Equivalent thermal analysis and optimization method for three-dimensional lattice structure
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摘要:
为了实现三维点阵结构高效、准确的热传导分析,基于热力学原理,推导了点阵结构的热传导等效计算公式,提出了热传导等效分析模型的建模方法。运用等效建模方法,建立了点阵结构的等效有限元模型,通过对比非等效有限元模型的计算结果,证明了等效有限元模型热传导分析的高效性与准确性。针对功能与性能要求下的点阵结构优化设计问题,结合所提出的热传导等效分析方法给出了点阵结构优化方法并建立优化数学模型,利用混合整数序列二次规划(MISQP)算法进行迭代计算,得到了最优设计方案,使点阵结构在满足均热性能约束的同时质量得到了降低。
Abstract:In order to achieve efficient and accurate thermal conduction analysis of three-dimensional lattice, based on the principle of thermodynamics, the equivalent heat conduction formula of lattice structure is deduced, and the modeling method of the equivalent heat conduction analysis model is proposed.The equivalent finite element model of lattice structure is established by using equivalent modeling method.Then the efficiency and accuracy of the heat conduction analysis of the equivalent model are proved by comparing with the results of the non-equivalent finite element model. Aimed at the optimization design of lattice structure under the requirement of function and performance, the lattice structure optimization method is given and the optimization mathematical model is established based on the proposed equivalent analysis method. The mixed integer sequential quadratic programming (MISQP) algorithm is used for iterative computation and the optimal design scheme is obtained, which makes the lattice structure meet the thermal performance constraints and mass has been reduced.
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表 1 材料热传导属性
Table 1. Heat conduction property of material
参数 数值 热传导率/(mW·mm-1·K-1) 201 密度/(t·mm-3) 2.81×10-9 比热容/(mJ·K-1) 9×108 表 2 点阵结构尺寸
Table 2. Size of lattice structure
点阵
类型结构尺寸/
(mm×mm×mm)杆件半径/
mm胞元数量 1 15×10×8 0.25 20×24×5=2 400 2 10×10×10 0.25 30×24×4=2 880 3 7.5×6×8 0.25 40×40×5=8 000 表 3 点阵结构等效热传导属性
Table 3. Equivalent heat conduction property of lattice structure
点阵
类型热传导率/(mW· mm-1·K-1) 密度/ (10-11t· mm-3) 比热容/ (108 mJ· K-1) kxx kyy kzz 1 1.50 0.667 0.427 3.627 35 9 2 0.911 0.911 0.911 3.822 58 9 3 1.97 1.26 2.25 7.663 09 9 表 4 等效有限元模型精度分析
Table 4. Precision analysis of equivalent finite element model
点阵类型 胞元数量 R2 RMSE 1 2 400 0.999 994 0.000 340 2 2 880 0.999 976 0.000 698 3 8 000 0.999 989 0.000 494 表 5 等效有限元模型单元数量
Table 5. Number of elements of equivalent finite element model
单元数 x、y、z方向的等效单元数 1 30×24×4=2 880 2 20×16×3=960 3 15×12×2=360 表 6 等效有限元模型精度对比
Table 6. Precision comparison of equivalent finite element model
等效有限元模型 节点数量 节点减少比例/% R2 RMSE 1 3 875 42.6 0.999 976 0.000 698 2 1 428 78.9 0.999 106 0.004 269 3 624 90.8 0.998 401 0.005 707 表 7 优化结果与初始设计对比
Table 7. Comparison of optimization results and initial design
设计状态 Nx, Ny, Nz tp/mm Varmax/K2 M/kg 优化前 30, 24, 4 0.5 5.364 0.373 优化后 23, 16, 2 0.599 5.000 0.361 -
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