Limit analysis and design of containment vessels

Abstract

In the introduction, the theory of plastic analysis of shells is briefly recalled. Minimum-volume design for assigned load factor at plastic collapse is then considered and optimality criteria are derived for plates and shells of continuously varying or piecewise-constant thickness. In the first part, containers made of metal are examined. Analytical and numerical limit analysis solutions and corresponding experimental results are considered for various types of vessels, including intersecting shells. Attention is given to experimental post-yield behavior. Some tests up to fracture are discussed. New theoretical and experimental results of limit analysis of stiffened cylindrical vessels are presented, in which reinforcing rings are treated as discrete structural element (no smearing out) and due account is taken of their strong curvature. Cases of collapse by instability under internal pressure are pointed out. Minimum-volume design of circular plates and cylindrical shells is then formulated and various examples are presented of sandwich and solid metal structures. Containers of piecewise-constant thickness are given particular attention. Available experimental evidence on minimum-volume design of plates and shells is reviewed and commented upon. The second part deals with reinforced concrete vessels. Cylindrical containers are studied, from both points of view of limit analysis and of limit design with minimum volume of reinforcement. The practical use of the latter solutions is discussed. A third part reviews other loading cases (including cyclic and impact loads) and gives indications on corresponding theories, formulations and solution methods. The last part is devoted to a discussion of the limitations of the methods presented, within the frame of the “limit states” design philosophy, which is first briefly recalled. Considerations on further research in the field conclude the paper.