P1‐nonconforming quadrilateral finite element for topology optimization

Jang, Gang-Won; Panganiban, Henry; Chung, Tae Jin

doi:10.1002/nme.2912

Cited by 9 publications

(14 citation statements)

References 19 publications

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“…In the introduced "truly-mixed" setting, C is written in terms of the complementary energy and computed from the stress unknowns according to Eqn. (11). Figure 4(a) shows that the relevant convergence curves find the same final value with a comparable rate of convergence.…”

Section: A Preliminary Investigation: "Truly-mixed" Element Vs Displamentioning

confidence: 71%

Topology optimization with mixed finite elements on regular grids

Bruggi

2016

Computer Methods in Applied Mechanics and Engineering

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Recently, new families of mixed finite elements have been proposed to address the analysis of linear elastic bodies on regular grids adopting a limited number of degrees of freedom per element. A twodimensional mixed discretization is implemented to formulate an alternative topology optimization problem where stresses play the role of main variables and both compressible and incompressible materials can be dealt with. The structural compliance is computed through the evaluation of the complementary energy, whereas the enforcement of stress constraints is straightforward. Numerical simulations investigate the features of the proposed approach: comparisons with a conventional displacement-based scheme are provided for compressible materials; stress-constrained solutions for structures made of incompressible media are introduced.

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Section: A Preliminary Investigation: "Truly-mixed" Element Vs Displamentioning

confidence: 71%

Topology optimization with mixed finite elements on regular grids

Bruggi

2016

Computer Methods in Applied Mechanics and Engineering

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“…The state of each finite element is determined by the design variable χ r ; the acoustical properties and inverse permeability of each element are parameterized with respect to χ r as

1 MathClass-bin∕ ρ_{r} (χ_{r}) MathClass-rel= 1 MathClass-bin∕ ρ_{air} MathClass-bin+ χ_{r} ((), 1 MathClass-bin∕ ρ_{rigid} MathClass-bin- 1 MathClass-bin∕ ρ_{air}) MathClass-punc,

1 MathClass-bin∕ K_{r} (χ_{r}) MathClass-rel= 1 MathClass-bin∕ K_{air} MathClass-bin+ χ_{r} ((), 1 MathClass-bin∕ K_{rigid} MathClass-bin- 1 MathClass-bin∕ K_{air}) MathClass-punc,

γ_{r} (χ_{r}) MathClass-rel= γ_{fluid} MathClass-bin+ ((), γ_{solid} MathClass-bin- γ_{fluid}) MathClass-bin\cdot χ_{r} \frac{1 MathClass-bin+ q}{χ_{r} MathClass-bin+ q} MathClass-punc,

where the subscripts ‘air’ and ‘rigid’ in Equations and stand for air and rigid body material, respectively, in acoustical topology optimization, and ‘solid’ and ‘fluid’ in Equation denote solid and fluid materials, respectively, in fluid topology optimization. The penalty parameter q in Equation is used to facilitate the convergence of the design variable to 0 or 1 ( q = 0.1 is used in this study.…”

Section: Multiobjective Topology Optimization Setup For Muffler Designmentioning

confidence: 99%

“…The state of each finite element is determined by the design variable r ; the acoustical properties and inverse permeability of each element are parameterized with respect to r as [4,15,19]…”

Section: Topology Optimization Formulationmentioning

confidence: 99%

“…An example of such a mechanical system is acoustic silencers such as reactive mufflers used in electric home appliances; they require not only high noise reduction but also a low pressure drop.The finite element method and a gradient-based topology optimization scheme are employed in the proposed multiobjective topology optimization. Finite element equations for acoustic and flow analyses are developed from the Helmholtz equation and the Stokes equation [4,15], respectively, under the assumption that the input flow is very slow. One design variable is assigned to each finite element to control the state of the element as a fluid (acoustic media) or solid (rigid body).…”

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confidence: 99%

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Topology design of reactive mufflers for enhancing their acoustic attenuation performance and flow characteristics simultaneously

Lee

Jang

2012

Numerical Meth Engineering

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SUMMARY When seeking to enhance the acoustic attenuation performance of a reactive muffler, it is necessary to ensure that the flow resistance does not increase significantly. To date, there have been very few attempts to simultaneously optimize the transmission loss and pressure drop of a muffler. In this study, a multiobjective topology optimization problem is formulated to maximize the transmission loss at a target frequency and minimize the pressure drop simultaneously. The objective function in the formulation is given as the sum of weighted transmission loss and weighted pressure drop. The effect of the weighting factors on the optimal topologies of a muffler is investigated. Furthermore, the physical interpretation of partition layouts of optimized mufflers is discussed. The proposed muffler design method involving multiobjective topology optimization is compared with the previous muffler design method that involves single‐objective topology optimization to maximize only the transmission loss. The most important advantage of this study is shown by considering numerical results; the proposed muffler design method is applicable to nonconcentric expansion chamber mufflers, unlike the previous muffler design method. Copyright © 2012 John Wiley & Sons, Ltd.

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“…Achieved results of Borrvall and Petersson (2003;Figs. 7, 11, and 13 of the study) have been approved by other scientists (Guest & Prévost, 2006a;Challis & Guest, 2009;Jang et al, 2010), however, with slightly different optimal objec- Layout synthesis of fluid channels tive values but significant changes in the required computational power and time. The registered time by Challis and Guest (2009), who have used a level set topology optimization method, is considered for comparison with results achieved with the developed method in this study.…”

Section: Benchmark Examplesmentioning

confidence: 99%

Layout synthesis of fluid channels using generative graph grammars

Hooshmand

Campbell

2014

AIEDAM

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This paper presents a new technique for shape and topology optimization of fluid channels using generative design synthesis methods. The proposed method uses the generative abilities of graph grammars with simulation and analysis power of conventional computational fluid dynamics methods. The graph grammar interpreter GraphSynth is used to carry out graph transformations, which define different topologies for a given multiple-inlet multiple-outlet problem. After evaluating and optimizing the generated graphs, they are first transformed into meaningful three-dimensional shapes. These solutions are then analyzed by a computational fluid dynamics solver for final evaluation of the possible solutions. The effectiveness of the proposed method is checked by solving a variety of available test problems and comparing them with those found in the literature. Furthermore, by solving very complex large-scale problems, the robustness and effectiveness of the method is tested. To extend the work, future research directions are presented.

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P1‐nonconforming quadrilateral finite element for topology optimization

Cited by 9 publications

References 19 publications

Topology optimization with mixed finite elements on regular grids

Topology optimization with mixed finite elements on regular grids

Topology design of reactive mufflers for enhancing their acoustic attenuation performance and flow characteristics simultaneously

Layout synthesis of fluid channels using generative graph grammars

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