For Finite Element Model Research Articles

Investigation of optimal parameters for finite element solution of the forward problem in magnetic field tomography based on magnetoencephalography

This paper presents an investigation of optimal parameters for finite element (FE) solution of the forward problem in magnetic field tomography (MFT) brain imaging based on magnetoencephalography (MEG). It highlights detailed analyses of the main parameters involved and evaluates their optimal values for various cases of FE model solutions (e.g., steady-state, transient, etc.). In each case, a detail study of some of the main parameters and their effects on FE solution and its accuracy are carefully tested and evaluated. These parameters include: total number and size of 3D FE elements used, number and size of elements used in surface discretisation (of both white and grey matters of the brain), number and size of elements used for approximation of current sources, number of anisotropic properties used in steady-state and transient solutions, and the time steps used in transient analyses. The optimal values of these parameters in relation to solution accuracy and mesh convergence criteria have been found and presented.

The interval intersection method for FE model updating

In this work a method for finite element (FE) model updating based on interval analysis is presented. The interval analysis inclusion theorem is exploited to achieve a solution of the model updating problem. The solution algorithm is implemented in the automatic procedure named interval intersection method (INTIM). A basic and a refined version of the method and their implementations are presented. Solutions of a numerical example are provided to show the method capabilities compared with a classical sensitivity method.

The biomechanical behaviour of the hyalinized periodontal ligament in dogs during experimental orthodontic tooth movement

During orthodontic tooth movement, the mechanical behaviour of the extracellular matrix of the periodontal ligament (PDL) determines the cellular processes involved in turnover of the PDL and alveolar bone. This mechanical behaviour is the basis for finite element (FE) models and FE analyses. Five young adult male beagle dogs were used to test the null hypothesis that the mechanical behaviour of the PDL is identical in normal and hyalinized PDL. Therefore, tooth transposition was measured after standardized force application by super-elastic nickel titanium (NiTi) coil springs, exerting a constant force of 100 cN for 5 hours in both conditions. A rapid transposition during the first few seconds was found. However, it was significantly less for hyalinized than for non-hyalinized PDL. Subsequently, a short-lived creep movement was found for hyalinized PDL, while creep persisted at the non-hyalinized sides (analysis of variance and Tukey's multiple comparisons post hoc tests). The results showed substantial biomechanical differences between hyalinized and non-hyalinized PDL at different time points (Mann-Whitney). This indicates that FE models in the study of long-term orthodontic tooth movement, which are based solely on the characteristics of normal PDL should be reconsidered.

A New Framework for the Accurate FE Model of Bone Tissue Based on CT Images

The frameworks for finite element (FE) model of bone tissue available in pervious literatures, to some extent, are expert-oriented and give rise to a considerable deviation in geometric model and assignment of material property. The objective of this study is to develop a new framework to reconstruct accurate individual bone FE model based on CT images rapidly and conveniently. In image-processing, automatic segmentation of the region of interest (ROIs) improves the efficiency. The idea of enclosed volume of interest (VOI) overcomes the drawback of geometric ambiguity in Marching Cube (MC) method. Geometric model is easily obtained by a STL translator and smooth operator in home-made program. In the material property assignment, two templates for hexahedron and tetrahedron FE models, respectively, are put forth to smoothing an abrupt change of material property in the region from cortical to cancellous. K-mean algorithm is introduced to cluster material properties to improve partition performance. Finally, the new framework is demonstrated by the implementation of a femoral FE model.

Handling of Constraints in Finite-Element Response Sensitivity Analysis

In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.

Thermal structural analysis of SST-1 vacuum vessel and cryostat assembly using ANSYS

Steady state super-conducting tokamak-1 (SST-1) is a medium sized tokamak, which has been designed to produce a ‘D’ shaped double null divertor plasma and operate in quasi steady state (1000 s). SST-1 vacuum system comprises of plasma chamber (vacuum vessel, interconnecting rings, baking and cooling channels), and cryostat all made of SS 304L material designed to meet ultra high vacuum requirements for plasma generation and confinement. Prior to plasma shot and operation the vessel assembly is baked to 250/150 °C from room temperature and discharge cleaned to remove impurities/trapped gases from wall surfaces. Due to baking the non-uniform temperature pattern on the vessel assembly coupled with atmospheric pressure loading and self-weight give rise to high thermal-structural stresses, which needs to be analyzed in detail. In addition the vessel assembly being a thin shell vessel structure needs to be checked for critical buckling load caused by atmospheric and baking thermal loads. Considering symmetry of SST-1, 1/16th of the geometry is modeled for finite element (FE) analysis using ANSYS for different loading scenarios, e.g. self-weight, pressure loading considering normal operating conditions, and off-normal loads coupled with baking of vacuum vessel from room temperature 250 °C to 150 °C, buckling and modal analysis for future dynamic analysis. The paper will discuss details about SST-1 vacuum system/cryostat, solid and FE model of SST-1, different loading scenarios, material details and the stress codes used. We will also present the thermal structural results of FE analysis using ANSYS for various load cases being investigated and our observations under different loading conditions.

