Inverse Finite Element Method Research Articles

Isogeometric mindlin-reissner inverse-shell element formulation for complex stiffened shell structures

Structural health monitoring (SHM) is a technology that is used to improve the safety, stability, and availability of large engineering structures. One important aspect of SHM is the ability to perform real-time reconstruction of the full-field structural displacements, also known as shape sensing. The inverse Finite Element Method (iFEM) is a technique that has been used for three-dimensional shape sensing of structures using strain data. On the other hand, Isogeometric Analysis (IGA) is a method that utilizes smooth spaces of functions, such as non-uniform rational B-splines, to solve structural problems and has gained significant attention in recent times. In this study, the authors propose a new method for shape sensing of complex stiffened shell structures by combining IGA with the iFEM method. The goal of this research is to accurately reconstruct the complex geometry of the structure without the need for a fine numerical discretization or mesh. To achieve this, the authors have developed an isogeometric Mindlin-Reissner inverse-shell element (IgaiMin) to implement the coupling between IGA and iFEM. The proposed method is validated by solving problems involving simple plates, tee junctions, and partly clamped stiffened panels representing ship structures.

Full-field deformation reconstruction of beams using the inverse Finite Element Method: Application to thin-walled structures

This work presents a methodology for the real-time structural deformation reconstruction of solid or thin-walled prismatic beams using discrete strains. Based on the 1D inverse Finite Element Method (iFEM), the approach combines the beam kinematics of Timoshenko theory, strain–displacement relations, and the finite element discretisation framework to reconstruct the full-field deformations of beams with any general cross-section. Although applicable for any general class of beams, the present work investigates its experimental application specifically to conventionally and additively manufactured thin-walled beams discretised using various low- and high-order inverse beam elements. The results demonstrate the method’s accuracy and robustness, albeit influenced by the element discretisation scheme and the number of strain sensors used.

Inverse finite element method with energy-based regularization for deformation reconstruction and structural health monitoring

Distributed Fiber Optical Sensing (DFOS) can be used to perform compact, low-invasive and large-scale strain measurements, providing an important tool for strain-based deformation reconstruction and Structural Health Monitoring (SHM). However, most current deformation reconstruction methods are difficult to apply to the sparse uniaxial strain measurement conditions associated with DFOS, especially for structures with complex geometries. This work introduces an energy-based regularization method, i.e., a priori assumption that the actual deformation state is close to the state with the minimum deformation energy under the premise of satisfying the strain constraints, into inverse finite element method to perform load-independently deformation reconstruction under the condition of sparse uniaxial strain measurement. The Inverse Finite Element Method with Energy-based Regularization (iFEM-EBR) can naturally construct the DFOS-based deformation reconstruction model with quasi-forward finite element analysis without introducing additional mathematical processing. The sensitivity of this method to structural characteristics, such as material parameters, makes it a unique prospect in SHM.

A methodology for applying isogeometric inverse finite element method to the shape sensing of stiffened thin-shell structures

The capability of reconstructing the displacement field of a structure based on in-situ strain measurements is referred to as “shape sensing” and constitutes a fundamental unit for the real-time monitoring of critical structural components. The Inverse Finite Element Method (iFEM) is one of the most promising innovative techniques for accomplishing this task. This study explores the application of iFEM in conjunction with Isogeometric Analysis (IGA) for the shape sensing of stiffened thin-shell structures. The use of IGA allows for the exact representation of computational geometry, simplifies mesh refinement, and potentially reduces the number of installed sensors. In the context of IGA, when the geometry of a structure is composed of multiple surfaces, non-conforming interfaces are typically involved. To overcome this issue, we propose an assembly process based on the Lagrange multiplier method to jointly apply iFEM and IGA to shell structures assemblies. The methodology is numerically validated using FEM models both to generate the in-situ strain data and as a comparison for iFEM reconstruction results. The case studies include a T-beam, a reinforced hyperbolic paraboloid, and a wingbox. Convergence analyzes are performed to investigate the shape sensing accuracy as the number of inverse elements increases. Additionally, contour plots of displacement field components are compared with the reference solution, revealing a high degree of agreement.

