Transient Boundary Element Method Research Articles

Probabilistic chloride diffusion modelling in cracked concrete structures by transient BEM formulation

Abstract Reinforcement corrosion is a concern in the structural engineering domain, since it triggers several pathological manifestations, reducing the structural service life. Chloride diffusion has been considered one of main causes of reinforcements' corrosion in reinforced concrete. Corrosion starts when the chloride concentration at the reinforcements interface reaches the threshold content, leading to depassivation, whose assessment of its time of starts is a major challenge. This study applied the transient Boundary Element Method (BEM) approach for modelling chloride diffusion in concrete pores. The subregion BEM technique effectively represented the cracks inherent to the material domain, and environmental effects were also considered. Because of the inherent randomness of the problem, the service life was evaluated within the probabilistic context; therefore, Monte Carlo Simulation (MCS) assessed the probabilistic corrosion time initiation. Three applications demonstrated the accuracy and robustness of the model, in which the numerical results achieved by BEM were compared against numerical, analytical, and experimental responses from the literature. The probabilistic modelling substantially reduced the structural service life when the cracks length was longer than half of concrete cover thickness in highly aggressive environments.

Theoretical Analysis of Impact Noise Based on the Transient Boundary Element Method and Its Application in Offshore Drilling

Theoretical Analysis of Impact Noise Based on the Transient Boundary Element Method and Its Application in Offshore Drilling

Study on the influence of damping plates on structural vibration and radiation characteristics of the railway box girder

The influence of damping plates on structural vibration, noise and the contribution of the box girder bridge panels was analysed using the model test and numerical calculation methods. In this paper, a 1/10 scale box girder model test system was designed and constructed using a simply supported 32 m box girder from the Beijing–Shanghai high-speed railway as a prototype, and damping plates were laid on the box girder web side after the model was verified as being similar to the prototype by means of a series of model tests. The effects of the damping plates on the reduction of the structural vibration and noise were evaluated according to scaled model acoustic tests. In addition, the influence of the damping plates on the sound contribution of the panel was analysed based on the transient boundary element method. The study shows that the damping plates had an obvious vibration reducing effect on the concrete box girder, though their noise reduction properties were less than ideal. The vibration level reduction and time–history noise level reduction were kept within 10.2–29.5 dB and around 1.0 dB (A), respectively. The noise would decrease to its lowest value at 250 Hz – down to 4.0 dB. The damping plates were helpful in effectively reducing the sound power contribution and the sound pressure contribution of the concrete panel. At the peak frequencies of 17 Hz and 251 Hz, the sound power contributions of the panel on the damper side were reduced by 3.4 dB and 3.7 dB, respectively, compared with the normal side, while the sound pressure contributions on the panel decreased by 4.9 dB and 4.2 dB, respectively.

Theoretical and numerical investigation on impact noise radiated by collision of two cylinders

Impact noise characterized by high peak value and short duration is very common source of noise in the industries and in many cases can be summed up in the noise radiated by collision of two cylinders. In order to precisely predict the impact noise radiated by collision of two cylinders, a modified theoretical prediction model was established based on the Palmgren’s cylinder contact empirical model and acoustics theory. Then a numerical simulation method combining the finite element method (FEM) and the transient boundary element method (TBEM) had been presented to verify the modified theoretical model and further discuss the mechanism of impact noise. Both the contact force and impact noise of collision cylinders by the modified theoretical model were compared with the numerical results as well as the prediction results by the original theoretical model. It indicated that the results by modified theoretical prediction model are in good agreement with the numerical results, indicating better prediction superior to the original model. The impact noise radiated by collision cylinders is attributed to the rigid body acceleration. Furthermore, the experimental validations were conducted to verify the modified theoretical prediction model and numerical simulation results.

