NONLINEAR RESPONSE OF LONG ORTHOTROPIC TUBES UNDER BENDING INCLUDING THE BRAZIER EFFECT

A nonlinear solution to the Brazier problem of cross-sectional flatten ing for infinitely long tubes under bending is formulated using classi cal nonlinear shell theory along with semimembrane constitutive relati ons. It is shown that traditional cylindrical shell equations are not sufficient to accurately model the nonlinearity of the Brazier effect, and the suitable corrections to the shell equations are derived. This approach gives greater physical insight into the problem than traditi onal variational methods, and it yields a highly nonlinear ordinary di fferential equation for infinite length cylinders with orthotropic mat erial properties. This resulting equation is solved numerically using finite difference techniques, and an approximate analytical solution i s also obtained, which corresponds to Brazier's original solution. Col lapse loads as a result of limit points and local instability are comp ared with classical failure estimates, and the influences of laminate stacking sequence and internal pressure are explored, Also, a collapse parameter is introduced that gives a relative measure of the buckling load to that of the limit load for orthotropic structures, and it is shown that, for low values of this parameter, the limit moment is not a suitable estimate for the collapse load of long cylinders.