A piecewise inverse finite element method for shape sensing of the morphing wing fishbone

The shape sensing technology plays a significant role in enhancing the structural performance and flight efficiency of the morphing aircraft by providing feedback to actuation and control systems in real time. The inverse finite element method (iFEM) is a fast, accurate, and robust shape-sensing method based on in-situ surface strain measurements. However, the conventional iFEM becomes less effective when applied to real engineering structures. Thus, this paper proposes a piecewise iFEM (P-iFEM) based on a two-node inverse Hermite beam element (iHB2) for the load-bearing structure of the morphing wing. The P-iFEM method discretizes the structure into a combination of rigid and elastic parts, based on the geometry of the structure when assembling the inverse elements. The Hermite polynomial shape function in iHB2 is adopted to increase the reconstruction efficiency, as only one degree of freedom of deflection is required to achieve the C1-continuity to reconstruct the displacement fields. The high accuracy and efficiency of the proposed method are validated with a numerical fishbone model. Finally, the proposed method is applied to a fishbone structure of a real adaptive deformed wing with high accuracy.

A two-dimensional four-node quadrilateral inverse element for shape sensing and structural health monitoring

The inverse finite element method (iFEM) is a powerful tool for shape sensing and structural health monitoring and has several advantages with respect to some other existing approaches. In this study, a two-dimensional four-node quadrilateral inverse finite element formulation is presented. The element is suitable for thin structures under in-plane loading conditions. To validate the accuracy and demonstrate the capability of the inverse element, four different numerical cases are considered for different loading and boundary conditions. iFEM analysis results are compared with regular finite element analysis results as the reference solution, and very good agreement is observed between the two solutions demonstrating the capability of iFEM approach.

Algorithmically designed flaps in tongue reconstruction: a feasibility analysis.

Despite the significance and complexity of tongue reconstruction surgery, a digital tool for flap design is currently lacking. This study investigates the effectiveness of employing inverse finite element method (IFEM) for meticulously designing the geometric characteristics of harvested tissue (free flap) for tongue reconstruction. In the case of an artificially simulated hemiglossectomy, IFEM algorithm was applied for algorithmic flap design. The method's effectiveness was evaluated by assessing flap deformation in a simplified virtual reconstruction, focusing on parameters such as stress, strain, and thickness. The IFEM algorithm successfully generated an optimal flap design for the intended surgical removal. Analysis of the flap's overall surface area, deformation characteristics, and safety margins demonstrated the feasibility of the deformation. Notably, the stress and thickness assessments suggested that the flap's tension post-surgery would not adversely affect the mobility of the reconstructed tongue, suggesting a positive outcome for functional recovery. The IFEM demonstrates significant potential as a tool for precise free flap design in tongue reconstruction surgeries. Its application could lead to improved surgical accuracy and better quality of life for patients undergoing such procedures.

Shape Sensing in Plate Structures through Inverse Finite Element Method Enhanced by Multi-Objective Genetic Optimization of Sensor Placement and Strain Pre-Extrapolation.

The real-time reconstruction of the displacement field of a structure from a network of in situ strain sensors is commonly referred to as "shape sensing". The inverse finite element method (iFEM) stands out as a highly effective and promising approach to perform this task. In the current investigation, this technique is employed to monitor different plate structures experiencing flexural and torsional deformation fields. In order to reduce the number of installed sensors and obtain more accurate results, the iFEM is applied in synergy with smoothing element analysis (SEA), which allows the pre-extrapolation of the strain field over the entire structure from a limited number of measurement points. For the SEA extrapolation to be effective for a multitude of load cases, it is necessary to position the strain sensors appropriately. In this study, an innovative sensor placement strategy that relies on a multi-objective genetic algorithm (NSGA-II) is proposed. This approach aims to minimize the root mean square error of the pre-extrapolated strain field across a set of mode shapes for the examined plate structures. The optimized strain reconstruction is subsequently utilized as input for the iFEM technique. Comparisons are drawn between the displacement field reconstructions obtained using the proposed methodology and the conventional iFEM. In order to validate such methodology, two different numerical case studies, one involving a rectangular cantilevered plate and the other encompassing a square plate clamped at the edges, are investigated. For the considered case studies, the results obtained by the proposed approach reveal a significant improvement in the monitoring capabilities over the basic iFEM algorithm with the same number of sensors.

