Multi-material proportional topology optimization based on the modified interpolation scheme

Cui, Mingtao; Zhang, Yifei; Yang, Xi; Luo, Chenchun

doi:10.1007/s00366-017-0540-z

Cited by 33 publications

(15 citation statements)

References 35 publications

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“…The interpolation function of the multivariable approach varies depending on the number of employed materials. [19][20][21][22][23][24][25] (18) and (19), respectively, to match the material properties in the PSM application shown in Figures 7A and 7B. Such formulations require that several design variables should be equally 1 to represent a specific material property, eg, 1 ∼ 4 = 1 for E 1 in Equation (19).…”

Section: Comparison With Multivariable-based Design Resultsmentioning

confidence: 99%

“…Those studies introduce "m − 1" variables to demonstrate "m" materials (or phases) including voids. [20][21][22][23][24] An alternating active-phase algorithm is proposed to convert binary topology optimization into multiphase easily; however, it requires subproblem iterations. 25 The multivariable issue has been also applied to the level-set design method by introducing multiple level-set functions to define the phase combination of several materials.…”

Section: Introductionmentioning

confidence: 99%

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Multiphase topology optimization with a single variable using the phase‐field design method

Seong¹,

Kim²,

Yoo³

et al. 2019

Numerical Meth Engineering

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In this study, a multimaterial topology optimization method using a single variable is proposed by combining the solid isotropic material with penalization method and the reaction-diffusion equation. Unlike ordinary multimaterial optimization, which requires several variables depending on the number of material types, this method intends to represent various materials as one variable. The proposed method combines two special functions in the sensitivity analysis of the objective function to converge the design variable into prespecified density values defined for each of the multimaterials. The composition constraint based on a normal distribution function is also introduced to estimate the distribution of each target density value in a single variable. It enables density exchange between multiple materials by increasing or decreasing the amount of a specific material. The proposed method is applied to structural and electromagnetic problems to verify its effectiveness, and its usefulness is also confirmed from the viewpoint of cost and computation time. KEYWORDScomposition constraint, multimaterial design, reaction-diffusion equation, solid isotropic material with penalization method, topology optimization 334

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Section: Comparison With Multivariable-based Design Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiphase topology optimization with a single variable using the phase‐field design method

Seong¹,

Kim²,

Yoo³

et al. 2019

Numerical Meth Engineering

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show abstract

“…The main point of the method is that material is distributed proportionally to the compliance value calculated at each finite element. PTO was then further developed for multi-material optimization by Cui et al [23]. However, both [22] and [23] are limited to 2D elastic problems.…”

Section: Introductionmentioning

confidence: 99%

“…PTO was then further developed for multi-material optimization by Cui et al [23]. However, both [22] and [23] are limited to 2D elastic problems. 3D topology optimization based on sensitivity analysis has been introduced by Liu and Tovar [24] using SIMP.…”

Section: Introductionmentioning

confidence: 99%

A Non-Gradient Approach for Three Dimensional Topology Optimization

Nguyen

Tran

2021

JST

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The present work is devoted to the extension of the non-gradient approach, namely Proportional Topology Optimization (PTO), for compliance minimization of three-dimensional (3D) structures. Two schemes of material interpolation within the framework of the solid isotropic material with penalization (SIMP), i.e. the power function and the logistic function are analyzed. Through a comparative study, the efficiency of the logistic-type interpolation scheme is highlighted. Since no sensitivity is involved in the approach, a density filter is applied instead of sensitivity filter to avoid checkerboard issue

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“…It is found that the PTO method is an efficient algorithm to acquire the final results under topology optimization and more facile to implement the algorithm than the OC method. The PTO also applied to the robust topology optimization [21] and multimaterial optimization [22] under the SIMP approach. Most of the studies on the PTO have been applied this algorithm to optimize the structure under the material nonlinearity only.…”

Section: Introductionmentioning

confidence: 99%

Optimization on mechanical structure for material nonlinearity based on proportional topology method

Kongwat

Hasegawa

2019

JASSE

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Topology optimization is one complex method due to a final layout obtained by an initial shape is not a consideration. This paper purposes a proportional technique to determine an optimal layout by employing the topology optimization method. The objective function is to maximize an internal energy density by stress constraint based on the bi-linear elastoplasticity material properties. Fully stress design criterion is concerned to be a factor of the proportional technique for updating the design variable. Finally, the optimal layout acquires from the proportional technique and results are faster to converge with an over-relaxation factor which applied to the fully stress design.

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Multi-material proportional topology optimization based on the modified interpolation scheme

Cited by 33 publications

References 35 publications

Multiphase topology optimization with a single variable using the phase‐field design method

Multiphase topology optimization with a single variable using the phase‐field design method

A Non-Gradient Approach for Three Dimensional Topology Optimization

Optimization on mechanical structure for material nonlinearity based on proportional topology method

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