A Design Method for Conformal Lattice Variable Density Control of Irregular Structures
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edited-by
(Contributed by HAO Peng, M.AMM Editorial Board)-
摘要: 针对异形承载结构中存在的共形点阵建模填充复杂、大规模单胞导致设计变量激增、优化困难的问题，提出了一种基于函数描述的共形点阵变密度调控设计方法. 通过发展基于网格变形的共形点阵参数化建模方法，可实现异形结构的点阵快速填充；进一步提出了基于分段三次Hermite插值多项式的点阵单胞尺寸调控方法和基于代理模型的点阵杆径调控方法，可实现点阵的精细调控和设计变量降维；在此基础上，建立了基于自适应更新动态代理模型的点阵结构优化设计框架，实现了点阵调控参数的快速优化设计. 通过两个工程算例开展了算例验证，包括火箭有效载荷适配器应变能优化、飞行器异形承载舱段结构屈曲优化，综合计算结果表明了所提方法对于不同问题的有效性.Abstract: To address the challenges of complex modeling and filling of conformal lattices in irregular load-bearing structures, as well as the difficulty in optimization caused by a surge in design variables due to large-scale unit cells, a conformal lattice variable density control design method based on functional descriptions was proposed. The parametric modeling method for conformal lattices based on mesh deformation was developed, enabling rapid lattice filling for irregular structures. Furthermore, a lattice unit cell size control method based on piecewise cubic Hermite interpolating polynomials and a lattice rod diameter control method based on surrogate models were proposed, to achieve fine control of the lattice and dimensionality reduction of design variables. On this basis, an optimization design framework for lattice structures based on an adaptively updated dynamic surrogate model was established, to realize rapid optimization design of lattice control parameters. Two engineering case studies, including the strain energy optimization of rocket payload adapters and the buckling optimization of irregular load-bearing cabin structures for aircraft, validates the proposed method. The comprehensive computational results show the effectiveness of the proposed method for different problems.
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Key words:
- irregular structure lattice filling /
- conformal lattice modeling /
- variable density control design /
- surrogate model optimization
edited-byedited-by1) (我刊编委郝鹏来稿) -
图 1 点阵结构参数化建模流程
Figure 1. The parameterized modeling process for the lattice structure
图 2 通过网格变形的点阵共形过程
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 2. The lattice deformation process through grid deformation
图 3 通过设计I-A线形状实现点阵单胞尺寸调控
Figure 3. Realization of the lattile unit cell size control by designing the shape of the I-A line
图 5 代理模型与点阵杆径粗细间的对应关系示意图
Figure 5. Schematic of the correspondence between the proxy model and the thickness of the lattice rod diameter
图 9 点阵夹芯圆台结构的应变能优化迭代图
Figure 9. Iterative diagram of strain energy optimization for the lattice sandwich truncated cone structure
图 10 点阵夹芯椭圆舱段结构的屈曲优化模型
Figure 10. The buckling optimization model for lattice sandwich elliptical cabin structures
图 11 点阵夹芯椭圆舱段结构的屈曲优化迭代图
Figure 11. Iterative diagram of buckling optimization for lattice sandwich elliptical cabin structures
表 1 点阵夹芯圆台结构应变能优化结果
Table 1. Optimization results of strain energy for lattice sandwich truncated cone structures
initial lattice structure optimized by the proposed method optimized by differential method lattice structure 
strain energy/mJ 1 645 1 248 1 330 strain energy reduction rate/% - 24.13 19.15 mass/kg 51.3 50.7 51.3 θ/(°) 46.5 40.0 46.5 number of iterations - 596 50 number of analysis - 596 5 000 
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表 2 点阵夹芯椭圆舱段结构屈曲特征值优化结果
Table 2. Optimization results of buckling eigenvalues for lattice sandwich elliptical cabin structures
initial lattice structure optimized with the proposed method lattice structure 
1st-order buckling eigenvalue 1.14 1.94 eigenvalue increase rate/% - 70.2 mass/kg 19.1 18.9 θ/(°) 39.2 40.2 number of iterations - 361
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