Dynamic analysis of bridge–vehicle system with uncertainties based on the finite element model

A new method of dynamic analysis on the bridge–vehicle interaction problem considering uncertainties is proposed in this paper. The bridge is modeled as a simply supported Euler–Bernoulli beam with Gaussian random elastic modulus and mass density of material with moving forces on top. These forces are time varying with a coefficient of variation at each time instance and they are considered as Gaussian random processes. The mathematical model of the bridge–vehicle system is established based on the finite element model in which the Gaussian random processes are represented by the Karhunen–Loéve expansion and the equations will be solved by the Newmark  -β$\beta$ method. The proposed method is compared with the Monte Carlo method in numerical simulations with good agreements for cases with different vehicle speed and level of uncertainties in the excitation and system parameters. The mean value and variance of the structural responses are found to be very accurate even with large uncertainties in the excitation forces. The proposed method is also found to have superior performance in the computational efficiency compared with the Monte Carlo method.     

3-D boundary element–finite element method for the dynamic analysis of piled buildings

A boundary element–finite element model is presented for the three-dimensional dynamic analysis of piled buildings in the frequency domain. Piles are modelled as compressible Euler–Bernoulli beams founded on a linear, isotropic, viscoelastic, zoned-homogeneous, unbounded layered soil, while multi-storey buildings are assumed to be comprised of vertical compressible piers and rigid slabs. Soil–foundation–structure interaction is rigorously taken into account with an affordable number of degrees of freedom. The code allows the direct analysis of multiple piled buildings, so that the influence of other constructions can be taken into account in the analysis of a certain element. The formulation is outlined before presenting validation results and an application example.     

Fracture analysis of epoxy/SWCNT nanocomposite based on global–local finite element model

A global–local multiscale finite element method (FEM) is proposed to study the interaction of nanotubes and matrix at the nanoscale near a crack tip. A 3D FE model of a representative volume element (RVE) in crack tip is built. The effects of the length and chirality of single walled carbon nanotube (SWCNT) in a polymer matrix on the fracture behavior were studied in the presence of van der Waals (vdW) interaction as inter-phase region. Detailed results show that with increasing the weight percentage of SWCNT, fracture toughness improves. Three situations of nanotube directions with respect to crack are considered. Results show that bridging condition has minimum stress intensity factor. In addition, it can be seen that the crack resistance improves by increasing the length and chirality for all kinds of nanotubes. Finally, epoxy/SWCNT 10 wt.% has lower stress intensity factor compared to epoxy/halloysite 10 wt.% in similar loading state.     

Mechanical property analysis of kenaf–glass fibre reinforced polymer composites using finite element analysis

Nowadays, natural fibres are used as a reinforcing material in polymer composites, owing to severe environmental concerns. Among many different types of natural resources, kenaf plants have been extensively exploited over the past few years. In this experimental study, partially eco-friendly hybrid composites were fabricated by using kenaf and glass fibres with two different fibre orientations of 0° and 90°. The mechanical properties such as tensile, flexural and impact strengths of these composites have been evaluated. From the experiment, it was observed that the composites with the 0° fibre orientation can withstand the maximum tensile strength of 49.27 MPa, flexural strength of 164.35 MPa, and impact strength of 6 J. Whereas, the composites with the 90° fibre orientation hold the maximum tensile strength of 69.86 MPa, flexural strength of 162.566 MPa and impact strength of 6.66 J. The finite element analysis was carried out to analyse the elastic behaviour of the composites and to predict the mechanical properties by using NX Nastran 9.0 software. The experimental results were compared with the predicted values and a high correlation between the results was observed. The morphology of the fractured surfaces of the composites was analysed using a scanning electron microscopy analysis. The results indicated that the properties were in the increasing trend and comparable with pure synthetic fibre reinforced composites, which shows the potential for hybridization of kenaf fibre with glass fibre.     

Efficient parallel algorithms for elastic–plastic finite element analysis

This paper presents our new development of parallel finite element algorithms for elastic–plastic problems. The proposed method is based on dividing the original structure under consideration into a number of substructures which are treated as isolated finite element models via the interface conditions. Throughout the analysis, each processor stores only the information relevant to its substructure and generates the local stiffness matrix. A parallel substructure oriented preconditioned conjugate gradient method, which is combined with MR smoothing and diagonal storage scheme are employed to solve linear systems of equations. After having obtained the displacements of the problem under consideration, a substepping scheme is used to integrate elastic–plastic stress–strain relations. The procedure outlined controls the error of the computed stress by choosing each substep size automatically according to a prescribed tolerance. The combination of these algorithms shows a good speedup when increasing the number of processors and the effective solution of 3D elastic–plastic problems whose size is much too large for a single workstation becomes possible.     

