Combined Finite-element Boundary-element Research Articles

Dynamic Damage Quantification of Slab Tracks—Finite Element Models on Winkler Soil and Finite-Element Boundary-Element Models on Continuous Soil

Train passages over intact or damaged slab tracks on different soils were calculated by two methods. The finite element method (FEM) uses a Winkler soil under the track model by adding a thin “soil layer”. The combined finite-element boundary-element method has a continuous soil model that is included by the boundary element method. The basic results are the distributions of the track (rail, track plate, and base layer) displacements along the track for a single axle load. These solutions were superposed to a complete train load and transformed to time histories. The influence of track and soil parameters was analysed. The main interest was the influence of the track damage. A gap between the track plate and base layer of different lengths was studied for changes in amplitudes and widths of deflection. A best fit to measured track displacements was found so that the track damage could be identified and quantified. The FEM model with the Winkler soil cannot be fitted to the amplitude and width with the same soil parameters. Therefore, the FEBEM model is preferable for these railway track problems.

Compliance and damping of piles for wind tower foundation in non-homogeneous soils by the finite-element boundary-element method

A combined finite-element boundary-element method for the dynamic interaction of the soil with flexible structures such as single piles or complete wind energy towers has been developed. Flexible piles in different soils are analysed in frequency domain. The different parameters such as the stiffness of the soil, the bending stiffness and the radius of the hollow pile are analysed for their influence on the complex compliances. The results have been determined as specific power laws which are different for the different load cases (horizontal, rocking, coupling) and for the different soil models (Winkler, continuum with constant, root-parabolic and proportional-linear stiffness variation). The strongest influence of the soil stiffness can be found for the homogeneous soil and the horizontal component. Winkler soils have a weaker influence than the corresponding continuous soils. An offshore wind energy tower has been modeled and calculated for wind and wave loads.

Scoping assessment of free-field vibrations due to railway traffic

The number of railway lines both operational and under construction is growing rapidly, leading to an increase in the number of buildings adversely affected by ground-borne vibration (e.g. shaking and indoor noise). Post-construction mitigation measures are expensive, thus driving the need for early stage prediction, during project planning/development phases. To achieve this, scoping models (i.e. desktop studies) are used to assess long stretches of track quickly, in absence of detailed design information. This paper presents a new, highly customisable scoping model, which can analyse the effect of detailed changes to train, track and soil on ground vibration levels. The methodology considers soil stiffness and the combination of both the dynamic and static forces generated due to train passage. It has low computational cost and can predict free-field vibration levels in accordance with the most common international standards. The model uses the direct stiffness method to compute the soil Green's function, and a novel two-and-a-half dimensional (2.5D) finite element strategy for train-track interaction. The soil Green's function is modulated using a neural network (NN) procedure to remove the need for the time consuming computation of track-soil coupling. This modulation factor combined with the new train-track approach results in a large reduction in computational time. The proposed model is validated by comparing track receptance, free-field mobility and soil vibration with both field experiments and a more comprehensive 2.5D combined finite element-boundary element (FEM-BEM) model. A sensitivity analysis is undertaken and it is shown that track type, soil properties and train speed have a dominant effect on ground vibration levels. Finally, the possibility of using average shear wave velocity introduced for seismic site response analysis to predict vibration levels is investigated and shown to be reasonable for certain smooth stratigraphy's.

Force and ground vibration reduction of railway tracks with elastic elements

The reduction of train-induced ground vibration by elastic elements such as rail pads and sleeper pads has been analyzed by a combined finite-element boundary-element method. The dynamic compliance of the track, the transfer function of the total force on the ground and the ground vibration ratios have been calculated for a variety of isolated and un-isolated track systems. It has been found that the soil force transfer, which describes the excitation force of the soil, is an appropriate quantity to predict the reduction of the ground vibration and the effectiveness of isolated tracks. All force transfer functions of isolated tracks display a vehicle–track resonance where the wheelset on the compliant track is excited by wheel and track irregularities. At higher frequencies, considerable reductions of the amplitudes are observed as the benefit of the resilient element. The influence of the stiffness of the rail or sleeper pads, the ballast and the soil, and the mass of the sleeper and the wheelset on the resonance frequency and the reduction has been investigated. Sleeper pads are advantageous due to the higher mass that is elastically supported compared to the rail-pad track system. The combination of elastic rail and sleeper pads has been found to be disadvantageous, as the second resonance occurs in the frequency range of intended reduction.

Response to harmonic wave excitation of finite or infinite elastic plates on a homogeneous or layered half-space

The soil–structure interaction of elastic plates on homogeneous or layered soils excited by horizontally propagating waves is analysed. Large plates are modelled by a combined finite-element boundary-element method (FEBEM), whereas the response of infinitely long plates is calculated by a numerical integration in the frequency–wavenumber domain. The finite-element boundary-element method yields the complete soil–plate transfer function of frequency and distance whereas the frequency–wavenumber solution of the infinitely long plate can serve as an approximation for long distances on a finitely long plate. The soil–plate transfer function starts to decrease strongly at the coincidence frequency, where the bending stiffness equals the plate inertia. A strong decrease follows at mid frequencies and a strong reduction of less than 0.1 of the ground vibration is reached at high frequencies. Rules for the characteristic frequencies are derived from the numerical results clearly indicating the strongest influence of the soil stiffness and the weaker influence of the bending stiffness of the plate. The influence of the mass, length and width of the plate are shown to be limited in case of realistic parameters, but it should be noted that the reduction effects are less effective for layered soils and for nearer observation points.

