Topology optimization using regularized intermediate density control

Borrvall, Thomas; Petersson, Joakim

doi:10.1016/s0045-7825(00)00356-x

Cited by 157 publications

(85 citation statements)

References 13 publications

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“…Restriction methods for density based topology optimization problems can roughly be divided into three categories: 1) mesh-independent filtering methods, constituting sensitivity filters (Sigmund, 1994(Sigmund, , 1997Sigmund and Petersson, 1998) and density filters (Bruns and Tortorelli, 2001;Bourdin, 2001); 2) constraint methods such as perimeter control (Ambrosio and Buttazzo, 1993;Haber et al, 1994), global gradient control (Bendsøe, 1995;Borrvall, 2001), local gradient control (Niordson, 1983;Petersson and Sigmund, 1998;Zhou et al, 2001), regularized penalty methods (Borrvall and Petersson, 2001) and integral filtering (Poulsen, 2003); and 3) other methods like wavelet parameterizations (Kim and Yoon, 2000;Poulsen, 2002), phase-field approaches (Bourdin and Chambolle, 2003;Wang and Zhou, 2004) and level-set methods (Sethian and Wiegmann, 2000;Wang et al, 2003;Allaire et al, 2004) 1 . The filtering methods in group 1 are probably the most popular ones due to their ease of implementation and their efficiency.…”

Section: Introductionmentioning

confidence: 99%

Morphology-based black and white filters for topology optimization

Sigmund

2007

Struct Multidisc Optim

1,396

801

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In order to ensure manufacturability and mesh-independence in density-based topology optimization schemes it is imperative to use restriction methods. This paper introduces a new class of morphology based restriction schemes which work as density filters, i.e. the physical stiffness of an element is based on a function of the design variables of the neighboring elements. The new filters have the advantage that they eliminate grey scale transitions between solid and void regions. Using different test examples, it is shown that the schemes in general provide black and white designs with minimum length-scale constraints on either or both minimum hole sizes and minimum structural feature sizes. The new schemes are compared with methods and modified methods found in the literature.

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Section: Introductionmentioning

confidence: 99%

Morphology-based black and white filters for topology optimization

Sigmund

2007

Struct Multidisc Optim

1,396

801

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“…However, in this case the difficulty for selecting α is transferred to the selection of the constraint value. A variation of the explicit penalization is proposed in [22] where the density ρ in Equation 6 is replaced with a density average which imposes a length scale on the design, however, with the same challenges in selecting α as for the expression given by Equation 6.…”

Section: Interpolation Schemes In Topology Optimizationmentioning

confidence: 99%

“…and Table 7, respectively. In the first row of each table the most eroded and the most dilated designs are obtained using the Harmonic mean filter given by Equation 21 and Equation 22, respectively. The filter radius for the Harmonic filter is set to 2.17L/200.…”

Section: Topology Optimization Under Geometrical Uncertaintiesmentioning

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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“…Bourdin [2001] proposed a filtering technique by regularizing the density field through the use of a convolution operator to replace the point-wise element densities. Borrvall and Petersson [2001] also implemented a different density filter through regularized density control. Then, Wang and Wang [2005] developed a bilateral filtering technique to perform checkerboard-free, mesh dependent, edge preserving topology optimization.…”

Section: Layout Optimization Issuesmentioning

confidence: 99%

Application of layout and topology optimization using pattern gradation for the conceptual design of buildings

Stromberg

Beghini

Baker

et al. 2010

Struct Multidisc Optim

114

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This work explores the use of manufacturing-type constraints, in particular pattern gradation and repetition, in the context of layout optimization. By placing constraints on the design domain in terms of number and size of repeating patterns along any direction, the conceptual design for buildings is facilitated. To substantiate the potential future applications of this work, examples within the context of high-rise building design are presented. Successful development of such ideas will lead to practical engineering solutions, especially during the building design process. Throughout this work, a continuous topology optimization formulation is utilized with compliance as the objective function and constraints on the pattern geometry. Examples are given to illustrate the ideas developed both in two-dimensional and three-dimensional building configurations.ii To my father, Barry and my mother, Kathy.iii

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Topology optimization using regularized intermediate density control

Cited by 157 publications

References 13 publications

Morphology-based black and white filters for topology optimization

Morphology-based black and white filters for topology optimization

Length scale and manufacturability in density-based topology optimization

Application of layout and topology optimization using pattern gradation for the conceptual design of buildings

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