Full-scale Finite Element Analysis Research Articles

Laboratory and numerical analyses on polyurethane–scrap rubber-reinforced base layer

Previous studies have explored using scrap rubber in constructing the ballasted track and showed tremendous potential to mitigate noise and vibration. However, its application for slab tracks has not been extensively investigated. This study intends to utilise scrap rubber in the base layer of the slab track; however, the high stress below base layer of the slab track may render its use unsuitable. The addition of scrap rubber would improve the damping performance but reduce the elastic modulus and cause excessive settlement of the track. This paper utilises an experimental programme comprising static and cyclic triaxial testing and numerical analyses to assess the suitability of four mixes, e.g., mix-A (soil), mix-B (soil mixed with rubber), mix-C (polyurethane-treated soil), and mix-D (polyurethane-treated soil mixed with rubber), as a base layer in slab tracks. The laboratory investigations reveal that the best performance in terms of improved damping ratio and resilient modulus, and lowered excess pore water pressure and vertical strains are shown by mix-D. These experimental test findings were supplemented with the results from three-dimensional full-scale finite element analyses, which showed a drastic reduction in the vibration levels of the track with mix-D as a base layer instead of conventional lean-mix concrete.

Accelerated multiscale mechanics modeling in a deep learning framework

Microstructural heterogeneity affects the macro-scale behavior of materials. Conversely, load distribution at the macro-scale changes the microstructural response. These up-scaling and down-scaling relations are often modeled using multiscale finite element (FE) approaches such as FE-squared (FE2). However, FE2 requires numerous calculations at the micro-scale, which often renders this approach intractable. This paper reports an enormously faster machine learning (ML) based approach for multiscale mechanics modeling. The proposed ML-driven multiscale analysis approach uses an ML-model that predicts the local stress tensor fields in a linear elastic fiber-reinforced composite microstructure. This ML-model, specifically a U-Net deep convolutional neural network (CNN), is trained separately to perform the mapping between the spatial arrangement of fibers and the corresponding 2D stress tensor fields. This ML-model provides effective elastic material properties for up-scaling and local stress tensor fields for subsequent down-scaling in a multiscale analysis framework. Several numerical examples demonstrate a substantial reduction in computational cost using the proposed ML-driven approach when compared with the traditional multiscale modeling approaches such as full-scale FE analysis, and homogenization based FE2 analysis. This approach has tremendous potential in efficient multiscale analysis of complex heterogeneous materials, with applications in uncertainty quantification, design, and optimization.

Thermal-mechanical coupling topology optimization of multi-phase infill structures with a non-gradient porosity optimization method

Mechanical structures in the real world are often subject to different types of physics which affect their performance and reliability. Recent studies have revealed that porous structures can be an ideal solution for multiphysics problems due to their multifunctionality. In this paper, a full-scale topology optimization method of multi-phase infill structures, i.e. non-gradient porosity optimization method, is proposed to exploit the advantages of different phase materials and solve multiphysics problems efficiently. The method builds upon a unified multi-material density-based topology optimization framework to interpolate the thermal stress coefficient in order to characterize the dependence of the thermal stress load upon the design variables. To generate sparse but stable structures distributed in the interior of a given shape, the upper bound of the solid material volume fraction in the neighborhood of each element in the design domain is constrained. In particular, the influence radius of each element is considered as a separate variable to be optimized, which is calculated directly from field functions in finite element analysis (FEA) without additional sensitivity analysis. In the proposed method, the element pseudo-density and porosity are optimized simultaneously, which further expands the design space and improves the performance of infill structures. Subsequently, the improved weighting method is used to aggregate multiple objective functions. The whole analysis and optimization process are based on a full-scale FEA, thus avoiding scale separation and naturally ensuring the optimized spatial gradient infills to be connected smoothly. Numerical examples with different thermal and mechanical load conditions are presented to demonstrate the feasibility and effectiveness of the proposed method.

