Boundary Element Method Model Research Articles

A Coupled Smoothed Finite Element-Boundary Element Method for Structural-Acoustic Analysis of Shell

Abstract Nowadays, the finite element method (FEM) - boundary element method (BEM) is used to predict the performance of structural-acoustic problem, i.e. the frequency response analysis, modal analysis. The accuracy of conventional FEM/BEM for structural-acoustic problems strongly depends on the size of the mesh, element quality, etc. As element size gets greater and distortion gets severer, the deviation of high frequency problem is also clear. In order to improve the accuracy of structural-acoustic problem, a smoothed finite-element/boundary-element coupling procedure (SFEM/BEM) is extended to analyze the structural-acoustic problem consisting of a shell structure interacting with the cavity in this paper, in which the SFEM and boundary element method (BEM) models are used to simulate the structure and the fluid, respectively. The governing equations of the structural-acoustic problems are established by coupling the SFEM for the structure and the BEM for the fluid. The solutions of SFEM are often found to be much more accurate than those of the FEM model. Based on its attractive features, it was decided in the present work to extend SFEM further for use in structural-acoustic analysis by coupling it with BEM, the present SFEM/BEM is implemented to predict the vehicle structure-acoustic frequency response analysis, and two numerical experiments results show that the present method can provide more accurate results compared with the standard FEM/BEM using the same mesh. It indicates that the present SFEM/BEM can be widely applied to solving many engineering noise, vibration and harshness (NVH) problems with more accurate solutions.

Spark-generated bubble near an elastic sphere

The interaction between a spark-generated bubble and an elastic sphere is investigated. A spark-generated bubble is created at various distances horizontally away from a suspended elastic sphere made of silicone rubber or super absorbent polymer (of shear modulus of elasticity G of between 5 and 312kPa), using a low-voltage spark discharge method. We observe pronounced deformation and elongation of the elastic sphere when the spark-bubble is generated very close to a sphere. This happens when the elastic sphere has a small modulus of elasticity and a small size ratio R’ between the bubble and the elastic sphere (i.e. the bubble and the sphere have similar radii). Numerical simulations are also conducted using a Boundary Element Method (BEM) model coupled with a Finite Element Method (FEM) solver. The simulation results compare well with the experimental data. The numerical model is then extended to study the effects of elasticity and experimental parameters, such as the dimensionless stand-off distance H’, and size ratio R’, on the degree of deformation of the elastic cell and the dynamics of the bubble.

Tectonic role of margin-parallel and margin-transverse faults during oblique subduction in the Southern Volcanic Zone of the Andes: Insights from Boundary Element Modeling

Obliquely convergent subduction margins develop trench-parallel faults shaping the regional architecture of orogenic belts and partitioning intra-plate deformation. However, transverse faults also are common along most orogenic belts and have been largely neglected in slip partitioning analysis. Here, we constrain the sense of slip and slip rates of differently oriented faults to assess whether and how transverse faults accommodate plate-margin slip arising from oblique subduction. We implement a forward 3D boundary element method (BEM) model of subduction at the Chilean margin evaluating the elastic response of intra-arc faults during different stages of the Andean subduction seismic cycle (SSC). Our model results show that the margin-parallel, NNE-striking Liquine-Ofqui Fault System (LOFS) accommodates dextral-reverse slip during the interseismic period of the SSC, with oblique slip rates ranging between 1-7 mm/yr. NW-striking faults exhibit sinistral-reverse slip during the interseismic phase of the SSC, displaying a maximum oblique slip of 1.4 mm/yr. ENE-striking faults display dextral strike-slip, with a slip rate of 0.85 mm/yr. During the SSC coseismic phase, all modeled faults switch their kinematics: NE-striking fault become sinistral whereas NW-striking faults are normal-dextral. Because coseismic tensile stress changes on NW faults reach 0.6 MPa at 10-15 km depth, it is likely that they can serve as transient magma pathways during this phase of the SSC. Our model challenges the existing paradigm wherein only margin-parallel faults account for slip partitioning: transverse faults are also capable of accommodating a significant amount of plate-boundary slip arising from oblique convergence.

A new simple multidomain fast multipole boundary element method

A simple multidomain fast multipole boundary element method (BEM) for solving potential problems is presented in this paper, which can be applied to solve a true multidomain problem or a large-scale single domain problem using the domain decomposition technique. In this multidomain BEM, the coefficient matrix is formed simply by assembling the coefficient matrices of each subdomain and the interface conditions between subdomains without eliminating any unknown variables on the interfaces. Compared with other conventional multidomain BEM approaches, this new approach is more efficient with the fast multipole method, regardless how the subdomains are connected. Instead of solving the linear system of equations directly, the entire coefficient matrix is partitioned and decomposed using Schur complement in this new approach. Numerical results show that the new multidomain fast multipole BEM uses fewer iterations in most cases with the iterative equation solver and less CPU time than the traditional fast multipole BEM in solving large-scale BEM models. A large-scale fuel cell model with more than 6 million elements was solved successfully on a cluster within 3 h using the new multidomain fast multipole BEM.

