An adaptive mesh‐adjustment strategy for continuum topology optimization to achieve manufacturable structural layout

Wang, Hongxin; Liu, Jie; Wen, Guilin

doi:10.1002/nme.6001

Cited by 15 publications

(7 citation statements)

References 35 publications

(37 reference statements)

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“…The resulting topology was free from grey elements on the boundaries, small holes, and thin elements, which is desirable from the point of view of the manufacturing technology. This effect was gained without additive filtering, in contrast to the studies presented in [38].…”

Section: Topology Optimization For a Multiple Load Casecontrasting

confidence: 61%

CARMA—Cellular Automata with Refined Mesh Adaptation—The Easy Way of Generation of Structural Topologies

Tajs-Zielińska¹,

Bochenek²

2020

Applied Sciences

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This paper is focused on the development of a Cellular Automata algorithm with the refined mesh adaptation technique and the implementation of this algorithm in topology optimization problems. Traditionally, a Cellular Automaton is created based on regular discretization of the design domain into a lattice of cells, the states of which are updated by applying simple local rules. It is expected that during the topology optimization process the local rules responsible for the evaluation of cell states can drive the solution to solid/void resulting structures. In the proposed approach, the finite elements are equivalent to cells of an automaton and the states of cells are represented by design variables. While optimizing engineering structural elements, the important issue is to obtain well-defined solutions: in particular, topologies with smooth boundaries. The quality of the structural topology boundaries depends on the resolution level of mesh discretization: the greater the number of elements in the mesh, the better the representation of the optimized structure. However, the use of fine meshes implies a high computational cost. We propose, therefore, an adaptive way to refine the mesh. This allowed us to reduce the number of design variables without losing the accuracy of results and without an excessive increase in the number of elements caused by use of a fine mesh for a whole structure. In particular, it is not necessary to cover void regions with a very fine mesh. The implementation of a fine grid is expected mainly in the so-called grey regions where it has to be decided whether a cell becomes solid or void. The benefit of the proposed approach, besides the possibility of obtaining high-resolution, sharply resolved fine optimal topologies with a relatively low computational cost, is also that the checkerboard effect, mesh dependency, and the so-called grey areas can be eliminated without using any additional filtering. Moreover, the algorithm presented is versatile, which allows its easy combination with any structural analysis solver built on the finite element method.

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Section: Topology Optimization For a Multiple Load Casecontrasting

confidence: 61%

CARMA—Cellular Automata with Refined Mesh Adaptation—The Easy Way of Generation of Structural Topologies

Tajs-Zielińska¹,

Bochenek²

2020

Applied Sciences

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“…9 This approach can be applied also to meshless optimization methods, which do not require mesh connectivity nevertheless maintaining a sufficient accuracy and numerical stability. 15,16 Interpolation or projection methods can be used to realize mesh adaptive [17][18][19] or multiresolution 12,[20][21][22] topology optimization approaches to increase the results definition while reducing computational time. These methods decouple the discretization on the design variables from the discretization for the displacement field to obtain high resolution results with relatively coarse meshes.…”

Section: Introductionmentioning

confidence: 99%

“…Interpolation or projection methods can be used to realize mesh adaptive 17‐19 or multiresolution 12,20‐22 topology optimization approaches to increase the results definition while reducing computational time. These methods decouple the discretization on the design variables from the discretization for the displacement field to obtain high resolution results with relatively coarse meshes.…”

Section: Introductionmentioning

confidence: 99%

A shape function based interpolation approach for nodal design variable based structural optimization

Previati

Ballo

Gobbi

2022

Numerical Meth Engineering

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In this article, a novel density interpolation scheme for topological optimization based on nodal density variables is presented. The method relies on the definition of an independent interpolation mesh for the description of the density field. This mesh is used for the interpolation of the density field at the Gauss points of the design domain mesh. Provided that the interpolation mesh is realized by linear elements, the proposed scheme is range restricted and assures physically meaningful values of the interpolated density. Explicit analytical sensitivity expressions can be derived. The utilization of an independent interpolation mesh allows for the utilization of any element type and geometry on the body for the computation of the displacements. It is also shown that the chosen interpolation scheme has interesting properties of volume and material volume conservation with respect to the mesh utilized on the body and the domain of the interpolation mesh can differ from the domain of the mesh for the displacements computation. This allows for the realization of very regular interpolation meshes even in case of very complex shapes of the domain of the body to be optimized. Examples are provided showing the performance of the proposed interpolation scheme.

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“…Recently proposed morphable moving component/void (MMC/MMV) [29,30,31] methods have the ability to seamlessly integrate topology optimization in CAD modeling systems, which can overcome problem (1). For problem (2), numerous methods, including employing higher-order finite elements or refined meshes [32,33,34], mesh adaptive strategies [35,36], and high-resolution techniques [37,38] have been proposed. Note that level-set methods can inherently produce structures with smooth edges [39,40].…”

Section: Introductionmentioning

confidence: 99%

Topological Design of a Lightweight Sandwich Aircraft Spoiler

Liu

et al. 2019

Materials

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In this study, a lightweight sandwich aircraft spoiler (AS) with a high stiffness-to-weight ratio was designed. Excellent mechanical properties were achieved by the synthetic use of topology optimization (TO), lattice structure techniques, and high-performance materials, i.e., titanium alloy and aluminum alloy. TO was first utilized to optimize the traditional aircraft spoiler to search for the stiffest structure with a limited material volume, where titanium alloy and aluminum alloy were used for key joints and other parts of the AS, respectively. We then empirically replaced the fine features inside the optimized AS with 3D kagome lattices to support the shell, resulting in a lightweight sandwich AS. Numerical simulations were conducted to show that the designed sandwich AS exhibited good mechanical properties, e.g., high bending rigidity, with a reduction in weight by approximately 80% when compared with that of the initial design model. Finally, we fabricated the designed model with photosensitive resin using a 3D printing technique.

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An adaptive mesh‐adjustment strategy for continuum topology optimization to achieve manufacturable structural layout

Cited by 15 publications

References 35 publications

CARMA—Cellular Automata with Refined Mesh Adaptation—The Easy Way of Generation of Structural Topologies

CARMA—Cellular Automata with Refined Mesh Adaptation—The Easy Way of Generation of Structural Topologies

A shape function based interpolation approach for nodal design variable based structural optimization

Topological Design of a Lightweight Sandwich Aircraft Spoiler

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