Finite element modeling of piezoelectric elements with complex electrode configuration

It is well known that the material properties of piezoelectric materials stronglydepend on the state of polarization of the individual element. While an unpolarizedmaterial exhibits mechanically isotropic material properties in the absence of globalpiezoelectric capabilities, the piezoelectric material properties become transversallyisotropic with respect to the polarization direction after polarization. Therefore, forevaluating piezoelectric elements the material properties, including the couplingbetween the mechanical and the electromechanical behavior, should be addressedcorrectly. This is of special importance for the micromechanical description ofpiezoelectric elements with interdigitated electrodes (IDEs). The best knownrepresentatives of this group are active fiber composites (AFCs), macro fibercomposites (MFCs) and the radial field diaphragm (RFD), respectively. While thematerial properties are available for a piezoelectric wafer with a homogeneouspolarization perpendicular to its plane as postulated in the so-called uniform fieldmodel (UFM), the same information is missing for piezoelectric elements withmore complex electrode configurations like the above-mentioned ones with IDEs.This is due to the inhomogeneous field distribution which does not automaticallyallow for the correct assignment of the material, i.e. orientation and property. Avariation of the material orientation as well as the material properties can beaccomplished by including the polarization process of the piezoelectric transducer in thefinite element (FE) simulation prior to the actual load case to be investigated. Acorresponding procedure is presented which automatically assigns the piezoelectricmaterial properties, e.g. elasticity matrix, permittivity, and charge vector, forfinite element models (FEMs) describing piezoelectric transducers according tothe electric field distribution (field orientation and strength) in the structure. Acorresponding code has been realized for a commercial finite element programallowing for an automatic assignment of different material properties for two- andthree-dimensional FEMs with arbitrary electrode configurations. Examples of piezoelectrictransducers with complex electrode configurations are presented and the influence ofthe material description on the behavior of the modeled element is discussed.Furthermore, as an attempt at verification of the FEM simulation, a comparison ofsimulated stress concentrations with experimental investigations is presented.

Modeling the properties of closed-cell cellular materials from tomography images using finite shell elements

Closed-cell cellular materials exhibit several interesting properties. These properties are, however, very difficult to simulate and understand from the knowledge of the cellular microstructure. This problem is mostly due to the highly complex organization of the cells and to their very fine walls. X-ray tomography can produce three-dimensional (3-D) images of the structure, enabling one to visualize locally the damage of the cell walls that would result in the structure collapsing. These data could be used for meshing with continuum elements of the structure for finite element (FE) calculations. But when the density is very low, the walls are fine and the meshes based on continuum elements are not suitable to represent accurately the structure while preserving the representativeness of the model in terms of cell size. This paper presents a shell FE model obtained from tomographic 3-D images that allows bigger volumes of low-density closed-cell cellular materials to be calculated. The model is enriched by direct thickness measurement on the tomographic images. The values measured are ascribed to the shell elements. To validate and use the model, a structure composed of stainless steel hollow spheres is firstly compressed and scanned to observe local deformations. The tomographic data are also meshed with shells for a FE calculation. The convergence of the model is checked and its performance is compared with a continuum model. The global behavior is compared with the measures of the compression test. At the local scale, the model allows the local stress and strain field to be calculated. The calculated deformed shape is compared with the deformed tomographic images.

EFFECT OF CALIBRATION AND SCANNING PROTOCOLS FOR CASE SPECIFIC FINITE ELEMENT ANALYSIS

When quantitative computed tomography (CT) is used as basis for finite element (FE) modelling of bones, it is essential to correctly derive bone density from the scans using a calibration phantom. Various methods are described in the literature as how to link CT data to mechanical properties of the FE model. It is known that clear differences exist between CT data sets from bones scanned either in a water basin or in a (cadaver) body [Keyak, 2003]. We, therefore, addressed the following questions: 1. What are the differences in bone density derived from CT-data between femora scanned in situ, in a water basin, and in an anatomically shaped physical model? 2. What is the influence of different calibration methods on bone density, and on stiffness and failure load predictions by FE modelling?