Efficient characterization of dynamic response variation using multi-fidelity data fusion through composite neural network

Uncertainties in a structure is inevitable, which generally lead to variation in dynamic response predictions. For a complex structure, brute force Monte Carlo simulation for response variation analysis is infeasible since one single run may already be computationally costly. Data driven meta-modeling approaches have thus been explored to facilitate efficient emulation and statistical inference. The performance of a meta-model hinges upon both the quality and quantity of training dataset. In actual practice, however, high-fidelity data acquired from high-dimensional finite element simulation or experiment are generally scarce, which poses significant challenge to meta-model establishment. In this research, we take advantage of the multi-level response prediction opportunity in structural dynamic analysis, i.e., acquiring rapidly a large amount of low-fidelity data from reduced-order modeling, and acquiring accurately a small amount of high-fidelity data from full-scale finite element analysis. Specifically, we formulate a composite neural network fusion approach that can fully utilize the multi-level, heterogeneous datasets obtained. It implicitly identifies the correlation of the low- and high-fidelity datasets, which yields improved accuracy when compared with the state-of-the-art. Comprehensive investigations using frequency response variation characterization as case example are carried out to demonstrate the performance.

Full-scale finite element analysis of deformation and contact of a wire-wrapped fuel bundle subject to realistic thermal and irradiation conditions

The fuel bundle in a fast breeder reactor (FBR) is wrapped with wires for guiding the flow of liquid metal. Under operation condition with irradiation and high temperature, the wrapped bundle undergoes complex contact so that the flow channel of liquid will be affected. There are mainly four factors involved: radiation swelling, thermal expansion, radiation creep and thermal creep. In the present study, a full-scale finite element model (FEM) is established to consider the effect of these factors on the complex contact during operation. The established model can capture the contact separation, spacer wire’s dispersion, oval distortion and bowing details of fuel pins. The results show that the local contact dispersion caused by the wire slip can alleviate the severe transverse bending deformation of the bundle. What is more important, we find out that the dispersion of contact points in the peripheral direction of the bundle is another key factor for alleviating the severe deformation of the bundle during operation, this new mechanism – peripheral dispersion of contact – has not been achieved in previous studies.

Assessment of the shock adsorption properties of bike helmets: a numerical/experimental approach

In this paper, a numerical and experimental study of the shock absorption properties of bike helmets is presented. Laboratory compression and tensile tests were carried out on samples of expanded polystyrene (EPS) and polycarbonate (PC), respectively constituting the internal shock absorption layer and the external hard shell of composite helmets. The measured responses of the two materials were then exploited to calibrate the relevant elasto-plastic constitutive models, adopted in full-scale finite element analyses of a helmet subject to standardized impacts. The simulations allowed assessing the time evolution of the acceleration measured inside the headform (according e.g., to EN 1078) and the failure mechanisms of the helmet, if any, as induced by the localization of plastic deformations.

Nonlinear Vibration of Sandwich Beams with Functionally Graded Negative Poisson’s Ratio Honeycomb Core

This paper investigates the nonlinear flexural vibration of sandwich beams with functionally graded (FG) negative Poisson’s ratio (NPR) honeycomb core in thermal environments. The novel constructions of sandwich beams with three FG configurations of re-entrant honeycomb cores through the beam thickness direction are proposed. The temperature-dependent material properties of both face sheets and core of the sandwich beams are considered. 3D full-scale finite element analyses are conducted to investigate the nonlinear vibration, and the variation of effective Poisson’s ratio (EPR) of the sandwich beams in the large deflection region. Numerical simulations are carried out for the sandwich beam with FG-NPR honeycomb core in different thermal environmental conditions, from which results for the same sandwich beam with uniform distributed NPR honeycomb core are obtained as a basis for comparison. The effects of FG configurations, temperature changes, boundary conditions, and facesheet-to-core thickness ratios on the nonlinear vibration ratio curves and EPR–deflection curves of sandwich beams are discussed in detail.

