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Journal of Graphics ›› 2023, Vol. 44 ›› Issue (5): 1013-1020.DOI: 10.11996/JG.j.2095-302X.2023051013

• Digital Design and Manufacture • Previous Articles     Next Articles

A lattice-solid hybrid structure topology optimization method for support-free additive manufacturing

YUN Feng1,2(), WANG You-zhi1,2, SONG Jiao1,2, GENG Lei1,2, ZHANG Cheng-hu3, LIU Ji-kai3()   

  1. 1. State Key Laboratory of Engine Reliability, Weifang Shandong 261071, China
    2. Weichai Power Co., Ltd., Weifang Shandong 261071, China
    3. School of Mechanical Engineering, Shandong University, Jinan Shandong 250013, China
  • Received:2023-05-10 Accepted:2023-08-01 Online:2023-10-31 Published:2023-10-31
  • Contact: LIU Ji-kai (1987-), professor, Ph.D. His main research interests cover topology optimization, computer aided design and additive manufacturing, etc. E-mail:jikai_liu@sdu.edu.cn
  • About author:YUN Feng (1988-), senior engineer, master. His main research interests cover structural topology optimization and generative design. E-mail:yunf@weichai.com
  • Supported by:
    State Key Laboratory of Engine Reliability(skler-202001);Natural Science Foundation of Shandong Province(ZR2020QE165)


In light of the development of advanced design methods and additive manufacturing technologies, the design and manufacturing of multi-scale structures have been extensively investigated. Extensive research has been conducted on multi-scale structural optimization with both variable density lattices and topologically freeform micro structures. Their additively manufactured counterparts have undergone testing, showcasing excellent mechanical properties, as reported in a vast number of publications. Recently, by introducing solid phase into the design, it is found that the resulted mechanical performance of the multi-scale structures can be further enhanced. The lattice-solid hybrid multi-scale structures possess lightweight, high-performance, and multifunctional characteristics, demonstrating great potentials in applications and scientific research. Hence, in this paper, a topology optimization method on lattice-solid hybrid structures for support-free additive manufacturing was proposed. By proposing a novel hierarchical material interpolation model, this method defined two sets of densities: the external densities defining the overall material distribution for support-free effect and the internal relative densities defining the local structural details for lattice-solid phase interpolation. PDE filter is applied to smooth density distribution and thus eliminate the check board issue. Heaviside projection is adopted to create the clear cut structural boundary, preventing hard to process grey elements. Additive manufacturing filter was applied to the external densities to ensure the support-free capability by restricting the overhang inclination angle beyond 45 degree. The effective elastic properties of the lattice-solid materials were evaluated through numerical homogenization, and polynomial fittings were performed to establish the surrogate models of the equivalent elastic matrix components on the internal relative densities. One important characteristic of the above interpolation was that the material option could automatically switch between the lattice and solid phases, thus enabling the smooth gradient-based design optimization. Then, the optimization problem is formulated similar to the density based topology optimization scheme and sensitivities of both the objective and constraint functions are derived with the adjoint method. The method of moving asymptotes are adopted for design updating the two sets of density variables. Finally, the effectiveness of the proposed method was verified through a numerical case study. The numerical result indicated that the support-free lattice-solid hybrid structure outperformed the conventional single-scale self-support topological design in terms of load-bearing capability.

Key words: lattice structure, design optimization, topology optimization, multi-scale design, additive manufacturing

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