Length scale and manufacturability in density-based topology optimization

Lazarov, Boyan Stefanov; Wang, Fengwen; Sigmund, Ole

doi:10.1007/s00419-015-1106-4

Cited by 237 publications

(160 citation statements)

References 168 publications

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“…Furthermore, numerical artifacts, similar to the well-known checkerboard patterns, need to be omitted from the solution space. To do so, several established filter methods are used in our model, such as the sensitivity filter, the density filter, the density filter with projection, and robust topology optimization [22]. The description of each of these filters and their corresponding sensitivities can be found in Appendix A.…”

Section: Static Condensationmentioning

confidence: 99%

Higher‐order multi‐resolution topology optimization using the finite cell method

Groen

Langelaar

Sigmund

et al. 2016

Numerical Meth Engineering

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SUMMARYThis article presents a detailed study on the potential and limitations of performing higher-order multiresolution topology optimization with the finite cell method. To circumvent stiffness overestimation in high-contrast topologies, a length-scale is applied on the solution using filter methods. The relations between stiffness overestimation, the analysis system, and the applied length-scale are examined, while a highresolution topology is maintained. The computational cost associated with nested topology optimization is reduced significantly compared with the use of first-order finite elements. This reduction is caused by exploiting the decoupling of density and analysis mesh, and by condensing the higher-order modes out of the stiffness matrix.

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Section: Static Condensationmentioning

confidence: 99%

Higher‐order multi‐resolution topology optimization using the finite cell method

Groen

Langelaar

Sigmund

et al. 2016

Numerical Meth Engineering

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“…Regarding M ND , the optimized designs presented in Section 5.3 outperforms those obtained by state of the art techniques for imposing minimum length scales presented in the review by Lazarov et al (2016). In what way the proposed method benefits from extra penalization of intermediate densities has not been fully investigated.…”

Section: Discussionmentioning

confidence: 88%

“…The plate is held at zero temperature along the boundary portion D and is thermally insulated along the rest of the boundary N . For the minimum heat compliance problem, using standard SIMP with p = 3 and standard filtering schemes to impose NEL on one of the phases yields designs with large M ND (Lazarov et al 2016). Moreover, there are numerical evidence that, for this problem-unlike the cantilever beam example-, an open-close filtering strategy (combined with adequate penalization of intermediate conductivities) fails to provide designs with NELs on both phases (Hägg and Wadbro 2017).…”

Section: Minimum Heat Compliancementioning

confidence: 99%

“…Related to constraints on minimum length scale are so called robust formulations aiming at designs that are robust toward geometrical uncertainties (Lazarov et al 2016). Robust formulations typically require multiple solves of the state equation at each design iteration and are therefore in general computationally demanding.…”

Section: Overview On Minimum Length Scale Control In Density Based Tomentioning

confidence: 99%

“…A comprehensive review on different techniques based on density filtering has recently been given by Lazarov et al (2016).…”

Section: Overview On Minimum Length Scale Control In Density Based Tomentioning

confidence: 99%

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On minimum length scale control in density based topology optimization

Hägg

Wadbro

2018

Struct Multidisc Optim

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This is the published version of a paper published in Structural and multidisciplinary optimization (Print). Citation for the original published paper (version of record):Hägg, L., Wadbro, E. (2018) On minimum length scale control in density based topology optimization AbstractThe archetypical topology optimization problem concerns designing the layout of material within a given region of space so that some performance measure is extremized. To improve manufacturability and reduce manufacturing costs, restrictions on the possible layouts may be imposed. Among such restrictions, constraining the minimum length scales of different regions of the design has a significant place. Within the density filter based topology optimization framework the most commonly used definition is that a region has a minimum length scale not less than D if any point within that region lies within a sphere with diameter D > 0 that is completely contained in the region. In this paper, we propose a variant of this minimum length scale definition for subsets of a convex (possibly bounded) domain. We show that sets with positive minimum length scale are characterized as being morphologically open. As a corollary, we find that sets where both the interior and the exterior have positive minimum length scales are characterized as being simultaneously morphologically open and (essentially) morphologically closed. For binary designs in the discretized setting, the latter translates to that the opening of the design should equal the closing of the design. To demonstrate the capability of the developed theory, we devise a method that heuristically promotes designs that are binary and have positive minimum length scales (possibly measured in different norms) on both phases for minimum compliance problems. The obtained designs are almost binary and possess minimum length scales on both phases.

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Topology Optimization

Maute

2017

Encyclopedia of Computational Mechanics Second Edition

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Topology optimization is a computational approach to systematically optimize the conceptual layout and the geometry of a body on the basis of a basic description of a design problem. In contrast to other design optimization methods, the outer shape of the body and the geometry of the material interfaces within the body may undergo radical changes in the optimization process, including both shape and topological changes. This unique feature reduces significantly the dependence of the optimized design on the initial guess from which the optimization process is started and allows finding nonintuitive solutions for complex design problems. Formulating optimization problems that yield meaningful, practical designs requires a solid understanding of the physical phenomena that dominate the body's functionality, as well as insight into the mathematical characteristics of the high‐dimensional design spaces used in topology optimization. Topology optimization methods involve a broad variety of computational techniques for describing the geometry of the body, predicting the physical phenomena of interest, and searching for the optimum design. This chapter provides an introduction to modern topology optimization. Instead of providing a comprehensive overview, the most important and widely used approaches are discussed in sufficient detail to provide the reader with a basic understanding of the state of the art of topology optimization.

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Length scale and manufacturability in density-based topology optimization

Cited by 237 publications

References 168 publications

Higher‐order multi‐resolution topology optimization using the finite cell method

Higher‐order multi‐resolution topology optimization using the finite cell method

On minimum length scale control in density based topology optimization

Topology Optimization

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