Preface

Post-buckling analysis of functionally graded multilayer graphene platelet reinforced composite cylindrical shells under axial compression

“…The first equilibrium equation (2.17 a ) is solved analytically first, and then the last three equilibrium equations (2.17 b )–(2.17 d ) are solved by Galerkin's method. The existing experimental study indicated that the post-buckling of axial compressed cylindrical shells can divided into two categories: symmetric mode and asymmetric mode [8]. Therefore, to perform the post-buckling analysis of axial compressed cylindrical shells, two types of displacement functions are adopted here, i.e.…”

“…However, with the development of the manufacturing technology, some experimental studies [7] on nearly perfect cylindrical shells still captured the remarkable decline of critical loads in the process of post-buckling. In view of those experimental observations, Yamaki [8] turned to the nonlinear post-buckling theory and rebuilt the displacement expressions based on the deformation measured in the experiment, and finally obtained a full post-buckling equilibrium path consisting of a series of wave-like deformations with stepwise reduced circumferential wavenumbers. After the above continuous efforts, the post-buckling models of the isotropic thin cylindrical shells which could predict the more accurate critical loads were well established.…”

“…For the singular perturbation method, the accuracy of solutions can only be guaranteed in a small range of deformation near the critical buckling state. According to the experimental study [7,8], the secondary buckling occurs with the further loading and the mode-jumping phenomenon appears with the decreasing circumferential wavenumber. These phenomena cannot be predicted by the singular perturbation method.…”

“…Therefore, it will greatly reduce the accuracy and convergence of the solutions.In the existing literature carried out by the energy method, the displacement functions are usually assumed to be a fixed form, such as w ( x , y ) = f 0 + f 1 sin αx sin βy + f 2 sin 2 αx [15,16,18,20], w = W mn sin α m x cos β n y [17] and w = W sin β m x sin δ n y [19,36], which are independent of the calculation parameters. However, according to the previous experimental study [7,8], there may exist two kinds of post-buckling modes (symmetric or asymmetric modes) which are highly depend on the calculation parameters. Therefore, it is necessary to develop two groups of displacement functions for the two different post-buckling modes.…”

Buckling and post-buckling behaviour of elastic seven-layered cylindrical shells – FEM study

“…The selected important papers and monographs related to these problems in chronological order are as follows: Hutchinson and Koiter [18], Budiansky [19], Grigoluk and Kabanov [20], Yamaki [21], Bushnell [22], Simitses [4], Bažant and Cedolin [23], Teng [24] and van der Heijden [25]. A review of recent studies on stability of liquid-containment shells of revolution is presented by Zingoni [26].…”