Original Finite Element Model Research Articles

An enhanced AMLS method and its performance

Abstract In this paper, we present an effective new component mode synthesis (CMS) method based on the concept of the automated multi-level substructuring (AMLS) method. Herein, the original transformation matrix of the AMLS method is enhanced by considering the residual mode effect, and the resulting unknown eigenvalue in the formulation is approximated by employing the idea of the improved reduced system (IRS) method. Using the newly defined transformation matrix, we develop an enhanced AMLS method by which original finite element (FE) models can be more precisely approximated by reduced models, and their solution accuracy is significantly improved. The formulation details of the enhanced AMLS method is presented, and its accuracy and computational cost is investigated through numerical examples.

Reduced-Order Models of Finite-Element Systems Featuring Shape and Material Parameters

Since typical finite-element systems are of high dimension, the analysis of parameter-dependent microwave structures over broad frequency bands tends to be very time-consuming. This issue is addressed by parametric order reduction, which provides a systematic methodology for constructing surrogate models that are cheap to evaluate and feature low and controllable levels of error. This article presents an order reduction technique for finite-element models that depends on the operating frequency and features explicit and implicit parameters for material properties and shape, respectively. It uses polynomial interpolation to resolve implicit parameter dependencies and employs parameter-dependent bases defined on sub-domains of parameter space. The resulting reduced-order models are of very small dimension and preserve the structure and frequency dependency of the original finite-element model. Numerical results demonstrate that the proposed method reduces solution times by several orders of magnitude compared to the underlying finite-element model at very low error.

Theoretical Efficacy of Preventive Measures for Pathologic Fracture After Surgical Removal of Mandibular Lesions Based on a Three-Dimensional Finite Element Analysis

Pathologic fracture of the mandible after removal of a lesion historically has been a clinical problem. The present study aimed to evaluate mandibular strength after removal of a lesion and to illustrate the theoretical efficacy of preventive measures against pathologic fracture based on a 3-dimensional finite element (FE) analysis. A computed tomographic (CT)-based FE model of the mandible of a patient with a dentigerous cyst including a third molar was constructed. Using this model, the decrease of mandibular strength after virtual removal of the lesion was analyzed. The effect of the decrease of occlusal force and reinforcement by a miniplate was analyzed using a simple FE model of the mandible. Based on these analyses, removal of the cyst with the third molar was performed with a decrease of occlusal force and reinforcement by a miniplate. The validity of these procedures was analyzed using a CT-based FE model constructed after surgery. The von Mises stress in a CT-based FE model after virtual removal of the cyst with the third molar was markedly greater than that in the original FE model. In the analysis using a simple FE model, the stress around the fenestrated area was decreased after premolar loading compared with that after molar loading. In addition, miniplate placement around the fenestrated area markedly decreased the stress. Based on these results, the cast crowns of the first and secondmolars were removed and the fenestrated area of the mandible was reinforced with a 1.5-mm locking miniplate in the actual surgery. The von Mises stress in the fenestrated area was decreased and primarily borne by the miniplate in the analysis of a CT-based FE model constructed after surgery. The present study illustrated the theoretical efficacy of plate application for the decrease of stress on the mandible after surgical removal of a cyst including a third molar based on a simulation by FE analysis.

SRSM-Based Stochastic Model Updating Method

With the combination of stochastic response surface model (SRSM) and Monte Carlo simulation (MCS)-based inverse error propagation method, a computational efficiency stochastic model updating approach has been proposed. The SRSM of original finite element model is determined using the Hermite polynomial chaos expansion and regression-based efficient collocation method. The efficiency of this method is demonstrated as a large number of computational demanding full model simulations are no longer essential, and instead, the updating of parameter mean values and variances is implemented on explicit SRSM. The effectiveness of this approach is validated through a bolt-jointed double-hat structure numerical example. The proposed method can be applied on stochastic uncertainty quantification of complex engineering structures.

