Optimal shapes of mechanically motivated surfaces

Subject of this contribution is form finding of “optimal” structural shapeswith regard to the load carrying behaviour of surface structures undercertain load cases. In general, those optimal shapes prefer a membranestate of stress to transfer loading. Bending is omitted as much as possible.It will be focused on two different disciplines and related numerical approacheswhich deal with solutions of the mentioned task: form finding of prestressedmembranes and general shape optimization. As design is an inverse problemboth approaches share similar problematic properties as e.g. indeterminatein-plane location of surface discretization or necessary regularizationand filtering of sensitivity and other data. As it will turn out, thoseremedies found for the very special methods of membrane design can be abstractedand transferred to general optimization procedures. That merges into elegant,numerical shape optimal design techniques which combine advantages of bothapproaches and allow for effective and efficient shape optimization offree formed surfaces, directly on the finite element mesh and for a largenumber of variables. Typical applications are, for example, membrane design,free form architecture and structural engineering, and metal sheet design.     «

Subject of this contribution is form finding of “optimal” structural shapeswith regard to the load carrying behaviour of surface structures undercertain load cases. In general, those optimal shapes prefer a membranestate of stress to transfer loading. Bending is omitted as much as possible.It will be focused on two different disciplines and related numerical approacheswhich deal with solutions of the mentioned task: form finding of prestressedmembranes and general shape optimization. As design i...     »