Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, 34956 Istanbul, Turkey.
Integrated Manufacturing Technologies Research and Application Center, Sabanci University, Tuzla, 34956 Istanbul, Turkey.
Sensors (Basel). 2020 Jul 8;20(14):3808. doi: 10.3390/s20143808.
In this study, we methodologically compare and review the accuracy and performance of C-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.
在这项研究中，我们从形状、应变和应力监测以及不同加载和约束条件下各种平面和曲面几何形状的损伤检测的角度，比较和评估了 C 连续平面和曲面逆壳单元（即 iMIN3、iQS4 和 iCS8）的准确性和性能，用于逆有限元方法（iFEM）。为此，提出了四个不同的基准问题，即锥形板、四分之一圆柱壳、加筋曲面板和刚度降低材料区域的曲面板，代表损伤。这些测试案例的复杂性得到了系统地增加，以揭示不同传感器密度部署下元素的优缺点。基准问题中使用的参考位移解和应变传感器数据是通过直接有限元分析数值建立的。在进行形状、应变和应力传感分析之后，将参考解与 iMIN3、iQS4 和 iCS8 模型的重构解进行比较。对于稀疏传感器配置的平面几何形状，这三个元素提供了相当接近的重构位移场，而使用 iCS8 比使用 iMIN3/iQS4 时，应力传感更为准确。在曲面几何形状上证明，与单对角线网格策略（例如，利用两个 iMIN3 元素在四边形元素中）相比，四边形元素模式的交叉对角线网格（例如，导致四个 iMIN3 元素）提高了位移重建的准确性，利用 iMIN3 元素。然而，无论任何几何形状、传感器密度和网格策略如何，iQS4 在形状和应力传感方面都优于 iMIN3。随着问题复杂性的提高，iCS8 元素在形状和损伤检测方面的预测能力明显优于平面逆壳元素（例如，iMIN3 和 iQS4）。总之，我们预计本文提出的精心选择的测试案例集可以成为测试/验证/比较新开发的逆元素功能的可靠基准。
