Incorporating Topological Derivatives into Level Set Methods for Structural Topology Optimization

2004 ◽  
Author(s):  
Xiaoming Wang ◽  
Yulin Mei ◽  
Michael Wang
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Level Set Methods ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Topological Derivatives

Level-set methods for structural topology optimization: a review

2013 ◽  
Vol 48 (3) ◽  
pp. 437-472 ◽  
Author(s):  
N. P. van Dijk ◽  
K. Maute ◽  
M. Langelaar ◽  
F. van Keulen
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Level Set Methods ◽  
Structural Topology Optimization ◽  
Structural Topology

scholarly journals Level set band method: A combination of density-based and level set methods for the topology optimization of continuums

2020 ◽  
Vol 15 (3) ◽  
pp. 390-405
Author(s):  
Peng Wei ◽  
Wenwen Wang ◽  
Yang Yang ◽  
Michael Yu Wang
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Level Set Methods ◽  
Boundary Representation ◽  
Structural Topology ◽  
Topology Changes ◽  
Practical Engineering ◽  
Band Method ◽  
2D And 3D ◽  
Level Set Framework

Abstract The level set method (LSM), which is transplanted from the computer graphics field, has been successfully introduced into the structural topology optimization field for about two decades, but it still has not been widely applied to practical engineering problems as density-based methods do. One of the reasons is that it acts as a boundary evolution algorithm, which is not as flexible as density-based methods at controlling topology changes. In this study, a level set band method is proposed to overcome this drawback in handling topology changes in the level set framework. This scheme is proposed to improve the continuity of objective and constraint functions by incorporating one parameter, namely, level set band, to seamlessly combine LSM and density-based method to utilize their advantages. The proposed method demonstrates a flexible topology change by applying a certain size of the level set band and can converge to a clear boundary representation methodology. The method is easy to implement for improving existing LSMs and does not require the introduction of penalization or filtering factors that are prone to numerical issues. Several 2D and 3D numerical examples of compliance minimization problems are studied to illustrate the effects of the proposed method.

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