Surface response meta-models for the assessment of embankment frictional angle stochastic properties from monitoring data: An application to harbour structures

For several decades, many structures have been monitored during maintenance or during their service lives to analyse long-term behaviour. A large number of sensors, properly distributed in the structure, are necessary, especially if the structure is complex and includes significant spatial variability. When probabilistic modelling is applied, because of intrinsic uncertainties in the model as well as uncertain physical parameters, monitoring measurements can be used to identify the parameters of the structural model. This paper presents a monitoring example of a pile-supported wharf in which tie rods are instrumented and the geotechnical characteristics of the soil embankment are identified. The modelling is performed using a meta-model fitted with a numerical database obtained from direct simulations with a finite element model implemented with Plaxis. A full quadratic response surface model (RSM) is the most efficient approximation to fit the original finite element model. The identified soil parameters enable the model to describe the variability of the measured loading in the tie rods.

Bearing parameter identification of rotor-bearing system based on Kriging surrogate model and evolutionary algorithm

Bearing dynamic parameters are important factors governing the vibration characteristics of rotating machinery, but they are usually unknown in the modeling. In this paper, an effective method is proposed to identify the bearing parameters and unbalance information of a rotor-bearing system based on the Kriging surrogate model and evolutionary algorithm (KSMEA). The initial Kriging surrogate model is constructed by the samples of various identification parameters (bearing parameters and magnitude of mass unbalance) and measured unbalance responses, which substitutes the original finite element model. It effectively reduces the computational expense of identification. In order to search for the global optimal solution exactly, one of the evolutionary algorithms, differential evolution (DE) algorithm is employed based on the constructed Kriging surrogate model. The effect on different numbers of samples is discussed to improve the accuracy of the Kriging surrogate model. Both numerical example and experimental results indicate that the proposed method can identify the bearing parameters and unbalance information of rotor-bearing system accurately and reliably.

Evaluation of Bridge Load Carrying Capacity Using Updated Finite Element Model and Nonlinear Analysis

The integrity of ageing bridges is in doubt because of increasing traffic loads, deterioration of materials, possible damage during service, and revised code requirements. Traditional methods in prediction of load varying capacity of bridges are usually based on the design blueprints and may not reflect the bridge condition as is. In this paper, the nonlinear finite element analysis, incorporating the model updating technique, is used to predict the behaviour of a 30-year-old slab-girder bridge. The original finite element model based on the design drawings is updated by modifying the stiffness parameters of the girders, slab, shear connectors and bearings so that the vibration properties of the model match the field vibration measurement data. The updated model represents the present condition of the bridge better than the original model that is based on the design blueprints. The load carrying capacity of the bridge is then calculated using the original and updated finite element models, respectively, with consideration of nonlinear material properties. The comparison shows that the bridge load carrying capacity under the present condition is lower than that under the design condition, whereas is still above the design requirement. The influence of the shear connectors on the load carrying capacity is specially investigated.

Finite Element Analysis of Large Capacity Endplate Steel Connections

Problem statement: Extended endplate connection is one of the most widely used beam-to column steel connections because of its fabrication simplicity, good overall performance and cost effectiveness compared with other connection types. The objective of this research is to develop three-dimensional finite element models to study the behavior of large capacity eight-bolt extended un-stiffened wide endplate steel connections, using current-technology elements instead of legacy elements which were previously used by other researchers. Approach: A finite element software package (ANSYS, version 11.0) was used to create and analyze three finite element models. Two of the finite element models were compared with previously reported experimental results to validate the accuracy of the finite element models. The third model was based on a modification of the second finite element model to improve bolt force distribution. Eight-node brick solid elements were used to model the connection members. The bolt shank was modeled using one three-dimensional spar element that connected the bolt head and nut together. Pretension in bolts, contact algorithm and material nonlinearity were considered in the finite element models. Results: Results of the first and the second finite element models were compared with experimental data. The comparison was based on moment-beam rotation and moment-endplate separation of the finite element models and the corresponding tested specimens. The results of the finite element models were used to compare the behavior of the bolts in the tension region adjacent to the beam bottom flange. Conclusion: The comparison showed good correlations between the finite element models and the corresponding tested specimens which confirmed the validity of the proposed models. Thus, a modified connection was proposed to improve the connection response. A finite element model of the modified connection was modeled, analyzed and compared to the original finite element model prior to modification to show their correlation.

