Shape optimization under uncertainty$$-$$a stochastic programming perspective.(English)Zbl 1176.49045

Summary: We present an algorithm for shape optimization under stochastic loading and representative numerical results. Our strategy builds upon a combination of techniques from two-stage stochastic programming and level-set-based shape optimization. In particular, usage of linear elasticity and quadratic objective functions permits us to obtain a computational cost which scales linearly in the number of linearly independent applied forces, which often is much smaller than the number of different realizations of the stochastic forces. Numerical computations are performed using a level set method with composite finite elements both in two and in three spatial dimensions.

MSC:

 49Q10 Optimization of shapes other than minimal surfaces 49N30 Problems with incomplete information (optimization) 74P05 Compliance or weight optimization in solid mechanics
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