Transient wave propagation phenomena at visco-elastic half-spaces under distributed surface loadings

This article analyzes the transient wave propagation phenomena that take place at 2D viscoelastic half-spaces subjected to spatially distributed surface loadings and to distinct temporal excitations. It starts with a fairly detailed review of the existing strategies to describe transient analysis for elastic and viscoelastic continua by means of the Boundary Element Method (BEM). The review explores the possibilities and limitations of the existing transient BEM procedures to describe dynamic analysis of unbounded viscoelastic domains. It proceeds to explain the strategy used by the authors of this article to synthesize numerically fundamental solutions or auxiliary states that allow an accurate analysis of transient wave propagation phenomena at the surface of viscoelastic half-spaces. In particular, segments with spatially constant and linear stress distributions over a halfspace surface are considered. The solution for the superposition of constant and discontinuous adjacent elements as well as linear and continuous stress distributions is addressed. The in uence of the temporal excitation type and duration on the transient response is investigated. The present study is based on the numerical solution of stress boundary value problems of (visco)elastodynamics. In a first stage, the solution is obtained in the frequency domain. A numerical integration strategy allows the stationary solutions to be determined for very high frequencies. The transient solutions are obtained, in a second stage, by applying the Fast Fourier Transform (FFT) algorithm to the previously synthesized frequency domain solutions. Viscoelastic effects are taken into account by means of the elastic-viscoelastic correspondence principle. By analyzing the transient solution of the stress boundary value problems, it is possible to show that from every surface stress discontinuity three wave fronts are generated. The displacement velocity of these wave fronts can be associated to compression, shear and Rayleigh waves. It is shown that the half-space transient displacement solutions present abrupt jumps or oscillations which can be correlated to the arrival of these wave fronts at the observation point. Such a detailed analysis connecting half-space transient responses to the wave propagation fronts in viscoelastic half-spaces have not been reported in the reviewed literature.

A Transient Boundary Element Method for Acoustic Scattering from Mixed Regular and Thin Rigid Bodies

Boundary Element Methods (BEMs) may be used to predict the scattering of sound by obstacles, which has accelerated the prototyping of new room acoustic treatments such as diffusers. Unlike the more popular frequency domain method, the time domain BEM is usually solved in an iterative manner which means it can exhibit instability, a crucial impediment to its widespread use. These instabilities are primarily associated with the resonance of cavities formed by closed surface sections, but may also be caused by discretisation or integration error corrupting physical damped resonances. Regular BEM implementations cannot model objects with thin sections due to a phenomenon known as Thin Shape Breakdown. This paper develops an algorithm which combines an accepted approach for modelling thin plates with the Combined Field Integral Equation which eradicates cavity resonances, thereby permitting models of mixed regular and thin bodies. Accuracy and stability are tested by comparison to verified frequency domain BEMs, examination of the transient response, and pole decomposition. This is done for a simple obstacle and a Schroeder diffuser, which comprises a series of wells separated by thin fins. The approach is successful but universal stability cannot be guaranteed for the diffuser. It is suggested that instability is caused by the lightly damped resonances of the wells being corrupted into divergent behaviour by numerical errors.

A transient boundary element method model of Schroeder diffuser scattering using well mouth impedance

Room acoustic diffusers can be used to treat critical listening environments to improve sound quality. One popular class is Schroeder diffusers, which comprise wells of varying depth separated by thin fins. This paper concerns a new approach to enable the modeling of these complex surfaces in the time domain. Mostly, diffuser scattering is predicted using steady-state single frequency methods. A popular approach is to use a frequency domain boundary element method (BEM) model of a box containing the diffuser, where the mouth of each well is replaced by a compliant surface with appropriate surface impedance. The best way of representing compliant surfaces in time domain prediction models, such as the transient BEM is, however, currently unresolved. A representation based on surface impedance yields convolution kernels which involve future sound, so is not compatible with the current generation of time-marching transient BEM solvers. Consequently, this paper proposes the use of a surface reflection kernel for modeling well behavior and this is tested in a time domain BEM implementation. The new algorithm is verified on two surfaces including a Schroeder diffuser model and accurate results are obtained. It is hoped that this representation may be extended to arbitrary compliant locally reacting materials.

A time domain boundary element method for compliant surfaces

The best way of representing compliant surfaces in time domain prediction models, such as the transient Boundary Element Method (BEM), is currently unresolved. This is not true of frequency‐domain, time‐invariant models, where the common practice is to represent the characteristics of a material by its surface impedance. A BEM may be used to predict the scattering of sound, and reduces the problem of modelling a volume of air to one involving surfaces conformal to the obstacles. Surface impedance is a convenient concept for inclusion in the frequency domain BEM as it abstracts the obstacle's characteristics into a property of the conformal surface. The time domain BEM predicts transient scattering of sound, and is usually solved in an iterative manner by marching on in time from known initial conditions. For surface impedance data to be utilised it must be Fourier transformed from a frequency dependent multiplication into a temporal convolution. This approach typically yields convolution kernels which involve future sound, hence is not compatible with time‐marching solvers. In this paper an alternative time domain representation of compliant locally reacting materials is proposed to overcome this problem, and its implementation and limitations discussed.

