@Article{cmes.2004.006.373,
AUTHOR = {Michael Yu Wang, Xiaoming Wang},
TITLE = {PDE-Driven Level Sets, Shape Sensitivity and Curvature Flow for Structural Topology Optimization},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {6},
YEAR = {2004},
NUMBER = {4},
PAGES = {373--396},
URL = {http://www.techscience.com/CMES/v6n4/24856},
ISSN = {1526-1506},
ABSTRACT = {This paper addresses the problem of structural shape and topology optimization. A level set
method is adopted as an alternative approach to the popular homogenization based methods. The paper focuses
on four areas of discussion: (1) The level-set model of
the structure’s shape is characterized as a region and
global representation; the shape boundary is embedded in
a higher-dimensional scalar function as its “iso-surface.”
Changes of the shape and topology are governed by a
partial differential equation (PDE). (2) The velocity vector of the Hamilton-Jacobi PDE is shown to be naturally
related to the shape derivative from the classical shape
variational analysis. Thus, the level set method provides
a natural setting to combine the rigorous shape variations
into the optimization process. (3) Perimeter regularization is incorporated in the method to make the optimization problem well-posed. It also produces an effect of
the geometric heat equation, regularizing and smoothing
the geometric boundaries as an anisotropic filter. (4) We
further describe numerical techniques for efficient and
robust implementation of the method, by embedding a
rectilinear grid in a fixed finite element mesh defined on
a reference design domain. This would separate the issues of accuracy in numerical calculations of the physical
equation and in the level-set model propagation. Finally,
the benefit and the advantages of the developed method
are illustrated with several 2D examples that have been
extensively used in the recent literature of topology optimization, especially in the homogenization based methods.},
DOI = {10.3970/cmes.2004.006.373}
}