Dung Beetle Optimization Algorithm for Predicting Damage to 2D Truss Structures

A reliable and accurate analytical model is desired for the printed circuit board (PCB) with IC package to predict the system response due to loadings such as shock and vibration simulation or even with thermal effect. This work addresses the procedure of model verification by the adoption of experimental modal analysis (EMA) to validate the finite element (FE) model constructed by FE commercial software. The PCB with one package adhered with the heating pad to emulate the heat effect is first considered for completely free boundary condition. The refined FE model of the PCB consists of detail components, such as the chip, substrate, compound and solder balls. The thermal effect on the PCB is simulated to conduct the temperature field analysis as well as the thermal stress. The modal analysis on the PCB with the heating in steady state is then performed to obtain the structural modal parameters, i.e. natural frequencies and mode shapes. The EMA is also carried out to determine the system modal properties that are used to update the analytical FE model. Through the comparison of frequency response functions and modal parameters between the analytical FE model and the real PCB structure, the refined FE model can be verified for material properties and thermal boundary conditions. The same procedure for model verification is then conducted via both EMA and FEA on the PCB in the fixed boundary that complies with the test fixture for the random vibration test of JEDEC specification. The verified equivalent FE model of the PCB can then be adopted to perform spectrum response analysis accordingly.

Damage identification of structures using incomplete mode shape and improved TLBO-PSO with self-controlled multi-stage strategy

Purpose The present paper aims to describe the model updating of a small aircraft dynamic finite element model (FEM) to improve its agreement with ground vibration test (GVT) data. Design/methodology/approach An automatic updating method using an optimization procedure is carried out. Instead of using dedicated updating tools, the procedure is implemented using standard MSC/NASTRAN because of wide availability of the software in small aircraft industries. The objective function is defined to minimize the differences in the natural frequency and the differences in the mode shape between the analytical model and the GVT data. Provision has been made to include the quantification of confidence in both the GVT data and in the initial model. Parameter grouping is carried out to reduce the number of design parameters during the optimization process. Findings The optimization module of standard finite element (FE) software can be effectively used to reduce the differences between the GVT and the FEM in terms of frequency and mode shape satisfactorily. The strategy to define the objective function based on minimizing the mode shape error can reduce the improvement in the frequency error. The required user interference can be kept low. Originality/value The most important contribution of the present paper concerns the combination of strategies to define the objective function and selection of the parameters.

Modal analysis is an approach to determine the dynamic behavior of a structure through numerical analysis or experimental approach. Nowadays, numerical analysis has been preferred by most researchers and engineers compared to experimental analysis to analyze the structure due to expenditure and time consuming factors of the research. Recently, numerical analysis is done computationally or well known as Finite Element Analysis (FEA) by using finite element (FE) model to replicate the real test structure. Instead of advantage of FE analysis, the trustworthiness of FE model has been questioned since simplification has been made during design stage for complex structure and inaccurate of geometry input of the model. Hence, this paper is carried out to reduce the discrepancies between numerical prediction results with measured test data on FE model of exhaust structure by implementing FE model updating using SOL200 algorithm. Initially, the FE model is running on normal mode analysis SOL103 to extract the modal parameters such as natural frequency and mode shape. Then, the numerical pre-diction result has been correlated and validated with measured test data obtained through Experimental Modal Analysis (EMA). Due to disagreement between numerical result and experimental data in correlation process, the FE model has been updated using SOL200 algorithm. The percentage error between numerical prediction result and measured test data is minimized from 5.67 to 3.23% after been updated. It’s shown the capability SOL200 algorithm in preparing the reliable FE model before been used for further analysis such as structural dynamic modification.KeywordsDynamic studyJoints strategyFinite element analysisExperimental modal analysisFE model updating

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.

