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

This study introduces a Bayesian model updating approach for analyzing the long-term performance of steel–concrete composite beams (SCBs). Two nominally identical SCBs (SCB-1 and SCB-2) were designed, fabricated, and subjected to modal testing. Despite their identical design parameters, notable differences were observed in their frequencies and mode shapes during testing. Initial finite element model (FEM) analyses, developed under testing conditions, revealed notable discrepancies between theoretically computed values and the results of modal testing. To resolve these differences, the FEM was updated using the Bayesian approach, integrating the dynamic test data to enhance model accuracy. The updated FEM was subsequently employed to assess the long-term performance of the SCBs, with a particular focus on the time-dependent effects of concrete shrinkage and creep in deflection calculations. The findings reveal substantial differences in the long-term deflection predictions between the updated and initial FEM. Specifically, the long-term deflection of SCB-1 increased by 13.1%, whereas that of SCB-2 decreased by 9.8%, leading to an overall difference of 25.3% between the two beams. These findings underscore the considerable impact of fabrication errors and material inhomogeneities on structural performance, highlighting the limitations of initial FEM based solely on test parameters in accurately capturing actual behavior. Consequently, the study emphasizes the critical role of model updating in accurately predicting the long-term performance of SCBs.

In various applications it is important to determine dynamically equivalent spatial finite element (FE) model of complex structures. For instance, obtaining the FE model of an existing aerospace structure is a major requirement for reliable aeroelastic analysis. In such applications a reliable FE model may not be always available, and when this is so a dynamically equivalent FE model derived from modal test will be very useful. This paper presents a noble method to determine spatial FE model of a structure by using experimentally measured modal data along with the connectivity information of measurement points. The method is based on the mass and stiffness orthogonality equations written using experimentally determined mode shapes and natural frequencies. These equations are solved for geometric and material properties constituting global spatial mass and stiffness matrices of an initial FE model. Starting from this initial FE model, mass and stiffness orthogonality equations are updated iteratively employing experimentally obtained natural frequencies and corresponding eigenvectors from the FE model. Iterations are continued until eigensolution of the updated FE model closely correlates with experimentally measured modal data. A simulated case study on GARTEUR scaled aircraft model is presented in order to demonstrate the applicability of the method.

In order to improve the machining precision, the carriage of the gantry machine tool must have high anti-vibration performance, and its mass should be as light as possible. Based on the finite element modal analysis, a precision gantry machine tool's carriage was taken as the study object, and a multi-objective optimization mathematical model of the carriage was built by taking the mass and the first four order natural frequencies of the carriage as the objective functions, and the thickness of stiffener plates as the design variables. The second-order response surface model for carriage's multi-objective optimization was established through orthogonal experimental design. The accuracy of the response surface model was verified by comparing the response surface model with finite element model. The optimal solution of carriage multi-objective optimization was obtained by solving the response surface optimization model, which made carriage's mass decreasing 9.63%, the first four natural frequencies increasing 6.48%, 7.41%, 8.36% and 10.32% respectively. Finally, the correctness of carriage's optimization design method proposed in this paper was verified by the static and dynamic experiments.

Structural safety assessment of bowstring type RC arch bridges using ambient vibration testing and finite element model calibration

A method for continuous box-girder bridge structure finite element (FE) model updating based on static-load testing is proposed. The procedure includes field static-load testing, FE modeling, FE model (parameter) updating, etc. Based on this procedure, the structure FE model updating for an expressway 5-span pre-stressed concrete continuous box-girder bridge is conducted. And the bridge structure static FE model, which is consistent with the static-load testing actual measure response, is gained. The updated FE model (parameter) is foundation of structural performance evaluation for the bridge.

The main objective of this work is to check the compatibility of Finite element method (FEM) to determine the modal parameters of the rotor system and to compare the results with analytical method. Current work is an attempt to implement different finite element (FE) models for the estimation of modal parameters. Two different order elements from Beam, Axisymmetric and Solid FE models are considered. The analysis is carried out on the rotor system and the accuracy of the results and the computation time of the FE models are estimated. The FE results are compared with the analytical method. It is observed that FE model can be used to simulate even at higher order frequencies, which is a limitation of analytical model. The analysis shows that the FE results closely match with analytical method and also the study summarizes that proper choosing of FE helps in developing rotor models in both a desirable accuracy and efficiency. Finally, a Campbell diagram is generated using the analytical method and FEM. The critical speeds are also calculated from the Campbell diagram. The closeness of the results between the two methods is checked.

Development and calibration of digital twins for human skin growth in tissue expansion.

Probabilistic finite element predictions of the human lower limb model in total knee replacement

An efficient method for constructing multiple candidate finite element (FE) models which are consistent with the measured dynamic properties of a civil structure is presented. A parameterised sensitivity-based FE model updating method was developed to permit a feasible FE model set for the target structure to be produced. In this method, an aggregated multi-objective function, which is defined by the weighted sum of the error functions, is parameterised by its relative weighting factors. By introducing multiple parameter sets for the weighting factors, a number of optimal updated FE models are produced that permit both the natural frequency errors and mode shape errors to be simultaneously minimised. The effectiveness of the proposed method is illustrated by an example using an existing cable-stayed bridge. The findings show that error-minimised, well-distributed FE models can be obtained in terms of modal frequency errors and mode shape errors. The high quality of the candidate model sets is also verified by observations showing that the distributions of the structural parameters are consistent through each updated FE models, and the characteristic features of the target structure such as non-symmetric mode shapes are relatively well captured.

