Presented by:
Anca-Maria Toader Universidade de Lisboa, Universidade de Lisboa
Date:
Tuesday 11th June 2019 - 10:00 to 11:00
Venue:
INI Seminar Room 1
Abstract:
Mimicking nature, an optimization method that makes the
link between microstructure and macrostructure is considered. Homogenization
theory is used to describe the macroscopic (effective) elastic properties of
the body.
The already known alternate optimization of shape and
topology of the model cell is a procedure that gives a limited flexibility to
the microstructure for adapting to the macroscopic loads.
Beyond that, one may vary the periodicity cell itself
during the optimization process, thus allowing the microstructure to adapt more
freely to the given loads.
What we propose is a method that combines the three
optimization 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 material properties as in functionally graded materials.
Numerical examples will be presented.
The problem is numerically heavy, since the optimization
of the macroscopic problem is performed by optimizing in simultaneous hundreds
or even thousands of periodic structures, each one using its own finite element
mesh on the periodicity cell. Parallel computation is used in order to
alleviate the computational burden.
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