A Study On Topology Optimization Using The
Level-set Function And BEM
Author(s)
T. Matsumoto, T. Yamada, S. Shichi & T. Takahashi
Abstract
A framework to solve topology optimization problems using a level-set based
approach and boundary element method (BEM) is presented. The objective
functional is assumed to be defined only on the boundary, thus the problem is
suitable for handling with BEM. The boundary of the structure is defined as
the isosurface of the level-set function. The distribution of the level-set function
is obtained by solving an evolution equation defined in a fixed design domain.
The evolution equation has a source term related to the topological sensitivity
of the objective functional. The sensitivity can be evaluated from BEM analysis
results both for the original physical variable and its adjoint variable. The shape
of the structure is defined as the isosurface of the level-set function defined in
a fixed design domain, and the boundary mesh is generated by extracting the
isosurface. Since the fixed design domain has a simple rectangular solid shape and
does not change its domain shape through iteration steps, the evolution equation
of the level-set function can be solved by FEM more efficiently than by BEM.
The effectiveness of the proposed approach is demonstrated through a minimum
compliance topology optimization problem.
Keywords: topology optimization, level-set function, adjoint method, boundary
element method.
1 Introduction
Because of the current development of fast boundary element algorithms [1, 2],
BEM may become a strong analysis tool not only for shape optimization problems
but also for topology optimization problems. In particular, BEM is effective for
linear problems and those with infinite domains.
Keywords
topology optimization, level-set function, adjoint method, boundary
element method.
Related Book
Other papers in this volume
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