High-Resolution Topology Optimization with Stress and Natural Frequency Constraints

Leader, Mark K.; Chin, Ting Wei; Kennedy, Graeme J.

doi:10.2514/1.j057777

Cited by 34 publications

(16 citation statements)

References 59 publications

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“…Nguyen-Xuan (2017) used a hierarchical data structure called polytree to selectively refine boundary elements, which improved the quality of the boundary. Leader et al (2019) and Chin et al (2019) interpolated the node design variables under coarse mesh to obtain a refined displacement mesh, which solved the multi-material and frequency response optimization problems in large-scale designs. In these methods, the resolution of the finite element mesh (displacement mesh) is not less than the design variable mesh, which means that FEA takes lot of time in the optimization.…”

Section: Method Moving Morphablementioning

confidence: 99%

An Efficient and High-Resolution Topology Optimization Method Based on Convolutional Neural Networks

Liu¹,

Liu²,

Wen³

et al. 2019

Preprint

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Topology optimization is a pioneering design method that can provide various candidates with high mechanical properties. However, the high-resolution for the optimum structures is highly desired, normally in turn leading to computationally intractable puzzle, especially for the famous Solid Isotropic Material with Penalization (SIMP) method. In this paper, we introduce the Super-Resolution Convolutional Neural Network (SRCNN) technique into topology optimization framework to improve the resolution of topology solutions with extremely high computational efficiency. Additionally, a pooling strategy is established to balance the number of finite element analysis (FEA) and the output mesh in optimization process. Considering the high training cost of 3D neural networks, several 2D neural networks are combined to deal with 3D topology optimization design problems. The combined treatment method used in 3D topology optimization design eliminates the expense of retraining 3D convolutional neural network and guarantees the quality of 3D design. Some typical examples justify that the high-resolution topology optimization method adopting SRCNN has excellent applicability and high efficiency.

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Section: Method Moving Morphablementioning

confidence: 99%

An Efficient and High-Resolution Topology Optimization Method Based on Convolutional Neural Networks

Liu¹,

Liu²,

Wen³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…(i) Nguyen-Xuan [36] used a hierarchical data structure called a polytree to refine boundary elements selectively; the structure improves the quality of the boundary. Leader et al [37] and Chin et al [38] interpolated the node design variables under a coarse mesh to obtain a refined displacement mesh that can solve multi-material and frequency response optimization problems in large-scale designs. In these methods, the resolution of the finite element mesh (displacement mesh) is not lower than that of the design variable mesh, which means that finite element analysis (FEA) devotes a large amount of time to optimization.…”

Section: Introductionmentioning

confidence: 99%

Efficient, high-resolution topology optimization method based on convolutional neural networks

Liu

Wen

et al. 2021

Front. Mech. Eng.

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Topology optimization is a pioneer design method that can provide various candidates with high mechanical properties. However, high resolution is desired for optimum structures, but it normally leads to a computationally intractable puzzle, especially for the solid isotropic material with penalization (SIMP) method. In this study, an efficient, high-resolution topology optimization method is developed based on the superresolution convolutional neural network (SRCNN) technique in the framework of SIMP. SRCNN involves four processes, namely, refinement, path extraction and representation, nonlinear mapping, and image reconstruction. High computational efficiency is achieved with a pooling strategy that can balance the number of finite element analyses and the output mesh in the optimization process. A combined treatment method that uses 2D SRCNN is built as another speed-up strategy to reduce the high computational cost and memory requirements for 3D topology optimization problems. Typical examples show that the high-resolution topology optimization method using SRCNN demonstrates excellent applicability and high efficiency when used for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.

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“…[29][30][31][32][33] Although several techniques were developed to handle this issue, there are few papers addressing large-scale three-dimensional stress-constrained topology optimization. To the authors' knowledge, the largest problem solved so far in the literature has been addressed by Leader et al, 34 with 14 million elements.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional manufacturing tolerant topology optimization with hundreds of millions of local stress constraints

Silva

Aage

Beck

et al. 2020

Numerical Meth Engineering

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In topology optimization, the treatment of stress constraints for very large scale problems (more than 100 million elements and more than 600 million stress constraints) has so far not been tractable due to the failure of robust agglomeration methods, that is, their inability to accurately handle the locality of the stress constraints. This article presents a three-dimensional design methodology that alleviates this shortcoming using both deterministic and robust problem formulations. The robust formulation, based on the three-field density projection approach, is extended and proved necessary to handle manufacturing uncertainty in three-dimensional stress-constrained problems. Several numerical examples are solved and further postprocessed with body-fitted meshes using commercial software. The numerical investigations demonstrate that: (1) the employed solution approach based on the augmented Lagrangian method is able to handle very large problems, with hundreds of millions of stress constraints; (2) three-dimensional stress-based results are extremely sensitive to slight manufacturing variations; (3) if appropriate interpolation parameters are adopted, voxel-based (fixed grid) models can be used to compute von Mises stresses with excellent accuracy; and (4) in order to ensure manufacturing tolerance in three-dimensional stress-constrained topology optimization, a combination of double filtering and more than three density field realizations may be required.

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High-Resolution Topology Optimization with Stress and Natural Frequency Constraints

Cited by 34 publications

References 59 publications

An Efficient and High-Resolution Topology Optimization Method Based on Convolutional Neural Networks

An Efficient and High-Resolution Topology Optimization Method Based on Convolutional Neural Networks

Efficient, high-resolution topology optimization method based on convolutional neural networks

Three‐dimensional manufacturing tolerant topology optimization with hundreds of millions of local stress constraints

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