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The real-time reconstruction of the displacement and stress fields from discrete-location strain measurements is a fundamental feature for monitoring systems, which is generally referred to as shape- and stress-sensing. Presented herein is a computationally efficient shape- and stress-sensing methodology that is ideally suited for applications to laminated composite and sandwich structures. The new approach employs the inverse Finite Element Method (iFEM) as a general framework and the Refined Zigzag Theory (RZT) as the underlying plate theory. Using a C0-discretization, a three-node inverse plate finite element is formulated. The element formulation enables robust and efficient modeling of plate structures instrumented with strain sensors that have arbitrary positions. The methodology leads to a set of linear algebraic equations that are solved efficiently for the unknown nodal displacements. These displacements are then used at the finite element level to compute full-field strains and stresses that may be in turn used to assess structural integrity. Numerical results for multilayered, highly heterogeneous laminates demonstrate the unique capability of this new formulation for shape- and stress-sensing.

The development of advanced needles for diagnostic and therapeutic purposes such as ablation and brachytherapy in the liver has offered minimally invasive therapies to patients that were previously untreatable. This thesis focuses on accurate placement of such needles guided by magnetic resonance imaging (MRI) to maximize the effect of the treatment and to minimize unwanted side-effects. To this end, an MRI-compatible steerable needle is developed which consists of a cable-actuated tip and a passively flexible shaft. The trajectory of this needle can be adjusted after the needle has been inserted. In addition, shape sensing based on optical strain sensors (fiber Bragg gratings or FBGs) is investigated aiming at feeding back information about the position and orientation of the needle tip in real-time. This is essential for accurate targeting, particularly when the needle trajectory is curved. Finally, steerability and shape sensing are integrated in a robotic system for needle steering in MRI-guided percutaneous interventions in the liver. The master-slave system comprises a steerable needle equipped with FBGs for tracking and a piezoelectric actuator unit. Needle insertion and steering is controlled by the physician through a master device, while FBG-based visual feedback of the needle shape is provided.

A robust and efficient computational method for reconstructing the elastodynamic structural response of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as “shape sensing”, this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving section strains (also known as strain measures) of Timoshenko theory for stretching, torsion, bending, and transverse shear. The present iFEM methodology is based on strain–displacement relations only, without invoking force equilibrium. Consequently, both static and time-varying displacement fields can be reconstructed without the knowledge of material properties, applied loading, or damping characteristics. Two finite elements capable of modeling frame structures are derived using interdependent interpolations, in which interior degrees of freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. Several example problems involving cantilevered beams and three-dimensional frame structures undergoing static and dynamic response are discussed. To simulate experimentally measured strains and to establish reference displacements, high-fidelity MSC/NASTRAN finite element analyses are performed. Furthermore, numerically simulated measurement errors, based on Gaussian distribution, are also considered in order to verify the stability and robustness of the methodology. The iFEM solution accuracy is examined with respect to various levels of discretization and the number of strain gauges.

Shape sensing, i.e., reconstruction of the displacement field of a structure from surface-measured strains, has relevant implications for the monitoring, control and actuation of smart structures. The inverse finite element method (iFEM) is a shape-sensing methodology shown to be fast, accurate and robust. This paper aims to demonstrate that the recently presented iFEM for beam and frame structures is reliable when experimentally measured strains are used as input data.The theoretical framework of the methodology is first reviewed. Timoshenko beam theory is adopted, including stretching, bending, transverse shear and torsion deformation modes. The variational statement and its discretization with C0-continuous inverse elements are briefly recalled. The three-dimensional displacement field of the beam structure is reconstructed under the condition that least-squares compatibility is guaranteed between the measured strains and those interpolated within the inverse elements.The experimental setup is then described. A thin-walled cantilevered beam is subjected to different static and dynamic loads. Measured surface strains are used as input data for shape sensing at first with a single inverse element. For the same test cases, convergence is also investigated using an increasing number of inverse elements. The iFEM-recovered deflections and twist rotations are then compared with those measured experimentally. The accuracy, convergence and robustness of the iFEM with respect to unavoidable measurement errors, due to strain sensor locations, measurement systems and geometry imperfections, are demonstrated for both static and dynamic loadings.

Steerable needles are a promising technology to provide safe deployment of tools through complex anatomy in minimally invasive surgery, including tumor-related diagnoses and therapies. For the 3-D localization of these instruments in soft tissue, fiber Bragg gratings (FBGs)-based reconstruction methods have gained in popularity because of the inherent advantages of optical fibers in a clinical setting, such as flexibility, immunity to electromagnetic interference, non-toxicity, the absence of line of sight issues. However, methods proposed thus far focus on shape reconstruction of the steerable needle itself, where accuracy is susceptible to errors in interpolation and curve fitting methods used to estimate the curvature vectors along the needle. In this study, we propose reconstructing the shape of the path created by the steerable needle tip based on the follow-the-leader nature of many of its variants. By assuming that the path made by the tip is equivalent to the shape of the needle, this novel approach paves the way for shape reconstruction through a single set of FBGs at the needle tip, which provides curvature information about every section of the path during navigation. We propose a Kalman Filter-based sensor fusion method to update the curvature information about the sections as they are continually estimated during the insertion process. The proposed method is validated through simulation, in vitro and ex vivo experiments employing a programmable bevel-tip steerable needle (PBN). The results show clinically acceptable accuracy, with 2.87 mm mean PBN tip position error, and a standard deviation of 1.63 mm for a 120 mm 3-D insertion.