Parallel Topology Optimization of Bi-Material Layout for Vibration Control in Plate Structures

This paper presents a parallel implementation process for the structural dynamic topology optimization problem. An energy flow analysis based topology optimization model is established for the objective of vibration control. The structural vibrations are excited by time-harmonic external mechanical loading with prescribed frequency and amplitude. Design variables are parameterized using Bi-material Solid Isotropic Material with Penalization (SIMP) models and Method of Moving Asymptotes (MMA) is applied for variable updating. A Parallel Finite Element (PFE) model is constructed by re-group the original finite element model. Each PFE will be computed by different processor, and then assembles together to get the global response. The efficiency and stability can be improved, which has been illustrated in the results discussion section in the end of the paper.

Orbital Stress Analysis, Part V

The progress in computer technology and the increased use of finite element analysis in the medical field by nonengineers and medical researchers lead us to believe that there is a need to develop a systematic approach to validate a finite element model (FEM), of a human orbit, that simulates part of the maxillofacial skeleton and to investigate the effects and the clinical significance of changing the geometry, boundary conditions, that is, muscle forces, and orthotropic material properties on the predictive outcome of an FEM of a human orbit. Forty-seven variables affecting the material properties, boundary conditions, and the geometry of an FEM of a human orbit including the globe were systematically changed, creating a number of FEMs of the orbit. The effects of the variations were quantified as differences in the principal strain magnitudes modeled by the original FEM (criterion standard), before the sensitivity analyses, and those generated by the changed FEMs. The material properties that had the biggest impact on the predicted principal strains were the shear moduli (up to 21%) and the absence of fatty tissue (up to 75%). The boundary condition properties that had the biggest impact on the predicted principal strains were the superior rectus muscle and canthal ligaments (up to 18% and 23%, respectively). Alterations to the geometry of the orbit, such as an increase in its volume, had the greatest effect on principal strain magnitudes (up to 52%). Changes in geometry, boundary conditions, and orthotropic material properties can induce significant changes in strain patterns. These values must therefore be chosen with care when using finite element modeling techniques. This study also highlights the importance of restoring the orbital fat and volume when reconstructing the orbital floor following a blunt injury. The possibility that the unrestored increase in the orbital volume and the resulting stresses may be a source of globe injuries, causing diplopia, cannot be excluded.

Optimal model-based state estimation in mechanical and structural systems

In many applications, such as control, monitoring, assessment, and failure detection in mechanical and structural systems, the state of the system is sought. However, in almost all cases, the full state vector is not directly measured, and it must be reconstructed from sparse measurements contaminated by noise. If in addition, the excitations are not (or cannot be) measured, such as the case with wind loads, wave loading, and others, the problem becomes more challenging and standard deterministic methods are not applicable. This paper presents a model-based state estimation algorithm for online reconstruction of the complete dynamic response of a partially instrumented structure subject to realizations of random loads. The proposed algorithm operates on noise-contaminated measurements of dynamic response, a finite element model of the system, and a spectral density description of the random excitation and noise. The main contribution of the paper is the development of a second-order estimator that can be directly implemented as a modified version of the finite element model of the system while minimizing the state error estimate covariance. The proposed observer results in a suboptimal Kalman filter that can be implemented as a modified version of the original finite element model of the system with added dampers and collocated forces that are linear combinations of the measurements. The proposed method is successfully illustrated and compared with the standard Kalman filter in a mass–spring–damper system under various ideal and nonideal conditions. Copyright © 2011 John Wiley & Sons, Ltd.

Multi-objective optimisation and sensitivity analysis of a paratransit bus structure for rollover and side impact tests

Paratransit buses are heavily used in the United States. A paratransit bus consists of custom passenger compartments mounted onto separate cutaway chassis. The lack of dedicated national crashworthiness standards, along with different construction methods used by paratransit fleet manufacturers, can result in a wide variance of passenger compartment structural strength. In August 2007, the Florida Department of Transportation (FDOT), to ensure adequate crashworthiness performance, introduced a standard stipulating that newly acquired buses must be tested for rollover and side impact conditions. The rollover test is performed using a tilt table test according to UN-ECE Regulation 66. The side impact test involves the impact of a bus by a common sport utility vehicle or pickup truck. In the current study, an original finite element model of a paratransit bus was used in LS-DYNA® simulations of both the rollover and the side impact testing procedures per FDOT standard. Using LS-OPT®, a metamodel-based approach was used to perform multi-objective optimisation of the bus structure for the rollover and the side impact tests. The linear ANOVA and the Sobol's indices approach were used for sensitivity analysis. The structural components of the bus having the greatest influence on the bus performance in the simulated test scenarios were identified. The simulation results show that the original bus design would pass the FDOT testing procedure. However, appropriate redistribution of the mass can noticeably increase its strength for the side impact case.

