Concurrent shape and topology optimization involving design‐dependent pressure loads using implicit B‐spline curves

Zhou, Ying; Zhang, Weihong; Zhu, Jihong

doi:10.1002/nme.6022

Cited by 15 publications

(4 citation statements)

References 47 publications

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“…The main challenge of such problems is how to accurately track pressure boundary during the design process. To solve this challenge, a direct idea is to use the boundarybased topology optimization methods, such as the level set method [4][5][6][7][8][9][10]. These kinds of methods provide an implicit description of material boundaries and also enable easier extraction of their geometric information (normal direction and curvature), and thus, are particularly suitable for structural boundary/interface-related design problems.…”

Section: Introductionmentioning

confidence: 99%

A Thermal-Solid–Fluid Method for Topology Optimization of Structures with Design-Dependent Pressure Load

Huang

Liu

et al. 2022

Acta Mech. Solida Sin.

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For the topology optimization of structures with design-dependent pressure, an intuitive way is to directly describe the loading boundary of the structure, and then update the load on it. However, boundary recognition is usually cumbersome and inaccurate. Furthermore, the pressure is always loaded either outside or inside the structure, instead of both. Hence, the inner enclosed and outer open spaces should be distinguished to recognize the loading surfaces. To handle the above issues, a thermal-solid–fluid method for topology optimization with design-dependent pressure load is proposed in this paper. In this method, the specific void phase is defined to be an incompressible hydrostatic fluid, through which the pressure load can be transferred without any needs for special loading surface recognition. The nonlinear-virtual thermal method (N-VTM) is used to distinguish the enclosed and open voids by the temperature difference between the enclosed (with higher temperature) and open (with lower temperature) voids, where the solid areas are treated as the thermal insulation material, and other areas are filled with the self-heating highly thermally conductive material. The mixed displacement–pressure formulation is used to model this solid–fluid problem. The method is easily implemented in the standard density approach and its effectiveness is verified and illustrated by several typical examples at the end of the paper.

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Section: Introductionmentioning

confidence: 99%

A Thermal-Solid–Fluid Method for Topology Optimization of Structures with Design-Dependent Pressure Load

Huang

Liu

et al. 2022

Acta Mech. Solida Sin.

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“…The mechanisms to impose a minimum size in (Zhang et al, 2016b;Hoang and Jang, 2017) are effective in preventing single-node hinges often seen in compliant mechanism design using free-form methods. Another application in elastostatic structures is an MMV method for design-dependent loading (Zhou et al, 2019). Stress constraints are incorporated in the geometry projection technique of Zhang et al (2017a) and in the MMV method of Zhang et al (2018b); and stresses were minimized in the former work and in the MMC method of Takalloozadeh and Yoon (2017), which uses the topological derivative to compute the design sensitivities of the stress function.…”

Section: Applicationsmentioning

confidence: 99%

A Review on Feature-Mapping Methods for Structural Optimization

Wein¹,

Dunning²,

Norato³

2019

Preprint

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In this review we identify a new category of structural optimization methods that has emerged over the last 20 years, which we propose to call feature-mapping methods. The two defining aspects of these methods are that the design is parameterized by a high-level geometric description and that features are mapped onto a fixed grid for analysis. The main motivation for using these methods is to gain better control over the geometry to, for example, facilitate imposing direct constraints on geometric features, while avoiding issues with re-meshing. The review starts by providing some key definitions and then examines the ingredients that these methods use to map geometric features onto a fixed-grid. One of these ingredients corresponds to the mechanism for mapping the geometry of a single feature onto a fixed analysis grid, from which an ersatz material or an immersed boundary approach is used for the analysis. For the former case, which we refer to as the pseudo-density approach, a test problem is formulated to investigate aspects of the material interpolation, boundary smoothing and numerical integration. We also review other ingredients of feature-mapping techniques, including approaches for combining features (which are required to perform topology optimization) and methods for imposing a minimum separation distance among features. A literature review of feature-mapping methods is provided for shape optimization, combined feature/free-form optimization, and topology optimization. Finally, we discuss potential future research directions for feature-mapping methods.

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“…-Surface pressure loads, which have attracted significant attention from researchers. These include hydrostatic pressure loads, considered by workers such as Hammer and Olhoff (2000), Bourdin and Chambolle (2003), Allaire et al (2004), Sigmund and Clausen (2007), Lee and Martins (2012), Xia et al (2015), Picelli et al (2019), Zhou et al (2019) and many others. The pressures produced by the weight of snow or by wind loading usually require similar approaches (see, for example, Chen and Kikuchi 2001).…”

Section: Introductionmentioning

confidence: 99%

On transmissible load formulations in topology optimization

Tyas

Gilbert

et al. 2021

Struct Multidisc Optim

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Transmissible loads are external loads defined by their line of action, with actual points of load application chosen as part of the topology optimization process. Although for problems where the optimal structure is a funicular, transmissible loads can be viewed as surface loads, in other cases such loads are free to be applied to internal parts of the structure. There are two main transmissible load formulations described in the literature: a rigid bar (constrained displacement) formulation or, less commonly, a migrating load (equilibrium) formulation. Here, we employ a simple Mohr’s circle analysis to show that the rigid bar formulation will only produce correct structural forms in certain specific circumstances. Numerical examples are used to demonstrate (and explain) the incorrect topologies produced when the rigid bar formulation is applied in other situations. A new analytical solution is also presented for a uniformly loaded cantilever structure. Finally, we invoke duality principles to elucidate the source of the discrepancy between the two formulations, considering both discrete truss and continuum topology optimization formulations.

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Concurrent shape and topology optimization involving design‐dependent pressure loads using implicit B‐spline curves

Cited by 15 publications

References 47 publications

A Thermal-Solid–Fluid Method for Topology Optimization of Structures with Design-Dependent Pressure Load

A Thermal-Solid–Fluid Method for Topology Optimization of Structures with Design-Dependent Pressure Load

A Review on Feature-Mapping Methods for Structural Optimization

On transmissible load formulations in topology optimization

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