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.

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.

Design of Mechanical Structures Considering Harmonic Loads Using Level Set-Based Topology Optimization

2012 ◽  
Author(s):  
Takayuki Yamada ◽  
Toshiro Matsumoto ◽  
Shinji Nishiwaki
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Design Method ◽  
Optimization Method ◽  
Adjoint Equations ◽  
Topology Optimization Problem ◽  
Level Set Function ◽  
Elastic Design ◽  
Objective Functional ◽  
Topology Optimization Method

This paper presents an optimum design method for mechanical structures considering harmonic loads using a level set-based topology optimization method and the Finite Element Method (FEM). First, we briefly discuss the level set-based topology optimization method. Second, a topology optimization problem is formulated for a dynamic elastic design problem using level set boundary expressions. The objective functional is set to minimize the displacement at specific boundaries. Based on this formulation, the topological sensitivities of the objective functional are derived. Next, a topology optimization algorithm is proposed that uses the FEM to solve the equilibrium and adjoint equations, and when updating the level set function. Finally, several numerical examples are provided to confirm the validity and utility of the proposed method.

Electromagnetic Design of In-Vehicle Reactor Using a Level-Set Based Topology Optimization Method

2014 ◽  
Author(s):  
Shintaro Yamasaki ◽  
Atsushi Kawamoto ◽  
Akira Saito ◽  
Masakatsu Kuroishi ◽  
Kikuo Fujita
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Design Problem ◽  
Design Method ◽  
Reactor Core ◽  
Optimization Method ◽  
State Variables ◽  
Boundary Tracking ◽  
Level Set Function ◽  
Topology Optimization Method

In this paper, we propose a level-set based topology optimization method for designing a reactor, which is used as a part of the DC-DC converter in electric and hybrid vehicles. Since it realizes a high-power driving motor and its performance relies on its component, i.e., reactor core, it is valuable to establish a reasonable design method for the reactor core. Boundary tracking type level-set topology optimization is suitable for this purpose, because the shape and topology of the target structure is clearly represented by the zero boundary of the level-set function, and the state variables are accurately computed using the zero boundary tracking mesh. We formulate the design problem on the basis of electromagnetics, and derive the design sensitivities. The derived sensitivities are linked with boundary tracking type level-set topology optimization, and as a result, a useful structural optimization method for the reactor core design problem is developed.

A topology optimization algorithm based on topological derivative and level-set function for designing phononic crystals

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Rolando Yera ◽  
Luisina Forzani ◽  
Carlos Gustavo Méndez ◽  
Alfredo E. Huespe
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Optimization Algorithm ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Lagrangian Function ◽  
Topological Derivative ◽  
Content Type ◽  
Level Set Function ◽  
Set Function

PurposeThis work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps.Design/methodology/approachThe resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtained through the dispersion relation of the phononic crystal.FindingsThe description of the optimization algorithm is emphasized, and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed.Originality/valueThe original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

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