共形映射
格子(音乐)
有限元法
几何学
二次方程
格点模型(金融)
数学
数学分析
材料科学
结构工程
物理
工程类
复合材料
声学
聚合物
作者
Yabo Liu,Zhipeng Qu,Yongfeng Li
标识
DOI:10.1002/adem.202101423
摘要
Lattice structures have superior mechanical properties, however the structures in practical engineering cannot be directly filled with periodic lattice structures because of their special‐shaped surface profile, which also restricts its practical application. Herein this work, a mapping design method of conformal lattice structures is proposed considering the part's shape profiles with different characteristics. The main idea behind this method is inspired from isoparametric element in finite element method (FEM), an irregular domain can be meshed and solved with arbitrary quadratic element by mapping the element from a regular element. By introducing geometric transformation into the design of lattice structures, lattice unit cell in irregular volume can be achieved through mapping from the regular lattice unit cell, which will establish the conformal lattice structures rapidly. Then, the mechanical properties of regular and conformal lattice structures under three‐point bending are compared using FEM. Both the yield force and ultimate force of conformal lattice structures are increased by 45.83% and 15.03%, respectively. It is hoped that this work can make a contribution to the application of lattice structures in practical engineering with irregular geometric shape.
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