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.