A generalized DCT compression based density method for topology optimization of 2D and 3D continua

Zhou, Pingzhang; Du, Jiuyu; Li, Zhenhua

doi:10.1016/j.cma.2018.01.051

Cited by 14 publications

(6 citation statements)

References 21 publications

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“…After this, 3D DCT can be seen, which is achieved by changing the dimension of sequence. Now, a sequence

is given in spatial domain, which needs to be processed by [ 43 ]:

…”

Section: Methodsmentioning

confidence: 99%

“…The compact form of 3D DCT can be directly derived by generalizing Equation (7) [ 43 ], taking into consideration the separability property of DCT.

…”

Section: Methodsmentioning

confidence: 99%

“…The 3D IDCT can be expressed by [ 43 ]:

where

;

and

can be calculated by substituting

, and

in place of

in Equation (6), respectively.…”

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Permeability Prediction of Nanoscale Porous Materials Using Discrete Cosine Transform-Based Artificial Neural Networks

You

Liao

et al. 2023

Materials

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The permeability of porous materials determines the fluid flow rate and aids in the prediction of their mechanical properties. This study developed a novel approach that combines the discrete cosine transform (DCT) and artificial neural networks (ANN) for permeability analysis and prediction in digital rock images, focusing on nanoscale porous materials in shale formations. The DCT effectively captured the morphology and spatial distribution of material structure at the nanoscale and enhanced the computational efficiency, which was crucial for handling the complexity and high dimensionality of the digital rock images. The ANN model, trained using the Levenberg–Marquardt algorithm, preserved essential features and demonstrated exceptional accuracy for permeability prediction from the DCT-processed rock images. Our approach offers versatility and efficiency in handling diverse rock samples, from nanoscale shale to microscale sandstone. This work contributes to the comprehension and exploitation of unconventional resources, especially those preserved in nanoscale pore structures.

show abstract

“…After this, 3D DCT can be seen, which is achieved by changing the dimension of sequence. Now, a sequence

is given in spatial domain, which needs to be processed by [ 43 ]:

…”

Section: Methodsmentioning

confidence: 99%

“…The compact form of 3D DCT can be directly derived by generalizing Equation (7) [ 43 ], taking into consideration the separability property of DCT.

…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Permeability Prediction of Nanoscale Porous Materials Using Discrete Cosine Transform-Based Artificial Neural Networks

You

Liao

et al. 2023

Materials

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show abstract

“…Recently, White et al proposed a novel method to represent the density field with a truncated Fourier representation, where the number of decision variables is reduced significantly. Du et al proposed a novel efficient topology optimization based on image compression techniques, where the number of design variables can be phenomenally reduced. In fact, geometry projection methods and Fourier representation can be classified into dimension reduction method.…”

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear topology optimization design with projection‐based ground structure method (P‐GSM)

Deng

2020

Numerical Meth Engineering

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A new topology optimization scheme called the projection-based ground structure method (P-GSM) is proposed for linear and nonlinear topology optimization designs. For linear design, compared to traditional GSM which are limited to designing slender members, the P-GSM can effectively resolve this limitation and generate functionally graded lattice structures. For additive manufacturing-oriented design, the manufacturing abilities are the key factors to constrain the feasible design space, for example, minimum length and geometry complexity. Conventional density-based method, where each element works as a variable, always results in complex geometry with large number of small intricate features, while these small features are often not manufacturable even by 3D printing and lose its geometric accuracy after postprocessing. The proposed P-GSM is an effective method for controlling geometric complexity and minimum length for optimal design, while it is capable of designing self-supporting structures naturally. In optimization progress, some bars may be disconnected from each other (floating in the air). For buckling-induced design, this issue becomes critical due to severe mesh distortion in the void space caused by disconnection between members, while P-GSM has ability to overcome this issue. To demonstrate the effectiveness of proposed method, three different design problems ranging from compliance optimization to buckling-induced mechanism design are presented and discussed in details. K E Y W O R D Sbuckling-induced design, functionally graded lattice, projection-based ground structure method, self-support design, topology optimization

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“…This technique can also be used for optimizing the topology of 3D structures with a significantly small number of design variables 9 . Also with the aiming of reducing the number of design variables, inspired by the idea of image compression, Zhou et al 10 proposed a novel approach based on discrete cosine transform and density interpolation. Considering the fact that the dominant part of computational cost is usually spent on the response analysis of a 3D topology optimization problem, many works have been devoted to saving the time involved in structural analysis.…”

Section: Introductionmentioning

confidence: 99%

A scaled boundary finite element based explicit topology optimization approach for three‐dimensional structures

Zhang

Xiao

Liu

et al. 2020

Numerical Meth Engineering

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This article proposes an efficient approach for solving three-dimensional (3D) topology optimization problem. In this approach, the number of design variables in optimization as well as the number of degrees of freedom in structural response analysis can be reduced significantly. This is accomplished through the use of scaled boundary finite element method (SBFEM) for structural analysis under the moving morphable component (MMC)-based topology optimization framework. In the proposed method, accurate response analysis in the boundary region dictates the accuracy of the entire analysis. In this regard, an adaptive refinement scheme is developed where the refined mesh is only used in the boundary region while relating coarse mesh is used away from the boundary. Numerical examples demonstrate that the computational efficiency of 3D topology optimization can be improved effectively by the proposed approach. K E Y W O R D S moving morphable component (MMC), scaled boundary finite element method (SBFEM), three-dimensional (3D) problem, topology optimization 4878

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A generalized DCT compression based density method for topology optimization of 2D and 3D continua

Cited by 14 publications

References 21 publications

Permeability Prediction of Nanoscale Porous Materials Using Discrete Cosine Transform-Based Artificial Neural Networks

Permeability Prediction of Nanoscale Porous Materials Using Discrete Cosine Transform-Based Artificial Neural Networks

Linear and nonlinear topology optimization design with projection‐based ground structure method (P‐GSM)

A scaled boundary finite element based explicit topology optimization approach for three‐dimensional structures

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