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Abstract In this thesis, three different models of elastic shape optimization are described. All models use phase fields to describe the elastic shapes and regularize the interface length on some level or scale to control fine-scale structures. First, the paradigm of stochastic dominance is transferred from finite dimensional stochastic programming to elastic shape optimization under stochastic loads. The shapes are optimized under the constraint, that they dominate a given benchmark shape in a certain stochastic order. This allows for a flexible risk aversion comparison. Risk aversion is handled in the constraint rather than the objective functional, which results in an optimization over a subset of admissible shapes only. Starting with the observation that unregularized elastic shape optimization methods create arbitrarily fine micro-structures in many scenarios, domains composited of a number of geometrical subdomains with prescribed boundary conditions are considered in the second model.
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