基于最小秩的结构有限元模型修正方法研究

发布时间：2018-06-30 02:26

本文选题：模型修正 + 最小秩　；参考：《哈尔滨工业大学》2014年硕士论文

【摘要】：随着经济和科技的发展，工程结构不断向大跨、高耸、组合结构方向发展，对大型复杂的重要工程结构进行健康监测已成为一个必然的发展趋势。结构损伤识别和结构有限元模型修正是结构健康监测领域的重要组成部分，而且结构损伤识别大多基于结构有限元模型，可见确保结构有限元模型的准确性至关重要，发展有限元模型修正技术是必要和迫切的。近年来结构有限元模型修正方法得到了快速发展，发展了一系列结构有限元模型修正方法，但大多有限元模型修正方法的修正结果过于平滑，不能凸显结构损伤的局部性。针对结构有限元模型损伤的局部性问题，本文研究了基于最小秩的结构有限元模型修正方法。本文的主要研究内容如下。针对结构有限元模型修正中损伤的局部性问题，发展了一种基于最小秩的结构有限元模型修正方法。同时分别采用模型缩聚和模态扩展方法，，研究实测自由度不完整情况下的最小秩模型修正方法，扩展了最小秩模型修正方法的应用。文中利用一级矩阵的概念推导了结构刚度连接矩阵，相比之前的灵敏度求解方法，使得计算过程变得简单、准确。同时改进了结构损伤单元数的判断方法，使损伤单元数的确定能够更加准确。最后利用平面钢桁架和平面简支梁有限元模型进行了数值模拟，模拟结果表明：在不同噪声水平下基于最小秩的结构有限元模型修正结果较准确，且能很好地凸显损伤的局部性；在实测自由度不完整的情况下，最小秩模型修正结果也能较好地凸显损伤的局部性。
[Abstract]:With the development of economy and science and technology, the engineering structure has been developing to the direction of long span, towering and composite structure. It has become an inevitable trend to monitor the health of large and complex important engineering structures. Structural damage identification and structural finite element model modification are important parts in the field of structural health monitoring, and structural damage identification is mostly based on structural finite element model, so it is very important to ensure the accuracy of structural finite element model. It is necessary and urgent to develop finite element model modification technology. In recent years, structural finite element model modification methods have been developed rapidly, and a series of structural finite element model correction methods have been developed. However, the results of most of the finite element model modification methods are too smooth to highlight the localization of structural damage. In order to solve the local damage problem of finite element model, a method of structural finite element model modification based on minimum rank is studied in this paper. The main contents of this paper are as follows. In order to solve the local damage problem in structural finite element model modification, a structural finite element model correction method based on minimum rank is developed. At the same time, the method of model condensation and modal expansion is used to study the minimum rank model correction method under the condition of incomplete measured degree of freedom, which extends the application of the minimum rank model correction method. In this paper, the stiffness connection matrix of structure is derived by using the concept of first-order matrix. Compared with the previous sensitivity solution method, the calculation process becomes simple and accurate. At the same time, the method of judging the number of structural damage elements is improved, so that the determination of the number of damaged elements can be more accurate. Finally, the finite element model of plane steel truss and plane simply supported beam is simulated. The simulation results show that the finite element model of structure based on minimum rank is more accurate under different noise levels. And it can highlight the locality of damage well, and the result of minimum rank model correction can also better highlight the localization of damage when the measured degree of freedom is not complete.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU317

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