Shape sensing for thin-shell spaceborne antennas with adaptive isogeometric analysis and inverse finite element method

Structural health monitoring of shell structures with preexisting cracks

In automobile panel manufacturing, the design of a feasible trimming line is crucial in obtaining an accurate edge profile after flanging. In this study, an effective method which combines the robust incremental development method and finite element inverse method is presented. The finite element inverse method is used to analyze the flanging process. In using the finite element inverse method, the main obstacle is the generation of the initial guess. An improved incremental development method is presented to handle badly-shaped element, various element sizes, and undercut parts. This method incrementally develops a 3D triangular mesh onto the drawing tool surface by layer-wise development and smoothing technique. The effectiveness of this method is verified by two numerical examples.

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.

The deformation of the gantry structure in heavy-duty machine tools is an important factor that affects machining accuracy. In order to realize real-time monitoring of the deformation of the gantry structure, which is statically indeterminate and complex in shape, the reconstruction algorithm based on inverse Finite Element Method (iFEM) is proposed and fiber Bragg grating (FBG) sensors are used to measure strain data. The elements of the gantry structure are divided and the displacement functions of each element are determined. The shape function is obtained by substituting degree of freedoms (DOF) of element nodes into displacement functions. Through a differential method, the relation between strain and DOF of element nodes is established by the strain matrices. Subsequently, the DOF of element nodes are obtained by minimizing an error functional defined as the least-squares error between the analytic strain data and the corresponding experimental strains. Considering coordinate transformation and problem-specific displacement boundary conditions, the total deformation of the gantry structure is obtained. Following this, the experiment was carried out. The deformation simulated by ANSYS was used to replace the experimentally measured deformation and then compared with the deformation reconstructed by iFEM under the same loading condition. The accuracy of iFEM for reconstructing deformation of the gantry structure in heavy-duty machine tools is verified. It provides a new view for improving the machining precision of heavy-duty machine tools.

Abstract. Spacecraft in orbit are gradually developing in the direction of large-scale, complex, and distributed. These aircraft structures will undergo complex thermal deformation because of time-varying and distributed thermal excitation in harsh operating environments. Real-time and accurate structural deformation monitoring is important to ensure the spacecraft's performance in orbit. The inverse Finite Element Method (iFEM) is the most promising strain-based deformation reconstruction algorithm for the independent of the material properties and external load information. However, iFEM needs to obtain the strain field of the structure and accurately define the geometry dimension and boundary displacements. For large deployable aerospace structures, the special characteristics of the unfolding mechanism lead to complex boundary constraints, leading to low shape-sensing accuracy of iFEM if characterized inaccurately. This paper proposed a shape-sensing method that combined iFEM with boundary parameters optimization to deal with the limitation. Based on the genetic algorithm, the parameters of boundary constraints in iFEM are optimized to achieve an accurate representation of complex boundary constraints and high-precision deformation reconstruction. The numerical experiment of a sub-panel structure with complex boundary constraints of a deployable Space-borne antenna was carried out to validate the effectiveness of the proposed method.

The inverse finite element method (iFEM) is a mechanics-based algorithm for dynamic tracking of full-field structural displacements. Accurate deformed structural-shape can be attained without any material properties and loading information, even when some discrete locations lack in-situ strain measurements. The structure is discretized by inverse finite elements, enabling superior predictive capability for complex structural deformations. These exclusive advantages make iFEM suitable for geotechnical deformation monitoring, but very few researches and applications are present in the existing literature. With this in mind, a novel inclinometer that employs iFEM methodology as its underlying design theory is developed in this paper. The inclinometer is fabricated by lowering the fiber optic shape sensor into the conventional inclinometer casing leveraging on sliding fixtures. Distributed strain measures are captured using self-developed fiber Bragg grating sensors and then input into the iFEM model to regenerate the internal displacement of soil structures. The present inclinometer serves to both increase the survival rate of the sensors while at the same time achieving the sensing element reuse. A series of indoor and field validation tests have been performed and demonstrated the high accuracy, robustness, and practical usefulness of the iFEM-based inclinometer.

ABSTRACTConstitutive behaviour of fusion‐relevant steels in the post‐necking regime is necessary for detailed design of future fusion device components. A finite element model updating (FEMU) procedure using digital image correlation (DIC), particle swarm optimisation (PSO) and a novel post‐necking constitutive law was developed. A DIC‐like strain filter was introduced within the optimisation loop to reduce cost function errors associated with spatial filtering of the DIC processing. The effects of the DIC process and experimental noise on the uncertainty of optimised parameters were quantified using synthetic image deformation techniques. For large plasticity problems, the effect of measurement system noise was found to be negligible. The FEMU method was applied to small‐scale specimens of Eurofer97 ferritic‐martensitic steel of two thicknesses. Strain rate sensitivity was found to be necessary to explain observed post‐UTS uniform strain due to delayed localisation onset. Local strain data from DIC measurements have been demonstrated to improve the accuracy of the identified constitutive model compared to global data alone. Additionally, DIC strain data can provide information to support the inclusion of additional model physics, such as rate sensitivity.

