Experimental Shape Sensing and Load Identification on a Stiffened Panel: A Comparative Study

Abstract

The monitoring of loads and displacements during service life is proving to be crucial for developing a modern Structural Health Monitoring framework. The continuous monitoring of these physical quantities can provide fundamental information on the actual health status of the structure and can accurately guide pro-active condition-based maintenance operations, thus reducing the maintenance costs and extending the service life of the monitored structures. Pushed by these needs and by the simultaneous development in the field of strain sensing technologies, several displacement reconstruction and load identification methods have been developed that are based on discrete strain measurements. Among the different formulations, the inverse Finite Element Method (iFEM), the Modal Method (MM) and the 2-step method, the latter being the only one able to also compute the loads together with the displacements, have emerged as the most accurate and reliable ones. In this paper, the formulation of the three methods is summarized in order to set the numerical framework for a comparative study. The three methods are tested on the reconstruction of the external load and of the displacement field of a stiffened aluminium plate starting from experimentally measured strains. A fibre optic sensing system has been used to measure surface strains and an optimization procedure has been performed to provide the best fibre pattern, based on five lines running along the stiffeners’ direction and with a back-to-back measuring scheme. Additional sensors are used to measure the applied force and the plate’s deflection in some locations. The comparison of the results obtained by each method proves the extreme accuracy and reliability of the iFEM in the reconstruction of the deformed shape of the panel. On the other hand, the Modal Method leads to a good reconstruction of the displacements, but also exhibits a sensitivity to the choice of the modes considered for the specific application. Finally, the 2-step approach is able to correctly identify the loads and to reconstruct the displacements with an accuracy that depends on the modeling of the experimental setup.

Hybrid Shell-Beam Inverse Finite Element Method for the Shape Sensing of Stiffened Thin-Walled Structures: Formulation and Experimental Validation on a Composite Wing-Shaped Panel

“…For each sensorized element, only strain sensors located at the centroid of the element are considered, according to the scheme adopted in Ref. [32]. Fiber-optic sensors are also used in this case, as shown by the blue dotted lines of the sensor configuration in Figure 11.…”

“…This inverse element repository has been successfully applied for various numerical and experimental shape-sensing studies featuring metallic and composite structures. The structures investigated include wing-shaped geometries [6,28,29], stiffened panels [30][31][32], wing boxes [33], and marine structures [34,35]. Moreover, the application of iFEM has been extended to geometrically non-linear problems in [36,37].…”

Identification of Time Variations of Moving Loads Applied to Plates Resting on Viscoelastic Foundation Using a Meshfree Method

“…where k f and c f are the stiffness and damping coefficients of the foundation, and q is the lateral distributed load. Upon substitution of Equations ( 5)- (7) into Equation (4), and performing necessary integration by parts on the time variable, the Hamilton's principle can be written as: Where K, U, and V are the kinetic energy, strain energy, and the work conducted by the external loads, respectively. The variation in these quantities for the plate of Figure 1 is defined as:…”

“…where f k and f c are the stiffness and damping coefficients of the foundation, and q is the lateral distributed load. Upon substitution of Equations ( 5)- (7) into Equation (4), and performing necessary integration by parts on the time variable, the Hamilton's principle can be written as:…”

“…Analysis of beams and plates resting on an elastic or viscoelastic foundation has many important applications in mechanical and aerospace engineering [1]. While direct analysis of plates under different conditions is still an active area of research [2][3][4], inverse analysis of plates for identification of applied loads has attracted the attention of many researchers [5][6][7]. Identification of a moving load can be carried out by a suitable inverse analysis and using measurement of dynamic structural responses such as displacement, velocity, or acceleration at some sampling points.…”