Optimal contours for heads of cylindrical pressure vessels are discussed. As opposed to the common method of preventing buckling in pressure vessel ends by means of increased wall thickness or local reinforcements, this paper proposes a design for “buckle-free” shapes in which the contour is established/adjusted so as to ensure stable behavior. A previous analysis by the authors, in which compressive stresses were eliminated, is extended so as to take into account the actual flexural rigidity of the wall. The shapes obtained from such buckle-free designs appear to be similar to standard ellipsoidal and torispherical ends and should be acceptable from various design and aesthetic viewpoints.

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