Updated Finite Element Model Research Articles

Performance assessment of steel cantilever beams based on connection behaviour using DIC technique and improved hybrid PSO algorithm

Cantilever beams can have various behaviour depending on the details of the connection. Partially-fixed connections have a different performance from conventionally-fixed connections, in which the exact information is not available. In this paper, using the finite element model updating (FEMU) of a steel cantilever beam, the support conditions of a partially-fixed connection and the behaviour of the beam are investigated. The FEMU is utilized as an appropriate technique for structural health monitoring, which requires the use of data acquisition methods from the structure. In this research, instead of using discrete sensors, displacement and strain information are continuously measured from the beam surface using the digital image correlation (DIC) method. The difference between the initial model and the data extracted from the DIC is determined by a cost function. A hybrid method called Powell particle swarm optimization is used to minimize the cost function. This method includes particle swarm optimization (PSO) as a global search technique and Powell optimization as a local search technique; the hybrid method achieves better performance by combining the two methods. A dynamic inertia weight is presented to improve the performance of the PSO algorithm. Abaqus software and Python programming have been used to carry out the FEMU process. Finally, the amount of rotation and displacement of support are calculated, and the dependency of beam behaviour on each of the variables is investigated. This method yields acceptable convergence of the results and can be extended to study other structural components.

High-fidelity numerical simulation and experimental validation of a 1600-mm-diameter axial loaded grid stiffened cylindrical shell

Stiffened cylindrical shells are commonly used in the launch vehicle, which are prone to buckling under axial compression load and extremely sensitive to imperfections. Establishing a high-fidelity finite element model is a prerequisite for correctly analyzing buckling load and imperfection sensitivity of stiffened cylindrical shells. This paper proposes a homogenization-based model updating approach for the grid stiffened cylindrical shell with many chamfers, which can establish a high-fidelity shell finite element model that maintains calculation efficiency and accuracy advantages. It uses the equivalent elastic constants of the unit cell as the link to modify the size parameters of the finite element model for the grid stiffened cylindrical shell. Moreover, the axially compressed buckling test of a 1.6-m-diameter orthogrid stiffened cylindrical shell is performed to verify the effectiveness of the proposed method. Through comparison, it could be found that the updated finite element model has a higher analysis accuracy. Specifically, the analysis error of the initial finite element model is −16.85% compared with the test result, while the error of the updated model is only −0.67%. The updated model can be used with full confidence for simulating mechanical performance such as the buckling process and the imperfection sensitivity analysis. Besides, it also indicates the necessity of considering the structural characteristics such as the chamfer in the optimization design process of the grid stiffened cylindrical shell structure.

Finite Element Model Updating of Steel Arch Bridge Based on First-Order Mode Test Data

In order to obtain an accurate finite element model of a steel arch bridge, a first-order modal finite element model updating method is proposed by using the measured first-order modal data of the bridge. Using the measured acceleration time history data under random excitation and the first-order mode updating method, the stiffness matrix of the finite element model is updated, and the first-order frequencies and first-order mode shapes before and after updating of the model are compared and analyzed. The state space method is used to compare and analyze the dynamic response and the reliability of the structure before and after the updating of the model. The results show that the difference of the first-order frequencies between the updated finite element model and the measured result is about 0.001, and the difference of the first-order mode shapes is less than 0.197, which meets the needs of engineering. Dynamic response values of the updated structural model are much larger than those of the structural model before updating. The theoretical model is different from the dynamic response of actual structure, so it is necessary to update the theoretical model. The finite element model updating method can provide a reliable analytical way for bridge structural health monitoring, state evaluation, and damage identification.