Stability behaviour and results of a transient boundary element method for exterior radiation problems

Based on the Helmholtz integral equation, a boundary element method in time domain (TD-BEM) can be formulated. Because of instability issues, this method is rarely used in numerical acoustics. The stability and accuracy of the method for exterior radiation problems is investigated using some simple examples. A connection between the internal resonances of the closed structure and the instable behaviour of the method is assumed, but it is mathematically unproven. Numerical evidence of this connection is presented. Because of the sparse structure of the resulting system matrix, the use of iterative solvers is advantageous. The performances of different solvers are compared with respect to stability and numerical costs. For testing purposes, the acoustic radiation from an open turbulent flame is calculated and compared with results of a frequency domain BEM calculation.

A stable transient boundary element method (BEM) for diffuser scattering

Boundary element methods (BEM) may be used to model scattering from hard rigid surfaces such as diffusers. They have the advantage over volumetric methods that only the surface need be meshed and the surface velocity potential found. Unlike the more widely used single frequency methodology, transient BEM discretizes integral equations to produce an iterative system that is marched on in time from known initial conditions to calculate how the velocity potential varies over time. This iterative process can be unstable, and this is one reason why transient BEM is not more widely used. Previous works on transient BEMs have focused on idealized surfaces, such as spheres and plates. However, little is published on the performance of these methods for more complex surfaces of interest, such as Schröder diffusers. Consequently, this paper presents an implicit scheme suitable for a surface comprising thin and solid sections. Such an implicit scheme has the benefits of not constraining time-step duration to the smallest surface detail, and brings stability benefits. Numerical integration is carried out efficiently and accurately by conversion to contour integrals. Accuracy and stability is investigated by comparison to a verified single frequency BEM.

A transient fictitious stress boundary element method for porothermoelastic media

The development of an indirect transient boundary element method for porothermoelastic media is described. Specifically, the fictitious stress method is extended to non-isothermal poroelasticity to solve coupled porothermoelastic problems. The fundamental solutions and numerical procedures are described and an application is presented. In particular, the model is used to study the stress and pore pressure distributions around a wellbore drilled in hot rock. There is good agreement between the numerical predictions and analytical results. The analysis is useful for determining the conditions for wellbore failure while drilling as well as for calculating the classical fracture initiation pressure for hydraulic fracturing. The results indicate that the transient formulation of the fictitious stress method is an accurate and suitable means for solving problems in porothermoelasticity.

A simple comparison between two 3D time domain elastodynamic boundary element formulations

The three-dimensional transient boundary element method for elastodynamic analysis is studied here to verify its performance concerning some required features when solving practical problems. The classical formulation was established more than 10 years ago and has already been applied several times, mainly in the context of infinite domain analysis. In this work the classical fundamental solution is compared with an alternative one in which a fundamental solution based on the unit impulse is assumed distributed over a time interval. Some interesting aspects of both solutions, regarding the result confidence for practical analysis, are also discussed in the paper.

Three-dimensional transient BEM analysis

In this work the three-dimensional transient boundary element method (BEM) is studied to show its applicability when solving several problems in engineering. A general technique to combine the BEM with the finite element method (FEM) is presented, with particular emphasis on studying building structures interacting with their foundations. In order to improve the stability of the developed numerical algorithm, a modified time dependent fundamental solution was derived. The article also shows a numerical scheme to deal with time singular integrals over flat triangular and quadrangular elements.

Influence of wall slip on extrudate swell: a boundary element investigation

This paper reports a numerical study of the extrudate swell by a transient Boundary Element Method (BEM). Furthermore the fluid, which is modeled by a differential constitutive equation, is allowed to slip at the wall, where the slip velocity is a prescribed function of the wall shear stress. This function is a curve fit of the extensive data of Ramamurthy on linear low density polyethylene which incorporates two parameters: a critical wall shear stress above which slip occurs, and another parameter which governs the shape of the slip velocity versus shear stress curve. The results show that wall slip reduces both the amount of extrudate swell and the critical Weissenberg number above which our numerical scheme no longer converges.