BUCKLING OF THIN LAMINATED ORTHOTROPIC COMPOSITE RINGs/LONG CYLINDERS UNDER EXTERNAL PRESSURE

The buckling of isotropic rings under external pressure has attracted the interest of researchers since late 1950s. The formula for critical fluid buckling pressure of thin rings is very well known. This formula was directly extended to account for homogeneous orthotropic rings as well. The buckling of orthotropic cylindrical shells was also a subject of interest since the 1960s. However, the formulations developed, to date, require numerical solutions to obtain the critical pressure. In this work, a generalized closed form analytical formula for the buckling of thin orthotropic multi-angle laminated rings/long cylinders is developed. Standard energy based formulation is used to express the kinematics and equilibrium equations. Classical lamination theory is implemented to introduce the constitutive equations of thin shells. These equations are statically condensed, in terms of the ring's boundary conditions, to produce effective axial, coupling and flexural rigidities for the cases of rings and long cylinders. The critical buckling pressure may be calculated by hand using the derived equation in terms of these effective elastic rigidities. Comparisons are made with some existing results. Parametric studies are conducted to compare the present results with those of the buckling equations implemented by design standards. Various fiber orientations and stacking sequences are considered.