There has been a growing demand for nonlinear model updating procedures in the structural dynamics community as advanced vehicles have started to incorporate nonlinearity into their designs. Finite element (FE) model updating is difficult for a nonlinear structure for several reasons: there may be many unknown parameters in the FE model so that multiple solutions may exist, and it is very expensive to compute the structure’s nonlinear normal modes from a full FE model that are an excellent metric to use for nonlinear updating. A recent work showed that some of these challenges can be overcome by updating a nonlinear reduced order model (ROM) rather than the full FE model. The updated ROM can be used to compute response statistics, stresses and ultimately life of the structure. However, one drawback of this approach is that one does not gain physical insight into which parameters in the FE model were in error, and so it is difficult to transfer the lessons learned to future FE models. This work explores the feasibility of updating a FE model to correlate with a ROM with a set of known parameters. The target ROM parameters consist of the linear stiffness and the nonlinear stiffness coefficients which have been identified previously by updating the ROM to correlate with experimental measurements. In this process an optimization routine is setup in which the free parameters are those of the FE model, such as boundary stiffness springs, imperfections, pre-stress, etc. The optimization procedure is wrapped around a ROM creation algorithm that iteratively tunes the FE parameters, creates a ROM, and evaluates the ROM parameters with respect to the target ROM in order to minimize the objective function. This work will demonstrate the procedure on a numerical example of a curved beam in order to verify its effectiveness on the nonlinear model updating.

This study investigates the feasibility of an alternative structural health monitoring (SHM) technique for an existing, post-tensioned, prestressed concrete bridge in Niigata, Japan. Currently, a static SHM system is in place to detect the progress of damages within the bridge. However, the existing system cannot properly monitor the structural health of the bridge including the periodic vibration, which is one of the damage-sensitive features of interest. Therefore, to effectively detect the real-time performances of the bridge, a three-dimensional (3D) Finite Element (FE) model was developed as a reference and verified using on-site load-deflection test results. After validating the reference FE model, different damage scenarios, such as degradation of concrete, corrosion & rupture of steel tendons and missing tendons, were incorporated in the FE models. Based on non-linear structural and Eigenvalue analyses, natural frequencies and mode shapes of the bridge remain constant even after careful consideration of all types of damages in the FE model. However, vertical displacements are observed to increase for the damage scenarios. Although the effect of tendon rupture and corrosion showed negligible influences on the vertical displacement, the deterioration of the concrete largely influenced the vertical displacement. Additionally, crack widths were found to vary with damage types. Brifely, this study recommends some effective indicators to monitor the structural conditions of the bridge using FE analysis (FEA).

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.

The vibrational effect is one of the primary considerations during construction due to the ambient excitation from the surrounding environment. Thus, it is necessary to find the most dependable Finite Element (FE) model for the actual structure to improve its quality and life span on site. In this context, the study included a 3-story building model that was analyzed using finite element analysis to determine its dynamic properties such as natural frequency and mode shape to avoid the resonance effect. It is due to the importance of obtaining a reliable and accurate model by verifying with the results of the Operational Modal Analysis (OMA). In general, the goal of this study is to update the FE model so that it is close to the actual scaled model based on the previous OMA study. As a result, an initial linear FE model of the 3-story building scaled model was created using CAD software based on actual geometry to describe the structure's physical properties. The FE model was then imported into CAE software, where the boundary condition and estimated material properties were assigned to determine the effect of random vibration. Through the pairing of Finite Element Analysis results and previous studies, 9 natural frequencies and 9 mode shapes were extracted. The Modal Assurance Criterion (MAC) was used to compare the mode shape of FE results against the OMA to determine the degree of consistency between paired mode shapes. A model updating process was carried out to reduce the discrepancy between the methods. The uncertainties arising from the initial conditions have been discussed in terms of the stiffness of the material used. The updated model allows for an evaluation of the structure's current actions as well as the development of models for a wide range of potential future research scenarios.

Finite element model updating from full-field vibration measurement using digital image correlation

Skull stiffness of children is of great significance to protect brain tissues during traffic accidents. In this paper, the effects of skull stiffness on traumatic brain injury (TBI) are investigated by using a validated 6-year-old child head finite element (FE) model according to Chinese standard GB/T 24550-2009 Results showed that the HIC value, intracranial pressure, Von Mises stress and shear strain of brain tissue increased with the decrease of skull stiffness during the impact of FE model with engine hood. Therefore, the injury risk of the child head decreases with the increase of skull stiffness. And the skull with higher stiffness can provide a better protection for brain tissues during traffic accidents.

