模型修正是结构损伤识别的一项重要工作，多采用有限元数值模型，但精细化建模往往导致计算效率低下。本文以钢筋混凝土T梁为研究对象，提出了一种高效的谱单元数值模型。首先利用Hamilton原理推导了位移控制方程组，利用快速傅里叶变换（FFT）将位移场从时域转换到频域，从而建立了谱单元模型，并提出了非线性静力计算框架。为验证模型的有效性，制作了钢筋混凝土T梁试件并开展了静载试验，并开展有限元数值模拟。最后利用谱单元模型作为基准数值模型，开展了基于模型修正的结构损伤识别。结果表明:谱单元模型仅用少量单元便完成了计算，计算效率远高于有限元模型，且精度较高；利用其开展模型修正时，可快速收敛于最终结果。谱单元模型为结构健康监测及损伤识别提供了一种高效可靠的分析手段。

Model updating is an important work in structural damage identification, mostly using finite element model, but refined modeling usually leads to computational inefficiency. In this paper, an effective spectral element model is proposed for reinforced concrete (RC) T-beam. Firstly, the displacement governing equations were derived by using Hamilton principle, the displacement field was transformed from time domain to frequency domain using Fast Fourier Transform (FFT). The spectral element model of RC T-beam was established, and a nonlinear static calculation framework was developed. In order to verify the validity of the model presented in this paper, a RC T-beam specimen was experimental tested and numerical simulation was carried out using finite element model. Finally, the structural damage identification based on model updating was carried out by using the proposed spectral element model. It shows that only 34 spectral elements were used to complete the calculation, thus, the computational efficiency of the spectral model is much higher than finite element model. Fast convergence can be achieved by using the spectral element model. In summary, the proposed spectral element model can be applied in model updating, which provides a reliable tool for structural health monitoring and damage identification.

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国家自然科学基金项目（52192663, 52078084）