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增材制造非均匀点阵结构热弹性耦合多目标拓扑优化
Thermoelastic coupling multi-objective topology optimization of additively manufactured non-uniform lattice structures
投稿时间:2024-04-17  修订日期:2024-05-08
DOI:
中文关键词:  非均匀点阵结构  等效热传导性能预测  热弹性耦合  几何建模  节点球光滑化
英文关键词:Non-uniform lattice structure  equivalent heat conductivity prediction  thermoelastic coupling  geometric modeling  node sphere smoothing
基金项目:
作者单位邮编
丛煜昊* 大连理工大学 116024
易斯男 北京机电工程研究所 
赵政 大连理工大学 
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中文摘要:
      本文面向航天结构轻量化、高承载和高导热设计需求,以具有高刚度质量比和多孔连通性等特点的Octet晶格构成的空间非均匀点阵结构为研究对象,基于密度法建立热弹性耦合多目标拓扑优化设计模型,获得承载与传热功能一体化结构设计。首先,基于均匀化方法给出拟合Octet晶格材料等效刚度与热传导率与其几何参数的函数关系。进而,基于所建立的点阵单胞等效性能预测模型,考虑结构热弹性应力载荷,以结构刚度与传热性能为优化目标,研究了给定温度场边界条件下的非均匀点阵结构多目标优化设计问题。其中,基于目标函数对单胞和宏观结构两个层次设计变量的灵敏度分析,同时对单胞设计参数和单胞在宏观结构中的空间分布进行优化。最后,针对非均匀点阵结构拓扑优化结果中局部几何突变问题,提出了相邻点阵单胞共有杆件保体积的等直径变换和共有节点处节点球光滑化的非均匀点阵结构几何后处理方法。数值算例验证了本文优化设计方法的有效性和优化结果的增材制造可行性。
英文摘要:
      This paper presents a thermoelastic coupled multi-objective topology optimization model for integrated design of spatially non-uniform lattice structures with load-bearing and heat transfer functionalities to fulfil the specific requirements of lightweight, high load-bearing capacity, and excellent thermal conductivity for aerospace engineering applications. To address the need for high stiffness-to-mass ratio and high-permeability configurations, the study focuses on relative density-based distribution of Octet unit cells in a lattice structure. First, the relationships between the equivalent stiffness, heat conductivity of Octet lattice cells and their geometric design parameters are established through homogenization and polynomial regression. Then, with the resulting property prediction models of the equivalent properties, the topology optimization problem of non-uniform lattice structures is formulated and solved with a gradient-based mathematical programing algorithm for determining the design variables in the unit cell level and the macro-structure level. Therein, the structural stiffness under mechanical and thermal loads, and the heat conduction performance, are simultaneously optimized. Further, a geometric post-processing approach is introduced to tackle the modeling issues related to abrupt local geometric changes in the optimized non-uniform lattice structures. The postprocess comprises of two steps: a volume-preserving equal-diameter transformation of shared rods of adjacent lattice unit cell, and a node sphere smoothing at shared nodes. Several numerical examples are presented to demonstrate the effectiveness of the optimization design method and the feasibility of additive manufacturing in realizing these intricate structures.
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