基于残余变形控制的增材制造自支撑结构拓扑优化设计方法

doi:10.3901/JME.260260

摘要/Abstract

摘要： 残余变形是导致增材制造构件开裂破坏的关键因素，提出一种在设计阶段同时考虑残余变形和悬垂角度约束的增材制造自支撑结构设计方法。首先基于固有应变法预测被打印件的残余变形；建立分层稳态传热模型，研究悬垂角度对构件温度的影响，引入最大温度约束以满足悬垂角度要求；以结构柔度和残余变形加权最小化为优化目标，以构件最大温度和体积分数为约束，采用密度法进行拓扑优化设计。通过悬臂梁和L形梁的典型算例验证所提出方法的有效性。结果表明，优化后构件的最大残余变形相较于传统设计大幅减少，满足悬垂角要求，符合自支撑设计需求；当构件的打印方向和传力路径方向一致时，可以有效地减少最大残余变形并提升刚度；传热模型的分层厚度越大，越容易生成细小分支，从而促进热量向基板传递。提出的设计方法为复杂结构的增材制造提供了技术指导。

关键词: 增材制造, 残余变形, 拓扑优化, 悬垂角约束, 自支撑结构

Abstract: Residual deformation is a critical factor causing cracking and failure in additively manufactured components. This study proposes a self-supported structure design method for additive manufacturing that simultaneously considers residual deformation and overhang angle constraints during the design phase. First, the residual deformation of the printed component is predicted based on the inherent strain method. A layered steady-state heat transfer model is established to investigate the influence of overhang angle on component temperature, with maximum temperature constraints introduced to satisfy overhang angle requirements. Taking structural compliance and weighted minimization of residual deformation as optimization objectives, and using maximum temperature and volume fraction as constraints, topology optimization design is implemented through the density method. The effectiveness of the proposed method is validated through representative case studies of cantilever beams and L-shaped beams. Results demonstrate that the optimized structure exhibits significantly reduced maximum residual deformation compared to conventional designs while meeting overhang angle requirements and aligning with self-supported design principles. When the component’s printing direction coincides with the force transmission path direction, maximum residual deformation can be effectively reduced and structural stiffness enhanced. Increasing the layer thickness of the heat transfer model facilitates the generation of fine branches, thereby improving heat transfer to the substrate. The proposed design method provides technical guidance for additive manufacturing of complex structures.

Key words: additive manufacturing, residual deformation, topology optimization, overhang angle constraint, self-supported structure

中图分类号:

TH122

杨建东, 丁晓红, 熊敏, 张横. 基于残余变形控制的增材制造自支撑结构拓扑优化设计方法[J]. 机械工程学报, 2026, 62(15): 555-565.

YANG Jiandong, DING Xiaohong, XIONG Min, ZHANG Heng. Topology Optimization Design Method of Self-supported Structures in Additive Manufacturing Based on Residual Deformation Control[J]. Journal of Mechanical Engineering, 2026, 62(15): 555-565.

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链接本文: http://www.cjmenet.com.cn/CN/10.3901/JME.260260