Macro and micro damage analysis and parameter inversion of HTPB adhesive Interface based on DIC and FEMU

ABSTRACT In order to realize the quantitative analysis of the structural integrity and damage evolution of hydroxyl-terminated polybutadiene (HTPB) composite solid propellant under external load, the loading failure experiments were carried out on the macro rectangular specimen and the micro specimen, and the numerical analysis of the strain evolution process in the region of interest (ROI) of the specimen was carried out using digital image correlation (DIC). At the same time, with the help of finite element model updating (FEMU) method, the mechanical and cohesion parameters of the specimen were inversed using the combination of adaptive particle swarm optimization (APSO), back propagation (BP) and Hooke-Jeeves algorithm, and the simulation of the whole process of propellant damage and fracture was realized from the microscopic point of view. The results show that inhibiting the debonding of propellant/liner interface is the key to maintain the structural integrity. It starts with the damage and fracture of the propellant side. A scanning electron microscope (SEM) in-situ dynamic tensile test shows that the initial damage occurs at the strain of 27.368%, and the through-type crack propagates along the interface when the strain reaches 43.276%. In addition, the use of combinatorial optimization algorithm can realize the global optimal inversion of 16 parameters divided into three types in 100 complete calculations, reduce the optimal objective function value to 0.0251, and assist the finite element calculation to realize the quantitative analysis and accurate simulation of the experimental process.

Finite Element Model Updating of Bridge Structures Based on Improved Response Surface Methods

An accurate and reasonable finite element model is essential for bridge structural health monitoring and safety assessment. To improve the accuracy and efficiency of the finite element model updating, this paper proposes a finite element model updating method for bridge structures based on an improved response surface method. By introducing the radial basis function as the augmentation term of the polynomial function, a response surface model based on the augmentation polynomial is established, and the fitting accuracy of the global response surface model is improved. The convergence speed and accuracy of the response surface model optimization solution are improved by improving the regression step and annealing strategy in the simulated annealing algorithm. The method is validated using the numerical case of a simply supported beam and the finite element model of the main bridge of the Tonghe Songhua River Highway Bridge (Tonghe Bridge), and the safety condition of the main bridge of the Tonghe Bridge is evaluated using the updated finite element model. The results show that the maximum relative error of the updated parameters of the simply supported beam decreased from 13.011% before improvement to 0.719% after improvement, and the maximum relative error of the natural frequencies decreased from 0.728% before improvement to 0.225% after improvement; the maximum relative error of the natural frequencies of the finite element model of the Tonghe Bridge main bridge decreased from 21.68% before improvement to 4.23% after improvement. In April, May, and June of 2021, the main bridge of the Tonghe Bridge operated well and had a good security reserve.

Structural performance assessment of RC flexural members through crack-based fibre beam-column model updating

For reinforced concrete (RC) structures in service, original finite element models (FEMs) based on design information usually deviate from actual structures due to structural damage such as cracks, displacement and material degradation. Although conventional FEMs can be updated to give results that match the response data used during the updating process, they can hardly predict the subsequent structural performance. In this study, an innovative fibre beam-column model updating method based on static deflection and crack width is proposed. First, the self-developed fibre beam-column finite element program COMPONA-MARC is modified to efficiently simulate the nonlinear cracking behaviour of RC flexural members. Second, sensitivity studies using the discrete central difference method based on the Lagrange interpolation function are conducted to select updating parameters. Third, with the combination of modified COMPONA-MARC and an automation program written in Python, plenty of sample data are obtained, and artificial neural networks (ANNs) are trained by Bayesian Regularization Backpropagation (BRB). Finally, the updated parameters are acquired by inputting the measured static deflections and crack widths. Typical RC beams and RC slabs from the literature are utilized to validate the proposed methodology and explore potential implementation scenarios. The results show that updated FEMs can satisfactorily predict mechanical behaviour and assess structural performance. The proposed method offers enlightening insights about combining structural health monitoring and inspection (SHMI) results with model updating, which can promote the applications of digital twins in performance assessments of RC structures.

Surrogate-assisted finite element model updating for detecting scour depths in a continuous bridge

In this study, the Kriging surrogate-assisted method is proposed to improve the computational efficiency in finite element model updating (FEMU) based scour depth detection for the first time. Unlike the conventional methods of FEMU that update the structural parameters by the frequency surrogate models, the proposed method further takes the mode shapes into account by constructing the modal assurance criterion (MAC) surrogate models. The bi-objective functions of the frequency discrepancies and MAC values are directly optimized by the nondominated sorting genetic algorithm II to circumvent the specification of weighting factors as required in single-objective optimization. The preferred solution is selected from the nondominated solutions by the criterion of minimum distance from the equilibrium point. As the sensitivity analysis indicates that the transverse vibration modes are sensitive to the bridge scour, the transverse mode shapes measured on the bridge piers are adopted in scour detection. The illustrative examples show that the proposed method can greatly reduce the computational time with a competitive estimation of the scour depth vector. The parametric study further demonstrates the ability of the proposed method to yield satisfactory results even using the modal parameters of the first two modes with three measurement points.

