基于测量应变的薄壁结构应变场重构与试验验证文献综述

 2023-08-08 04:08

文献综述（或调研报告）：

  1. 研究背景：

使役环境下的飞行器结构状态监测近年来成为研究的热点。美国NASA的朗利研究中心（NASA Langley Research Center）经过几十年的研究，发展了基于应变测量的飞行器结构位移、应变场重构技术，利用有限测点的结构应变响应信号，重构结构的全场位移和应变，并将该技术在某些型号上开展应用。

  1. 国内外研究综述：

利用有限测点的结构应变响应信号重构结构的全场位移和应变的关键在于构建合适的算法。目前主要有三种理论来构建重构算法：模态法、Ko位移理论、逆有限元法。

模态法的基本理论是模态叠加理论。通过实验或者有限元建模分析，得到结构的振型矩阵和相应的位移振型矩阵。通过对这两个矩阵进行计算可以得到位移—应变的转化矩阵，结合应变传感系统测得的结构应变场实现结构位移场的重构。但是这种算法有几个弊端。首先，这种方法十分依赖结构的准确建模和模态分析，如果建模不准或者模态分析出现问题，最终得到的结果的误差将十分巨大；其次，对结构的材料属性也提出了一定的要求，不同材料重构的精度也会有很大差异；最后就是对应变传感器的布置方式提出了很高要求，如果布置不合理，那么计算精度和计算效率就会变得很差。由于这种方法现有弊端较多，不予研究。

2004年Kim与Cho通过实验测得应变数据与施加荷载的关系，得到了一组连续的曲率函数，并对梁的挠度进行了评估【5】；2009年Ko等正式提出了Ko理论。Ko位移理论是指将将梁段离散化，通过分段连续的多项式获得梁的曲率函数，从而得到梁的变形，并将该理论扩展到不同载荷形式和不同结构上，如弯曲、扭转、组合变形等载荷形式，以及变截面梁、简支梁、曲梁、翼盒、板等不同结构形式【6-7】。但是该方法仅能实现单方向位移变形测量，对于考虑三维变形的框架结构的变形测量并不适用，而且只有在变形是以弯曲变形为主的情况下才能有很好的计算精度。虽然该方法有一定局限性，但是对于机翼等以弯曲变形为主的结构的重构还是具有很高的适用性。

逆有限元法是由Tessler和Spangler于2003年提出的，通过最小二乘变分原理对基于一阶剪切变形理论下的板壳结构进行了分析【8】，将测得的结构表面应变与理论分析应变进行最小二乘，得到应变与位移的关系式，该方法相比以上方法具有一次获得多个变形量的有点，同时该方法中一旦测量应变点位置选定，其位移结果只与应变信息相关，即可在结构材料属性、载荷情况未知的情况下准确估计出板壳结构的变形【9-11】。

2008年日本东京大学Nishio与德国弗劳恩霍夫无损检测研究所Mizutani基于布拉格光纤传感器的分布式应变数据对结构形状进行重构，通过在结构表面布置大量的光纤传感器测量应变，并对测量的应变进行拟合得到整个结构的应变信息，得到应变与位移关系【12-14】。2010年Gherlone等在Tessler提出的逆有限元法基础上，将该方法成功应用于梁单元【15-17】，该单元以Timosheno梁理论为理论基础，实现了梁结构的变形测量。2010年Tessler 等人提出了复合结构的位移场理论【18】，称为RZT，在一阶剪切变形理论基础上增加了多层复合对面内位移场的影响。2010年美国缅因大学R.Glaser等学者通过测量梁结构表面的应变或曲率，对梁结构的变形进行监测，通过仿真和实验验证了其方法的准确性【19】，但该方法针对复杂结构较难实现。2011年到2015年，意大利都灵理工大学Alioli与美国俄勒冈州立大学 Carpenter基于应变使用逆有限元法对薄膜结构的形变进行重构【20-23】，通过仿真验证了该方法的可行性。

2015年Cerracchio等人在RZT基础上将逆有限元法用在复合结构的变形测量上，完成了复合结构的位移与应力的监测【24】，并进行了复合结构热载荷下的变形监测【25】。2016年到2018年，Todd与Chadha基于应变应用连续介质力学对类似于绳索等细长结构进行变形测量，其利用局部线性方法对细长梁的变形进行重构，并通过实验验证了该方法的可靠性【26-28】。2015年起英国斯特拉斯克莱德大学的Kefal与Oterkus对逆有限元法进行改进，使其最开始的三节点逆壳单元发展成四节点单元，使其适用于航海结构的健康监测上【29-35】，该方法在美国、英国、意大利等地得到广泛重视与发展，目标将其应用在下一代航空航天等多领域的结构健康监测上。

  1. 研究目的：

目前我国对于重构方面的研究主要是关于Ko理论，对逆有限元法的研究较少。通过对外国相关文献的阅读，逆有限元法现在已经是主流的重构算法。它对应变传感器的布置没有太多要求，还可以在不知道材料属性的情况下依旧具有很高的计算精度。推动飞行器健康检测方面的研究，开展基于逆有限元法的应变场重构至关重要。

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