Finite element analysis model is the discretion and simplification of actual structure. Due to some uncertain factors in the process of modeling, such as element type, material properties, geometric shape, the uncertainty of boundary conditions and so on, the finite element analysis model tends to have certain error, which will affect the accuracy of the analysis results. Therefore, model updating and validation are needed to improve the accuracy and reliability of the model. Model updating method based on the first-order optimization was employed to update finite element models referring to experimental modal parameters in the paper. Taking an aero-engine simulation casing as the research object, modal test was carried out to obtain experimental modes. Then the finite element software was used to calculate the corresponding modal parameters. The calculated modal parameters were compared with the experimental ones. As the calculated results obtained by the finite element method may be not so accurate, the test modal data was utilized to update the finite element model, and the modal parameters were selected as references for optimization. With the correction of elastic moduli in each part of the finite element model, modal parameters of the updated finite element model were obtained, and modes of the revised model were in good agreement with the experimental modal parameters. The modal frequency differences between the calculated and experimental results were significantly reduced and the modal shapes of them were identical. The results demonstrated that model updating method based on the correction of elastic modulus is feasible and suitable for the accurate finite element modeling of large and complex structures in engineering.

Dynamic parametric modeling-based model updating strategy of aeroengine casings

The aircrafts with high aspect ratio wings made by a composite material have been developed, which enable high energy efficiency and long-term flight by reducing air resistance and structural weight. However, they have difficulties in securing the aeroelastic stability such as the flutter because of their long and flexible wings. The flutter is unstable self-excited-vibration caused by interaction between the structural dynamics and the aerodynamics. It should be verified analytically prior to first flight test that the flutter does not happen in the range of flight mission. Normally, the finite element model is used for the flutter analysis. So it is important to construct the finite element model representing dynamic characteristics similar to those of a real aircraft. Accordingly, in this research, to acquire dynamic characteristics experimentally the modal test of the aircraft with high aspect ratio composite wings was conducted. And then the modal parameters from the finite element analysis(FEA) were compared with those from the modal test. To make analysis results closer to test results, the finite element model was updated by means of the sensitivity analysis on variables and the optimization. Finally, it was proved that the updated finite element model is reliable as compared with the results of the modal test.

Carbon/carbon composites (C/Cs) are extensively utilized as structural materials and functional materials in the aerospace industry. Laser processing technology is an effective means of precision manufacturing C/Cs parts, with the advantages of no mechanical impact and high efficiency. Accurately predicting the material removal of C/Cs during laser processing is of great significance for the precision manufacturing of C/Cs parts. However, the numerical simulation models that can directly display the microstructure of C/Cs are still inadequate, and measuring the sublimation temperatures of two different phases of carbon is challenging. This paper establishes a three-dimensional microscopic heterogeneous finite element (FE) model of C/Cs, and the FE simulation of quasi-continuous wave (QCW) laser ablation of C/Cs is optimized using the restart method taking into account the residual temperature. Combining the optimized FE model, the material parameters of C/Cs are inverted using response surface methodology and genetic algorithm, resulting in the sublimation temperatures of the fiber phase being 4029.01 K and the matrix phase being 3481.86 K. After these parameters are substituted into the FE model, the resulting simulations are then compared with the experiments of QCW laser processing C/Cs, which reveals high correspondence between simulated morphology and experimental data, with the relative error of predicted ablation depth not exceeding 6.169%. The revised FE model can guide the laser processing of C/Cs, and the inverted material parameters can provide references for the theoretical study of the laser processing of C/Cs.

ABSTRACTThe structural stiffness of a blade changes when it is defective, which affects its modal parameters. Consequently, modal parameters can be crucial to investigating defects. Therefore, developing a model that can accurately analyze the modal parameters of healthy and defective blades is essential. This study proposes a high‐fidelity finite element (FE) model development method based on multiobjective optimization. Three 10‐kW‐class wind turbine blades were manufactured, and the modal parameter changes due to debonding damage were measured. The initial FE model was constructed using structural drawings and considering specific material properties. Subsequently, the modal analysis results were compared with the experimental results. The analysis errors of normal and abnormal blades were expressed as cost functions and multiobjective optimization was performed. Machine learning–based predictive models facilitated time‐ and cost‐effective optimization, enabling modal updating that simultaneously reflects modal parameter changes for various blade models. Because accurately predicting the dynamic characteristics of blades by various defect locations and sizes is crucial for blade damage detection, the proposed method is significant for damage detection research.

Updating the structural model of complex structures is time-consuming due to the large size of the finite element model (FEM). Using conventional methods for these cases is computationally expensive or even impossible. A two-level method, which combined the Kriging predictor and the component mode synthesis (CMS) technique, was proposed to ensure the successful implementing of FEM updating of large-scale structures. In the first level, the CMS was applied to build a reasonable condensed FEM of complex structures. In the second level, the Kriging predictor that was deemed as a surrogate FEM in structural dynamics was generated based on the condensed FEM. Some key issues of the application of the metamodel (surrogate FEM) to FEM updating were also discussed. Finally, the effectiveness of the proposed method was demonstrated by updating the FEM of a real arch bridge with the measured modal parameters.