Parallel Disturbance Force Compensator for Electrical Machines

The objective of the research is to diminish unwanted forces generated by rotation and unbalanced rotor mass on the rotor of an electrical machine. These forces, dependent on rotational speed, cause vibration that, when occurring in the machine's natural frequency, causes severe problems. Extra windings are built in the stator of the machine, and they are supplied with current to create an opposite force to the vibration. The main task is to develop a new controller to the system, in order to continuously provide the needed voltage input to the new actuator.The system was first modeled for finite element model (FEM) software, and based on FEM simulations a simplified state-space model was identified. Separate models for the rotor mechanics and for the actuator were created for convenience. Input to the actuator model was voltage given by the controller, and the output was the compensating force to the rotor. The rotor model mapped total input force of rotor to displacement, vibration. There was an internal feedback from rotor displacement to actuator, which was taken into account in the actuator model.Because the source of vibration is well known, the problem was attacked at the very source. A compensator was designed for balancing the forces in the rotor. The forces were not measured and remained thus unknown, but they could be estimated. The adaptive compensator was designed so that other controllers can be used parallel, without having to make any changes to the compensator.

Finite Element Modeling of the Tower of Runyang Cable-stayed Bridge Based on Ambient Vibration Test

In this paper, the multi level model updating method is put forward for finite element (FE) modeling of the bridge tower for long-span cable-stayed bridge, which includes model order updating, model structure updating, and model parameter updating. According to the design drawings of the tower of the Runyang Cable-stayed Bridge, the element numbers of the tower and calculation parameters for nodal rigid zone are both determined based on the analysis results of model order error and the structural modeling error. The FE model of the tower is further dynamically updated according to ambient vibration test through modal sensitivity based model updating method. Model updating verification results reveal that the model parameter updating should take nodal rigid zone and parameter modification restriction into account, on the basis of which the updated tower FE model can properly reflect the dynamic characteristics of the tower and can serve the baseline FE model for the purpose of structural health monitoring and safety evaluation.

Synchrotron X-ray measurement and finite element analysis of residual strain in tungsten inert gas welded aluminum alloy 2024

Residual strains have been measured in a tungsten inert gas (TIG) butt-welded 2024 aluminum alloy plate using synchrotron X-ray diffraction. Novel two-dimensional strain maps spanning the entire plate reveal steep gradients in residual stress and provide detailed validation data for finite element (FE) analysis. Two variants of a FE model have been used to predict the residual strain distributions, incorporating different levels of plate constraint. The model uses decoupled thermal and elastic-plastic mechanical analyses and successfully predicts the longitudinal and transverse residual strain field over the entire weld. For butt weld geometries, the degree of transverse constraint is shown to be a significant boundary condition, compared to simpler bead-on-plate analyses. The importance of transverse residual strains for detailed model validation is highlighted, together with the need for care in selecting the location for line scans. The residual stress is largest in the heat-affected zone (HAZ), being equal to the local postweld yield stress, though the strength increases subsequently by natural aging. In addition, a halving of the diffraction line width has been observed local to the weld, and this correlates with the microstructural changes in the region.

Stepwise reduction of functional spinal structures increase range of motion and change lordosis angle

Many investigators have performed studies on specific defect situations or determined the contribution on isolated structures. Investigating the contribution of functional structures requires obtaining the kinematic response directly on spinal segments. The purpose of this study was to quantify the function of anatomical components on lumbar segments for different loading magnitudes. Eight spinal segments (L4–5) with a median age of 52 years (ranging from 38 to 59 years) and a low degree of disc degeneration were utilized for the in vitro testing. Specimens were mounted in a custom-built spine tester and loaded with pure moments (1–10 N m) to move within three anatomical planes at a loading rate of 1.0°/s. Anatomy was successively reduced by: ligaments, facet capsules, joints and nucleus. Data were evaluated for range of motion, neutral zone and lordosis angle. Transection of posterior ligaments predominantly increased specimen flexion for all bending moments applied. Supraspinous ligament also indicated to resist in extension slightly, whereas the facet capsules did not. Facet joints contributed to axial rotation, but not in lateral bending. The anterior longitudinal ligament was found to slightly resist in axial rotation, but strongly in extension. Nucleotomy caused largest increase of all movements. The unloaded posture of the specimens changed after ligament dissection, indicating ligament pretension. The region of lumbar spine is interesting for finite element (FE) simulation due to the high evidence of disc degeneration and injuries. This study may help to understand the function of specific anatomical structures and assists in FE model calibration. We suggest to start a calibration procedure for such models with the smallest functional structure (annulus) and to cumulatively add further structures.

