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SUMMARY:Optimization of bodies with locally periodic microstructure by var
 ying the shape\, the topology and the periodicity pattern - Anca-Maria Toa
 der (Universidade de Lisboa\; Universidade de Lisboa)
DTSTART:20190611T090000Z
DTEND:20190611T100000Z
UID:TALK125980@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Mimicking nature\, an optimization method that makes the link 
 between microstructure and macrostructure is considered. Homogenization th
 eory is used to describe the macroscopic (effective) elastic properties of
  the body.  &nbsp\;  The already known alternate optimization of shape and
  topology of the model cell is a procedure that gives a limited flexibilit
 y to the microstructure for adapting to the macroscopic loads.  Beyond tha
 t\, one may vary the periodicity cell itself during the optimization proce
 ss\, thus allowing the microstructure to adapt more freely to the given lo
 ads.  &nbsp\;  What we propose is a method that combines the three optimiz
 ation techniques :  the shape\, the topology and the periodicity pattern. 
  By combining variations of these three ingredients\, the obtained optimal
  design approaches the homogenized structure of the body\, giving one the 
 possibility to obtain a manufacturable design with smooth transition of ma
 terial properties as in functionally graded materials.  &nbsp\;  Numerical
  examples will be presented.  The problem is numerically heavy\, since the
  optimization of the macroscopic problem is performed by optimizing in sim
 ultaneous hundreds or even thousands of periodic structures\, each one usi
 ng its own finite element mesh on the periodicity cell. Parallel computati
 on is used in order to alleviate the computational burden.
LOCATION:Seminar Room 1\, Newton Institute
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