Research Objective: Analysis and design problems characterized by moving interfaces and variable connectivity pose significant computational challenges. Boundary tracking methods require sophisticated meshing technologies and might suffer from mesh

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• Research Objective Analysis and design problems
  characterized by moving interfaces and variable
  connectivity pose significant computational
  challenges. Boundary tracking methods require
  sophisticated meshing technologies and might
  suffer from mesh tangling and numerical errors
  associated with remeshing. We seek new methods
  that circumvent these problems.
• Approach We are developing fictitiousdomain
  optimization methods that loosely couple implicit
  geometry models with finite element response
  models. We will use this technique to design
  two-phase microstructures that deliver specified
  homogenized material properties. An implicit
  geometry model describes the physical domain
  boundaries and internal material interfaces. For
  purposes of response analysis, we project the
  geometry onto a fictitious- domain described by a
  fixed finite element grid.

Design of microstructure to obtain specified
properties
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Significant results No remeshing is required to
accommodate boundary and topological variations.
Our method delivers unambiguous optimal
geometries that do not require post-processing,
and our formulation is suitable for adaptive
implementations. Broader Impact Our topology
optimization method is applicable to a broad
range of design problems, ranging from
large-scale civil engineering systems to micro
and nanoscale systems (e.g., MEMS, microfluidic
devices and nanoscale materials design). The
numerical techniques are also applicable to
modelling microstructure evolution, including
topological changes due to nucleation and
coarsening..
To illustrate our method, we show results for the
shape optimization of a transversely loaded
cantilever beam we minimize compliance subject
to a volume constraint. Some of the holes in the
initial design coalesce (in a process analogous
to coarsening in material microstructures) to
produce the optimal design configuration shown.