Nonlinear dynamic response of sandwich beams with functionally graded negative Poisson’s ratio honeycomb core

This paper investigates the nonlinear dynamic response of sandwich beams with functionally graded (FG) negative Poisson’s ratio (NPR) honeycomb core in thermal environments. The novel constructions of sandwich beams with four FG configurations of re-entrant honeycomb cores through the beam thickness direction are proposed for the first time. The temperature-dependent material properties of both face sheets and core of the sandwich beam are considered. 3D full scale finite element analyses are conducted to investigate the nonlinear dynamic response, and the variation of effective Poisson’s ratio (EPR) of the sandwich beam in the large deflection region. The numerical simulations are carried out for the sandwich beam with FG-NPR honeycomb core, from which results for the same sandwich beam with uniform distributed NPR honeycomb core are obtained as a comparator. Present results indicate that, when subjected to transverse dynamic pressure, the induced dynamic bending moment of the sandwich beam with core of positive EPR is much bigger than that of the sandwich beam with NPR core, and the thickness of which will extraordinarily increase. The effects of loading types, functionally graded configurations, temperature changes, boundary conditions, and length-to-thickness ratios on the deflection-time curves and EPR-deflection curves of sandwich beams are discussed in detail.

Nonlinear bending of sandwich beams with functionally graded negative Poisson’s ratio honeycomb core

This paper investigates the nonlinear bending behavior of sandwich beams with functionally graded (FG) negative Poisson’s ratio (NPR) honeycomb core in thermal environments. The novel constructions of sandwich beams with three FG configurations of re-entrant honeycomb cores through the beam thickness direction are proposed for the first time. The temperature-dependent material properties of both face sheets and core of the sandwich beam are considered. 3D full scale finite element analyses are conducted to investigate the nonlinear bending behavior and the variation of effective Poisson’s ratio (EPR) of the sandwich beam in the large deflection region. The numerical simulations are carried out for the sandwich beams with FG-NPR honeycomb core, from which results for the same sandwich beam with uniform distributed NPR honeycomb core are obtained as a comparator. Finite element results showed that the thickness change of sandwich beams with NPR honeycomb cores are distinctly out of ordinary, and the NPR sandwich beams have significantly lower load-bending moment curves compared with those with positive Poisson’s ratio cores. The effects of functionally graded configurations, load distribution types, boundary conditions, temperature changes and length-to-thickness ratios on the bending load-deflection curves and EPR-deflection curves of sandwich beams are discussed in detail.

Reduced modal state-space approach for low-velocity impact analysis of sandwich beams

Abstract The convergence problems of nonlinear dynamic impact analysis may be in some extent overcome by using the linear forms of contact laws. However, the full-scale finite element analysis of structures with linearized contact laws need high computational efforts. In this study, an efficient reduced modal state-space approach with low computational cost was introduced to predict the dynamic structural response of sandwich beams. A one degree of freedom spring-mass system was used to model the dynamics of projectile. Furthermore, the fully dynamic equations of the sandwich beam were obtained using a new high-order finite element formulation . The dimensions of the dynamic system were reduced based on the method of truncated combination of modes. Finally, the reduced dynamic equations were solved in the framework of state-space approach. The results obtained from the present formulation were compared with the available analytical and numerical results and good agreements found between them.

A Computational Model of Bio-Inspired Soft Network Materials for Analyzing Their Anisotropic Mechanical Properties

Soft network materials constructed with horseshoe microstructures represent a class of bio-inspired synthetic materials that can be tailored precisely to match the nonlinear, J-shaped, stress–strain curves of human skins. Under a large level of stretching, the nonlinear deformations associated with the drastic changes of microstructure geometries can lead to an evident mechanical anisotropy, even for honeycomb and triangular lattices with a sixfold rotational symmetry. Such anisotropic mechanical responses are essential for certain targeted applications of these synthetic materials. By introducing appropriate periodic boundary conditions that apply to large deformations, this work presents an efficient computational model of soft network materials based on the analyses of representative unit cells. This model is validated through comparison of predicted deformed configurations with full-scale finite element analyses (FEA) for different loading angles and loading strains. Based on this model, the anisotropic mechanical responses, including the nonlinear stress–strain curves and Poisson's ratios, are systematically analyzed for three representative lattice topologies (square, triangular and honeycomb). An analytic solution of the geometry-based critical strain was found to show a good correspondence to the critical transition point of the calculated J-shaped stress–strain curve for different network geometries and loading angles. Furthermore, the nonlinear Poisson's ratio, which can be either negative or positive, was shown to depend highly on both the loading angle and the loading strain.

