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A new technique to optimize the use of mode shape derivatives to localize damage in laminated composite plates

机译：优化模态形状导数以定位层压复合板损伤的新技术

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摘要

Damage localization in laminated composite structures is a very active area of research due to the role that these kind of structures play in the transport industries. The mode shape derivatives, like rotations (first derivative), curvatures (second derivative) and, more recently, third and four derivatives, have been used to localize damage in composite plates. The most used method to compute these derivatives is the application of finite differences. However, finite differences present several well-known problems, such as the error propagation and amplification. The magnitude of the error associated with the computed derivative is not easy to estimate, mainly because the numerical error associated with finite differences depends on the values of derivatives of higher order than the order of the derivative that one wants to compute. A new technique based on the Ritz method to estimate this error is proposed in this paper. The optimal spatial sampling for the numerical differentiation of the mode shapes are defined based on the minimization of the total error. The good performance of the optimal sampling is shown by applying it to the damage localization in a laminated composite plate.
机译：由于这类结构在运输行业中的作用，层压复合结构中的损伤局部化是一个非常活跃的研究领域。模态形状导数，如旋转（一阶导数），曲率（二阶导数），以及最近的三阶和四阶导数，已被用来定位复合板中的损伤。计算这些导数最常用的方法是应用有限差分。但是，有限的差异带来了几个众所周知的问题，例如错误传播和放大。与计算的导数相关的误差的大小不容易估计，主要是因为与有限差分相关的数值误差取决于比要计算的导数阶高的阶导数的值。提出了一种基于Ritz方法的误差估计新技术。基于总误差的最小化，定义了用于模式形状的数值微分的最佳空间采样。通过将其应用于层压复合板的损伤定位，可以显示最佳采样的良好性能。

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