Abstract
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.
Highlights
Thin shell structures with monolithic/stiffened curved and flat geometries are commonly utilized in diverse engineering applications including ships and marine platforms, aerospace vehicles, and civil structures, among others
Sudden damages lead to economic loss, environmental pollution, and even may cause human casualties. To prevent such events and predict these undesirable damages in real time, a structural health monitoring (SHM) system with a reliable and robust displacement and stress-monitoring capabilities should be installed in the structures aboard [1,2,3]
The above-stated shape-sensing methods encounter difficulties in dealing with structures with complex geometries and boundary conditions, and cannot be generalized for shape sensing of any structures
Summary
Thin shell structures with monolithic/stiffened curved and flat geometries are commonly utilized in diverse engineering applications including ships and marine platforms, aerospace vehicles, and civil structures, among others. For the solution of this inverse problem, various mathematical formulations and algorithms have been proposed and investigated experimentally and/or numerically for beam/plate/shell structures These algorithms can be classified into the following two main categories: (1) modal/analytical/curve-fitting approaches [14,15,16,17,18,19], and (2) inverse finite element method (iFEM) [20,21]. The above-stated shape-sensing methods encounter difficulties in dealing with structures with complex geometries and boundary conditions, and cannot be generalized for shape sensing of any structures Among these inverse-methods, the iFEM methodology has been demonstrated to be the most general shape-sensing algorithm because of its mathematical attributes, i.e., the utilization of a least-squares variational principle based on experimental and numerical strain–displacement relationships [20,21].
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