目的 建立一种通用、高效的设计方法,以实现从零泊松比到特定目标泊松比的三维点阵结构的自动化优化设计,为功能集成轻量化结构的制备提供理论基础与设计工具。方法 提出了一种基于正负泊松比单元组合的设计策略,通过将具有负泊松比效应的三维内凹点阵单元与具有正泊松比效应的体心立方支撑点阵单元进行拓扑组合,构建可调控泊松比的复合点阵结构。研究建立了一套集成参数化建模、有限元模拟与贝叶斯优化算法的自动化设计框架。具体流程如下：首先,利用Python脚本驱动Abaqus软件,实现点阵结构几何参数（如杆件直径、内凹角、单元尺寸等）的参数化建模;其次,在Abaqus中施加周期性边界条件,在单轴拉伸工况下进行静力学有限元分析,以精确计算结构的宏观等效泊松比;最后,将有限元分析结果作为响应,以目标泊松比（本研究以零泊松比为例）为优化目标,利用贝叶斯优化算法自动调整几何参数组合,进行多轮迭代寻优。该方法通过脚本自动化实现了“参数更新-模拟计算-性能评估-参数再优化”的闭环设计流程。结果 通过上述自动化设计框架对三维零泊松比点阵结构进行了优化设计。经过若干轮迭代后,通过贝叶斯优化算法成功寻得一组最优几何参数组合,经过有限元模拟及贝叶斯优化算法优化后,误差在10-4数量级,极为接近理论零值。有限元模拟结果显示,在该最优参数下,内凹单元在纵向拉伸时表现出明显的横向膨胀行为,而BCCZ单元在纵向拉伸时则表现为横向收缩行为。2种相反变形效应的叠加在宏观尺度上相互抵消,最终实现了结构整体的零泊松比特性。结论 成功验证了基于正负泊松比点阵单元组合设计策略的有效性,并结合参数化有限元与贝叶斯优化算法,构建了一套高效、可靠的三维可控泊松比点阵结构自动化设计体系。变形机制分析结果表明,通过精巧的拓扑设计,可以实现不同泊松比效应在宏观结构层面的相互补偿,从而达到精确调控整体泊松比的目标。
Abstract
The work aims to establish a general and efficient design approach to achieve automated optimization design of a three-dimensional lattice structure from zero Poisson's ratio to tunable Poisson's ratios, so as to provide a theoretical basis and design tools for the preparation of lightweight structures with functional integration. A design strategy based on the combination of positive and negative Poisson's ratio elements is proposed. By topological combination of three-dimensional concave lattice elements with negative Poisson's ratio effect and body-centered cubic support lattice elements with positive Poisson's ratio effect, a composite lattice structure with adjustable Poisson's ratio is constructed. By integrating parametric modeling, finite element simulation, and Bayesian optimization, an automatic design framework was established. Firstly, Python scripts was used to drive Abaqus to achieve parametric modeling of geometric parameters of lattice structures (such as member diameters, concave angles, element dimensions, etc.); Secondly, periodic boundary conditions were added in Abaqus, to carry out static finite element analysis under uniaxial tensile conditions to accurately calculate the macroscopic equivalent Poisson's ratio of the structure. Finally, with the finite element analysis results as responses and the target Poisson's ratio (zero Poisson's ratio was taken as an example in this study) as the optimization objective, the Bayesian optimization algorithm was used to automatically adjust the combination of geometric parameters for multiple rounds of iterative optimization. This method realized the closed-loop design process of “parameter update-simulation calculation-performance evaluation-parameter re optimization” through script automation. The three-dimensional zero Poisson's ratio lattice structure was optimized through the above-mentioned automated design framework. After several rounds of iterations, a set of optimal geometric parameter combinations was successfully found through the Bayesian optimization algorithm. After finite element simulation and optimization by the Bayesian optimization algorithm, the error was at the 10-4 order of magnitude, extremely close to the theoretical zero value. The finite element simulation results showed that under this optimal parameter, the concave element exhibited an obvious lateral expansion behavior during longitudinal stretching, while the BCCZ element showed a lateral contraction behavior during longitudinal stretching. The superposition of these two opposite deformation effects canceled each other out at the macroscopic scale, ultimately achieving the zero Poisson's ratio characteristic of the structure as a whole. In conclusion, the effectiveness of the design strategy based on the combination of positive and negative Poisson's ratio lattice elements is successfully verified. By combining parametric finite elements and Bayesian optimization algorithms, an efficient and reliable automated design system for three-dimensional controllable Poisson's ratio lattice structures is constructed. The analysis of the deformation mechanism shows that through ingenious topological design, different Poisson's ratio effects can be compensated for at the macroscopic structural level, thereby achieving precisely control of the overall Poisson's ratio.
关键词
点阵结构 /
泊松比 /
贝叶斯优化 /
有限元模拟 /
结构优化
Key words
lattice structures /
Poisson's ratio /
Bayesian optimization /
finite element simulation /
structure optimization
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基金
国家自然科学基金（12272245）; 清洁高效透平动力装备全国重点实验室开放基金（DEC8300CG202417229A1228117）
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