On the different formulations in linear bifurcation analysis of laminated cylindrical shells

The stability pattern of shells is governed by a set of nonlinear partial differential equations. The solution procedure can be simplified, and fast and accurate predictions of the critical buckling load obtained, with the aid of a multilevel approach. Under this approach the lower levels are implemented by means of the perturbation technique, with the nonlinear prebuckling deformation disregarded, and a linear set of equations solved for each state. It turns out, however, that in these circumstances the prediction may differ depending on the chosen formulation. In an attempt to find the reasons for these differences, the linear bifurcation buckling behavior of laminated cylindrical shells was examined via two well-known formulations, with u–v–w and w–F as the unknowns. A third, mixed formulation, was found the most reliable in predicting the buckling behavior.