Elastic metamaterial design based on deep learning and gradient optimization

doi:10.3785/j.issn.1008-973X.2024.09.014

Journal of ZheJiang University (Engineering Science)

2024, Vol. 58

Issue (9): 1892-1901 DOI: 10.3785/j.issn.1008-973X.2024.09.014

Elastic metamaterial design based on deep learning and gradient optimization

Li XIAO1,2(

),Zhigang CAO1,3,*(

),Haoran LU1,Zhijian HUANG1,Yuanqiang CAI1

1. Coastal and Urban Geotechnical Engineering Research Center, Zhejiang University, Hangzhou 310058, China
2. Center for Balance Architecture, Zhejiang University, Hangzhou 310028, China
3. The Architectural Design and Research Institute of Zhejiang University Co. Ltd, Hangzhou 310028, China

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Abstract

A novel design method based on deep learning and gradient optimization was proposed to establish a flexible and general framework for fast iterative design of elastic metamaterials and achieve simultaneous optimization of topology structure and material considering material discretization. The design network composed of variational autoencoders and band gap neural network was developed as the framework, and auto-differentiation techniques and gradient optimization algorithms were employed to iteratively tune the design variables with the gradient information. Furthermore, a co-optimization strategy was further proposed to consider the material discretization, so that the structure was optimized while the optimal material was selected from the material depot. Band gap width maximization under constraints and on-demand design were carried out respectively, and the effects of simultaneous optimization and topological configuration were explored. Results showed that the simultaneous optimization provided superior performance compared to separate optimization of materials and topology structures. Additionally, the multilayer configuration can achieve basic units with smaller sizes under the same objectives and material composition. Furthermore, the numerical simulation results of frequency and time domain analyses showed that the designed elastic metamaterials exhibited significant vibration damping performance in the target band gap range.

Key words： elastic metamaterial band gap deep learning gradient optimization material selection

Received: 05 August 2023 Published: 30 August 2024

CLC:	TB 34
	O 327

Fund: 国家自然科学基金资助项目（51978611）；浙江省杰出青年科学基金资助项目（LR21E080004）.

Corresponding Authors: Zhigang CAO E-mail: xiaoli1104@zju.edu.cn;caozhigang2011@zju.edu.cn

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Cite this article:

Li XIAO,Zhigang CAO,Haoran LU,Zhijian HUANG,Yuanqiang CAI. Elastic metamaterial design based on deep learning and gradient optimization. Journal of ZheJiang University (Engineering Science), 2024, 58(9): 1892-1901.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.09.014 OR https://www.zjujournals.com/eng/Y2024/V58/I9/1892

基于深度学习和梯度优化的弹性超材料设计

为了建立灵活通用的弹性超材料快速迭代设计框架，并实现考虑材料离散性的拓扑结构和材料参数同步优化，提出基于深度学习和梯度优化的设计方法. 以变分自动编码器和带隙神经网络组成的设计网络作为框架，采用自动微分技术和梯度优化算法，利用梯度信息迭代调整设计变量；提出协同优化策略以考虑材料离散性，使结构优化的同时在材料库中选择最佳材料. 基于所提方法分别进行约束条件下带隙宽度最大化和指定带隙区间设计，并探讨同步优化和拓扑构型的影响. 结果表明，与材料和拓扑结构的单独优化相比，同步优化具有更优越的性能；在相同带隙目标和材料组成下，多层构型可以设计出更小尺寸的元胞. 频域和时域分析的数值模拟结果表明，所设计的超材料结构在目标带隙范围内表现出明显的减振性能.

关键词： 弹性超材料, 带隙, 深度学习, 梯度优化, 材料选择

Fig.1 Schematic structure of one-dimensional elastic metamaterial

Tab.1 Several material parameters in material depot

Fig.2 Schematic diagram of variational autoencoders

Fig.3 Training convergence plots of generators

Fig.4 Schematic diagram of band gap neural network

Tab.2 Range of soil layer parameters

Fig.5 Comparison plot between predicted and actual band gap widths

Fig.6 Forward computation and back propagation process

Fig.7 Flow chart of co-optimization strategy

Tab.3 Design results for maximizing band gap width under constraints and comparison with genetic algorithm design

Fig.8 Convergence diagram and optimal material selection for Case 3

Fig.9 Results of on-demand band gap design under different site conditions

Tab.4 Site soil parameters (condition variables)

Fig.10 Results of 2D finite element analysis of metamaterial-soil systems


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