모델차수축소법을 이용한 프리스트레스 구조물의 효율적인 고유진동해석

It is necessary to use prestressed modal analysis to calculate the modal frequencies and mode shapes of a prestressed structure such as a spinning blade, a preloaded structure, or a thermally deformed pipe, because the prestress effect sometimes causes significant changes in the frequencies and mode shapes. When the finite element model under consideration has a very large number of degrees of freedom, repeated prestressed modal analyses for investigating the prestress effects might become too computationally expensive to finish within a reasonable design-process time. To alleviate these computational difficulties, a Krylov subspace-based model order reduction, which reduces the number of degrees of freedom of the original finite element model and speeds up the necessary prestressed modal analysis with the reduced order models (ROMs), is presented. The numerical process for the moment-matching model reduction is performed directly on the full order models (FOMs) (modeled in ANSYS) by the Arnoldi process. To demonstrate the advantages of this approach for performing prestressed modal analysis, the prestressed wheel and the compressor impeller under their high-speed rotation are considered as examples.

Response Surface–Based Finite-Element-Model Updating Using Structural Static Responses

With the aid of the response surface methodology, which is a combination of mathematical and statistical techniques, this paper presents a method for updating a finite-element model based on the measured static responses of structures. Unlike in the traditional model updating procedure, original finite-element models are replaced with response surface models constructed using the uniform design. By this means the complexity of a structure can be easily expressed by explicit functions with low dimensions. A parameter scope shrinking technique is also proposed to construct response surface models. The proposed method is verified against a numerical beam and an experimental full-scale continuous box-girder bridge. It is demonstrated that the proposed response surface–based finite-element-model updating in structural statics has the advantages of easy implementation, high cost-efficiency, and adequate updating accuracy. Once the response surface model that is formulated explicitly is constructed, no finite-el...

Finite element model updating in structural dynamics by using the response surface method

Fast-running response surface models that approximate multivariate input/output relationships of time-consuming physical-based computer models enable effective finite element (FE) model updating analyses. In this paper, a response surface-based FE model updating procedure for civil engineering structures in structural dynamics is presented. The key issues to implement such a model updating are discussed such as sampling with design of experiments, selecting the significant updating parameters and constructing a quadratic polynomial response surface. The objective function is formed by the residuals between analytical and measured natural frequencies. Single-objective optimization with equal weights of natural frequency residual of each mode is used for optimization computation. The proposed procedure is illustrated by a simulated simply supported beam and a full-size precast continuous box girder bridge tested under operational vibration conditions. The results have been compared with those obtained from the traditional sensitivity-based FE model updating method. The real application to a full-size bridge has demonstrated that the FE model updating process is efficient and converges fast with the response surface to replace the original FE model. With the response surface at hand, an optimization problem is formulated explicitly. Hence, no FE calculation is required in each optimization iteration. The response surface-based FE model updating can be easily implemented in practice with available commercial FE analysis packages.

Model order reduction of finite element models: improved component mode synthesis

The finite element (FE) approach constitutes an essential methodology when modelling the elastic properties of structures in various research disciplines such as structural mechanics, engine dynamics and so on. Because of increased accuracy requirements, the FE method results in discretized models, which are described by higher order ordinary differential equations, or, in FE terms, by a large number of degrees of freedom (DoF). In this regard, the application of an additional methodology, referred to as the model order reduction (MOR) or DoF condensation, is rather compulsory. Herein, a reduced dimension set of ordinary differential equations is generated, i.e. the initially large number of DoF is condensed, while aiming to keep the dynamics of the original model as intact as possible. In the commercially available FE software tools, the static and the component mode syntheses (CMS) are the only available integrated condensation methods. The latter represents the state of the art generating well-correlated reduced order models (ROMs), which can be further utilized for FE or multi-body systems simulations. Taking into consideration the information loss of the CMS, which is introduced by its part-static nature, the improved CMS (ICMS) method is proposed. Here the algorithmic scheme of the standard CMS is adopted, which is qualitatively improved by adequately considering the advantageous characteristics of another MOR approach, the so-called improved reduction system method. The ICMS results in better correlated reduced order models in comparison to all the aforementioned methods, while preserving the required structural properties of the original FE model.

