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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Multi-Scale and Risc Averse Stochastic Shape Optim
ization - Martin Rumpf (University of Bonn\; Unive
rsität Bonn)
DTSTART;TZID=Europe/London:20190613T100000
DTEND;TZID=Europe/London:20190613T110000
UID:TALK125926AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/125926
DESCRIPTION:This talk discusses the optimization for elastic m
aterials and elastic microstructures under differe
nt and in particular stochastic loading scenarios.
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
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