Uncertainty quantification in structural dynamic analysis using two-level Gaussian processes and Bayesian inference

A probabilistic framework for efficient uncertainty quantification in structural dynamic analysis is presented. This framework is built upon the combination of two-level Gaussian processes emulator and Bayesian inference technique. The underlying idea is to employ the two-level Gaussian processes emulator to integrate together small amount of high-fidelity data from full-scale finite element analysis and large amount of low-fidelity data from order-reduced analysis to improve the response variation prediction. As component mode synthesis (CMS) is adopted in order-reduced modeling, we then utilize the improved response variation prediction on modal characteristics to update the CMS model to facilitate the efficient probabilistic analysis of any responses of concern. The effectiveness of this framework is demonstrated through systematic case studies.

Vibration analysis of structure with uncertainty using two- level Gaussian processes and Bayesian inference

Vibration analysis of structure with uncertainty is computationally costly, especially when the finite element model involved has high dimensionality. In this research a combination of two-level Gaussian processes and Bayesian inference is employed to facilitate the development of an efficient and accurate probabilistic order-reduced model. We first employ the two-level Gaussian processes emulator to integrate together small amount of high- fidelity data from full-scale finite element analysis and large amount of low-fidelity data from order-reduced component mode synthesis (CMS) model to improve the response variation prediction. We then utilize the improved response variation prediction on modal characteristics to update the CMS model in the probabilistic sense. The effectiveness of this method is demonstrated through a case study.

Equation to predict maximum pipe stress incorporating internal and external loadings on buried pipes

Pipelines used for water and other services are very important lifelines in modern society. Commonly, these buried pipes are subjected to significant stresses due to external (traffic and earth) and internal (water pressure) loads. As many of these pipelines were laid sometime in the last century or earlier, in most cases their condition has deteriorated primarily by electrochemical and (or) microbiological corrosion. Corrosion activity (internal and external) can manifest in various forms, but in many cases will lead to reduced pipe thickness, which in turn leads to an increase in pipe stresses induced by the external and internal loads. Currently available analytical procedures to estimate pipe stresses are based on oversimplifications such as the two-dimensional (2-D) analysis based on Winkler springs, limiting their application to general pipe burial conditions. This paper describes the application of a three-dimensional (3-D) finite element method to analyse a buried pipe subjected to external and internal loads. Firstly, the finite element model is validated against the data from field tests conducted on the basis of a cast iron pipe that was laid in 1930 at Strathfield, Sydney, Australia. The results of these 3-D finite element analyses are then used to develop a closed-form expression to predict maximum stresses in pipes of different sizes buried in different soil types. Having obtained a good agreement between the proposed model outcomes and the 3-D finite element analysis results, the proposed model has been validated against the field test data under different internal and external loadings. The verified outcomes of the model reveal that it can be used to predict maximum stresses without conducting a full-scale finite element analysis, which often requires specific computational resources and computational skills. Furthermore, the proposed model can be used in probabilistic analyses, where a large number of calculations need to be carried out to account for the uncertainty of the input variables. The applications of the model are also discussed in relation to the assessment of pipe performance and remaining safe life.

Performance of a Prestressed Concrete Pedestrian Bridge System under Equivalent Static Lateral Impact Loads

The resistance of prestressed concrete through-girder (PCTG) pedestrian bridges to lateral loads was studied in response to the increasing number of vehicular impacts in the United States. This research was motivated by the lack of reported studies analyzing the behavior of such bridges to lateral impact loads, as well as their potential vulnerability in comparison with bridges that are better able to redistribute and transfer locally applied impact loads through alternate load paths. Pedestrian bridges are of lighter construction than highway bridges and they do not have the high degree of redundancy, making them more vulnerable to collapse in the event of vehicular impact. Results from static lateral load analyses using three-dimensional, geometrically nonlinear, full-scale finite element (FE) models of a typical bridge system and bridge subassemblages were used to evaluate the characteristics of the system. The FE models were calibrated with experimental test data on typical subassemblages and connection details for PCTG bridges. Results of the experimental part of the program have already been published elsewhere. This paper summarizes the observations obtained from nonlinear static FE analyses of a PCTG pedestrian bridge system subjected to lateral impact loads. The analyses indicated that the location of impact, the type of connector, and the flexibility of the end support details affected bridge performance. Improved connection details are suggested for enhanced PCTG pedestrian bridge performance.

