Shape optimization of shell structures

Shells are known to be optimal in many ways, provided certain basic shell oriented design rules are followed. The shape, thickness and material distribution play a dominant role. Minimum material, a specific frequency response, maximum load carrying capacity, a pure membrane stress state are typical design objectives. In the present contribution the form finding and thickness variation are embedded in the concept of structural optimization which combines design modelling, structural and sensitivity analyses and mathematical optimization schemes to a general design tool. The structural response may be based on linear elastic, eigenvalue and geometrically nonlinear analyses. In particular, the imperfection sensitivity with respect to buckling is discussed. A few selected examples demonstrate the versatility of optimization schemes in shell design, among these are the tuning of a bell and the form finding of a classical reinforced concrete dome shell.