To this end\, on the one hand we transfers co ncepts from finite-dimensional stochastic programm ing to elastic shape optimization.

Thereby\, t he paradigm of stochastic dominance allows for fle xible risk aversion via comparison with benchmark random variables\,

Rather than handling risk a version in the objective\, this enables

risk a version by including dominance constraints that si ngle out subsets of

nonanticipative shapes wh ich compare favorably to a chosen stochastic bench mark.

On the other hand\, we investigate multiscale shape optimization using mechanically simple\, parametrized microscopic

supporting structure those parameters have to be optimized.< br> An posteriori analysis of the discretization e rror and the modeling error is investigated

fo r a compliance cost functional in the context of t he optimization of composite elastic materials

and a two-scale linearized elasticity model. This error analysis includes a control of the

mode ling error caused when replacing an optimal neste d laminate microstructure by this considerably sim pler microstructure.

Furthermore\, an ela stic shape optimization problem with simultaneous and competitive optimization of domain and complem ent

is discussed. Such a problem arises in bi omechanics where a bioresorbable polymer scaffold is implanted in

place of lost bone tissue and in a regeneration phase new bone tissue grows in the scaffold complement via osteogenesis.

In fact\, the polymer scaffold should be mechanically stable to bear loading in the early stage regener ation phase

and at the same time the new bone tissue grown in the complement of this scaffold s hould as well bear the loading.

The talk is based on joint work with Sergio Conti\, Patric k Dondl\, Benedikt Geihe\, Harald Held\, Rü\;d iger Schultz\,

Stefan Simon\, and Sascha T&ou ml\;lkes. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR