Paper Title:
A Meshless Level Set Method for Shape and Topology Optimization
  Abstract

This paper proposes a meshless Galerkin level set method for structural shape and topology optimization of continua. To taking advantage of the implicit free boundary representation scheme, structural design boundary is represented through the introduction of a scalar level set function as its zero level set, to flexibly handle complex shape fidelity and topology changes by maintaining concise and smooth interface. Compactly supported radial basis functions (CSRBFs) are used to parameterize the level set function and also to construct the shape functions for mesh free function approximation. The meshless Galerkin global weak formulation is employed to implement the discretization of the state equations. This provides a pathway to simplify two numerical procedures involved in most conventional level set methods in propagating the discrete level set functions and in approximating the discrete equations, by unifying the two different stages at two sets of grids just in terms of one set of scattered nodes. The proposed level set method has the capability of describing the implicit moving boundaries without remeshing for discontinuities. The motion of the free boundary is just a question of advancing the discrete level set function by finding the design variables of the size optimization in time. One benchmark example is used to demonstrate the effectiveness of the proposed method. The numerical results showcase that this method has the ability to simplify numerical procedures and to avoid numerical difficulties happened in most conventional level set methods. It is straightforward to apply the present method to more advanced shape and topology optimization problems.

  Info
Periodical
Advanced Materials Research (Volumes 308-310)
Chapter
Intelligent Optimization Design
Edited by
Jian Gao
Pages
1046-1049
DOI
10.4028/www.scientific.net/AMR.308-310.1046
Citation
Y. Wang, Z. Luo, "A Meshless Level Set Method for Shape and Topology Optimization", Advanced Materials Research, Vols. 308-310, pp. 1046-1049, 2011
Online since
August 2011
Authors
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Price
$32.00
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