Optimization of conducting structures by using the homogenization method

Haslinger, Jaroslav; Hillebrand, Arne; Kärkkäinen, Tommi; Miettinen, Markku

doi:10.1007/s00158-002-0223-1

Cited by 26 publications

(9 citation statements)

References 10 publications

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“…Because the nodal coordinates of the boundary elements appear only in s and r of Equation (30) when solving Equation (36), we obtain the discretized boundary integral equation consisting of the nodal values of the Eulerian mesh by substituting Equations (12) and (18) into Equation (30). The nodal coordinates of the boundary elements disappear with this substitution; that is, the boundary element mesh is immersed in the Eulerian mesh.…”

Section: Immersed Boundary Element Methods For Static Elasticity Problemmentioning

confidence: 99%

An immersed boundary element method for level‐set based topology optimization

Yamasaki

Yamada

Matsumoto

2012

Numerical Meth Engineering

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SUMMARY In this paper, we propose a new BEM for level‐set based topology optimization. In the proposed BEM, the nodal coordinates of the boundary element are replaced with the nodal level‐set function and the nodal coordinates of the Eulerian mesh that maintains the level‐set function. Because this replacement causes the nodal coordinates of the boundary element to disappear, the boundary element mesh appears to be immersed in the Eulerian mesh. Therefore, we call the proposed BEM an immersed BEM. The relationship between the nodal coordinates of the boundary element and the nodal level‐set function of the Eulerian mesh is clearly represented, and therefore, the sensitivities with respect to the nodal level‐set function are strictly derived in the immersed BEM. Furthermore, the immersed BEM completely eliminates grayscale elements that are known to cause numerical difficulties in topology optimization. By using the immersed BEM, we construct a concrete topology optimization method for solving the minimum compliance problem. We provide some numerical examples and discuss the usefulness of the constructed optimization method on the basis of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Immersed Boundary Element Methods For Static Elasticity Problemmentioning

confidence: 99%

An immersed boundary element method for level‐set based topology optimization

Yamasaki

Yamada

Matsumoto

2012

Numerical Meth Engineering

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“…Haslinger et al [46] applied the original homogenization method for conducting structures. Although the paper had focused more on convergence analysis and approximation strategies, it has utilized rank-two laminated structures to demonstrate the optimal heat conductor configurations for its test problems.…”

Section: Prior To 2005mentioning

confidence: 99%

Heat Exchanger Design with Topology Optimization

Manuel¹,

Lin²

2017

Heat Exchangers - Design, Experiment and Simulation

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Topology optimization is proving to be a valuable design tool for physical systems, especially for structural systems. However, its application in the field of heat transfer is less evident but is constantly progressing. In this chapter, we would like to introduce topology optimization in the context of heat exchanger design to the general reader. We also provide a chronological review of available literature to see the current progress of topology optimization in the field of heat transfer and heat exchanger design. We expect that topology optimization will prove to be a valuable tool in heat exchanger design for the coming years.

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“…On the other hand, the heat conduction optimization problem has been handled from the early age of TO as a benchmark problem [2,20,21]. Steadystate heat conduction problems are the most basic problems [22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Structural topology optimization with strength and heat conduction constraints

Takezawa

Yoon

Jeong

et al. 2014

Computer Methods in Applied Mechanics and Engineering

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In this research, a topology optimization with constraints of structural strength and thermal conductivity is proposed. The coupled static linear elastic and heat conduction equations of state are considered. The optimization problem was formulated; viz., minimizing the volume under the constraints of p-norm stress and thermal compliance introducing the qp-relaxation method to avoid the singularity of stress-constraint topology optimization. The proposed optimization methodology is implemented employing the commonly used solid isotropic material with penalization (SIMP) method of topology optimization. The density function is updated using sequential linear programming

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Optimization of conducting structures by using the homogenization method

Cited by 26 publications

References 10 publications

An immersed boundary element method for level‐set based topology optimization

An immersed boundary element method for level‐set based topology optimization

Heat Exchanger Design with Topology Optimization

Structural topology optimization with strength and heat conduction constraints

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