Minimum length scale control in structural topology optimization based on the Moving Morphable Components (MMC) approach

Zhang, Weisheng; Li, Dong; Zhang, Jian; Gao, Xu

doi:10.1016/j.cma.2016.08.022

Cited by 107 publications

(33 citation statements)

References 42 publications

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“…In order to deal with this constraint, we discretize 0 with a set of points ∈ 0 ∩ D, = 1, … , and impose the constraints on these points (i.e., = 0 • − cos ̅ ≤ 0, = 1, … , ). For the sake of reducing the computational effort, these constraints are aggregate into an equivalent single global constraint function as in [17]. Actually, = 0 • − cos ̅ ≤ 0, = 1, … , is fully equivalent to…”

Section: Treatment Of Geometry Constraintsmentioning

confidence: 99%

“…Our motivation is from the consideration that since the constraints associated with the designing of self-supporting structures (e.g., overhang angle, minimum length scale) are actually geometrical in nature, it seems more appropriate to include more geometry information in the mathematical formulation of the considered problem and perform topology optimization in an geometrically explicit way (it is worth noting that topological design is usually achieved in an implicit way in tradition solution approaches such as variable density method and level set method, see [24][25][26][27][28][29] for more detailed discussions on this aspect). Recent years witnessed a growing interest in solving topology optimization problems by optimizing a set of geometrical parameters explicitly (i.e., a revival of shape optimization) [17,[24][25][26][27][28][29]. In particular, the so-called Moving Morphable Components (MMC) and Moving Morphable Voids (MMV) where a set of components (in MMC) or voids (in MMV) are used as basic building blocks of optimization have been developed.…”

Section: Introductionmentioning

confidence: 99%

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Self-supporting structure design in additive manufacturing through explicit topology optimization

Gao

Zhou

Zhang

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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255

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One of the challenging issues in additive manufacturing (AM) oriented topology optimization is how to design structures that are self-supportive in a manufacture process without introducing additional supporting materials. In the present contribution, it is intended to resolve this problem under an explicit topology optimization framework where optimal structural topology can be found by optimizing a set of explicit geometry parameters. Two solution approaches established based on the Moving Morphable Components (MMC) and Moving Morphable Voids (MMV) frameworks, respectively, are proposed and some theoretical issues associated with AM oriented topology optimization are also analyzed. Numerical examples provided demonstrate the effectiveness of the proposed methods.

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Section: Treatment Of Geometry Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Self-supporting structure design in additive manufacturing through explicit topology optimization

Gao

Zhou

Zhang

et al. 2017

Computer Methods in Applied Mechanics and Engineering

Self Cite

255

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show abstract

“…Moving components with variable thickness are used in [71], and the esartz material model is employed to enhance computational e ciency. In the work of Zhang et al [65] length scale control is achieved by directly controlling the component's minimal thickness. In Deng et al [12] the MMC approach is successfully implemented to solve various types of problems, like the design of compliant mechanisms and of low-frequency resonating micro devices.…”

Section: Introductionmentioning

confidence: 99%

Generalized Geometry Projection: A Unified Approach for Geometric Feature Based Topology Optimization

Coniglio

Morlier

Gogu

et al. 2019

Arch Computat Methods Eng

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Structural topology optimization has seen many methodological advances in the past few decades. In this work we focus on continuum-based structural topology optimization and more specifically on geometric feature based approaches, also known as explicit topology optimization, in which a design is described as the assembly of simple geometric components that can change position, size and orientation in the considered design space. We first review various recent developments in explicit topology optimization. We then describe in details three of the reviewed frameworks, which are the Geometry Projection method, the Moving Morphable Components with Esartz material method

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“…Within the Moving Morphable Components (MMC) approach (Guo et al 2014a) with trapezoidal components, a different notion of minimum length scale considering the individual sizes of the components and the sizes of their intersection regions was introduced by Zhang et al (2016).…”

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

confidence: 99%

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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Minimum length scale control in structural topology optimization based on the Moving Morphable Components (MMC) approach

Cited by 107 publications

References 42 publications

Self-supporting structure design in additive manufacturing through explicit topology optimization

Self-supporting structure design in additive manufacturing through explicit topology optimization

Generalized Geometry Projection: A Unified Approach for Geometric Feature Based Topology Optimization

On minimum length scale control in density based topology optimization

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