三周期极小曲面多孔结构全参数化设计与关联模型
刘海宇,万琴,许鑫,文兆隆,杨海峰,李洋,梅德庆

Fully parametric design and parameter correlation models of triply periodic minimal surface porous structures
Haiyu LIU,Qin WAN,Xin XU,Zhaolong WEN,Haifeng YANG,Yang LI,Deqing MEI
表 3 Sheet-TPMS多孔结构孔隙率与比表面积的数学关联模型
Tab.3 Mathematical correlation models for porosity and specific surface area of Sheet-TPMS porous structures
TPMS数学关联模型(C2 > C1)
P$ {\varphi }_{\rm{P}}=1-0.286\;27({C}_{2}-{C}_{1}) $
$ {S }_{{\rm{v}}{\text{-P}}}=[-0.062\;24({C}_{1}^{4}+{C}_{2}^{4})-0.177\;64({C}_{1}^{2}+{C}_{2}^{2})+2.351\;78]\cdot \omega $
G$ {\varphi }_{{\mathrm{G}}}=1-0.319\;85({C}_{2}-{C}_{1})-0.010\;45({C}_{2}^{3}-{C}_{1}^{3}) $
$ {S }_{{\rm{v}}{\text{-G}}}=[-0.122\;99({C}_{1}^{6}+{C}_{2}^{6})+0.158\;89({C}_{1}^{4}+{C}_{2}^{4})-0.378\;96({C}_{1}^{2}+{C}_{2}^{2})+3.105\;24]\cdot \omega $
D$ {\varphi }_{{\mathrm{D}}}=1-0.578\;26({C}_{2}-{C}_{1})-0.029\;3({C}_{2}^{3}-{C}_{1}^{3}) $
$ {S }_{{\rm{v}}{\text{-D}}}=[-3.225\;11({C}_{1}^{6}+{C}_{2}^{6})+0.605\;17({C}_{1}^{4}+{C}_{2}^{4})-1.309\;35({C}_{1}^{2}+{C}_{2}^{2})+3.843\;42]\cdot \omega $
IWP$ {\varphi }_{{\mathrm{IWP}}}=1-0.129\;32({C}_{2}-{C}_{1})-0.003\;49({C}_{2}^{2}-{C}_{1}^{2})-0.001\;77({C}_{2}^{3}-{C}_{1}^{3})-4.728\;57\times 10^{-4} \times ({C}_{2}^{4}-{C}_{1}^{4}) $
$ {S }_{{\rm{v}}\text{-IWP}}=[-0.006\;86({C}_{1}^{4}+{C}_{2}^{4})-0.010\;5({C}_{1}^{3}+{C}_{2}^{3})-0.036\;03({C}_{1}^{2}+{C}_{2}^{2})+0.042\;46({C}_{1}+{C}_{2}) +3.533\;92]\cdot \omega $
FRD$ {\varphi }_{{\mathrm{FRD}}}=1-0.213\;31({C}_{2}-{C}_{1})-0.018\;57({C}_{2}^{2}-{C}_{1}^{2})-0.004\;76({C}_{2}^{3}-{C}_{1}^{3}) $
${S }_{{\rm{v}}\text{-FRD}}=[-0.083\;17({C}_{1}^{5}+{C}_{2}^{5})-0.137\;23({C}_{1}^{4}+{C}_{2}^{4})+0.016\;8({C}_{1}^{3}+{C}_{2}^{3})-0.225\;55({C}_{1}^{2}+{C}_{2}^{2})+0.059\;39({C}_{1}+{C}_{2})+4.850\;04]\cdot \omega $