scholarly journals A topology optimization method based on the level set method incorporating a fictitious interface energy

2010 ◽  
Vol 199 (45-48) ◽  
pp. 2876-2891 ◽  
Author(s):  
Takayuki Yamada ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki ◽  
Akihiro Takezawa
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Optimization Method ◽  
Interface Energy ◽  
Topology Optimization Method

Level Set-Based Topology Optimization Method for Thermal Problems Considering Design-Dependent Boundary Effects

2009 ◽  
Author(s):  
Takayuki Yamada ◽  
Shinji Nishiwaki ◽  
Atsuro Iga ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Field Theory ◽  
Topology Optimization ◽  
Level Set ◽  
Phase Field ◽  
Three Dimensional ◽  
Optimization Method ◽  
Interface Energy ◽  
Total Potential ◽  
Level Set Function ◽  
Topology Optimization Method

This paper proposes a new level set-based topology optimization method for thermal problems that deal with generic heat transfer boundaries including design-dependent boundary conditions, based on the level set method and the concept of the phase field theory. First, a topology optimization method using a level set model incorporating a fictitious interface energy derived from the concept of the phase field theory is briefly discussed. Next, a generic optimization problem for thermal problems is formulated based on the concept of total potential energy. An optimization algorithm that uses the Finite Element Method when solving the equilibrium equation and updating the level set function is then constructed. Finally, several three-dimensional numerical examples are provided to confirm the utility and validity of the proposed topology optimization method.

3301 A topology optimization method based on the level set method Using shell elements

2014 ◽  
Vol 2014.24 (0) ◽  
pp. _3301-1_-_3301-3_
Author(s):  
Kenta YAMAGATA ◽  
Takayuki YAMADA ◽  
Kazuhiro IZUI ◽  
Shinji NISHIWAKI ◽  
Atsushi KAWAMOTO
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Optimization Method ◽  
Shell Elements ◽  
Topology Optimization Method

Parametric Structural Shape and Topology Optimization Method With Radial Basis Functions and Level-Set Method

2006 ◽  
Author(s):  
Peng Wei ◽  
Michael Yu Wang
Keyword(s):  
Topology Optimization ◽  
Radial Basis Functions ◽  
Level Set Method ◽  
Level Set ◽  
Optimization Method ◽  
Basis Functions ◽  
Structural Shape ◽  
Shape And Topology Optimization ◽  
And Topology ◽  
Topology Optimization Method

In this paper, a parametric structural shape and topology optimization method is presented. To solving structure optimization problems, the level-set method has become a powerful design tool and been widely used in many fields. Combined with the Radial Basis Functions (RBF), which is a popular tool in function approximation, the method of level-set can be represented in a parametric way with a set of advantages comparing with the conventional discrete means. Some numerical examples are presented to illustrate its advantages.

Topology Optimization for Stokes Problem Under Multiple Flow Cases Using an Improved Level Set Method

2013 ◽  
Author(s):  
Bin Zhang ◽  
Xiaomin Liu ◽  
Jinju Sun
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Stokes Problem ◽  
Flow Analysis ◽  
Slip Boundary Condition ◽  
Optimization Method ◽  
Slip Boundary ◽  
New Formula ◽  
Topology Optimization Method

We present a topology optimization method for the Stokes problem under multiple flow cases by an improved level set method. In the framework of level set method, an implicit reinitialization approach is developed by deriving a new formula for the smoothing parameter in the conventional reinitialization equation. And a spline-free parameterization re-meshing method is adopted to overcome the convergence difficulty in flow analysis and guarantee the direct loading of the no-slip boundary condition. The topology optimization method developed in this paper is used to implement the optimal design for Stokes flow with the different boundary conditions. Numerical examples demonstrate that the proposed approach is effective and robust for the topology optimization of Stokes problem under multiple flow cases.

A Level Set-Based Topology Optimization Method for Maximizing Thermal Diffusivity in Problems Including Design-Dependent Effects

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Takayuki Yamada ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki
Keyword(s):  
Topology Optimization ◽  
Thermal Diffusivity ◽  
Level Set ◽  
Design Method ◽  
Optimization Method ◽  
Interface Energy ◽  
Total Potential ◽  
Level Set Function ◽  
Set Function ◽  
Topology Optimization Method

This paper proposes an optimum design method, based on our level set-based topology optimization method, for maximizing thermal diffusivity in problems dealing with generic heat transfer boundaries that include design-dependent boundary conditions. First, a topology optimization method using a level set model incorporating a fictitious interface energy for regularizing the topology optimization is briefly discussed. Next, an optimization method for maximizing thermal diffusivity is formulated based on the concept of total potential energy. An optimization algorithm that uses the finite element method when solving the equilibrium equation and updating the level set function is then constructed. Finally, several numerical examples are provided to confirm the utility and validity of the proposed topology optimization method.

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