基于面积坐标形函数的阵列天线变形检测方法  

Array antenna deformation detection method based on area coordinate shape functions

作　　者：关迪 陈鸣 商晨 冷国俊 Guan Di;Chen Ming;Shang Chen;Leng Guojun(National Key Laboratory of Electromagnetic Space Security,Chengdu 610036,China;School of Electro-Mechanical Engineering,Xidian University,Xi′an 710071,China)

机构地区：[1]电磁空间安全全国重点实验室,成都610036 [2]西安电子科技大学机电工程学院,西安710071

出　　处：《仪器仪表学报》2024年第8期112-122,共11页Chinese Journal of Scientific Instrument

基　　金：国防科工局重大基础科研项目(JCKY2023210A004)资助。

摘　　要：本研究针对薄板变形的畸变问题,提出了基于面积坐标形函数的重构方法。不同于传统的基于雅克比矩阵的等参转换方法,该方法引入面积坐标作为等参坐标与笛卡尔坐标之间的过渡,确保线性转换关系和形函数的二阶完备性。消除了等参转换中因单元畸变造成的精度下降隐患,增强了复杂结构变形重构模型的普适性。并考虑到工程实际中的传感器粘贴限制,基于经典Kirchhoff板的一阶剪切变形理论,提出了单面应变的重构方法。通过建立多目标粒子群优化模型,得到传感器单面布置的最优方案。在天线结构模型的仿真和实验验证中,最大变形60 mm时,均方根误差RMSE为0.72 mm,百分比误差PD为2.89%。该方法实现了天线结构变形的高精度重构,有望应用于可变形天线结构的设计制造中。To address the distortion issues of the thin plate deformation reconstruction,this study developed a quadrilateral element model based on the area coordinate shape function.Unlike the traditional isoparametric transformation method reliant on the Jacobian matrix,this approach introduces area coordinates as an intermediary between isoparametric and Cartesian coordinates.This ensures linear conversion and second-order completeness of shape functions,eliminating precision degradation caused by element distortion in isoparametric transformations and enhancing the model′s adaptability for complex structures.Considering the practical limitations of sensor placement,the study also presents a reconstruction method based on single-surface strain,grounded in the first-order shear deformation theory of classical Kirchhoff plates.By developing a multi-objective particle swarm optimization model,the optimal sensor layout for single-surface arrangement was determined.Simulation and experimental validation on an antenna structure model demonstrated that with a maximum deformation of 60 mm,the root mean square error(RMSE)was 0.72 mm,and the percentage error(PD)was 2.89%.This method achieved high-precision deformation reconstruction of antenna structures and shows promise for application in the design and manufacturing of deformable antenna structures.

关 键 词：天线结构 变形重构 单元畸变 边界元理论 

分 类 号：TH89[机械工程—仪器科学与技术]