Optimal design of shells against buckling under overall bending and external pressure

In this paper, the problem of optimal design of shells against instability is considered. A thin-walled shell is loaded, in general, by an external pressure and lateral forces causing overall bending moment (which varies along the axis of a shell) and the appropriate shearing force. We look for the shape of meridian as well as the thickness of a shell, which ensure the maximal critical value of the loading parameter. As the equality constraints, the volume of material and the capacity of a shell are considered. The concept of a shell of uniform stability is applied.