Model Updating for a Continuous Concrete Girder Bridge Using Data from Construction Monitoring

Finite element (FE) model updating can guarantee the accuracy of the numerical analyses for civil structures. However, two deficiencies currently exist with the traditional FE model updating technique based on the measurements of modal parameters and/or the static structural responses of the built structure with respect to its reference information insufficiency and its non-unique solution generally obtained, hampering its extensive use. It becomes the goal of the whole engineering community to introduce new effective methods for the civil structural FE model update. To this end, an innovative FE model updating method using data from construction monitoring is proposed in this article. With regard to its theoretical novelty, the new method transforms the complicated multi-variable optimization mathematical problem with the traditional FE model updating technique into many simple single-variable parameter identification problems. Under the engineering background of Huangsha Harbor Bridge, a three-span concrete continuous box girder bridge constructed utilizing the symmetric cantilever casting method, the effectiveness and the efficiency of the new model updating practice were validated. It is demonstrated using quantitative data that the abundant data measured on Huangsha Harbor Bridge in construction stages can enhance the reference information for the more accurate FE model updating of the structure, and the uncertain parameters with the initial FE model of Huangsha Harbor Bridge can be progressively and easily identified for the proposed model updating method using many single-variable linear regression models, instead of one complicated multi-variable mathematical or numerical model employed by the traditional model updating approaches, which generally leads to non-unique solutions rendered by normal optimization algorithms.

Structural damage identification based on pattern matching using the flexibility change rate

AbstractIn this paper, a rapid identification method for postearthquake structural damage is proposed based on pattern matching using the flexibility change rate. In the first stage, a small number of dynamic signals are collected for extracting the modal information, which is used as a reference for model updating. Using the updated finite element model of the structure to be monitored, the characteristic vector of the flexibility change rate is calculated by modal analysis from the first two orders of modal information of various damage scenarios to establish a pattern database. For the real structure, the measured responses are used to identify the modal parameters to calculate the flexibility change rate characteristic vector, which is treated as the observed pattern. Then, the similarity between the observed pattern and the pattern in the pattern database is calculated using the Euclidean distance (ED). The damage location and severity of the measured structure are treated to be the same as the pattern corresponding to the minimum value of ED, so that the damage is identified. Numerical simulations and experiments of two types of concentrated mass structures, four floors, and six floors confirm that the proposed method can identify the damage well. In addition, the matching results based on different sensor combinations demonstrate that the method can quickly identify the damage location and severity of a structure even using a limited number of sensors. The proposed method can provide support for the government in rapid postearthquake emergency decision‐making.

Modelling Strategies for the Updating of Infilled RC Building FEMs Considering the Construction Phases

This paper deals with modelling strategies for the updating of Finite Element Models (FEMs) of infilled Reinforced Concrete (RC) frame buildings. As is known, this building typology is the most adopted worldwide for residential houses and strategic buildings, such as hospitals, schools, police stations, etc. The importance of achieving trustworthy numerical models for these kinds of structures, especially the latter ones, is clear. The updating procedure mainly consists in changing the geometrical and mechanical material properties of models until pre-determined convergence criteria are verified, the latter based on the comparison between numerical and experimental outcomes. In this work, the modelling strategies that can be adopted to refine FEMs of infilled RC buildings are treated in-depth, starting from the simple model usually developed for design purposes. Modelling techniques relevant to the geometry, the mechanical properties, the mass, and the restraint conditions of the model are discussed. Moreover, the approaches that can be adopted to calibrate numerical models during the construction process are addressed as well. Then, an application of the proposed strategies is provided with reference to a real building that was investigated during its construction. The proposed modelling strategies proved to be effective in the model updating of the considered building and provide useful support for the calibration of FEMs of this building typology in general.

