Topology optimization of 2-D mechanical metamaterials using a parametric level set method combined with a meshfree algorithm

2019 ◽  
Vol 229 ◽  
pp. 111318 ◽  
Author(s):  
L. Ai ◽  
X.-L. Gao
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Mechanical Metamaterials ◽  
Parametric Level Set Method

Parametric Shape and Topology Optimization: A New Level Set Approach Based on Cardinal Kernel Functions

2017 ◽  
Author(s):  
Long Jiang ◽  
Shikui Chen ◽  
Xiangmin Jiao
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Material Property ◽  
Kernel Function ◽  
Level Set Methods ◽  
Level Set Function ◽  
Set Function ◽  
Distance Regularization ◽  
Parametric Level Set Method

The parametric level set method is an extension of the conventional level set methods for topology optimization. By parameterizing the level set function, conventional levels let methods can be easily coupled with mathematical programming to achieve better numerical robustness and computational efficiency. Furthermore, the parametric level set scheme not only can inherit the original advantages of the conventional level set methods, such as clear boundary representation and high topological changes handling flexibility but also can alleviate some un-preferred features from the conventional level set methods, such as needing re-initialization. However, in the RBF-based parametric level set method, it was difficult to determine the range of the design variables. Moreover, with the mathematically driven optimization process, the level set function often results in significant fluctuations during the optimization process. This brings difficulties in both numerical stability control and material property interpolation. In this paper, an RBF partition of unity collocation method is implemented to create a new type of kernel function termed as the Cardinal Basis Function (CBF), which employed as the kernel function to parameterize the level set function. The advantage of using the CBF is that the range of the design variable, which was the weight factor in conventional RBF, can be explicitly specified. Additionally, a distance regularization energy functional is introduced to maintain a desired distance regularized level set function evolution. With this desired distance regularization feature, the level set evolution is stabilized against significant fluctuations. Besides, the material property interpolation from the level set function to the finite element model can be more accurate.

A Parametric Level Set Method for Topology Optimization based on Deep Neural Network (DNN)

2021 ◽  
pp. 1-14
Author(s):  
Hao Deng ◽  
Albert C. To
Keyword(s):  
Neural Network ◽  
Topology Optimization ◽  
Differential Equations ◽  
Level Set Method ◽  
Level Set ◽  
Deep Neural Network ◽  
Implicit Function ◽  
Zero Level ◽  
Fully Connected ◽  
Parametric Level Set Method

Abstract This paper proposes a new parametric level set method for topology optimization based on Deep Neural Network (DNN). In this method, the fully connected deep neural network is incorporated into the conventional level set methods to construct an effective approach for structural topology optimization. The implicit function of level set is described by fully connected deep neural networks. A DNN-based level set optimization method is proposed, where the Hamilton-Jacobi partial differential equations (PDEs) are transformed into parametrized ordinary differential equations (ODEs). The zero-level set of implicit function is updated through updating the weights and biases of networks. The parametrized reinitialization is applied periodically to prevent the implicit function from being too steep or too flat in the vicinity of its zero-level set. The proposed method is implemented in the framework of minimum compliance, which is a well-known benchmark for topology optimization. In practice, designers desire to have multiple design options, where they can choose a better conceptual design base on their design experience. One of the major advantages of DNN-based level set method is capable to generate diverse and competitive designs with different network architectures. Several numerical examples are presented to verify the effectiveness of proposed DNN-based level set method.

scholarly journals A Form Finding Method for Arch Bridges Using Parametric Level Set Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yadong Shen ◽  
Jianhu Feng ◽  
Xiaohan Cheng ◽  
Xuntao Wang ◽  
Changhao Zhang
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Optimization Technique ◽  
Design Stage ◽  
Force Transmission ◽  
Form Finding ◽  
Preliminary Design Stage ◽  
Arch Bridges ◽  
Parametric Level Set Method

Topology optimization has developed rapidly in the past three decades; as a creative and efficient optimization technique, it has been applied in engineering fields of aerospace and mechanical. However, there are a few attempts in bridge form design. In this paper, the parametric level set method is utilized to solve the form finding of arch bridges. The optimization model for minimizing the structural compliance under the volume constraint is built. Three numerical examples of form finding of arch bridges are studied. Results show that the optimal structures which have well-distributed stress and smooth force transmission are almost identical with the actual forms of arch bridges. The optimal forms can be treated as alternatives in the preliminary design stage, and topology optimization has a bright prospect in form finding of arch bridges.

Topology optimization of shell-infill structures using a distance regularized parametric level-set method

2018 ◽  
Vol 59 (1) ◽  
pp. 249-262 ◽  
Author(s):  
Junjian Fu ◽  
Hao Li ◽  
Mi Xiao ◽  
Liang Gao ◽  
Sheng Chu
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Parametric Level Set Method

Topology optimization for heat conduction by combining level set method and BESO method

2018 ◽  
Vol 127 ◽  
pp. 200-209 ◽  
Author(s):  
Qi Xia ◽  
Tielin Shi ◽  
Liang Xia
Keyword(s):  
Topology Optimization ◽  
Heat Conduction ◽  
Level Set Method ◽  
Level Set ◽  
Beso Method

Topology optimization of hyperelastic structures using a level set method

2017 ◽  
Vol 351 ◽  
pp. 437-454 ◽  
Author(s):  
Feifei Chen ◽  
Yiqiang Wang ◽  
Michael Yu Wang ◽  
Y.F. Zhang
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set
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