基于iBeam3单元的冂形结构变形场重构算法  

Deformation Field Reconstruction Algorithm of Frame Structure Based on iBeam3 Element

作　　者：李龙飞 陶翀骢 张超[1] 季宏丽[1] LI Longfei;TAO Chongcong;ZHANG Chao;JI Hongli(State Key Laboratory of Mechanics and Control for Aerospace Structures,Nanjing University of Aeronautics&Astronautics,Nanjing 210016,China)

机构地区：[1]南京航空航天大学航空航天结构力学及控制全国重点实验室,南京210016

出　　处：《南京航空航天大学学报(自然科学版)》2025年第1期120-129,共10页Journal of Nanjing University of Aeronautics & Astronautics

摘　　要：结构变形作为结构健康监测的重要指标之一,对结构强度的性能评估至关重要,在实际工程中,由于工程用途等原因,应变传感器的安装数量和位置受限,导致结构变形重构精度降低。为解决上述问题,本文提出一种基于二节点逆梁单元的应变场重构算法。首先采用二节点梁单元对结构进行离散,基于Timoshenko梁理论以及最小二乘误差理论构建单元内理论应变与实测应变的误差函数,通过离散应变测点重构结构应变场分布,并以此为基础重构结构变形。分别通过ABAQUS仿真分析与实验验证算法的有效性,结果表明,此算法在应变测点数量较少时,可以有效地重构结构变形,与直接使用测点应变数据相比,相对误差减小了5%,对结构健康监测具有重要意义。Structural deformation,as one of the important indicators of structural health monitoring,is crucial for evaluating structural strength performance.In practical engineering,due to engineering use and other factors,the number and placement of strain sensors are limited,resulting in reduced accuracy of structural deformation reconstruction.To address the above problem,this paper proposes a strain field reconstruction algorithm based on two‑node inverse beam elements.First,the structure is discretized using two‑node beam elements.An error function is constructed based on the principles of Timoshenko beam theory and least squares error theory,which evaluates the discrepancy between the theoretical strains within the element and the measured strains.The strain field distribution of the structure is reconstructed using discrete strain measurement points,and this serves as the foundation for reconstructing the structural deformations.The effectiveness of the algorithm is validated through simulations in ABAQUS and experimental tests.The results indicate that the algorithm can effectively reconstruct structural deformations even with a limited number of strain measurement points,reducing the relative error by 5%compared with directly using the strain data from measurement points.It has significant implications for structural health monitoring.

关 键 词：逆有限元法 逆梁单元 应变场重构 实测结构应变 变形重构 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]