Forming tubular hexahedral screws—Process development by means of a combined finite element-boundary element approach

Abstract The aim of the present paper is twofold: first, to propose a new forming process that is capable of producing hexahedral heads with washers in tubular screws and, second, to present a numerical approach to solve the plastic deformation of the tubular preforms and the elastic deformation of the dies. The methodology draws from independent determination of mechanical properties and fabrication of prototypes with a forming tool designed and fabricated by the authors to the development of a direct boundary integral element formulation for solving the elastic deformation of the dies inside an existing in-house finite element computer program. The performance of the proposed forming process is assessed by experimentation and results and observations are explained in the light of the proposed numerical approach based on the combination of the finite element (FE) with the boundary element (BE) methods. Because project and design of tooling is often only dependent on boundary solutions for the elastic deformation of dies and for the contact between the workpiece and the dies, the proposed FE–BE approach seems as a cost-effective methodology that avoids discretization of dies by finite elements, reduces the overall size and improves the performance of the resulting computer models.

Thin-Shell Formulation Applied to Superconducting Shields for Magnetic Field Mitigation

The thin-shell formulation is applied to a combined finite element-boundary element technique to study the magnetic shielding efficiency of superconducting layers and hybrid superconducting-ferromagnetic sandwich structures in 3-D domains. The behavior of the superconducting material, assumed to be in a Meissner-like state, is here described by the London model. The numerical simulations are validated by comparison with the experimental results obtained for magnesium diboride (MgB2) samples having different shapes (i.e., disk, cup) and immersed in uniform low dc magnetic fields.

Theoretical and experimental excitation force spectra for railway-induced ground vibration: vehicle–track–soil interaction, irregularities and soil measurements

Excitation force spectra are necessary for a realistic prediction of railway-induced ground vibration. The excitation forces cause the ground vibration and they are themselves a result of irregularities passed by the train. The methods of the related analyses – the wavenumber integration for the wave propagation in homogeneous or layered soils, the combined finite-element boundary-element method for the vehicle–track–soil interaction – have already been presented and are the base for the advanced topic of this contribution. This contribution determines excitation force spectra of railway traffic by two completely different methods. The forward analysis starts with vehicle, track and soil irregularities, which are taken from literature and axle-box measurements, calculates the vehicle–track interaction and gets theoretical force spectra as the result. The second method is a backward analysis from the measured ground vibration of railway traffic. A calculated or measured transfer function of the soil is used to determine the excitation force spectrum of the train. A number of measurements of different soils and different trains with different speeds are analysed in that way. Forward and backward analysis yield the same approximate force spectra with values around 1 kN for each axle and third of octave.

Dynamics of the railway track and the underlying soil: the boundary-element solution, theoretical results and their experimental verification

A combined finite-element boundary-element method is presented in detail to calculate the dynamic interaction of the railway track and the underlying soil. A number of results are shown for ballasted and slab track, demonstrating the influence of the stiffness of the soil and the rail pads on the vertical compliance of the track. The compliance of the track is combined with a simple model of the vehicle giving the transfer function of vehicle–track interaction. An experimental verification of the theoretical results is achieved by harmonic and impulse excitation with and without static (train-) load and by combined measurements of train–track–soil interaction. A clear vehicle–track resonance is found for the slab track with elastic rail pads and for higher frequencies at highspeed traffic, the dynamic axle loads due to sleeper passage are reduced.

Coupled thermo-mechanical analysis of metal-forming processes through a combined finite element-boundary element approach

This paper presents a new approach for obtaining the distribution of temperature in the dies during thermo-mechanical numerical analysis of metal forming problems. The proposed approach is based on a solution resulting from the combination of the finite element method with the boundary element method. The finite element method is used to perform the numerical modelling of the thermo-mechanical deformation of the workpiece, taking into account the geometrical and material non-linearities as well as the influence of the temperature distribution on the mechanical behaviour of the material. The boundary element method is applied for computing the distribution of temperatures in the dies. The combination of the two numerical methods is made using the finite element solution of the heat flow exchanged across the die–workpiece interface to define the boundary conditions to be applied on the thermal analysis of the dies. A numerical example of compression under plane-strain conditions is included to show the applicability of the proposed approach. © 1998 John Wiley & Sons, Ltd.

On the efficient analysis of shallow tunnels

The numerical analysis of shallow tunnels using a combined Finite Element-Boundary Element method is discussed. The theory of coupling the Boundary and Finite Element discretisation is presented and solutions obtained by the method compared with analytical results for near surface circular excavations. The coupled method is then applied to a practical problem in tunneling.