Friday, September 23, 2005
1:00pm – 2:00pm
Professor Michael Yu
Wang
Department of Automation & Computer-Aided Engineering
The Chinese University
of Hong Kong
ÒPhysical Modeling and Optimization of Heterogeneous Solids: Implicit
Models and Level Set MethodsÓ
Abstract:
A heterogeneous object is
referred to as a solid object made of different constituent materials. The
object is of a finite collection of regions of a set of prescribed material
classes of continuously varying material properties. These properties have a discontinuous
change across the interface of the material regions. We present a variational
framework for a well-posed formulation for the design of the heterogeneous
solids. We discuss two approaches to the modeling and optimization problem of
free-discontinuities: a multi-phase discrete level-set model and a
partition-of-unity radial basis function model, both to represent the
discontinuities implicitly. These models yield a computational system of
coupled geometric evolution and/or partial differential equations. Promising
features of the proposed method include strong regularity in problem
formulation, topological flexibility, and inherent capabilities of geometric,
physical and material modeling, incorporating dimension, shape, topology,
material properties, and even micro-structures within a common framework for
design and optimization of the heterogeneous solids. The proposed methods are
illustrated with several examples of optimization of multi-material structures,
materials design, and compliant mechanism synthesis. Further applications in
tissue modeling, flexonic MEMS, and drug diffusion and delivery MEMS will be
discussed.