A non-intrusive dynamic sensitivity-based substructure model updating method for nonlinear systems

In nonlinear finite element model updating (FEMU), one of the main challenges is how to improve the updating efficiency for large-scale structures. The computational time of updating depends on the degree-of-freedom of the finite element model, and the optimization algorithm that the user chooses. In this work, a novel dynamic response sensitivity-based nonlinear FEMU method using the substructures is presented to reduce the time consuming of computation and updating. Considering the residual structural modes, the enhanced Hurty/Craig-Bampton (EHCB) substructure method is developed to establish a more precise initial numerical model, which also has high computational efficiency. A non-intrusive algorithm based on the real and imaginary perturbation of updating parameters is implemented to compute the nonlinear substructural response sensitivities, and further reduce the iteration loops in the nonlinear FEMU process. Simulation examples with smooth and non-smooth localized nonlinearities are conducted to verify the accuracy, robustness, and efficiency of the proposed method. Results indicated that the proposed method can effectively and efficiently update the nonlinear finite element model with high accuracy.

Corrosion-related parameter estimation for RC structures using UKF-based Bayesian nonlinear finite element model updating with seismic data

Model updating based on field measurements (e.g., from ambient vibration) has proven to be an efficient approach for assessing the condition of reinforced concrete (RC) structures. Despite existing studies in the literature, no effort has been devoted to corrosion-related parameter estimation for RC structures based on Bayesian nonlinear finite element model updating (FEMU) with seismic data. To bridge this gap, this research work extends the application of nonlinear FEMU to corroded RC structures and provides a methodology to estimate the corrosion-related parameters from seismic measurement of RC structures with high nonlinearity. The essential idea of this approach is to integrate recursive Bayesian inference (i.e., unscented Kalman filter) with advanced finite element (FE) modeling of corroded RC structures to estimate corrosion-affected properties. The advanced FE modeling approach used in this study is an efficient modeling strategy that accounts for different aspects of the corrosion, particularly corroded bond-slip in RC structures. The capability of the approach in evaluating the corrosion-affected model parameters is examined by 13 case studies using an example RC column with simulated seismic data due to lack of real-word measurements. These study cases consider different corrosion levels, measurement noise levels, corroded features, seismic intensity levels, and types of measurement. The successful estimation of the corrosion-affected properties for the corroded column under various scenarios indicates that the proposed methodology can be employed to identify the unknown corroded properties of RC structures using recorded seismic response data. The updated FE model of a corroded RC structure can potentially be utilized for reliable seismic performance assessment, which assists in future decision-making for repair or retrofit of existing structures.

Design and validation of a heterogeneous interior notched specimen for inverse material parameter identification

Nowadays, virtual manufacturing, digitalisation and simulation predictions are essential for the design and the development of engineering parts and components, as well as companies’ productivity. The implemented constitutive model and the accuracy of the determined material parameters influence the reliability of these predictions. It is necessary to calibrate multiple parameters of a complex and robust constitutive model. This is a very time-consuming task and involves high costs when using a classical approach, in which several different homogeneous mechanical experiments are performed. The non-homogeneous mechanical tests can provide a larger variety of mechanical information in just one experiment, reducing the number of required tests for material characterisation. The aim of this work is to numerically design a specimen with an interior notch for a uniaxial loading test that presents strain heterogeneity. The shape of the interior notch is optimised to maximise the strain heterogeneity. The optimisation procedure is guided by a cost function established by several strain heterogeneity indicators. The best specimen shape exhibits numerically uniaxial tension and compression, pure shear and plane strain tension in the plastic region. The identifiability of Swift’s hardening law parameters was quantitatively investigated based on the partial derivative of the strain fields with respect to the sought parameters. Results show that the proposed design strategy enables to increase in strain heterogeneity. It is shown that the optimised specimen has significantly better identifiability compared to a tensile specimen with a circular hole. Finally, a comparison between a classical Finite Element Model Updating (FEMU) methodology and a FEMU-based approach that uses a DIC-levelling strategy was conducted in order to inversely identify the Swift hardening law parameters and validate the designed specimen. It was confirmed that the DIC-levelling method finds more accurate results than the classical approach, with the compromise of the computational time. It was also shown that the optimum designed specimen is adequate for inverse identification strategies. • Optimised heterogeneous specimen to test in standard tensile test machine. • Better hardening parameters’ identifiability than circular perforated specimen. • The strain states observed in FEA are exhibited in the virtual experiment. • Parameter identification using a DIC-levelled approach is more accurate than the classical. • On the reduction of time, resources and costs in the development of engineering parts.

