Topology Optimization for Designing Shell-multi-material Infill Structures

doi:10.3901/JME.260384

Abstract

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

CLC Number:

TH122

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.

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://www.cjmenet.com.cn/EN/10.3901/JME.260384

http://www.cjmenet.com.cn/EN/Y2026/V62/I7/375

References

[1] CLAUSEN A,AAGE N,SIGMUND O. Exploiting additive manufacturing infill in topology optimization for improved buckling load[J]. Engineering,2016,2(2):250-257.
[2] THOMSEN C,WANG Fengwen,SIGMUND O. Buckling strength topology optimization of 2D periodic materials based on linearized bifurcation analysis[J]. Computer Methods in Applied Mechanics and Engineering,2018,339:115-136.
[3] GU Dongdong,SHI Xinyu,POPRAWE R,et al. Material-structure-performance integrated laser-metal additive manufacturing[J]. Science,2021,372(6545):eabg1487.
[4] ZHANG Xiao,XIAO Mi,GAO Liang,et al. A T-splines-oriented isogeometric topology optimization for plate and shell structures with arbitrary geometries using Bézier extraction[J]. Computer Methods in Applied Mechanics and Engineering,2024,425:116929.
[5] WU Jiawei,ZHU Jiayi,GAO Jie,et al. A CAD-oriented parallel-computing design framework for shape and topology optimization of arbitrary structures using parametric level set[J]. Computer Methods in Applied Mechanics and Engineering,2024,431:117292.
[6] CLAUSEN A,AAGE N,SIGMUND O. Topology optimization of coated structures and material interface problems[J]. Computer Methods in Applied Mechanics and Engineering,2015,290:524-541.
[7] WU Jun,CLAUSEN A,SIGMUND O. Minimum compliance topology optimization of shell-infill composites for additive manufacturing[J]. Computer Methods in Applied Mechanics and Engineering,2017,326:358-375.
[8] GROEN J,WU Jun,SIGMUND O. Homogenization-based stiffness optimization and projection of 2d coated structures with orthotropic infill[J]. Computer Methods in Applied Mechanics and Engineering,2019,349:722-742.
[9] ZHOU Mingdong,LU Yufan,LIU Yichang,et al. Concurrent topology optimization of shells with self-supporting infills for additive manufacturing[J]. Computer Methods in Applied Mechanics and Engineering,2022,390:114430.
[10] LIU Yichang,ZHOU Mingdong,WEI Chuang,et al. Topology optimization of self-supporting infill structures[J]. Structural and Multidisciplinary Optimization,2021,63:2289-2304.
[11] 白影春,景文秀. 基于滤波/映射边界描述的壳-填充结构多尺度拓扑优化方法[J]. 机械工程学报,2021,57(4):121-129. BAI Yingchun,JING Wenxiu. Multiscale topology optimization method for shell-infill structures based on filtering/projection boundary description[J]. Journal of Mechanical Engineering,2021,57(4):121-129.
[12] 白影春,刘康,李超,等. 基于大规模并行计算的三维薄壁填充结构特征频率拓扑优化设计[J]. 机械工程学报,2024,60(11):32-40. BAI Yingchun,LIU Kang,LI Chao,et al. Eigenfrequency topology optimization of 3D shell-infill structures based on large-scale parallel computing[J]. Journal of Mechanical Engineering,2024,60(11):32-40.
[13] LUO Yunfeng,LI Quhao,LIU Shutian. Topology optimization of shell-infill structures using an erosion-based interface identification method[J]. Computer Methods in Applied Mechanics and Engineering,2019,355:94-112.
[14] WANG Yaguang,KANG Zhan. A level set method for shape and topology optimization of coated structures[J]. Computer Methods in Applied Mechanics and Engineering,2018,329:553-574.
[15] FU Junjian,LI Hao,XIAO Mi,et al. Topology optimization of shell-infill structures using a distance regularized parametric level-set method[J]. Structural and Multidisciplinary Optimization,2019,59:249-262.
[16] FU Junjian,LI Hao,GAO Liang,et al. Design of shell-infill structures by a multiscale level set topology optimization method[J]. Computers & Structures,2019,212:162-172.
[17] 张横,李昊,丁晓红,等. 基于贴体网格的高分辨率三维结构拓扑优化研究[J]. 机械工程学报,2022,58(5): 136-143. ZHANG Heng,LI Hao,DING Xiaohong,et al. Numerical study on the body-fitted topology optimization for three-dimensional high resolution structure design[J]. Journal of Mechanical Engineering,2022,58(5):136-143.
[18] WANG Yu,WANG Xiaoming. “Color” level sets:A multi-phase method for structural topology optimization with multiple materials[J]. Computer Methods in Applied Mechanics and Engineering,2004,193(6-8):469-496.
[19] WANG Yu,CHEN Shikui,WANG Xiaoming,et al. Design of multimaterial compliant mechanisms using level-set methods[J]. Journal of Mechanical Design,2005,127(5):941-956.
[20] WANG Yiqiang,LUO Zhen,KANG Zhan,et al. A multi-material level set-based topology and shape optimization method[J]. Computer Methods in Applied Mechanics and Engineering,2015,283:1570-1586.
[21] SIGMUND O,TORQUATO S. Design of materials with extreme thermal expansion using a three-phase topology optimization method[J]. Journal of the Mechanics and Physics of Solids,1997,45(6):1037-1067.
[22] YIN L,ANANTHASURESH GK. Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme[J]. Structural and Multidisciplinary Optimization,2001,23:49-62.
[23] GAO Tong,ZHANG Weihong. A mass constraint formulation for structural topology optimization with multiphase materials[J]. International Journal for Numerical Methods in Engineering,2011,88(8):774-796.
[24] WU Chi,FANG Jianguang,LI Qing. Multi-material topology optimization for thermal buckling criteria[J]. Computer Methods in Applied Mechanics and Engineering,2019,346:1136-1155.
[25] ZUO Wenjie,KAZUHIRO S. Multi-material topology optimization using ordered simp interpolation[J]. Structural and Multidisciplinary Optimization,2017,55:477-491.
[26] XU Shuzhi,LIU Jikai,ZOU Bin,et al. Stress constrained multi-material topology optimization with the ordered simp method[J]. Computer Methods in Applied Mechanics and Engineering,2021,373:113453.
[27] ZHANG Yan,XIAO Mi,LI Hao,et al. Multiscale concurrent topology optimization for cellular structures with multiple microstructures based on ordered simp interpolation[J]. Computational Materials Science,2018,155:74-91.
[28] BAI Jiantao,ZUO Wenjie. Multi-material topology optimization of coated structures using level set method[J]. Composite Structures,2022,300:116074.
[29] LAZAROV B,SIGMUND O. Filters in topology optimization based on Helmholtz-type differential equations[J]. International Journal for Numerical Methods in Engineering,2011,86(6):765-781.