Fully stressed head of a pressure vessel

This work is devoted to a head of a vessel charged with internal uniform pressure. The analysis is aimed at finding a shape of the head that ensures its full charge with stresses. In a classical torispherical or ellipsoidal head the region of its joint with the cylindrical shell is loaded with shear force and bending moment as a result of the forced consistency of displacements of both parts of a vessel. The load causes high bending stresses in the area of the joint. Therefore, a shape of a head meridian is sought for which the shear force and the bending moment approach zero. Only membrane state stresses should occur in such a structure. The mathematical description is based on the theory of shells, taking account of boundary disturbances. The numerical solution determines the sought-after shape of the head and its minimal relative convexity.