@INCOLLECTION{AtCoGe12,
author = {Atwal, Pradeep and Conti, Sergio and Geihe, Benedict and Pach, Martin
and Rumpf, Martin and Schultz, R{\"{u}}diger},
title = {On shape optimization with stochastic loadings},
booktitle = {Constrained Optimization and Optimal Control for Partial Differential
Equations},
publisher = {Springer},
year = {2012},
editor = {Leugering, G{\"{u}}nter and Engell, Sebastian and Griewank, Andreas
and Hinze, Michael and Rannacher, Rolf and Schulz, Volker and Ulbrich,
Michael and Ulbrich, Stefan},
volume = {160},
series = {International Series of Numerical Mathematics},
chapter = {2},
pages = {215--243},
address = {Basel},
abstract = {This article is concerned with different approaches to elastic shape
optimization under stochastic loading. The underlying stochastic
optimization strategy builds upon the methodology of two-stage stochastic
programming. In fact, in the case of linear elasticity and quadratic
objective functionals our strategy leads to a computational cost
which scales linearly in the number of linearly independent applied
forces, even for a large set of realizations of the random loading.
We consider, besides minimization of the expectation value of suitable
objective functionals, also two different risk averse approaches,
namely the expected excess and the excess probability . Numerical
computations are performed using either a level set approach representing
implicit shapes of general topology in combination with composite
finite elements to resolve elasticity in two and three dimensions,
or a collocation boundary element approach, where polygonal shapes
represent geometric details attached to a lattice and describing
a perforated elastic domain. Topology optimization is performed using
the concept of topological derivatives. We generalize this concept,
and derive an analytical expression which takes into account the
interaction between neighboring holes. This is expected to allow
efficient and reliable optimization strategies of elastic objects
with a large number of geometric details on a fine scale.},
doi = {10.1007/978-3-0348-0133-1_12},
pdf = {http://numod.ins.uni-bonn.de/research/papers/public/AtCoGe10.pdf},
isbn = {978-3-0348-0133-1},
keywords = {SHAPE_OPT},
url = {http://dx.doi.org/10.1007/978-3-0348-0133-1_12}
}