Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework

Guo, Xu; Zhang, Weisheng; Zhong, Wenliang

doi:10.1115/1.4027609

Cited by 771 publications

(271 citation statements)

References 20 publications

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“…Discussion on the similarities and differences of these approaches has recently been reported in Sigmund and Maute (2013). We note also another recently proposed topology optimization approach using moving morphable components (Guo et al 2014;Zhang et al 2015Zhang et al , 2016.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary topology optimization of elastoplastic structures

Xia

Fritzen

Breitkopf

2016

Struct Multidisc Optim

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We have recently proposed in (Fritzen et al., Int J Numer Methods Eng 106 (6): 2016) an evolutionary topology optimization model for the design of multiscale elastoplastic structures, which is in general independent of the applied material law. Facing the variability of the final design for minor parameter changes when dealing with plastic structural designs, we further improve the robustness and the effectiveness of the BESO optimization procedure in this work by introducing a damping scheme on sensitivity numbers and by progressively reducing the sensitivity filtering radius. The damping scheme constraining the variance of the sensitivity numbers stabilizes the topological evolution process in particular for dissipative structural designs. By setting initially a large filter radius value and reducing it gradually, the emergence of the redundant structural branches, which are to be eliminated afterwards and Liang Xia are the main reasons deteriorating the design process, could be avoided. The robustness and the effectiveness of the improved model has been validated by means of benchmark numerical examples of conventional homogeneous structures.

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Section: Introductionmentioning

confidence: 99%

Evolutionary topology optimization of elastoplastic structures

Xia

Fritzen

Breitkopf

2016

Struct Multidisc Optim

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“…The details of this approach are described further in Section 2 as we make the minor modifications to the method of Norato et al 15 necessary to extend it to consider designs with cylindrical rods in 3 dimensions. This geometry projection method is similar to the recent 2-dimensional level set methods of Guo et al 17 and Guo et al, 18 which also restrict the design to assemblies of bar-like members. In Guo et al , 17 this is realized by enforcing a constraint on the average distance between each member's medial surface and the zero level cut; the resulting members have approximately constant thickness, compared to exactly constant thickness in this geometry projection method.…”

Section: Introductionmentioning

confidence: 92%

A geometric projection method for designing three‐dimensional open lattices with inverse homogenization

Watts

Tortorelli

2017

Numerical Meth Engineering

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Summary Topology optimization is a methodology for assigning material or void to each point in a design domain in a way that extremizes some objective function, such as the compliance of a structure under given loads, subject to various imposed constraints, such as an upper bound on the mass of the structure. Geometry projection is a means to parameterize the topology optimization problem, by describing the design in a way that is independent of the mesh used for analysis of the design's performance; it results in many fewer design parameters, necessarily resolves the ill‐posed nature of the topology optimization problem, and provides sharp descriptions of the material interfaces. We extend previous geometric projection work to 3 dimensions and design unit cells for lattice materials using inverse homogenization. We perform a sensitivity analysis of the geometric projection and show it has smooth derivatives, making it suitable for use with gradient‐based optimization algorithms. The technique is demonstrated by designing unit cells comprised of a single constituent material plus void space to obtain light, stiff materials with cubic and isotropic material symmetry. We also design a single‐constituent isotropic material with negative Poisson's ratio and a light, stiff material comprised of 2 constituent solids plus void space.

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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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Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework

Cited by 771 publications

References 20 publications

Evolutionary topology optimization of elastoplastic structures

Evolutionary topology optimization of elastoplastic structures

A geometric projection method for designing three‐dimensional open lattices with inverse homogenization

On minimum length scale control in density based topology optimization

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