Macro-indentation testing of soft biological materials and assessment of hyper-elastic material models from inverse finite element analysis

Mechanical characterization of hydrogels and ultra-soft tissues is a challenging task both from an experimental and material parameter estimation perspective because they are much softer than many biological materials, ceramics, or polymers. The elastic modulus of such materials is within the 1 - 100 kPa range, behaving as a hyperelastic solid with strain hardening capability at large strains. In the current study, indentation experiments have been performed on agarose hydrogels, bovine liver, and bovine lymph node specimens. This work reports on the reliable determination of the elastic modulus by indentation experiments carried out at the macro-scale (mm) using a spherical indenter. However, parameter identification of the hyperelastic material properties usually requires an inverse finite element analysis due to the lack of an analytical contact model of the indentation test. Hence a comprehensive study on the spherical indentation of hyperelastic soft materials is carried out through robust computational analysis. Neo-Hookean and first-order Ogden hyperelastic material models were found to be most suitable. A case study on known anisotropic hyperelastic material showed the inability of the inverse finite element method to uniquely identify the whole material parameter set.

A digital twin for ship structures—R&D project in Japan

Abstract In order to clarify and visualize the real state of the structural performances of ships in operation and establish a more optimal, data-driven framework for ship design, construction and operation, an industry-academia joint R&D project on the digital twin for ship structures (DTSS) was conducted in Japan. This paper presents the major achievements of the project. The DTSS aims to grasp the stress responses over the whole ship structure in waves by data assimilation that merges hull monitoring and numerical simulation. Three data assimilation methods, namely, the wave spectrum method, Kalman filter method, and inverse finite element method were used, and their effectiveness was examined through model and full-scale ship measurements. Methods for predicting short-term extreme responses and long-term cumulative fatigue damage were developed for navigation and maintenance support using statistical approaches. In comparison with conventional approaches, response predictions were significantly improved by DTSS using real response data in encountered waves. Utilization scenarios for DTSS in the maritime industry were presented from the viewpoints of navigation support, maintenance support, rule improvement, and product value improvement, together with future research needs for implementation in the maritime industry.

Enhanced Strain Field Reconstruction in Ship Stiffened Panels Using Optical Fiber Sensors and the Strain Function-Inverse Finite Element Method

Accurately reconstructing the strain field within stiffened ship panels is crucial for effective structural health monitoring. This study presents a groundbreaking approach to strain field reconstruction in such panels, utilizing optical fiber sensors in conjunction with the strain function-inverse finite element method (SF-iFEM). A novel technique for solving nodal strain vectors, based on the element strain function, has been devised to improve the accuracy of strain reconstruction using the inverse finite element method (iFEM), addressing the limitations associated with traditional nodal displacement vector solutions. Moreover, the proposed method for determining the equivalent neutral layer of stiffened ship panels not only reduces the number of elements effectively but also establishes a strain function between the inner and outer surfaces of the structure. Using this function, a layout scheme for optical fiber sensors on the inner side of ship stiffened panels is provided, overcoming the symmetrical arrangement constraints of iFEM for sensor placement on both the inner and outer sides of the structure. The results demonstrate a significant improvement in strain reconstruction accuracy under bending and bending–torsion deformations compared to conventional iFEM. Consequently, the findings of this research will contribute to enhancing the engineering applicability of iFEM in ship structure health monitoring.

A Two-Dimensional Eight-Node Quadrilateral Inverse Element for Shape Sensing and Structural Health Monitoring.

The inverse finite element method (iFEM) is a powerful tool for shape sensing and structural health monitoring and has several advantages with respect to some other existing approaches. In this study, a two-dimensional eight-node quadrilateral inverse finite element formulation is presented. The element is suitable for thin structures under in-plane loading conditions. To validate the accuracy and demonstrate the capability of the inverse element, four different numerical cases are considered for different loading and boundary conditions. iFEM analysis results are compared with regular finite element analysis results as the reference solution and very good agreement is observed between the two solutions, demonstrating the capability of the iFEM approach.

Characterizing atherosclerotic tissues: in silico analysis of mechanical properties using intravascular ultrasound and inverse finite element methods.

