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.
Key words
lattice structures /
Poisson's ratio /
Bayesian optimization /
finite element simulation /
structure optimization
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Funding
National Natural Science Foundation of China (12272245); The fund of State Key Laboratory of Clean and Efficient Turbomachinery Power Equipment (DEC8300CG202417229A1228117)
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