Shape Optimization Under Uncertainty—A Stochastic Programming Perspective

Authors:
Sergio Conti;Harald Held;Martin Pach;Martin Rumpf;Rüdiger Schultz
Affiliations:
sergio.conti@uni-bonn.de and held@math.uni-duisburg.de and pach@math.uni-duisburg.de and schultz@math.uni-duisburg.de;-;-;-;-
Venue:
SIAM Journal on Optimization
Year:
2009

Citing 0
Cited 3

Risk Averse Shape Optimization

SIAM Journal on Control and Optimization
Classification approach for reliability-based topology optimization using probabilistic neural networks

Structural and Multidisciplinary Optimization
Minmax topology optimization

Structural and Multidisciplinary Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.