Bend-free shells under uniform pressure with variable-angle tow derived anisotropy

Shells of variable radius of curvature may develop bending stress-resultants through the thickness under internal pressure. The severity of which depends on the rate of change of curvature of the mid-plane and the state of the boundary conditions [1]. In particular elliptical cylinders will develop relatively large bending stresses and curvatures under internal pressure. A bend-free shell is a specially designed structure, in which the external loading results in a zero bending stress resultant and a zero change in curvature. This work investigates the possibility of creating such states in composite shells by steering the fibre-tows, and hence tailoring the local orthotropy. In particular, the simple ellipsoid of revolution is studied, and solutions found in terms of the spatial trajectories of the lamination parameters VjI. Elliptical cylinders are also studied and the possibility of reducing bending deformation by tailoring extension-bend coupling explored. In general it was found that if the membrane hypothesis can be applied, then a totally bend-free shell may be designed by appealing to the materials constitutive equation. Doubly curved surfaces were found to be more amenable to the technique, while the moments in cylindrical shells were found to be impossible to suppress in the absence of additional secondary loading.