Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell. Part I: Prediction under axial compression

A boundary layer theory for the buckling and postbuckling of anisotropic laminated thin shells is developed. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. It is also assumed that the well-known von Kármán nonlinear strain–displacement relationships are valid. The governing equations with transverse displacement and stress function as independent variables are deduced to a boundary layer type, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell. A postbuckling analysis is presented for axially loaded, perfect and imperfect, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The joint effects played by anisotropy, nonlinear prebuckling deformations, as well as initial geometric imperfections are studied. The new finding is that there exists a compressive stress along with an associate shear stress and twisting when the anisotropic laminated cylindrical shell is subjected to axial compression, and all the results published previously need to be re-examined.