Minimum-Weight Design for Pressure Vessels Reinforced With Inextensible Fibers

Strong, lightweight pressure vessels can be constructed by winding glass fiber around supporting shells. Zickel1 and Fraser2 have discussed some of the advantages of isotensoid designs, in which every fiber is under the same tension, and geodesic designs, in which the fibers lie along geodesics on the supporting shell. The shell is taken to be cylindrically symmetrical. Zickel1 considered fibers lying along geodesics which intersect the equator of the shell at a single given angle, and derived the shape of the surface for which the design is isotensoid as well as geodesic. Fraser2 extended this work by considering designs with several families of fibers, intersecting the equator at various given angles, and again derived the surface shape for which the design is isotensoid.