Structural damage identification using strain mode differences by the iFEM based on the convolutional neural network (CNN)

The realization of an efficient Structural Health Monitoring (SHM) system strongly depends on the availability of tools that can accurately detect the structural condition during operational life. This detection can be achieved by means of physical sensors, which can provide information on the mechanical state of a structure. However, the installation of several sensors is often impractical or even impossible for systems operating in complex environments, such as aerospace, marine, and civil structures. In this context, the inverse Finite Element Method (iFEM) was developed. This algorithm is based on the finite element discretization of the structural domain. iFEM is able to reconstruct two physical quantities crucial for assessing the health status of a structure, the displacement and the stress fields, from a reduced number of easily installable physical strain sensors and without the need to know the loading conditions and the material properties. The method is extremely accurate and computationally efficient. These characteristics make it suitable for the real-time monitoring of structures and crucial for feeding the SHM framework with sufficient data using only a few sensors installed. Several works have proved the method’s accuracy when strain data are collected and processed offline. For the first time, this work presents an overview of the implementation of structural digital twins of several structures through the use of iFEM as a real-time monitoring system. In this study, both simple structures, such as a cantilevered beam, and more complex ones, such as a half-wing, are monitored live. In the presented applications, the data from the real structure is broadcast through an internet network so that the data from the sensors can feed the digital twin model remotely. These applications demonstrate that iFEM enables real-time monitoring, representing a significant step forward in the realization of the digital twin paradigm.

Material properties such as hardness can be dependent on the size of the indentation load when that load is small, a phenomenon known as the indentation size effect (ISE). In this work an inverse finite element method (IFEM) is used to investigate the ISE, with reference to experiments with a Berkovich indenter and an aluminium test material. It was found that the yield stress is highly dependent on indentation depth and in order to simulate this, an elastoplastic constitutive relation in which yielding varies with indentation depth/load was developed. It is shown that whereas Young's modulus and Poisson's ratio are not influenced by the length scale over the range tested, the amplitude portion of yield stress, which is independent of hardening and corresponds to the initial stress for a bulk material, changes radically at small indentation depths. Using the proposed material model and material parameters extracted using IFEM, the indentation depth-time and load-depth plots can be predicted at different loads with excellent agreement to experiment; the relative residual achieved between FE modelling displacement and experiment being less than 0.32%. An improved method of determining hardness from nanoindentation test data is also presented, which shows goof agreement with that determined using the IFEM.

Inverse finite element modeling of shells using the degenerate solid approach

The paper presents an experimental study of aeroelastic shape sensing and control based on strain data measured in fiber-optic sensors (FOSs). Past studies demonstrated how FOS strain data could be used to reconstruct the static and dynamic deformed shapes of a flexible wing. The current study further develops these capabilities and demonstrates wing shape control. Specifically, FOS-measured strain data are used in an optimization scheme, with a target of keeping the wing’s elastic deformations small, below a user-defined threshold, while maintaining a constant lift value (as required for trimmed flight) and with minimal usage of the control surfaces. The method is demonstrated computationally and experimentally on a wing model with four control surfaces. The wing was designed for this study, fabricated using additive manufacturing, and wind-tunnel tested. The trim optimization is performed both computationally and experimentally, following the same procedures but using strain and strain-modes data from finite element analysis and experiments. The wind-tunnel study demonstrated how a flexible wing’s shape could be controlled based on experimental strain data only, without resorting to a computational model. In both the computational and experimental parts of the study, considerable control-surface deformations were required. This primarily indicates that large control surfaces are not the optimal means for wing shape control. However, the same strain-based technique can be used with other effectors, such as distributed control surfaces, strain actuators, etcetera. The study opens a path to using FOSs to optimize winged unmanned-aerial-vehicle performance, and thus design lighter and more efficient platforms.

The study of corneal biomechanics has gained interest due to its applications on predicting refractive surgery outcomes and the study of a number of pathologies affecting the cornea. In this regard, non-contact tonometry (NCT) has become a popular diagnostic tool in ophthalmology and as an alternative method to characterize corneal biomechanics. Since identification of material parameters using NCT tests rely on the inverse finite element method, accurate and reliable simulations are required. In this work, we present a full fluid structure simulation of a NCT test accounting for the eff ect of the presence of the humors. The results indicate that when inertial effects are considered, not including humors may lead to overestimating corneal displacement, and therefore, to an overestimation of the actual corneal stiffness when using the inverse finite element method.

Shape sensing methods: Review and experimental comparison on a wing-shaped plate

To address the degradation in reconstruction accuracy of inverse finite element methods (iFEMs) for wing deformation—caused by discrepancies between the simulation model and the physical system, including model simplifications, mismatched loading conditions, and strain sensor installation errors—as well as the high cost and complexity associated with optical-based error identification and compensation systems, this study proposes an inertial measurement unit (IMU) -assisted calibration approach. A deformation field function is first constructed from strain data using iFEM, establishing a mapping from the field to the angular deflection at each measurement point. The actual angles measured by IMUs are then compared to the theoretical predictions to define an error criterion. Based on this criterion, the degree-of-freedom (DOF) errors in the deformation field are identified through a least-squares-based inverse solution. Finally, by incorporating multi-condition training data, a nonlinear mapping is established between strain inputs and DOF errors. Importantly, once this calibration model is built, only strain measurements are required during service, enabling compensation of iFEM reconstruction errors without the need for IMUs. The proposed method is experimentally validated using a wing loading platform. Results demonstrate that even without relying on optical devices, the method significantly improves the accuracy of deformation reconstruction, while maintaining low cost and strong engineering applicability.