Accurate representation of bolted joints in the finite element (FE) model of a built-up structure is a crucial factor in ensuring the accuracy and reliability of the dynamic behaviour prediction of the structure. Modelling of bolted joints in industrial structures has not been widely and thoroughly studied, especially in the dynamic response of the bolted joint itself. The aim of this work is to investigate several flexibility formulae for the calculation of the stiffnesses of CBUSH elements for the modelling of the bolted joints. The flexibility formulae used in this work are attributed to Huth, Tate & Rosenfeld, Boeing, Swift and Grumman. The results of the normal modes analysis of the FE models with different flexibility formulae were compared with those obtained from the experimental modal analysis (EMA). EMA was performed to measure the natural frequencies and mode shapes of the structure with bolted joints. The total errors calculated from the comparisons between FE and EMA were recorded for all flexibility formulae. The results of the investigation demonstrated that there are noticeable variations in the total errors recorded using different flexibility formulas for the CBUSH element representing the bolts in the FE model of the structure with bolted joints. It was found that the Swift’s flexibility formula is the most appropriate for the prediction of the natural frequencies of the structure with bolted joints.Accurate representation of bolted joints in the finite element (FE) model of a built-up structure is a crucial factor in ensuring the accuracy and reliability of the dynamic behaviour prediction of the structure. Modelling of bolted joints in industrial structures has not been widely and thoroughly studied, especially in the dynamic response of the bolted joint itself. The aim of this work is to investigate several flexibility formulae for the calculation of the stiffnesses of CBUSH elements for the modelling of the bolted joints. The flexibility formulae used in this work are attributed to Huth, Tate & Rosenfeld, Boeing, Swift and Grumman. The results of the normal modes analysis of the FE models with different flexibility formulae were compared with those obtained from the experimental modal analysis (EMA). EMA was performed to measure the natural frequencies and mode shapes of the structure with bolted joints. The total errors calculated from the comparisons between FE and EMA were recorded for all fle...

While linear finite element (FE) model updating has been successfully applied for predicting structural damage as loss of effective stiffness, nonlinear FE model updating can provide improved and more accurate damage identification (i.e., a more comprehensive measure of damage) and can additionally be used as a tool for damage prognosis. The current study is focused on characterizing the nonlinear material behavior in a FE model of a three-story infilled frame using the identified instantaneous natural frequencies and mode shapes. The 2/3-scale, 3-story, 2-bay reinforced concrete frame with masonry infills was subjected to large amplitude earthquake base excitations on a shake table. The deterministic stochastic subspace identification method is used for estimating the instantaneous (during short-time windows) modal parameters of the structure based on the nonlinear response of structure during a seismic base excitation. Parameters of a priori selected hysteretic models (Bouc-Wen) at different finite elements of the structural model are calibrated to minimize the misfit between the identified modal parameters and those from the FE model. The accuracy of the calibrated FE model is assessed through the comparison of the predicted response and natural frequencies obtained from the model with those of the specimen.

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.

As part of the FalconSAT student-built small satellite program at the United States Air Force Academy, a structural engineering model (SEM) was constructed to simulate the mass and stiffness properties of the flight model. The SEM was dynamically characterized using a scanning laser velocimeter that quickly collected data from several thousand closely-spaced points on the surface of the satellite. Orthogonal mode shape vectors were then extracted from the measured frequency response functions and used to evaluate an initial a priori finite element (FE) model created from the solid model geometry files from which the SEM was machined. Visual and Modal Assurance Criteria comparisons of the measured and modeled mode shapes and frequencies indicated a need to update the FE model. An optimization was then run in which an objective cost function consisting of the error in first three natural frequencies and second mode shape was minimized, resulting in a very accurate FE model of the first three modes (less than 1% frequency errors, greater than 0.95 MAC values) – the modes that experience the greatest deflection under launch loads and are therefore potentially damaging to the satellite and booster. The high-density experimental data collected here is vital to the extension of the FE model tuning beyond the first three modes to create a model that is accurate over a wide range of frequencies and a large number of modes.