Abstract
Based on the coordinate system, the equilibrium conditions of bandwidths or fibers and matrix on the surface of the winding pattern will be represented in this paper. From these conditions, calculate the equilibrium equations for a shell of revolution under internal pressure; define a governing equation determines the change of winding angle, the shape of the dome, weight and total volume of the vessel; the solution of these equations for determining the rules and deformation of the dome in the non-geodesic trajectories. Thereby, the equations of the thick-walled composite cylinder and dome (using helical and hoop winding) depend on the winding angle, destructive pressure and strength of materials can be given.