Atherosclerosis is a prevalent cause of acute coronary syndromes that consists of lipid deposition inside the artery wall, creating an atherosclerotic plaque. Early detection may prevent the risk of plaque rupture. Nowadays, intravascular ultrasound (IVUS) is the most common medical imaging technology for atherosclerotic plaque detection. It provides an image of the section of the coronary wall and, in combination with new techniques, can estimate the displacement or strain fields. From these magnitudes and by inverse analysis, it is possible to estimate the mechanical properties of the plaque tissues and their stress distribution. In this paper, we presented a methodology based on two approaches to characterize the mechanical properties of atherosclerotic tissues. The first approach estimated the linear behavior under particular pressure. In contrast, the second technique yielded the non-linear hyperelastic material curves for the fibrotic tissues across the complete physiological pressure range. To establish and validate this method, the theoretical framework employed in silico models to simulate atherosclerotic plaques and their IVUS data. We analyzed different materials and real geometries with finite element (FE) models. After the segmentation of the fibrotic, calcification, and lipid tissues, an inverse FE analysis was performed to estimate the mechanical response of the tissues. Both approaches employed an optimization process to obtain the mechanical properties by minimizing the error between the radial strains obtained from the simulated IVUS and those achieved in each iteration. The second methodology was successfully applied to five distinct real geometries and four different fibrotic tissues, getting median R 2 of 0.97 and 0.92, respectively, when comparing the real and estimated behavior curves. In addition, the last technique reduced errors in the estimated plaque strain field by more than 20% during the optimization process, compared to the former approach. The findings enabled the estimation of the stress field over the hyperelastic plaque tissues, providing valuable insights into its risk of rupture.

A two-dimensional inverse crack tip element for shape sensing and structural health monitoring

inverse Finite Element Method (iFEM) is a powerful tool for shape sensing and structural health monitoring of marine structures and has several advantages with respect to some other existing approaches. However, current iFEM formulation is not suitable for marine structures having pre-existing cracks due to stress singularities at the crack tip. In this study, a two-dimensional inverse crack tip element formulation is presented. The element is suitable for thin structures under in-plane loading conditions. The inverse crack tip element allows determination of Stress Intensity factor values at the crack tip. To validate the accuracy and demonstrate the capability of the inverse crack tip element, six different numerical cases are considered for different geometry, loading and boundary conditions. iFEM analysis results are compared with regular finite element analysis results as the reference solution and very good agreement is observed between the two solutions demonstrating the capability of the current iFEM approach.

Parametric Design and Shape Sensing of Geared Back Frame Shell Structure for Floating Cylindrical Reflector Antenna off the Coast

At present, numerous reflector antennas have been constructed worldwide on land. However, there are few applications of reflector antennas directly set off the coast. To expand the application region of reflector antennas, a floating cylindrical reflector antenna (FCRA) driven by the moving mass was developed to implement the elevation angle adjustment. Firstly, the structure design is introduced in detail. The design parameters are stated and analyzed to obtain the kinematic relationship while considering the water surface constraint. Then, the effects of each variable on the rotation capacity and structural stability are discussed. Further, the feasibility of the elevation angle adjustment process is demonstrated by using a prototype model test and software simulation. Finally, the deformation analyses and shape sensing of the back frame are carried out on the basis of the inverse finite element method (iFEM). We concluded that this new structure is feasible and expected to sit off the coast. In addition, the iFEM algorithm with sub-region reconstruction was proved to be suitable for the shape sensing of the over-constrained FCRA during the angle adjustment process via several quasi-static sampling moments.

Engineering the perfect mattress: The influence of substrate mechanics on deep tissue stresses in supine

BackgroundWith increasing global interest in sleep hygiene, sleep ergonomics is an area that has been largely understudied. During sleep individuals turn over during the night to restore blood flow in occluded blood vessels, indicating that control of local tissue pressure may play a role in improving sleep comfort. This study investigates the influence of mattress stiffness on tissue compressive stresses during supine lying. MethodsA subject-specific 3D finite element (FE) model of the pelvis area has been developed to simulate supine lying on substrates of varying firmness. Constitutive parameters for the adipose-skin tissue and muscle-organ tissue were calibrated using a novel application of the inverse finite element method. FindingsThe compressive stress was consistently greatest in the muscle interfacing the sacrum at 18.5 kPa on the soft foam, and 30.9 kPa on the firm foam. From soft to firm, the compressive stress increased by 67% at the sacrum, 20% at the ischium, 42% at the lesser trochanter, and 50% at the skin. InterpretationThe non-linearity of the foam substrate had a pressure distributing effect, relieving the peak compressive stresses at the sacrum, indicating that it may be possible to design arrays of foam substrates that can provide most efficient pressure relief.

