Equilibrium glass-plastic pressure vessels of minimum mass with a nongeodesic winding

A lens-shaped vessel having various central apertures made by a continuous winding process is considered. Using the methods of variational calculus, the optimum winding trajectory (yielding a structure of minimum mass) is established, subject to certain limitations regarding the angle of geodesic deviation and the stress level in the filaments. The shape of the base is determined with due allowance for the trajectory found in this way, which comprises sections of geodesic lines and lines of limiting deviation.