Rigorous buckling of laminated cylindrical shells

The effect of pre-buckled nonlinearity on the bifurcation point of laminated cylindrical shells is examined on the basis of Donnell's shell theory. The eigenvalue problem is solved iteratively about the nonlinear equilibrium state up to the bifurcation point. An algorithm is presented for the real buckling behavior, dispensing with the need to cover the entire nonlinear pattern. This algorithm is very important for structures characterized by a softening process in which the pre-buckled nonlinearity depresses the buckling level relative to the classical one.The procedure involves nonlinear partial differential equations, which are separated into two sets (using the perturbation technique) for the pre-buckled and buckled states, respectively, and solved with the variable expanded in Fourier series in the circumferential direction, and by finite differences in the axial direction. A special purpose computer code NBLCS (Nonlinear Buckling of Laminated Cylindrical Shells) was developed, for calculating the bifurcation point of laminated cylindrical shell.