基于最小作用量原理的多孔结构性能映射关系

Mapping Relationship for the Performance of Porous Structures Based on the Principle of Least Action

为拓展现有拓扑构型下多孔结构的优化设计方法,受物理学中最小作用量原理(The principle of least action,PLA)的启发,提出了一种基于PLA的多孔结构映射关系。结合体心立方(Body-centered cubic,BCC)多孔结构结点优化曲率存在的极值现象与自然界多数极值现象常采用PLA进行揭示的特点,通过多孔结构的力学模型和影响因素,建立了基于PLA多孔结构力学性能的映射关系。为验证该映射关系的有效性与合理性,构建了系列不同优化半径的BCC多孔结构,并采用仿真分析与实验相结合的手段探讨了结构的曲率演变趋势与力学性能。研究结果表明,不同优化半径下BCC多孔结构的平均曲率演化特点符合极值现象,且该极值现象对应的等效弹性模量、屈服强度分别有效提升26.29%、9.53%;SLM制造多孔结构样件的实验表明,极值曲率对应多孔结构的等效弹性模量和峰值强度比优化前分别高出18.81%、20.14%,验证了基于PLA原理多孔结构映射关系的有效性与合理性。该成果为多孔结构的设计及其多功能应用提供了新的优化思路,并为自然演化的优化方法在多孔结构中的进一步创新研究提供了理论基础与依据。

To expand the optimization design method of porous structures under existing topological configurations,a mapping relationship of mechanical characteristic for porous structures based on PLA is proposed inspired by PLA in physics.Combined with the extreme phenomenon of curvature for the BCC with different node optimized radius and most extreme phenomena in nature often revealed by PLA,a mapping relationship based on the mechanical properties of PLA porous structure is established through the mechanical model and influencing factors of porous structure.To verify the effectiveness and rationality of the mapping relationship,a series of BCC porous structures with different optimization radius are constructed,and the curvature evolution trend and mechanical properties of the structure are discussed by combining simulation analysis and experiment.The results indicate that the average curvature evolution characteristic of samples show an extreme value phenomenon,and the equivalent elastic modulus and yield strength corresponding to the extreme value phenomenon can be effectively increased by 26.29%,9.53%;and the experiments of porous structure samples manufactured by SLM show that the equivalent elastic modulus and first peak strength of the porous structure are 18.81%and 20.14%higher than the unoptimized structure,respectively.Moreover,this study provides a new optimization idea for the design or multifunction application of porous structures and offers the theoretical basis for further innovative research of natural evolution optimization methods in porous structures.