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Carbon fibers and resin used in manufacturing carbon fiber-reinforced plastic composite structures flow before the resin solidifies, resulting in disrupted fiber orientation and non-uniform thickness. This process, known as consolidation, is critical for the quality of the composite structure, but no technology exists to measure the deformation in situ. This study proposes a strip-type embeddable shape sensor based on fiber optics for in situ monitoring of consolidation deformation. The sensor consists of a thin, flexible sheet with optical fibers embedded in the upper and lower surfaces of the sheet, and it can monitor out-of-plane bending deformation in composite materials during consolidation. Finite element analysis and experiments are used to evaluate the basic performance of the shape sensor before it is applied to composite gap/lap monitoring. For the first time, the relaxation of consolidation deformation due to the flow of fiber-resin suspension is measured. The proposed sensor will be a powerful tool for elucidating consolidation mechanisms and for validating composite manufacturing simulations.

This study investigates the application of the inverse finite element method (iFEM) in fracture mechanics by developing a novel two‐dimensional six‐node triangular inverse crack‐tip element. With its simplified formulation, the proposed inverse element is computationally efficient and ensures strain singularity at the crack tip by repositioning midside nodes. Its displacement‐based stress intensity factor (SIF) computation methodology integrates seamlessly with the existing iFEM framework, making it highly suitable for real‐time health assessment of structures with pre‐existing cracks. The inverse element has been rigorously validated for shape‐sensing and mixed‐mode SIF calculations by considering various crack geometries and mixed‐mode loading conditions. The triangular inverse element demonstrates superior flexibility in handling structured and unstructured discretizations in mapping regular and complex geometries, particularly high‐stress gradient areas like crack tips. The study also explores the variational least squares method for optimal sensor placement within the inverse element domain, ensuring accurate shape‐sensing and SIF computations with fewer onboard strain sensors. The proposed inverse formulation, with its accurate shape‐sensing capabilities and precise reconstruction of fracture parameters, represents a significant advancement in the real‐time Structural Health Monitoring of engineering structures with pre‐existing cracks.

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.

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

Shape sensing is one of most crucial components of typical structural health monitoring systems and has become a promising technology for future large-scale engineering structures to achieve significant improvement in their safety, reliability, and affordability. The inverse finite element method (iFEM) is an innovative shape-sensing technique that was introduced to perform three-dimensional displacement reconstruction of structures using in situ surface strain measurements. Moreover, isogeometric analysis (IGA) presents smooth function spaces such as non-uniform rational basis splines (NURBS), to numerically solve a number of engineering problems, and recently received a great deal of attention from both academy and industry. In this study, we propose a novel “isogeometric iFEM approach” for the shape sensing of thin and curved shell structures, through coupling the NURBS-based IGA together with the iFEM methodology. The main aim is to represent exact computational geometry, simplify mesh refinement, use smooth basis/shape functions, and allocate a lower number of strain sensors for shape sensing. For numerical implementation, a rotation-free isogeometric inverse-shell element (isogeometric Kirchhoff–Love inverse-shell element (iKLS)) is developed by utilizing the kinematics of the Kirchhoff–Love shell theory in convected curvilinear coordinates. Therefore, the isogeometric iFEM methodology presented herein minimizes a weighted-least-squares functional that uses membrane and bending section strains, consistent with the classical shell theory. Various validation and demonstration cases are presented, including Scordelis–Lo roof, pinched hemisphere, and partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined and the high accuracy and practical aspects of isogeometric iFEM analysis for linear/nonlinear shape sensing of curved shells are clearly demonstrated.

Fiber-optic shape sensing enables real-time monitoring of structural deformation across a wide range of applications. For large-scale structures, Brillouin-based distributed sensing, typically implemented through Brillouin Optical Time Domain Analysis (BOTDA), offers an extended range for quasi-static measurements, albeit its limited spatial resolution degrades reconstruction accuracy. This study addresses this fundamental limitation through the introduction of a novel error compensation algorithm, particularly suited for a Brillouin-based shape sensing system, yet agnostic with respect to the sensing technology. The method leverages both the initial and final points of the sensing path, performing both forward and backward reconstructions and fusing the two trajectories by testing several polynomial and exponential weighting strategies. The algorithm is experimentally validated on a 28.91 m four-core shape sensing fiber cable (length = L), interrogated through BOTDA operating at 50 cm spatial resolution, and reconstructed through the Frenet–Serret frame formulation. Calibration procedures include radial-offset tuning and segment alignment via a hotspot reference. A non-trivial S-shaped geometry is adopted as a case study, specifically addressing curvature discontinuities arising from mixed straight and curved segments. Reconstruction accuracy is quantified through a Euclidean-distance-based Figure of Merit (FOMs). The cubic weighting strategy demonstrates improvements exceeding 86% in all FOMs compared to classical methods without compensation. Specifically, it achieves an RMSE of 0.145 m (0.50% of L), a MAE of 0.109 m (0.38% of L), and a maximum error of 0.341 m (1.18% of L). Remarkably, these percentage errors are of the same order of magnitude as those reported in the literature for Fiber Bragg Grating (FBG) and Optical Frequency Domain Reflectometry (OFDR) systems, indicating that the proposed compensation strategy enables BOTDA-based shape sensing to achieve comparable reconstruction accuracy despite its lower spatial resolution.

