In this study, we methodologically compare and review the accuracy and performance of C⁰-continuous flat and curved inverse-shell elements (i.e., iMIN3, iQS4, and iCS8) for inverse finite element method (iFEM) in terms of shape, strain, and stress monitoring, and damage detection on various plane and curved geometries subjected to different loading and constraint conditions. For this purpose, four different benchmark problems are proposed, namely, a tapered plate, a quarter of a cylindrical shell, a stiffened curved plate, and a curved plate with a degraded material region in stiffness, representing a damage. The complexity of these test cases is increased systematically to reveal the advantages and shortcomings of the elements under different sensor density deployments. The reference displacement solutions and strain-sensor data used in the benchmark problems are established numerically, utilizing direct finite element analysis. After performing shape-, strain-, and stress-sensing analyses, the reference solutions are compared to the reconstructed solutions of iMIN3, iQS4, and iCS8 models. For plane geometries with sparse sensor configurations, these three elements provide rather close reconstructed-displacement fields with slightly more accurate stress sensing using iCS8 than when using iMIN3/iQS4. It is demonstrated on the curved geometry that the cross-diagonal meshing of a quadrilateral element pattern (e.g., leading to four iMIN3 elements) improves the accuracy of the displacement reconstruction as compared to a single-diagonal meshing strategy (e.g., two iMIN3 elements in a quad-shape element) utilizing iMIN3 element. Nevertheless, regardless of any geometry, sensor density, and meshing strategy, iQS4 has better shape and stress-sensing than iMIN3. As the complexity of the problem is elevated, the predictive capabilities of iCS8 element become obviously superior to that of flat inverse-shell elements (e.g., iMIN3 and iQS4) in terms of both shape sensing and damage detection. Comprehensively speaking, we envisage that the set of scrupulously selected test cases proposed herein can be reliable benchmarks for testing/validating/comparing for the features of newly developed inverse elements.

中文翻译：

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使用iFEM元素的C0连续族的扁平/弯曲壳几何形状的形状和应力传感的比较和回顾研究。

在这项研究中，我们从方法上比较和审查了C ⁰的准确性和性能连续有限的平面和弯曲反壳元件（即，iMIN3，iQS4和iCS8），用于形状，应变和应力监控以及在受到不同应力的各种平面和弯曲几何形状上的损坏检测方面的逆有限元方法（iFEM）加载和约束条件。为此，提出了四个不同的基准问题，即，锥形板，四分之一的圆柱壳，刚性的弯曲板和刚性降低的材料区域代表损坏的弯曲板。这些测试用例的复杂性会系统地增加，以揭示不同传感器密度部署下元件的优缺点。利用直接有限元分析，数值建立基准问题中使用的参考位移解和应变传感器数据。在执行形状，应变和应力感应分析后，将参考解决方案与iMIN3，iQS4和iCS8模型的重构解决方案进行比较。对于具有稀疏传感器配置的平面几何，这三个元素提供了相当接近的重建位移场，使用iCS8的应力感应比使用iMIN3 / iQS4的感应场稍微精确一些。在弯曲的几何结构上证明，与单对角网格化策略（例如，两个iMIN3元素）相比，四边形元素图案的对角网格（例如，导致四个iMIN3元素）提高了位移重建的精度。四边形元素）利用iMIN3元素。尽管如此，无论任何几何形状，传感器密度和网格划分策略如何，iQS4都比iMIN3具有更好的形状和应力感应。随着问题复杂性的提高，就形状感测和损伤检测而言，iCS8元素的预测能力明显优于平面反壳元素（例如，iMIN3和iQS4）。概括地说，我们设想这里提出的一组精心选择的测试用例可以是可靠的基准，用于测试/验证/比较新开发的逆向元素的特征。