On nonlinear bending and instability of imperfect cylindrical tubes

In this paper, the nonlinear bending and instability of initial geometrical imperfect cylindrical tubes subjected to pure bending load are studied. The imperfection is assumed to be a small ovality expressed as Timoshenko initial noncircularity function. A set of new nonlinear differential equations is developed, through a virtual work principle with a Lagrange multiplier, and solved asymptotically by means of a perturbation method. The asymptotical expressions for a nonlinear moment–curvature relationship and a critical moment are obtained. The effect of the noncircularity on the bending and instability are examined. The results of numerical calculations are presented by curves and compared with available theoretical and experimental data.