The field of continuum robotics is rapidly developing. The development of new kinematic structures, locomotion principles and control strategies is driving the development of new types of sensors and sensing methodologies. The sensing in continuum robots can be divided into shape perception and environment perception. The environment perception is focusing on sensing the interactions between the robot and environment. These sensors are often embedded on an outer layer of the robots, so the interactions can be detected. The shape perception is sensing the robot’s shape using various principles. There are three main groups of sensors that use the properties of electricity, magnetism and optics to measure the shape of the continuum robots. The sensors based on measuring the properties of electricity are often based on measuring the electrical resistance or capacitance of the flexible sensor. Sensors based on magnetism use properties of permanent magnets or coils that are attached to the robot. Their magnetic field, flux or other properties are then tracked, and shape reconstruction can be performed. The last group of sensors is mostly based on leveraging the properties of traveling light through optical fibers. There are multiple objectives of this work. Objective number one is to clearly categorize the sensors and make a clear distinction between them. Objective number two is to determine the trend and progress of the sensors used in continuum robotics. And finally, the third objective is to define the challenges that the researchers are currently facing. The challenges of sensing the shape or the interaction with the environment of continuum robots are currently in the miniaturization of existing sensors and the development of novel sensing methods.

Civil structural health monitoring (CSHM) has become significantly more important within the last decades due to rapidly growing construction volume worldwide as well as aging infrastructure and longer service lifetimes of the structures. The utilization of distributed fiber optic sensing (DFOS) allows the assessment of strain and temperature distributions continuously along the installed sensing fiber and is widely used for testing of concrete structures to detect and quantify local deficiencies like cracks. Relations to the curvature and bending behavior are however mostly excluded. This paper presents a comprehensive study of different approaches for distributed fiber optic shape sensing of concrete structures. Different DFOS sensors and installation techniques were tested within load tests of concrete beams as well as real-scale tunnel lining segments, where the installations were interrogated using fully-distributed sensing units as well as by fiber Bragg grating interrogators. The results point out significant deviations between the capabilities of the different sensing systems, but demonstrate that DFOS can enable highly reliable shape sensing of concrete structures, if the system is appropriately designed depending on the CSHM application.

This paper investigated the effect of sensor density and alignment for three-dimensional shape sensing of an airplane-wing-shaped thick panel subjected to three different loading conditions, i.e., bending, torsion, and membrane loads. For shape sensing analysis of the panel, the Inverse Finite Element Method (iFEM) was used together with the Refined Zigzag Theory (RZT), in order to enable accurate predictions for transverse deflection and through-the-thickness variation of interfacial displacements. In this study, the iFEM-RZT algorithm is implemented by utilizing a novel three-node C°-continuous inverse-shell element, known as i3-RZT. The discrete strain data is generated numerically through performing a high-fidelity finite element analysis on the wing-shaped panel. This numerical strain data represents experimental strain readings obtained from surface patched strain gauges or embedded fiber Bragg grating (FBG) sensors. Three different sensor placement configurations with varying density and alignment of strain data were examined and their corresponding displacement contours were compared with those of reference solutions. The results indicate that a sparse distribution of FBG sensors (uniaxial strain measurements), aligned in only the longitudinal direction, is sufficient for predicting accurate full-field membrane and bending responses (deformed shapes) of the panel, including a true zigzag representation of interfacial displacements. On the other hand, a sparse deployment of strain rosettes (triaxial strain measurements) is essentially enough to produce torsion shapes that are as accurate as those of predicted by a dense sensor placement configuration. Hence, the potential applicability and practical aspects of i3-RZT/iFEM methodology is proven for three-dimensional shape-sensing of future aerospace structures.

Abstract Introduction: Lung cancer remains the leading cause of cancer death worldwide. Subsolid nodules (SSN), including ground-glass nodules (GGNs) and part-solid nodules (PSNs), are slow-growing but have a higher risk for malignancy. Therefore, timely diagnosis is imperative. Shape-sensing robotic-assisted bronchoscopy (ssRAB) has emerged as reliable diagnostic procedure, but data on SSN and how ssRAB compares to other diagnostic interventions such as CT-guided transthoracic biopsy (CTTB) are scarce. In this study, we compared diagnostic yield of ssRAB versus CTTB for evaluating SSN. Methods: A retrospective study of consecutive patients who underwent either ssRAB or CTTB for evaluating GGN and PSN with a solid component less than 6 mm from February 2020 to April 2023 at Mayo Clinic Florida and Rochester. Clinicodemographic information, nodule characteristics, diagnostic yield, and complications were compared between ssRAB and CTTB. Results: A total of 66 nodules from 65 patients were evaluated: 37 PSN and 29 GGN. Median size of PSN solid component was 5 mm (IQR: 4.5, 6). Patients were divided into two groups: 27 in the ssRAB group and 38 in the CTTB group. Diagnostic yield was 85.7% for ssRAB and 89.5% for CTTB (p = 0.646). Sensitivity for malignancy was similar between ssRAB and CTTB (86.4% vs. 88.5%; p = 0.828), with no statistical difference. Complications were more frequent in CTTB with no significant difference (8 vs. 2; p = 0.135). Conclusion: Diagnostic yield for SSN was similarly high for ssRAB and CTTB, with ssRAB presenting less complications and allowing mediastinal staging within the same procedure.