Topology optimization method for interior flow based on transient information of the lattice Boltzmann method with a level-set function

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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A Level Set-Based Topology Optimization Using the Lattice-Boltzmann Method

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C ◽

10.1299/kikaic.79.2152 ◽

2013 ◽

Vol 79 (802) ◽

pp. 2152-2163 ◽

Cited By ~ 2

Author(s):

Kentaro YAJI ◽

Takayuki YAMADA ◽

Masato YOSHINO ◽

Toshiro MATSUMOTO ◽

Kazuhiro IZUI ◽

...

Keyword(s):

Topology Optimization ◽

Lattice Boltzmann Method ◽

Level Set ◽

Lattice Boltzmann ◽

Boltzmann Method

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

Volume 3: 38th Design Automation Conference, Parts A and B ◽

10.1115/detc2012-70235 ◽

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.

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

Volume 5: 35th Design Automation Conference, Parts A and B ◽

10.1115/detc2009-86618 ◽

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.

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