The inverse Finite Element Method (iFEM) is a state-of-the-art methodology originally introduced by Tessler and Spangler for real-time reconstruction of full-field structural displacements in plate and shell structures that are instrumented by strain sensors. This inverse problem is commonly known as shape sensing. In this effort, a new four-node quadrilateral inverse-shell element, iQS4, is developed that expands the library of existing iFEM-based elements. This new element includes hierarchical drilling rotation degrees-of-freedom (DOF) and further extends the practical usefulness of iFEM for shape sensing analysis of large-scale structures. The iFEM/iQS4 formulation is derived from a weighted-least-squares functional that has Mindlin theory as its kinematic framework. Two validation problems, (1) a cantilevered plate under static transverse force near the free tip, and (2) a short cantilever beam under shear loading, are solved and discussed in detail. Following the validation cases, the applicability of the iQS4 element to more complex structures is demonstrated by the analysis of a thin-walled cylinder. For this problem, the effects of noisy strain measurements on the accuracy of the iFEM solution are examined using strain measurements that involve five and ten percent random noise, respectively. Finally, the effect of sensor locations, number of sensors, the discretization of the geometry, and the influence of noise on the strain measurements are assessed with respect to the solution accuracy

The inverse finite element method (iFEM) is an innovative framework for dynamic tracking of full-field structural displacements and stresses in structures that are instrumented with a network of strain sensors. In this study, an improved iFEM formulation is proposed for displacement and stress monitoring of laminated composite and sandwich plates and shells. The formulation includes the kinematics of Refined Zigzag Theory (RZT) as its baseline. The present iFEM methodology minimizes a weighted-least-squares functional that uses the complete set of strain measures of RZT. The main advantage of the current formulation is that highly accurate through-the-thickness distributions of displacements, strains, and stresses are attainable using an element based on simple C0-continuous displacement interpolation functions. Moreover, a relatively small number of strain gauges is required. A three-node inverse-shell element, named i3-RZT, is developed. Two example problems are examined in detail: (1) a simply supported rectangular laminated composite plate and (2) a wedge structure with a hole near one of the clamped ends. The numerical results demonstrate the superior capability and potential applicability of the i3-RZT/iFEM methodology for performing accurate shape and stress sensing of complex composite structures

The inverse Finite Element Method (iFEM) is a revolutionary methodology for real - time reconstruction of full-field structural displacements and stresses in plate and shell structures that are instrumented by strain sensors. This inverse problem is essential for structural health monitoring systems and commonly referred as ‘displacement and stress monitoring’ or ‘shape-and stress-sensing’. In this study, displacement and stress monitoring of a Panamax containership is performed based on the iFEM methodology. A simple, efficient, and practically useful four-node quadrilateral inverse-shell element, iQS4, is used for the numerical implementation of the iFEM algorithm. Hydrodynamic analysis of the containership is performed for beam sea waves in order to calculate v ertical and horizontal wave bending moments, and torsional wave moments acting on parallel mid-body of the containership. Several direct FEM analyses of the parallel mid-body are performed using the hydrodynamic wave bending and torsion moments. Then, experimentally measured strains are simulated by strains obtained from high-fidelity finite element solutions. After that, three different iFEM case studies of the parallel mid-body are performed utilizing the simulated sensor strains. Finally, the effect of sensor locations and number of sensors are assessed with respect to the solution accuracy

Real-time reconstruction of full field structural displacements, strains, and stresses by using surface strain measurements obtained from on-board strain sensors is commonly referred to as shape- and stress-sensing. For this purpose, a computationally accurate, robust, and rapid algorithm named as inverse Finite Element Method (iFEM) was recently developed. The main goal of this study is to perform displacement and stress monitoring of a typical chemical tanker mid-ship based on iFEM methodology. The numerical implementation of the iFEM algorithm is done by considering four-node inverse quadrilateral shell (iQS4) element. In order to demonstrate the capability of the current approach, a long barge that has a cross-section identical to a typical chemical tanker is modeled with iQS4 elements. Then, hydrodynamic loads of the barge for a certain frequency of waves are calculated by using in-house hydrodynamic software. Then, these forces are applied to a FEM model of barge and structural response is computed by using in-house finite element software. The results obtained from FEM analysis is utilized as a source to simulate in-situ strain data used in iFEM analysis as input. Finally, iFEM and FEM displacements are compared and the effects of locations and number of sensors on iFEM solution accuracy are discussed