Stability of anisotropic laminated rings and long cylinders subjected to external hydrostatic pressure

The problem of buckling of rings under external pressure has attracted interest since the late 1950s; however, the formulations developed, to date, to obtain the critical pressure are limited to special cases of orthotropic laminated construction. In this work, analytical and numerical treatments are carried out to provide results on the buckling of thin and moderately thick anisotropic rings and long cylinders. A generalized closed-form analytical formula for the buckling of thin anisotropic laminated rings is developed. Standard energy-based formulation and classical lamination theory are used to obtain the equilibrium equations assuming an intermediate class of deformation. The constitutive equations are statically condensed, in terms of the ring's boundary conditions, to produce the effective axial, coupling, and flexural rigidities. In addition, a three-dimensional (3D) tube finite-element model is developed for nonlinear analysis of anisotropic laminated composite rings or long cylinders. The element accounts for prebuckling ring twist and first-order shear deformations. Fourier series expansions are used to express the in-plane and out-of-plane components of deformation and geometry at the three nodes of the cylindrical element. Isoparametric quadratic shape functions are used to interpolate the displacement field in between. Comparisons of the analytical and numerical results show excellent agreement for thin rings. Parametric studies are also conducted to address the effects of lamination, shell thickness, and initial out-of-roundness imperfection on the external buckling pressure.