Rough surface contact analysis by means of the Finite Element Method and of a new reduced model

This article presents two approaches of a normal frictionless mechanical contact between an elastoplastic material and a rigid plane: a full scale finite element analysis (FEA) and a reduced model. Both of them use a representative surface element (RSE) of an experimentally measured surface roughness. The full scale FEA is performed with the Finite Element code Zset using its parallel solver. It provides the reference for the reduced model. The ingredients of the reduced model are a series of responses that are calibrated by means of FEA on a single asperity and phenomenological rules to account for asperity–asperity interaction. The reduced model is able to predict the load–displacement curve, the real contact area and the free volume between the contacting pair during the compression of a rough surface against a rigid plane. The CPU time is a few seconds for the reduced model, instead of a few days for the full FEA.

TWO-SCALE ANALYSIS OF HONEYCOMBS INDENTED BY FLAT PUNCH

The fully implicit incremental homogenization scheme developed by Asada and Ohno (2007) for elastoplastic periodic solids is applied to two-scale analysis of honeycomb blocks subjected to flat punch indentation. To this end, the scheme is rebuilt by introducing half unit cells based on the point-symmetric distributions of stress and strain in unit cells, so that analysis domains in unit cells are reduced by half. Then, by assuming the zigzag and armchair types of cell-arrangements, the two-scale analysis of honeycomb blocks is performed. The corresponding full-scale finite element analysis is also performed to reveal the cell-arrangement dependence of cell deformation in the honeycomb blocks. It is shown that the two-scale analysis is macroscopically successful in spite of microscopic limitations.

Repair of Bridge Girder Damaged by Impact Loads with Prestressed CFRP Sheets

A sound repair on a 40 year old four-span prestressed concrete girder bridge is performed with an innovative strengthening method using prestressed carbon fiber reinforced polymer (CFRP) sheets. In fact, this application is the first North American field application of its type. An adequate repair design is conducted based on the American Association of State Highway and Transportation Officials Load Resistance Factor Design (AASHTO LRFD) and the Canadian Highway Bridge Design Code. To ensure the feasibility of the site application using prestressed CFRP sheets, tests are conducted and closed-form solutions are developed to investigate the behavior of the anchor system that is necessary for prestressing the CFRP sheets. A full-scale finite-element analysis (FEA) is performed to investigate the flexural behavior of the bridge in the undamaged, damaged, and repaired states. The AASHTO LRFD exhibits conservative design properties as compared to the FEA results. The repaired bridge indicates that the flexural...

A reduced eigenvalue method for broadband analysis of a structure with vibration absorbers possessing rotatory inertia

Multi-tuned vibration absorbers are attractive in reducing vibration and noise over a broadband. Here, an efficient and robust dynamic reanalysis algorithm is presented for predicting the dynamic response of a base structure to which are attached multiple absorbers. The ‘reduced eigenvalue method’ uses the modal analysis results of the base structure without absorbers, computed just once, to obtain the response of the modified structure. The method presented has two salient features. One is that the resonances of the modified structure are provided, and can be summed directly to estimate broadband measures of the dynamic response. The other is that rotatory inertia of the absorbers is properly captured, which has been found from experiment to be significant when an absorber is attached to a point on the base structure undergoing rotation. The method is contrasted with the impedance-based approaches. The method is used to model a three-dimensional absorber on a structure, which has been built, and is shown to correlate with experiment and full-scale finite element analysis.

Approximate Prediction of Hoop Stresses at Major Sections of Tee Intersections of Cylindrical Shells Subjected to Internal Pressure

An approximate method is formulated to predict elastic hoop stresses in the longitudinal plane of unreinforced pressurized tees using axisymmetric solutions from plate-cylindrical shell intersections. These stresses are compared with experimental data and finite element results. Correspondence of values is such that the present method may be preferred to a full-scale finite element analysis for some cases. A comparison is also made between the hoop stresses in the transverse plane of tees and those in sphere-cylinder intersections. Hoop stresses from these two solutions do not compare.