Density filters for topology optimization based on the Pythagorean means

Svanberg, Krister; Svärd, Henrik

doi:10.1007/s00158-013-0938-1

Cited by 83 publications

(60 citation statements)

References 13 publications

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“…Penalization schemes can decrease their appearance to some extend, however, some post processing of the design might be necessary if the final goal of the optimization process it pure black and white design. Aiming at reducing the intermediate transition regions between solid and void, various alternative filtering schemes based on projections [61], on morphological operators [124] and more recently on Pythagorean means [135] have been proposed in the literature.…”

Section: Projectionsmentioning

confidence: 99%

Length scale and manufacturability in density-based topology optimization

2016

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Since its original introduction in structural design, density based topology optimization has been applied to a number of other fields like microelectromechanical systems, photonics, acoustics and fluid mechanics. The methodology has been well accepted in industrial design processes where it can provide competitive designs in terms of cost, materials and functionality under a wide set of constraints. However, the optimized topologies are often considered as conceptual due to loosely defined topologies and the need of post processing. Subsequent amendments can affect the optimized design performance and in many cases can completely destroy the optimality of the solution. Therefore, the goal of this paper is to review recent advancements in obtaining manufacturable topology optimized designs. The focus is on methods for imposing minimum and maximum length scale, and ensuring manufacturable, well defined designs with robust performances. The overview discusses the limitations, the advantages and the associated computational costs. The review is completed with optimized designs for minimum compliance, mechanism design and heat transfer.

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Section: Projectionsmentioning

confidence: 99%

Length scale and manufacturability in density-based topology optimization

2016

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“…Here we consider density filtering methods, where the design variables are filtered and the filtered design variables are mapped to the coefficients that enter the governing equation. A disadvantage of the original linear density filter is that it produces designs with relatively large areas of (Guest et al 2004(Guest et al , 2011Sigmund 2007;Svanberg and Svärd 2013;Wadbro and Hägg 2015;Hägg and Wadbro 2017). In addition to providing mesh independent solutions, filtering of the design variables can relieve the strong self penalization discussed in the previous section.…”

Section: Filteringmentioning

confidence: 99%

“…To pursue nonlinear filtering of the design variables, we substitute f k (·) in expression (11) by harmonic functions as proposed by Svanberg and Svärd (2013) for elasticity problems. More precisely, we use functions of the form…”

Section: Non-linear Filtermentioning

confidence: 99%

“…In addition, the harmonic filter operator have bounded derivatives as the nonlinearity parameter α tends to zero. We refer to the study by Svanberg and Svärd (2013) for a comprehensive comparison between the harmonic mean filters and other kinds of filters.…”

Section: Non-linear Filtermentioning

confidence: 99%

“…The first phase aims mainly to counteract the self penalization issue by filtering the design variables using a standard linear density filter combined with a continuation approach over a successively reduced filter size-but only down to a predefined finite size corresponding to the selected feature size. The second phase uses a nonlinear filtering of the design variables, based on a sequence of parameterized harmonic mean filters (Svanberg and Svärd 2013), which in the limit yields binary designs, while at the same time Fig. 1 A 50-Ohm coaxial cable is connected to the rear end of an a ×b rectangular waveguide.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Topology optimization of compact wideband coaxial-to-waveguide transitions with minimum-size control

Hassan

Wadbro

Hägg

et al. 2017

Struct Multidisc Optim

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This paper presents a density-based topology optimization approach to design compact wideband coaxialto-waveguide transitions. The underlying optimization problem shows a strong self penalization towards binary solutions, which entails mesh-dependent designs that generally exhibit poor performance. To address the self penalization issue, we develop a filtering approach that consists of two phases. The first phase aims to relax the self penalization by using a sequence of linear filters. The second phase relies on nonlinear filters and aims to obtain binary solutions and to impose minimum-size control on the final design. We present results for optimizing compact transitions between a 50-Ohm coaxial cable and a standard WR90 waveguide operating in the X-band (8-12 GHz).

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Homogenization‐based design of surface textures in hydrodynamic lubrication

Waseem

Temizer

Kato

et al. 2016

Numerical Meth Engineering

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SUMMARYAn optimization framework is developed for surface texture design in hydrodynamic lubrication. The microscopic model of the lubrication interface is based on the Reynolds equation, and the macroscopic response is characterized through homogenization. The microscale setting assumes a unilateral periodic texture but implicitly accounts for the bilateral motion of the surfaces. The surface texture in a unit cell is described indirectly through the film thickness, which is allowed to vary between prescribed minimum and maximum values according to a morphology variable distribution that is obtained through the filtering of a design variable. The design and morphology variables are discretized using either element-wise constant values or through first-order elements. In addition to sharp textures, which are characterized by pillars and holes that induce sudden transitions between extreme film thickness values, the framework can also attain a variety of non-standard smoothly varying surface textures with a macroscopically isotropic or anisotropic response.

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Density filters for topology optimization based on the Pythagorean means

Cited by 83 publications

References 13 publications

Length scale and manufacturability in density-based topology optimization

Length scale and manufacturability in density-based topology optimization

Topology optimization of compact wideband coaxial-to-waveguide transitions with minimum-size control

Homogenization‐based design of surface textures in hydrodynamic lubrication

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