Experimental and numerical study of angular error in wire-EDM taper-cutting

Wire electro discharge machining (WEDM) has become one of the most popular processes for producing precise geometries in hard materials, such as those used in the tooling industry. The so-called taper-cutting involves the generation of inclined ruled surfaces, and it is especially important in the manufacturing of tooling requiring draft angles. In this paper a new approach to the prediction of angular error in wire-EDM taper-cutting is presented. A systematic analysis of the influence of process parameters on angular error is carried out using Design of Experiments (DoE) techniques. A quadratic equation for the prediction of angular error that takes into account electrical parameters and part geometry is derived. Validation results reveal a dominant influence of the mechanical behaviour of the wire, rather than that of EDM regime. Following this assertion an original finite element model (FEM) to describe the mechanical behaviour of soft wires, typically used in taper-cutting operations, has been developed taking into account non-linear phenomena such as contact mechanics, plastic behaviour, stress-stiffening and large displacements. Both the results of DoE techniques and FEM simulation have been validated through experimental tests in industrial conditions. Deviations of accuracy of WEDM-tapered parts can be reduced to values below 4′ using these models.

축소된 유한요소모델을 이용한 하드디스크 구동부의 고유치 및 주파수응답 해석

In the case of control for mechanical systems, it is highly useful to be able to provide a compact model of the mechanical system to control engineers using the smallest number of state variables, while still providing an accurate model. The reduced mechanical model can then be inserted into the complete system models and used for extended system-level dynamic simulation. In this paper, moment-matching based model order reductions (MOR) using Krylov subspaces, which reduce the number of degrees of freedom of an original finite element model via the Arnoldi process, are presented to study the eigenvalue and frequency response problems of a HDD actuator and suspension system.

Development of a three‐dimensional finite element model of a human mandible containing endosseous dental implants. II. Variables affecting the predictive behavior of a finite element model of a human mandible

The purpose of this study was to propose a systematic approach to validate a finite element model (FEM) of the human mandible and to investigate the effects of changing the geometry and orthotropic material properties on the FEM predictions. Thirty-eight variables affecting the material properties, boundary conditions, and the geometry of a FEM of a human mandible, including two dental implants, were systematically changed, creating a number of FEMs of the mandible. The effects of the variations were quantified as differences in the principal strain magnitudes modeled by the original FEM (gold standard), prior to the sensitivity analyses, and those generated by the changed FEMs. The material properties that had the biggest impact on the predicted cortical principal strain were the shear moduli (up to 31% in difference from the unchanged state), and the absence of cancellous bone (up to 34%). Alterations to the geometry of the mandibular cross section, such as an increase in corpus dimensions, had the greatest effect on principal strain magnitudes (up to 16%). Changes in the cortical thickness in relation to the width of the corpus section modified strain more than alterations to the corpus depth (14% and 5%, respectively). The relatively small difference (up to 13.5%) between the predicted and measured interimplant distances indicates the accuracy of the FEM. Changes in geometry and orthotropic material properties could induce significant changes in strain patterns. These values must therefore be chosen with care when using finite element techniques for predicting stresses, strains, and displacements.

A new structural damage identification method

A new method is presented to provide an insight in to the characterizations of structural damages. The present algorithm makes use of an original finite element model and a subset of measured eigenvalues and eigenvectors. The proposed method detects damages in a decoupled fashion. First, a theory is developed to determine the number of damaged elements. With the damage number determined, the localization and quantification algorithms are then developed. A plane truss structure is analyzed as a numerical example to verify the present method. Results show that the method is accurate and robust in structural damage identification when the number of measured modes is more than the number of damaged elements with or without noise.