针对海洋平台结构健康状态难以实时监测的问题，提出一种利用应变信息重构位移场的逆有限元方法。基于Timoshenko梁和最小二乘变分理论，通过提取结构表面应变计算截面中性轴应变，推导应变场及位移场函数，并将应变信息作为逆有限元重构的输入条件，对结构变形进行回构。为提升该方法的容差性，分析了应变片位置偏差及信号噪声对精度的影响。以海洋平台立柱为试验对象，分别利用有限元分析结果及实测结构应变信息来重构位移场。试验结果表明，提出的逆有限元法在不同载荷形式下均有较高的重构精度。
An inverse finite element method for reconstructing the displacement field using strain information is proposed to address the problem that the structural health status of an offshore platform is challenging to monitor in real-time. This paper is based on Timoshenko beams and least squares variational theory to calculate the neutral axis strain in a section by extracting the strain from the surface of the structure. The strain field and displacement field functions are also derived and the strain information is used as an input condition for the inverse finite element method to reconstruct the structural deformation. To improve the tolerance of the proposed method, the effects of strain gauge position deviation and signal noise on the accuracy are analyzed. The finite element analysis results and the measured structural strain information are used to reconstruct the displacement field using the marine platform column as the test object, respectively. The test results show that the proposed inverse finite element method has a high reconstruction accuracy under different load forms.
2024,46(5): 133-140 收稿日期：2022-11-02
DOI：10.3404/j.issn.1672-7649.2024.05.024
分类号：U661.43
基金项目：船舶总体性能创新研究开放基金资助项目（33122233）
作者简介：徐庚辉(1997-),男,硕士研究生,研究方向为海洋结构物健康监测
参考文献：
[1] 李永胜, 王纬波, 陶沙, 等. 海洋平台结构振动超标分析方法研究[J]. 舰船科学技术, 2021, 43(15): 99–104
[2] 董科, 李友龙. 半潜式海洋平台受浮冰撞击作用损伤分析[J]. 舰船科学技术, 2018, 40(1): 57–61
[3] 马栋梁, 王德禹. 基于加速度和卷积神经网络的船体板裂纹损伤检测[J]. 船舶力学, 2022, 26(8): 1180–1188
[4] 张大朋, 白勇, 朱克强. UKF-PID模式下动力定位海洋平台-立管系统的动力学分析[J]. 应用力学学报, 2022, 39(2): 312–323
[5] 汪雪良, 朱全华, 张涛, 等. 船舶结构监测技术研究进展[J]. 船舶力学, 2022, 26(8): 1246–1253
[6] 黄辉. 基于逆有限元方法的板梁结构变形重构的研究[D]. 武汉：华中科技大学, 2021.
[7] FOSS G C, HAUGSE E D. Using modal test results to develop strain to displacement transformations[C]//Proceedings of the 13th international modal analysis conference. 1995, 2460: 112.
[8] KO W L, RICHARDS W L, FLEISCHER V T, Applications of KO displacement theory to the deformed shape predictions of the doubly-tapered ikhana wing number [R]. California: Dryden Flight Research Center, 2009.
[9] 吴懋琦, 谭述君, 高飞雄. 基于绝对节点坐标法的平面梁有限变形下变形重构[J]. 力学学报, 2021, 53(10): 2776–2789
[10] TESSLER A. A variational principle for reconstruction of elastic deformations in shear deformable plates and shells[M]. National aeronautics and space administration, langley research center, 2003.
[11] GHERLONE M, CERRACCHIO P, MATTONE M, et al. An inverse finite element method for beam shape sensing: theoretical framework and experimental validation[J]. Smart Materials and Structures, 2014, 23(4): 045027
[12] DING G, YAN X, GAO X, et al. Reconstruction of propeller deformation based on FBG sensor network[J]. Ocean Engineering, 2022, 249: 110884
[13] HE W, LIU P, CHENG H, et al. Displacement reconstruction of beams subjected to moving load using data fusion of acceleration and strain response[J]. Engineering Structures, 2022, 268: 114693
[14] 赵飞飞, 曹开拓, 保宏, 等. Timoshenko梁的变形场重构及传感器位置优化[J]. 机械工程学报, 2020, 56(20): 1–11
[15] 贾连徽, 任慧龙, 孙树政, 等. 船体结构应力监测点的选取方法研究[J]. 船舶力学, 2013, 17(4): 389–397
[16] 蔡智恒, 周金柱, 唐宝富, 等. 面向结构形变重构的应变传感器优化布局[J]. 振动与冲击, 2019, 38(14): 83–88+124
