Reaction-diffusion equation based topology optimization combined with the modified conjugate gradient method

Seong, Hong Kyoung; Shin, Hyun Soo; Yoo, Jeonghoon; Yamada, Takayuki; Nishiwaki, Shinji

doi:10.1016/j.finel.2017.11.009

Cited by 11 publications

(4 citation statements)

References 36 publications

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“…Therefore, it is meaningful to adapt the side length d of finite elements to the interface parameter L c . Similar observations are reported in the work of Seong et al In this example, we find that

d < \frac{L_{c}}{2}

should be ensured to obtain the topology with 6 voids. Then, the optimized topology is not sensitive concering the choice of K 0 here.…”

Section: Preceding Numerical Testssupporting

confidence: 92%

A phase field model for stress‐based evolution of load‐bearing structures

Muench

Gierden

Wagner

2018

Numerical Meth Engineering

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Summary We present a continuum‐type optimality algorithm for the evolution of load‐bearing solid structures with linear elastic material. The objective of our model is to generate structures with help of a sensitivity function accounting for equivalent stress. Similar to Evolutionary Structural Optimization, a threshold of equivalent stress is evaluated. However, we do not consider a material rejection ratio. The evolution process is governed by an Allen‐Cahn equation in the context of phase field modeling. The steady state of phase transition is the final geometry of the structure. The model accounts for the desired filling level, geometry of the design space, static loadings, and boundary conditions. Our variational approach drops conservation of mass and couples density as well as stiffness of the continuum by a sophisticated function to the phase field variable. Continuous regions of voids and material evolve from the initial state of homogeneously distributed material. The complexity of evolving structures depends on two numerical parameters, which we discuss in several examples.

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d < \frac{L_{c}}{2}

should be ensured to obtain the topology with 6 voids. Then, the optimized topology is not sensitive concering the choice of K 0 here.…”

Section: Preceding Numerical Testssupporting

confidence: 92%

A phase field model for stress‐based evolution of load‐bearing structures

Muench

Gierden

Wagner

2018

Numerical Meth Engineering

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“…On the contrary, the RD equation can solve the Laplacian and the steepest descent method simultaneously because it implies both concepts in a single partial differential equation. 11,14 It can also reduce computing load by performing two roles in a single step.…”

Section: Design Variable Update Based On the Rd Equationmentioning

confidence: 99%

“…12,13 The generation of the grayscale area has been reduced by using the conjugate gradient method as the design variable update scheme. 14 The RD equation-based topology optimization proves its effectiveness through several studies to various physics problems, such as compliant mechanism design, structural vibration, electromagnetics, heat, magnetics, and so on. [15][16][17][18][19] Studies on topology optimization, generally composed of a single material, have been expanded to derive structures composed of multimaterials.…”

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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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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“…Based on resilient propagation, Andersson et al 31 used a modified gradient descent search, which has less sensitivity to local optimal and faster convergence than traditional gradient descent. In order to overcome the problem of slow convergence of the reaction–diffusion equation near the optimal value of the steepest descent method, Seong et al 32 proposed a modified conjugate gradient method. Fang et al 33 presented a novel global and local fuzzy image fitting model for image segmentation and developed a direct method to update the level set function.…”

Section: Introductionmentioning

confidence: 99%

A sweeping optimization algorithm for the global cosine fitting energy image segmentation model

Zou

Chen

et al. 2021

Concurrency and Computation

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Image segmentation plays a pivotal role in image processing. Level set model is a traditional variation image segmentation method. In order to achieve level set evolution equation, the level set energy functionals are minimized with the gradient descent methods and then the partial differential equation (PDE) was solved by finite difference scheme. Slow speed is one of its disadvantages. We propose a sweep optimization algorithm based on global cosine fitting (GCF) energy. Instead of calculating the PDE and the curvature, the proposed sweeping algorithm directly calculates the energy change when a pixel moves from one side of evolving contour to the other. It checks whether the GCF energy is decreased or not. The proposed algorithm has many advantages. For example, independent of initial level set contour positions and parameters, need not consider the Courant Friedrichs Lew condition and the regularization energy term. The proposed algorithm can be easily extended to high dimension image segmentation. The experiments on synthetic images, noise images and real images demonstrate the effectiveness of the proposed sweeping optimization algorithm.

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Reaction-diffusion equation based topology optimization combined with the modified conjugate gradient method

Cited by 11 publications

References 36 publications

A phase field model for stress‐based evolution of load‐bearing structures

A phase field model for stress‐based evolution of load‐bearing structures

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

A sweeping optimization algorithm for the global cosine fitting energy image segmentation model

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