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SUMMARY:Topology optimization of modulated and oriented periodic microstru
 ctures by the homogenization method in 2-d and in 3-d - Perle Geoffroy (É
 cole Polytechnique)
DTSTART:20190611T133000Z
DTEND:20190611T143000Z
UID:TALK125830@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The work presented here is motivated by the optimization of so
 -called lattice materials which are becoming increasingly popular in the c
 ontext of additive manufacturing. We propose a method for topology optimiz
 ation of structures made of periodically perforated material\, where the m
 icroscopic periodic cell can be macroscopically modulated and oriented in 
 the working domain.<br> This method is made of three steps. The first step
  amounts to compute the homogenized properties of an adequately chosen par
 ametrized microstructure (here\, a cubic lattice with varying bar thicknes
 ses). The second step optimizes the homogenized formulation of the problem
 \, which is a classical problem of parametric optimization. The third\, an
 d most delicate\, step projects the optimal oriented microstructure at<br>
  a desired length scale. In 2-d case\, rotations are parametrized by a sin
 gle angle\, to which a conformality constraint can be applied. A conformal
  diffeomorphism is then computed from the orientation field\, thanks which
  each periodic cell is well oriented in the final structure. The 3-d case 
 is more involved and requires new ingredients. In particular\, the full ro
 tation matrix is regularized (instead of just one angle in 2-d) and the pr
 ojection map which deforms the periodic lattice is computed component by c
 omponent.
LOCATION:Seminar Room 1\, Newton Institute
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