Full-field deformation reconstruction for large-scale cryogenic composite tanks with limited strain monitoring data

Online deformation monitoring, while of paramount importance in safety evaluation for aerospace composite tanks, is highly challenging due to the complex strain distributions in the composite tank and the strict restrictions of sensor placement. In this study, full-field deformation of large-scale cryogenic composite tanks were reconstructed under thermo-mechanical coupling conditions. In essence, the inner surface strains in the junction area of the head and cylindrical shell of the tank, defined as the ‘H-C portion’, was derived theoretically based on outer-surface strain measurement. The inverse finite element method (iFEM) was then applied using the measured and derived strains to reconstruct the full-field deformed shape of the tank. A systematic and efficient parametric discussion was conducted using an orthotropic model equivalent with composite laminated models with different lay-ups. The influences of various factors relevant to the material and geometries of the tank on the accuracy of deformation reconstruction were unveiled. Finally, a numerical experiment was carried out to reconstruct the full-field deformation of a large-scale aerospace composite tank with a specific lay-up, where limited strain data analogous to those sparely measured using distributed optical fiber sensors was used. It was found that the sensor placement strategy markedly affects the accuracy of deformation reconstruction.

A Large-Scale Sensor Layout Optimization Algorithm for Improving the Accuracy of Inverse Finite Element Method.

The inverse finite element method (iFEM) based on fiber grating sensors has been demonstrated as a shape sensing method for health monitoring of large and complex engineering structures. However, the existing optimization algorithms cause the local optima and low computational efficiency for high-dimensional strain sensor layout optimization problems of complex antenna truss models. This paper proposes the improved adaptive large-scale cooperative coevolution (IALSCC) algorithm to obtain the strain sensors deployment on iFEM, and the method includes the initialization strategy, adaptive region partitioning strategy, and gbest selection and particle updating strategies, enhancing the reconstruction accuracy of iFEM for antenna truss structure and algorithm efficiency. The strain sensors optimization deployment on the antenna truss model for different postures is achieved, and the numerical results show that the optimization algorithm IALSCC proposed in this paper can well handle the high-dimensional sensor layout optimization problem.

An inverse method for elastic constants identification of two-layer hyperelastic bodies with suction loading

Some soft tissues of the human body and biomaterials are considered as multi-layer structures with layer-specific material properties. Identification of the material parameters of these distinct layers is challenging and has attracted considerable attention in recent decades. In this research, an inverse finite element method, which uses the data obtained from simulated suction experiments, is developed. The method employs a limited number of surface-measured data to recover the layer-specific hyperelastic material parameters of a two-layer structure. The Gauss-Newton method is employed to minimize a cost function, which is defined in terms of the difference between measured and calculated displacements of the surface points. The sensitivity analysis during the optimization process is carried out by the finite difference method. The effects of pipette diameter, noise in experimental data, the initial guess and the hyperelastic material model, on the robustness and efficiency of the inverse method are investigated.

Delamination Detection and Localization in Vibrating Composite Plates and Shells Using the Inverse Finite Element Method.

Delamination damage is one of the most critical damage modes of composite materials. It takes place through the thickness of the laminated composites and does not show subtle surface effects. In the present study, a delamination detection approach based on equivalent von Mises strains is demonstrated for vibrating laminated (i.e., unidirectional fabric) composite plates. In this context, the governing relations of the inverse finite element method were recast according to the refined zigzag theory. Using the in situ strain measurements obtained from the surface and through the thickness of the composite shell, the inverse analysis was performed, and the strain field of the composite shell was reconstructed. The implementation of the proposed methodology is demonstrated for two numerical case studies associated with the harmonic and random vibrations of composite shells. The findings of this study show that the present damage detection method is capable of real-time monitoring of damage and providing information about the exact location, shape, and extent of the delamination damage in the vibrating composite plate. Finally, the robustness of the proposed method in response to resonance and extreme load variations is shown.