High-Accuracy Finite Element Model Updating a Framed Structure Based on Response Surface Method and Partition Modification

In this paper, a finite element model updating (FEMU) method is proposed based on the response surface model (RSM) and genetic algorithm (GA) to establish a high-precision finite element (FE) model of space station scientific experiment racks. First, the fine solid and mixed FE models are established, respectively, and a comparison of the modal test results is conducted. Then, an orthogonal experimental design is used to analyze the significance of the parameters, and the variables to be modified are determined. The design parameters are sampled via the Latin hyperbolic method and are substituted into the FE model to obtain the modal parameters of the scientific experiment rack. The mapping relationship between the design and modal parameters is fitted by constructing the Kriging function, and the RSM is established. The design parameters of the scientific experiment rack are optimized via GA, and the initial FE model is updated, which has the advantage of improving the computing efficiency. Finally, the updated FE model of the experiment rack is verified by frequency sweep and random vibration tests. The experimental results show that the proposed approach has high precision and computing efficiency, and compared with the test results, the modal frequency errors of the updated model are within 5%, and the vibration response errors under random excitation of the updated model are within 7%.

Numerical identification of the elasticity tensor of heterogeneous materials made of Silicon Carbide and Titanium by the Finite Element Model Updating (FEMU)

This work is subjected to the development of a method to identify the elasticity tensor of homogeneous and heterogeneous materials. The materials are created in the form of checkerboards. We solved the direct problem to obtain the strain field using the finite element method, after obtaining this strain field, we created synthetic experimental displacement data by simulation. A re-calibration of the created experimental and simulated data is done based on the principle of the finite element model updating (FEMU), used in almost all domains, in the inverse problem. The minimization of the cost function obtained by FEMU is done by Levenberg-Marquardt algorithm which is very fast and elegant algorithm. A complete study has been done by studying the sensitivity of the identified values with respect to the refinement of the mesh and with respect to the level of disturbance.

Estimation of thermophysic properties of a bimaterial by temperature field measurement and finite element model updating

The aim of this study is to identify simultaneously the thermal conductivity tensor and the heat capacity per unit volume of a bimaterial, whose heat conduction obeys Fourier’s law. This approach is validated by numerical simulation. The simulated temperature fields are obtained by the direct resolution of the heat conduction equation solved numerically with the help of finite element method formulation. To identify the parameters, an inverse method is developed by using the finite element model updating (FEMU) based on the Levenberg-Marquardt algorithm. This inverse finite element method approach allowed us to estimate the thermophysical parameters sought. We validated the numerical procedure by using noiseless temperature fields at different time and space steps and two types of material: an homogeneous and a bimaterial one. To be close to real conditions, the influence of the noise on the temperature fields is also studied and shows the efficiency of the inverse method. The results of this procedure show that the identified parameters are very less sensitive to the number of infra-red images varying from 40 to 80 and the number of elements ranging from 20 to 50 for a specimen size equals to 36.6 × 36.6 mm2.

Finite element model updating with quantified uncertainties using point cloud data

AbstractWhile finite element (FE) modeling is widely used for ultimate strength assessments of structural systems, incorporating complex distortions and imperfections into FE models remains a challenge. Conventional methods typically rely on assumptions about the periodicity of distortions through spectral or modal methods. However, these approaches are not viable under the many realistic scenarios where these assumptions are invalid. Research efforts have consistently demonstrated the ability of point cloud data, generated through laser scanning or photogrammetry-based methods, to accurately capture structural deformations at the millimeter scale. This enables the updating of numerical models to capture the exact structural configuration and initial imperfections without the need for unrealistic assumptions. This research article investigates the use of point cloud data for updating the initial distortions in a FE model of a stiffened ship deck panel, for the purposes of ultimate strength estimation. The presented approach has the additional benefit of being able to explicitly account for measurement uncertainty in the analysis. Calculations using the updated FE models are compared against ground truth test data as well as FE models updated using standard spectral methods. The results demonstrate strength estimation that is comparable to existing approaches, with the additional advantages of uncertainty quantification and applicability to a wider range of application scenarios.

