scholarly journals Level Set Based Topological Shape Optimization of Hyper-elastic Nonlinear Structures using Topological Derivatives

2012 ◽  
Vol 25 (6) ◽  
pp. 559-567 ◽  
Author(s):  
Min-Geun Kim ◽  
Seung-Hyun Ha ◽  
Seonho Cho
Keyword(s):  
Shape Optimization ◽  
Level Set ◽  
Nonlinear Structures ◽  
Topological Derivatives ◽  
Hyper Elastic

scholarly journals A Level Set Method in Shape and Topology Optimization for Variational Inequalities

2007 ◽  
Vol 17 (3) ◽  
pp. 413-430 ◽  
Author(s):  
Piotr Fulmański ◽  
Antoine Laurain ◽  
Jean-Francois Scheid ◽  
Jan Sokołowski
Keyword(s):  
Topology Optimization ◽  
Variational Inequalities ◽  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Energy Functional ◽  
Optimization Techniques ◽  
Shape And Topology Optimization ◽  
And Topology ◽  
Topological Derivatives

A Level Set Method in Shape and Topology Optimization for Variational InequalitiesThe level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.

scholarly journals Level set method with topological derivatives in shape optimization

2008 ◽  
Vol 85 (10) ◽  
pp. 1491-1514 ◽  
Author(s):  
Piotr Fulmanski ◽  
Antoine Laurain ◽  
Jean-François Scheid ◽  
Jan Sokołowski
Keyword(s):  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Topological Derivatives
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