A study of the geogrid–subballast interface via experimental evaluation and discrete element modelling

This paper presents a study of the interface of geogrid reinforced subballast through a series of large-scale direct shear tests and discrete element modelling. Direct shear tests were carried out for subballast with and without geogrid inclusions under varying normal stresses of \(\sigma _n =6.7\) to \(45\hbox { kPa}\). Numerical modelling with three-dimensional discrete element method (DEM) was used to study the shear behaviour of the interface of subballast reinforced by geogrids. In this study, groups of 25–50 spherical balls are clumped together in appropriate sizes to simulate angular subballast grains, while the geogrid is modelled by bonding small spheres together to form the desired grid geometry and apertures. The calculated results of the shear stress ratio versus shear strain show a good agreement with the experimental data, indicating that the DEM model can capture the interface behaviour of subballast reinforced by geogrids. A micromechanical analysis has also been carried out to examine how the contact force distributions and fabric anisotropy evolve during shearing. This study shows that the shear strength of the interface is governed by the geogrid characteristics (i.e. their geometry and opening apertures). Of the three types of geogrid tested, triaxial geogrid (triangular apertures) exhibits higher interface shear strength than the biaxial geogrids; and this is believed due to multi-directional load distribution of the triaxial geogrid.     

Natural element analysis of the Cahn–Hilliard phase-field model

We present a natural element method to treat higher-order spatial derivatives in the Cahn–Hilliard equation. The Cahn–Hilliard equation is a fourth-order nonlinear partial differential equation that allows to model phase separation in binary mixtures. Standard classical C⁰{{mathcal{C}}^0}-continuous finite element solutions are not suitable because primal variational formulations of fourth-order operators are well-defined and integrable only if the finite element basis functions are piecewise smooth and globally C¹{{mathcal{C}}^1}-continuous. To ensure C¹{{mathcal{C}}^1}-continuity, we develop a natural-element-based spatial discretization scheme. The C¹{{mathcal{C}}^1}-continuous natural element shape functions are achieved by a transformation of the classical Farin interpolant, which is basically obtained by embedding Sibsons natural element coordinates in a Bernstein–Bézier surface representation of a cubic simplex. For the temporal discretization, we apply the (second-order accurate) trapezoidal time integration scheme supplemented with an adaptively adjustable time step size. Numerical examples are presented to demonstrate the efficiency of the computational algorithm in two dimensions. Both periodic Dirichlet and homogeneous Neumann boundary conditions are applied. Also constant and degenerate mobilities are considered. We demonstrate that the use of C¹{{mathcal{C}}^1}-continuous natural element shape functions enables the computation of topologically correct solutions on arbitrarily shaped domains.     

Determination of the Young’s modulus of porous ß-type Ti–40Nb by finite element analysis

Macroporous ß-type Ti–40Nb compacts with particularly low stiffness suitable for biomedical applications were successfully processed by a space-holder sintering method with a total porosity range of 50–60%. The microstructure of these samples as well as their phase composition and their mechanical properties were carefully analyzed. The samples comprise macropores with 100–300 μm size formed by NaCl space-holder particles and micropores of 1–3 μm size within the sintered Ti–Nb alloy. The correlation between the mesoscopic Young’s modulus and the microporosity of the alloy was analyzed by combining compression tests, microcomputer tomography (μCT), and finite element analysis (FE). The derived relationship permits to predict the macroscopic Young’s modulus of macroporous compacts for a known morphology of the macroporosity.     

Low-velocity impact response of fibre–metal laminates – Experimental and finite element analysis

In this contribution, the impact dynamic response and failure modes of fibre–metal laminated panels subjected to low velocity impact were investigated and presented. The fibre–metal laminate in this paper comprised of a layer of glass fibre-reinforced plastics sandwiched between two layers of aluminium alloy. Two different types of glass fibre-reinforced plastics were used for the fabrication: unidirectional and woven. A fairly extensive experimental investigation was conducted in conjunction with a detailed finite element analysis. The experiments were conducted using a standard drop-weight test machine and the finite element analysis was carried out using a commercially available finite element software. The results of maximum contact force, contact duration and corresponding failure modes are presented, compared and discussed in this technical paper.     

Space–time SUPG finite element computation of shallow-water flows with moving shorelines

We show that combination of the Deforming-Spatial-Domain/Stabilized Space–Time and the Streamline-Upwind/Petrov–Galerkin formulations can be used quite effectively for computation of shallow-water flows with moving shorelines. The combined formulation is supplemented with a stabilization parameter that was originally introduced for compressible flows, a compressible-flow shock-capturing parameter adapted for shallow-water flows, and remeshing based on using a background mesh. We present a number of test computations and provide comparisons to theoretical results, experimental data and results computed with nonmoving meshes.     

The analysis on transverse tensile behavior of SiC/Ti–6Al–4V composites by finite element method

A two-dimensional finite element model is created to investigate the effects of temperature and residual stress on transverse tensile behaviors for SiC/Ti–6Al–4V composites with square fiber array. The spring elements are used to simulate interfacial debonding when interfacial radial stress, composed of residual radial stress and radial stress introduced by the applied transverse tensile stress, reaches interfacial bonding strength. The results indicate that temperature has an obvious influence on the collapse stress of composites due to the change of matrix strength with temperature. And the higher temperature is, the lower collapse stress is. Residual radial stress can increase the applied stress required to cause interfacial debonding, but has a little influence on the collapse stress of the composites.     