A Novel Multiobjective Function for Finite-Element Model Updating of a Long-Span Cable-Stayed Bridge Using In Situ Static and Dynamic Measurements

The traditional objective function (TOF) of bridge model updating is usually defined on the basis of the structural response residuals between numerically calculated and experimentally measured values. However, this model finds it difficult to determine the weighting factors, and the updated model lacks accuracy. To offset these disadvantages, this study proposes a novel objective function (NOF) for finite-element model updating of a long-span cable-stayed bridge using in situ static and dynamic measurements. The proposed NOF comprises the residual functions of the displacement assurance criterion, the position of the neutral axis, and the natural frequency. The global sensitivity analysis–based model updating uses the Kriging model as the surrogate model to save computational costs. The nondominated sorting genetic algorithm II is employed to find the Pareto solutions. The updating results with the TOF defined directly using displacement, stress, and frequency are listed for the purposes of comparison. The results show that the NOF avoids determining the weighting factors and provides more accurate results than the TOF. The updated displacement curves, the position of the neutral axis, and the frequencies obtained from the NOF are all closer to the experimentally measured ones than those obtained from the TOF. After model updating, the displacement’s relative errors are around 5% without considering the displacement values under 10 mm. The relative errors of the first four frequencies are all less than 10%. The updated model can serve as the baseline finite-element model of the bridge.

Damage Detection of FRP Composite Plates from Dynamical Responses using Finite Element Model Updating: Equivalent Material Properties as Parameters

Fibre reinforced plastic (FRP) composite structures are extensively used in weight sensitive applications, such as in aircrafts, ships, etc. Such structures are susceptible to damages during their usual operation or during extreme loading from environment. Due to the anisotropic nature of FRP composite plates, damage detection is difficult for such layered materials particularly when the damage site is inaccessible. The localised loss of stiffness resulting from damage is reflected into the global dynamic responses of such structures. Finite element model updating is a convenient inverse approach in which these changes in stiffness due to damages are estimated from measured dynamical responses using optimization. The equivalent stiffness changes can be expressed in terms of either geometric or material property or both. In most of the cases, changes in geometric parameters physically represent the actual damage scenario with larger sensitivity. On the other hand, material property changes in the damaged area are a very convenient parameter to deal with. In the present work, updating parameters in the finite element model updating procedure are chosen in terms of material property. Detection of local stiffness changes from experimentally measured natural frequencies, mode shapes and/or frequency response functions are investigated. Experimental modal testing is performed on a rectangular FRP composite plate both in its undamaged and damaged state. Baseline finite element model of the composite plate is correlated with experimental model, followed by a sensitivity based finite element model updating algorithm. The results show the rapid convergence and accurate determination of local stiffness change in terms of elastic material parameters alone in all three orthogonal directions. This indicates that material properties like the in-plane Young’s moduli and in-plane Shear modulus within the localised region of damage, can well be used as convenient means for detecting equivalent stiffness loss in damaged structures.

A sequential finite element model updating routine to identify creep parameters for filament wound composite cylinders in aggressive environments

In this paper, a Finite Element Model Updating (FEMU) procedure is developed to find the best creep parameters for filament-wound cylinders under radial compression in harsh environmental conditions. Three winding angles are considered, each under three different hygrothermal conditions. The two–stage creep model captures i) primary creep through a time–hardening approach whilst ii) secondary creep is captured by Norton’s law. Given the high number of parameters in this two–stage creep model and the complexity of determining them experimentally, the FEMU routine utilises an optimisation scheme that sequentially couples a Genetic Algorithm (GA) with a gradient-based (GB) Levenberq-Marquardt Algorithm (LMA) to find all required creep input parameters to feed the model that best simulates experimental results. This framework finds the global optimum through an initial screening of the optimum area within the design space with GA, clearing the path to allow the GB algorithm to find the global optimum, substantially reducing the chance or even avoiding falling in local minima. The global search is driven by experimental data of cylinders loaded in radial compression under aggressive environments. The numerical results show excellent agreement with experimental results with reasonably low computational efforts.