Topological shape optimization of geometrically nonlinear structures using level set method

2005 ◽  
Vol 83 (27) ◽  
pp. 2257-2268 ◽  
Author(s):  
Juho Kwak ◽  
Seonho Cho
Keyword(s):  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures

scholarly journals Stiffness optimization of geometrically nonlinear structures and the level set based solution

2016 ◽  
Vol 7 ◽  
pp. A3 ◽  
Author(s):  
Qi Xia ◽  
Tielin Shi
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Optimization Problem ◽  
Two Dimensions ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Element Analysis ◽  
Topology Optimization Problem ◽  
Stiffness Optimization ◽  
Ks Function

Load-normalized strain energy increments between consecutive load steps are aggregated through the Kreisselmeier-Steinhauser (KS) function, and the KS function is proposed as a stiffness criterion of geometrically nonlinear structures. A topology optimization problem is defined to minimize the KS function together with the perimeter of structure and a volume constraint. The finite element analysis is done by remeshing, and artificial weak material is not used. The topology optimization problem is solved by using the level set method. Several numerical examples in two dimensions are provided. Other criteria of stiffness, i.e., the end compliance and the complementary work, are compared.

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 Shape optimization with the level-set-method using local volume constraints

2017 ◽  
Vol 57 (1) ◽  
pp. 115-130
Author(s):  
Simon H. Hesse ◽  
Lukas F. Leidinger ◽  
Johannes Kremheller ◽  
Dirk Lukaszewicz ◽  
Fabian Duddeck
Keyword(s):  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Local Volume
Sign in / Sign up

Export Citation Format

Share Document