Hybrid molecular dynamics–finite element simulations of the elastic behavior of polycrystalline graphene

In this paper, we develop an efficient multiscale molecular dynamics (MD)–finite element (FE) modeling scheme capable of determining the elastic and fracture properties of polycrystalline graphene. The local elastic properties of a grain boundary (GB) connecting two adjacent graphene grains, with different lattice orientations, were first determined using MD simulations. In a two-dimensional medium, randomly distributed grains connected with GBs were then created using the Voronoi tessellation method. The constructed Voronoi diagrams were used to create FE models of the polycrystalline graphene, where the GBs were represented by interphase regions with their local properties determined using MD. The grains were modeled as pristine graphene and the accuracy of the polycrystalline FE model was validated with MD simulations of a geometrically identical polycrystalline graphene. The results reveal good agreement between MD and FE simulations. They further show that the elastic and fracture properties of polycrystalline graphene are greatly influenced by the grain size and the misorientation angle. They also indicate that the predicted elastic properties are in agreement with earlier reported experimental and MD results. We believe that this newly proposed multiscale scheme could be easily integrated into current design software to model graphene based nano- and micro-devices.     

A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner–Mindlin plates. The discrete weak form of the NS-FEM is obtained based on the strain smoothing technique over smoothing domains associated with the nodes of the elements. The discrete shear gap (DSG) method together with a stabilization technique is incorporated into the NS-FEM to eliminate transverse shear locking and to maintain stability of the present formulation. A so-called node-based smoothed stabilized discrete shear gap method (NS-DSG) is then proposed. Several numerical examples are used to illustrate the accuracy and effectiveness of the present method.     

Development of a scalable finite element solution to the Navier–Stokes equations

A scalable numerical model to solve the unsteady incompressible Navier–Stokes equations is developed using the Galerkin finite element method. The coupled equations are decoupled by the fractional-step method and the systems of equations are inverted by the Krylov subspace iterations. The data structure makes use of a domain decomposition of which each processor stores the parameters in its subdomain, while the linear equations solvers and matrices constructions are parallelized by a data parallel approach. The accuracy of the model is tested by modeling laminar flow inside a two-dimensional square lid-driven cavity for Reynolds numbers at 1,000 as well as three-dimensional turbulent plane and wavy Couette flow and heat transfer at high Reynolds numbers. The parallel performance of the code is assessed by measuring the CPU time taken on an IBM SP2 supercomputer. The speed up factor and parallel efficiency show a satisfactory computational performance.The authors wish to acknowledge Mr. W. K. Kwan of The University of Hong Kong for his help in using the IBM SP2 supercomputer.     

Distinct element analysis of the effect of temperature on the bulk crushing of α-lactose monohydrate

Cryogenic milling could reduce the ductility in the milling operations of semi-brittle and relatively ductile pharmaceutical particles. However, to achieve a better application of this technology, it is necessary to establish the relationship between the influence of temperature on the mechanical properties and breakage characteristics of the single particle and the bulk crushing behavior of these types of material. The focus of this paper is on the analysis of bulk crushing behavior of α-lactose monohydrate particles in response to temperature variations, based on single particle mechanical properties and side crushing strength at different temperatures and the use of distinct element analysis. The effect of temperature on the side crushing strength of the particles has been quantified by quasistatic side crushing tests. The experimental results show a significant increase in the strength of the single particles by decreasing the temperature. These results are used in the distinct element analysis to simulate the bulk crushing behavior of pharmaceutical particles as affected by the temperature. The predictions are compared with the experimental results, for which a reasonable agreement is found for the ambient temperature case. There are some differences for the case of −20°C, due to lack of reliable data for Young's modulus.     

Structural contribution of open-graded friction course mixes in mechanistic–empirical pavement design

Open-graded friction course (OGFC) is often believed to have no contribution to the structural capacity of flexible pavement. In this study, five types of OGFC mixtures were prepared and tested for rutting potentials, and three of them were tested for dynamic moduli, which were further used to analyse pavement's response and performance based on the procedures in the mechanistic–empirical pavement design guide (MEPDG). It was found that the tensile strain at the bottom of asphalt concrete layers and the compressive strain at the top of sub-grade layer are sensitive to the availability of OGFC, regardless of mixture type. The fatigue and permanent deformation damages of a flexible pavement can be effectively reduced after adding the OGFC layer, due to the alteration of loading frequency, thermal gradient and modulus ratio. Trial designs using MEPDG software in two different climates verify the above observations.     

Macrotexture influence on vibrational mechanisms of the tyre–road noise of an asphalt rubber pavement

The road surface is one of the most important factors that have influence on the current traffic noise. Usually, for dense surfaces, impacts of the tyre on the pavement generate vibrations which are the dominant mechanisms in the tyre–road noise. In this study, the effect of muffling these vibrations, by the incorporation of crumb rubber (CR) from wasted tyres into asphalt pavements, has been evaluated acoustically. Close proximity measurements have been carried out to register the sound emission generated in the contact zone between a reference tyre and an experimental asphalt pavement with CR. The analysis of the measurements indicates that the incorporation of CR as well as the air voids content has less influence than the macrotexture of the road surface on the acoustical behaviour of this experimental asphalt pavement.