http://www.cjmenet.com.cn/CN/Y2026/V62/I15/555

参考文献

[1] 张桥，张卫红，朱继宏. 动力响应约束下的结构拓扑优化设计[J]. 机械工程学报，2010，46(15)：45-51. ZHANG Qiao，ZHANG Weihong，ZHU Jihong. Topology optimization of structures under dynamic response constraints[J]. Journal of Mechanical Engineering，2010，46(15)：45-51.
[2] LIU J，GAYNOR A T，CHEN S，et al. Current and future trends in topology optimization for additive manufacturing[J]. Structural and Multidisciplinary Optimization，2018，57(6)：2457-2483.
[3] 朱继宏，周涵，王创. 面向增材制造的拓扑优化技术发展现状与未来[J]. 航空制造技术，2020，63(10)：24-31. ZHU Jihong，ZHOU Han，WANG Chuang. Status and future of topology optimization for additive manufacturing[J]. Aeronautical Manufacturing Technology，2020，63(10)：24-31.
[4] ZHANG X，XIAO M，GAO L，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] LIN D，GAO L，GAO J. The Lagrangian-Eulerian described particle flow topology optimization (PFTO) approach with isogeometric material point method[J]. Computer Methods in Applied Mechanics and Engineering，2025，440：117892.
[6] XIE D，LV F，YANG Y. A review on distortion and residual stress in additive manufacturing[J]. Chinese Journal of Mechanical Engineering：Additive Manufacturing Frontiers，2022，1(3)：100039.
[7] WU K，VAN KEULEN F，WU J. Residual stress-constrained space–time topology optimization for multi-axis additive manufacturing[J]. Computer Methods in Applied Mechanics and Engineering，2025，440：117913.
[8] 宗子凯，肖蜜，周冕，等. 考虑局部过热约束的自支撑结构等几何拓扑优化[J]. 机械工程学报，2024，60(11)：41-52. ZONG Zikai，XIAO Mi，ZHOU Mian，et al. Isogeometric topology optimization of self-supported structures considering local overheating constraint[J]. Journal of Mechanical Engineering，2024，60(11)：41-52.
[9] PARRY L A，ASHCROFT I A，WILDMAN R D. Geometrical effects on residual stress in selective laser melting[J]. Additive Manufacturing，2019，25：166-175.
[10] ALLAIRE G，JAKABČIN L. Taking into account thermal residual stresses in topology optimization of structures built by additive manufacturing[J]. Mathematical Models and Methods in Applied Sciences，2018，28(12)：2313-2366.
[11] BOISSIER M，ALLAIRE G，TOURNIER C. Additive manufacturing scanning paths optimization using shape optimization tools[J]. Structural and Multidisciplinary Optimization，2020，61(6)：2437-2466.
[12] MIKI T，YAMADA T. Topology optimization considering the distortion in additive manufacturing[J]. Finite Elements in Analysis and Design，2021，193：103558.
[13] ZHANG H，SHI S，DING X，et al. Topology optimization for rudder structures considering additive manufacturing and flutter effects[J]. Computation，2025，13(9)：208.
[14] KRYSKO A V，AWREJCEWICZ J，PAVLOV S P. Topological optimization of thermoelastic composites with maximized stiffness and heat transfer[J]. Composites Part B：Engineering，2019，158：319-327.
[15] CHEN Q，LIU J，LIANG X. A level-set based continuous scanning path optimization method for reducing residual stress and deformation in metal additive manufacturing[J]. Computer Methods in Applied Mechanics and Engineering，2020，360：112719.
[16] GIRALDO-LONDOÑO O，MIRABELLA L，DALLORO L，et al. Multi-material thermomechanical topology optimization with applications to additive manufacturing：design of main composite part and its support structure[J]. Computer Methods in Applied Mechanics and Engineering，2020，363：112812.
[17] FU Y，HU D，WANG Y. High-order structure-preserving algorithms for the multi-dimensional fractional nonlinear Schrödinger equation based on the SAV approach[J]. Mathematics and Computers in Simulation，2021，185：238-255.
[18] LANGELAAR M. An additive manufacturing filter for topology optimization of print-ready designs[J]. Structural and Multidisciplinary Optimization，2017，55(3)：871-883.
[19] ZHANG K，CHENG G. Three-dimensional high resolution topology optimization considering additive manufacturing constraints[J]. Additive Manufacturing，2020，35：101224.
[20] BI M，TRAN P，XIE Y M. Topology optimization of 3D continuum structures under geometric self-supporting constraint[J]. Additive Manufacturing，2020，36：101422.
[21] WHITE J D. Weld shrinkage prediction[J]. Welding and Metal Fabrication，1980，1980：587-596.
[22] SIEWERT M，NEUGEBAUER F，EPP J，et al. Validation of mechanical layer equivalent method for simulation of residual stresses in additive manufactured components[J]. Computers & Mathematics with Applications，2019，78(7)：2407-2416.
[23] SIGMUND O. A 99 line topology optimization code written in Matlab[J]. Structural and Multidisciplinary Optimization，2001，21：120-127.
[24] XU S，LIU J，MA Y. Residual stress constrained self-support topology optimization for metal additive manufacturing[J]. Computer Methods in Applied Mechanics and Engineering，2022，389：114380.
[25] MERTENS R，CLIJSTERS S，KEMPEN K，et al. Optimization of scan strategies in selective laser melting of aluminum parts with downfacing areas[J]. Journal of Manufacturing Science and Engineering，2014，136(061012).
[26] ADAM G A O，ZIMMER D. Design for additive manufacturing-element transitions and aggregated structures[J]. CIRP Journal of Manufacturing Science and Technology，2014，7(1)：20-28.
[27] RANJAN R. Controlling local overheating in topology optimization for additive manufacturing[J]. Structural and Multidisciplinary Optimization，2022，65：162.
[28] DAS M N，RANJAN R，WU K，et al. A physics-motivated geometric method for overheating prevention in topology optimization for additive manufacturing[J]. Computer Methods in Applied Mechanics and Engineering，2025，447：118363.
[29] RANJAN R，AYAS C，LANGELAAR M，et al. Fast detection of heat accumulation in powder bed fusion using computationally efficient thermal models[J]. Materials，2020，13(20)：4576.
[30] SVANBERG K. The method of moving asymptotes—a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering，1987，24(2)：359-373.