A POSTERIORI ERROR ESTIMATION AND H-ADAPTIVE REFINEMENT TECHNIQUES FOR TRANSIENT DYNAMIC ANALYSIS OF STIFFENED PLATE/SHELL PANELS

This paper presents a posteriori error estimation and h-adaptive refinement techniques for transient dynamic analysis of stiffened plates/shells using the finite element method (FEM). We furnish the formulation of stiffness and mass matrices for finite element (FE) models, QL9S2 and QUAD4S2 for dynamic analysis of plates/shells with arbitrarily-located concentric/eccentric stiffeners. Procedures for computing a posteriori errors for spatial and temporal errors have been presented for transient dynamic problems. An h-adaptive refinement strategy for stiffened plate/shell panels by employing QL9S2 and QUAD4S2 FE models has been discussed. An adaptive time stepping scheme, which is to be used with the time errors for quality control of the time steps, has also been presented. Numerical studies have been conducted to evaluate the efficacy of the error estimators and the adaptive mesh refinement and time stepping algorithm. The spatial error estimator for transient dynamic analysis is found to exhibit monotonic convergence at all time steps. The temporal error estimator for transient dynamic analysis in association with the adaptive time stepping is able to compute more accurate and reliable time steps to keep the time errors within the specified tolerance limits.

A two-level neural network approach for dynamic FE model updating including damping

This paper presents a two-level neural network scheme for finite element (FE) model updating in which both the structural parameters and the damping ratios are updated. Considering the fact that in a lightly damped system the damping has only negligible influence on the resonance and antiresonance frequencies of the system, in the first-level updating the model is assumed to be free of damping and the structural parameters are updated using the natural and antiresonance frequencies as the response data. With the updated structural parameters from the above first-level updating, the second-level updating procedure deals only with the damping ratios, using the integrals of frequency response function (FRF) as reference responses. For the selection of a proper response configuration, a sensitivity analysis scheme is proposed, taking into account the carry-over error during the first-level updating in addition to the anticipated error in the measured FRF data. Through a numerical example it is shown that the approach is effective and efficient. It is also shown that by means of a noise injection learning the neural network can acquire considerable noise-resisting ability, resulting in about 50% reduction of the errors in the updated parameters as compared to the anticipated errors from the sensitivity analysis.

FREQUENCY–DOMAIN CRITERIA FOR CORRELATING AND UPDATING DYNAMIC FINITE ELEMENT MODELS

This paper discusses the use of frequency–domain criteria for finite element (FE) model correlation and updating. The criteria, which can be local or global, are either shape or amplitude based. The former are sensitive to mode shape differences but not to relative scales, and the latter depend on the actual response amplitudes. The updating objective function is formulated in such a way that two global correlation criteria are satisfied simultaneously. A sensitivity-based updating problem is expressed as a set of linear equations where the coefficient matrix contains the partial derivatives of the correlation functions with respect to the chosen design variables. The formulation has the advantage of being able to deal with incomplete measurements and there is no critical selection of updating frequency points. The correlation criteria were used successfully to quantify the initial closeness between 4 increasingly detailed FE models of an automotive oil pan. The updating of the second most detailed model, using simulated response functions from the most detailed model, exhibited quick convergence properties and yielded a very good match between the target and updated frequency response functions. However, the initial FE model was corrected in a curve-fitting/minimisation sense since actual modelling deficiencies were compensated by adjusting a small number of pre-selected design parameters.

Two-Step Identification Approach for Damped Finite Element Models

The application of well-established identification procedures in the time domain for finite element (FE) models with a larger number of degrees of freedom (DOF) in general causes quite severe difficulties; i.e., the solution diverges in most cases and the procedures are computationally too demanding. In this paper, a two-step identification approach is presented that is especially suitable for FE models with many DOF. The two complementary approaches are a least-square-based method and a special form of the Extended Kalman Filter. Both approaches use modal decomposition as a key for avoiding the initially mentioned problems. To enable the identification of local damping phenomena, nonclassically damped structures are assumed throughout the computational procedures, implying the solution of the complex eigenvalue problem. For this purpose, a subspace iteration is used for solving the eigenvalue problem advantageously.