A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions
A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions
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用于识别二维刚度分布的基于傅里叶级数的虚拟场方法
DOI：
10.1002/nme.4665
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发表时间：
2014
影响因子：
2.9
通讯作者：
Nguyen T
中科院分区：
文献类型：
--
作者：
Nguyen T
虚拟场法（VFM）是一种从实验确定的位移场计算材料性质空间分布的强大技术。本文提出了基于傅里叶级数的VFM扩展（F - VFM），其中未知刚度分布在空间频域参数化，而不是在经典VFM中使用的空间域参数化。本文提出了具有已知边界条件的弹性各向同性薄结构的F - VFM理论。提出了一种基于二维快速傅立叶变换（FFT）的高效数值算法，与直接实现典型实验数据集相比，该算法将计算时间减少了三到四个数量级。通过使用适当的滤波策略，可以在很大程度上消除F‐VFM特有的伪影（在模不连续点附近的最高空间频率处振铃）。在输入位移场中不同噪声水平下的三种刚度分布情况下，利用F - VFM重构刚度分布进行了验证。即使在位移噪声高于典型试验场的情况下，也能实现鲁棒重建。版权所有©2014 John Wiley & Sons， Ltd。
The virtual fields method (VFM) is a powerful technique for the calculation of spatial distributions of material properties from experimentally determined displacement fields. A Fourier‐series‐based extension to the VFM (the F‐VFM) is presented here, in which the unknown stiffness distribution is parameterised in the spatial frequency domain rather than in the spatial domain as used in the classical VFM. We present in this paper the theory of the F‐VFM for the case of elastic isotropic thin structures with known boundary conditions. An efficient numerical algorithm based on the two‐dimensional Fast Fourier Transform (FFT) is presented, which reduces the computation time by three to four orders of magnitude compared with a direct implementation of the F‐VFM for typical experimental dataset sizes. Artefacts specific to the F‐VFM (ringing at the highest spatial frequency near to modulus discontinuities) can be largely removed through the use of appropriate filtering strategies. Reconstruction of stiffness distributions with the F‐VFM has been validated on three stiffness distribution scenarios under varying levels of noise in the input displacement fields. Robust reconstructions are achieved even when the displacement noise is higher than in typical experimental fields.Copyright © 2014 John Wiley & Sons, Ltd.