Shaping of a middle surface of a dished head of a circular cylindrical pressure vessel

The paper is devoted to a dished head of a pressure vessel subject to internal uniform pressure. A short survey of optimal design of the pressure vessel and its head is presented. The problem of shaping of the middle surface of the dished head with the use of trigonometric series is depicted. As a criterion of the shaping process, the continuity of curvatures of the surfaces in the joint of the circular cylindrical shell and the dished head is assumed. Results of the numerical calculation for optimal shapes of the head are presented in figures.