蒙皮-多材料内填充结构拓扑优化设计

doi:10.3901/JME.260384

机械工程学报 ›› 2026, Vol. 62 ›› Issue (7): 375-384.doi: 10.3901/JME.260384

• 数字化设计与制造 • 上一篇

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蒙皮-多材料内填充结构拓扑优化设计

张横¹, 胡天男², 丁晓红¹, 罗云锋³, 李海东⁴, 倪维宇¹

1. 上海理工大学机械工程学院上海 200093;
2. 京都大学大学院工学研究科京都 6158540 日本;
3. 山东大学机械工程学院济南 250061;
4. 上海机电工程研究所上海 201109

收稿日期:2025-06-04 修回日期:2025-12-10 发布日期:2026-05-25
作者简介:张横，男，1988年出生，副教授。主要研究方向为多尺度拓扑优化，高性能计算。E-mail:zhanghengsh@usst.edu.cn
胡天男(通信作者)，男，1996年出生，博士研究生。主要研究方向为多物理场拓扑优化，高性能计算。E-mail:htn0571@163.com
基金资助:
国家自然科学基金(52375257)和上海市白玉兰人才计划浦江(24PJD073)资助项目。

Topology Optimization for Designing Shell-multi-material Infill Structures

ZHANG Heng¹, HU Tiannan², DING Xiaohong¹, LUO Yunfeng³, LI Haidong⁴, NI Weiyu¹

1. School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093;
2. Department of Mechanical Engineering and Science, Kyoto University, Kyoto, 6158540 Japan;
3. School of Mechanical Engineering, Shandong University, Jinan 250061;
4. Shanghai Electro-Mechanical Engineering Institute, Shanghai 201109

Received:2025-06-04 Revised:2025-12-10 Published:2026-05-25

摘要/Abstract

摘要： 针对多材料内填充结构设计问题，基于有序SIMP方法提出了一种蒙皮-多材料内填充结构拓扑优化设计框架。首先，通过两个引入特殊的Heaviside投影函数实现空/实体材料域的识别，在此基础上通过两步滤波和投影，有效实现外部蒙皮和内部填充域的分离。然后，在有序SIMP框架下，通过将内填充域与分段Heaviside投影得到的多材料分布场相乘，得到多材料内填充域的材料分布。利用基于PDE过滤和标准Heaviside投影，可以有效实现外部蒙皮厚度的定量设计。所提设计方法都是基于常用的过滤和投影手段，算法实现较为容易，鲁棒性较好。同时，所提设计方法，继承了有序SIMP方法的优点，具有很高的计算效率和稳定的迭代性能。最后，通过考虑不同蒙皮厚度和不同设计参数的设计算例，验证了方法的有效性。优化结果表明，所提设计方法可有效实现蒙皮-多材料内填充结构的设计，同时设计结果也表明在蒙皮-多材料内填充结构相较于单材料内填充结构具有很大优势。

关键词: 拓扑优化, 蒙皮-多材料内填充, 多材料设计, 有序SIMP模型

Abstract: A novel topology optimization method for the design of coated structures infilled with multiple materials is proposed, where a new material interpolation model for the topology description is developed based on the ordered SIMP scheme. With the introduction of two special Heaviside projections into the two-step filtering and projection procedure, the external coating and the substrate region can be well identified by using several modified density fields. Then, the material distribution of the multi-material infilling is obtained by multiplying the infill identification field with the piece-wisely projected design variables and optimized via the mathematical programming algorithm under the ordered SIMP framework. Using an eroded density field and its original field, the uniform thickness of the external coating can be well controlled. The proposed approach for optimizing coated structures with multi-phase infill materials is easy to implement due to its implementation relying on those frequently-used filtering and projection operations. Besides, without introducing any additional design variables, the method developed in this paper inherits the advantages of the ordered SIMP method and has great calculation efficiency and stable iteration performance. With the consideration of several issues such as different coating thicknesses and different design parameters, several 2D numerical examples are studied to demonstrate the effectiveness of the proposed approach, as well as a 3D example. The optimization results illustrate that the method developed in this paper is effective for the design of coated structures infilled with multiple materials and the advantages of considering multiple infill materials are also validated.

Key words: topology optimization, shell-multi-material infill structures, multi-material design, ordered SIMP method

中图分类号:

TH122

张横, 胡天男, 丁晓红, 罗云锋, 李海东, 倪维宇. 蒙皮-多材料内填充结构拓扑优化设计[J]. 机械工程学报, 2026, 62(7): 375-384.

ZHANG Heng, HU Tiannan, DING Xiaohong, LUO Yunfeng, LI Haidong, NI Weiyu. Topology Optimization for Designing Shell-multi-material Infill Structures[J]. Journal of Mechanical Engineering, 2026, 62(7): 375-384.

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蒙皮-多材料内填充结构拓扑优化设计

Topology Optimization for Designing Shell-multi-material Infill Structures

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