Shape Sensing of Plate Structures Using the Inverse Finite Element Method: Investigation of Efficient Strain–Sensor Patterns

Abstract

Methods for real-time reconstruction of structural displacements using measured strain data is an area of active research due to its potential application for Structural Health Monitoring (SHM) and morphing structure control. The inverse Finite Element Method (iFEM) has been shown to be well suited for the full-field reconstruction of displacements, strains, and stresses of structures instrumented with discrete or continuous strain sensors. In practical applications, where the available number of sensors may be limited, the number and sensor positions constitute the key parameters. Understanding changes in the reconstruction quality with respect to sensor position is generally difficult and is the aim of the present work. This paper attempts to supplement the current iFEM modeling knowledge through a rigorous evaluation of several strain–sensor patterns for shape sensing of a rectangular plate. Line plots along various sections of the plate are used to assess the reconstruction quality near and far away from strain sensors, and the nodal displacements are studied as the sensor density increases. The numerical results clearly demonstrate the effectiveness of the strain sensors distributed along the plate boundary for reconstructing relatively simple displacement patterns, and highlight the potential of cross-diagonal strain–sensor patterns to improve the displacement reconstruction of more complex deformation patterns.

Coupling of peridynamics and inverse finite element method for shape sensing and crack propagation monitoring of plate structures

“…The underlying idea on derivations of Eqs. (40)(41)(42)(43) is that energies required to break all associated bonds crossing unit crack between particles within the same ply or two adjacent plies of a laminate are the same with related critical energy release rate. It is also important to note that the bonds are assumed to fail only in tension because of the predominant mechanism of the delamination/fiber/matrix failure modes of a laminate.…”

“…The most attractive ones including iMIN3 [32], iQS4 [33], and iCS8 [34] inverse-shell elements employ C 0 -continuous interpolation functions in accordance with the firstorder shear deformation theory (FSDT). Particularly, the iQS4 element has recently gained a popularity for shape sensing applications on simple/complex geometries, e.g., ship and offshore structures [35][36][37][38][39] and stiffened aerospace panels [40][41], due to its merits for practical modelling of large-scale structures with low-cost sensor measurement and highly accurate displacement estimations [42][43]. Several studies have shown the superior applications of iFEM/iQS4 approach Coupling of peridynamics and inverse finite element method for shape sensing and crack propagation monitoring of plate structures for damage identification in monolithic/stiffened structures having isotropic/orthotropic material properties [44][45][46][47][48][49].…”

Sensor Placement Optimization for Shape Sensing of Plates and Shells Using Genetic Algorithm and Inverse Finite Element Method

“…Despite the available literature on the optimum sensor placement in vibration-based structural health monitoring, the lack of a comprehensive method to define the optimum placement in strain-based SHM is evident. The primary strategy of the inverse finite element method is to collect data from the strain rosette sensors and employ it through the iFEM formulation to regenerate the real-time full-field deformation [ 58 , 59 , 60 , 61 , 62 , 63 ]; thus, the location of these strain gauges plays an essential role in the certainty of the results. In this regard, Kefal et al [ 58 ], in the endeavor of introducing a new inverse eight-node element (iCS8) to shape sensing curved structural components of marine structures, investigated the effect of the sensor sparsity and its effect on the accuracy of the results.…”

“…Kefal et al [ 60 ] employed isogeometric iFEM analysis for shell structures to improve the displacement results of coarse mesh with a few sensors compared to the results of high-fidelity FEM analysis. Roy et al [ 61 ] struggled to suggest a proper position for sensors on a rectangular plate. They explored various sensor patterns, taking a specified volume fraction for sensors and implemented them in such locations to achieve the best result and the minimum displacement error.…”

Online monitoring for floating raft structure displacement based on optimal placement of measuring points

“…Although many types of optimization problems and their applications have been proposed, few researchers have dealt with the deformation sensing of the raft. At present, more studies on structures with simple constrained boundaries such as bridges, cantilever beams, frame structure, and slabs at home and abroad, [16][17][18][19][20] but fewer paper about complex constrained boundary conditions, such as plate-like structures with multiflexible support on both sides.…”