalue equation is derived and the buckling mode is given by means of the displacement method and complex number method. Moreover, a hybrid Genetic Algorithm combining modern intelligent optimization algorithms and classical iteration algorithms is put forward to solve the eigenvalue equation. This new algorithm sufficiently exerts the advantages of Genetic Algorithm such as good global convergence and classical iteration algorithms such as high convergence rate. So it has high reliability and computation efficiency. All roots of the equation can be obtained by using the new algorithm. The numerical results show that the hybrid Genetic Algorithm can be used to solve nonlinear algebraic equations successfully. Some computational examples also show the influence of the boundary conditions on the stability of composite cylindrical shells with different long-radius ratio.Secondly, the influence of typical axisymmetrical initial geometrical imperfections on the stability of composite cylindrical shells under axial compression is discussed. Based on the previous part, the buckling governing equations of the imperfect shells are established. Galerkin method is employed to derive the eigenvalue equation of the shells containing axisymmetrical initial geometrical imperfections. Then the eigenvalue equation is converted into a high order algebraic equation with one variable. All roots can be obtained by using the hybrid Genetic Algorithm previously designed. The smallest real positive root is the buckling critical load. The final results verify that the buckling mode of composite cylindrical shells is unaxisymmetrical in most cases. Moreover, the influence of the fiber orientations on the buckling critical loads of the shells containing initial geometrical imperfections with different amplitude is studied.Finally, the influence of typical unaxisymmetrical initial geometrical imperfections on the stability of composite cylindrical shells under axial compression is discussed and the sensitivity to initial geometrical imperfections ofthe shells is also analyzed. Based on Koiter' theory, the initial post-bucklingcoefficients, which can reflect imperfection sensitivity, are determined by means of a half-analytic method. Galerkin method is used to deduce the relation between the buckling critical load and the number of axial or circumferential half-waves. The buckling critical load can be obtained by searching the number of half-waves. The relation between the buckling critical load of imperfect shells and that of perfect shells is established. The results show that the shells under axial compression are more sensitive to initial geometrical imperfections than those under external compression. Moreover, the relation among the buckling critical load under axial compression, the fiber orientations and imperfection sensitivity is investigated. In addition, the stabilities of the cylindrical shells made of several common composite materials are briefly compared.