Aeroacoustic Scattering Using a Particle Accelerated Computational Fluid Dynamics/Boundary Element Technique

A particle accelerated computational fluid dynamics/boundary element method technique to predict the sound pressure field produced by low Mach number flow past a rigid body is presented. An incompressible computational fluid dynamics solver is used to calculate the transient hydrodynamic flowfield. A near-field formulation based on Lighthill’s analogy is coupled with a particle condensation technique to predict the incident acoustic field and its normal derivative on the body. The near-field formulation involves singular surface and volume integrals, which are regularized via singularity subtraction. A particle condensation technique is applied to accelerate the incident field computations and reduce the amount of data that must be stored during the computational fluid dynamics analysis. The incident field is then combined with a boundary element method model of the body, and the scattered sound pressure field is obtained by solving the Burton–Miller boundary integral equations. The accuracy and computational cost of the particle accelerated computational fluid dynamics/boundary element method approach is demonstrated by calculating the incident acoustic field on a cylinder in crossflow under laminar and turbulent flow conditions as well as predicting the scattered and far-field sound pressures.

Response of deformation patterns to reorganization of the southern San Andreas fault system since ca. 1.5 Ma

Between ~1.5 and 1.1Ma, the southern San Andreas fault system underwent a major reorganization that included initiation of the San Jacinto fault zone and termination of slip on the extensional West Salton detachment fault. The southern San Andreas fault itself has also evolved since this time, with several shifts in activity among fault strands within San Gorgonio Pass. We use three-dimensional mechanical Boundary Element Method models to investigate the impact of these changes to the fault network on deformation patterns.A series of snapshot models of the succession of active fault geometries explore the role of fault interaction and tectonic loading in abandonment of the West Salton detachment fault, initiation of the San Jacinto fault zone, and shifts in activity of the San Andreas fault. Interpreted changes to uplift patterns are well matched by model results. These results support the idea that initiation and growth of the San Jacinto fault zone led to increased uplift rates in the San Gabriel Mountains and decreased uplift rates in the San Bernardino Mountains. Comparison of model results for vertical-axis rotation to data from paleomagnetic studies reveals a good match to local rotation patterns in the Mecca Hills and Borrego Badlands. We explore the mechanical efficiency at each step in the modeled fault evolution, and find an overall trend toward increased efficiency through time. Strain energy density patterns are used to identify regions of incipient faulting, and support the notion of north-to-south propagation of the San Jacinto fault during its initiation.

Resonance and cancellation phenomena caused by equidistant moving loadings in a periodic structure — A pile-supported periodic viaduct

Abstract In this paper, the resonance and cancellation phenomena occurring in a periodic structure-- a pile-supported periodic viaduct subjected to multiple equidistant moving loadings (MEML) are investigated. For this purpose, the representation for the dynamic response of the periodic viaduct to a single moving loading (SML) is introduced first. In order to take account of the pile-soil-structure interaction when evaluating the response of the periodic viaduct to a SML, a wavenumber domain boundary element method (WDBEM) model for the pile-row-soil system is employed to determine the compliances of the piles. By superposing the responses of the viaduct to all SMLs constituting the MEML, the representation for the dynamic response of the periodic viaduct to the MEML is obtained. With the representation for the MEML response of the viaduct, the resonance and cancellation conditions for the viaduct are derived. For the high speed MEML, when the time interval between two neighboring moving loadings is equal to the integer or half-integer multiples of the period of one of the dominant resonance peaks of the corresponding SML response of the viaduct, resonance or cancellation occurs. The predicted resonance and cancellation phenomena are confirmed by the numerical results presented in this paper.

Topology Optimization of a Bounded Space for a Vibroacoustical Problem in a Low Frequency

The article deals with the problem of a space with vibroacoustical source generating inside specific conditions, which form a field of some values. All applies to an acoustic field in particular, characterized by an acoustic pressure or field of displacements in vibration problems. In general the field is described by specific dependent variable w(t) in all points of space, whose location are defined by coordinates r. The first aspect of this work relates to the modeling of an induced field, which can be alternative to finite element method (FEM) or boundary element method (BEM) in a low range of frequency. The second aspect is connected with minimization of some significant factor level related to dependent variable w(t) and subsequently to control field inside bounded space in order to get required state. In this work, it is assumed that the field distribution can be described by using modal analysis assumptions. Therefore, the dependent variable w(t) is defined by a modal expansion i.e. the sum over a set of a space’s eigenfunctions Ψ(r) (normal modes, characteristic functions) and time components (modal amplitudes, generalized coordinates). If the assumption of the highest values of acoustical or mechanical impedance of the space boundaries (damping properties of boundaries) is made, the modal coupling can be neglected. Such approach results in the vibroacoustical model being faster than alternative FEM or BEM models and suitable for the optimization procedure by using genetic algorithms, in the case when a computational cost is high. Thereafter, the topology optimization problem is formulated, where the influence of boundaries, represented by their impedance and the shape of space, represented by eigenfunctions are considered as the design variables. The genetic algorithm method is applied in order to find a minimum of objective function. In this case the function returns some functional value. As the result of the optimization a topology of the investigated space is obtained in the form of its shape and simultaneously configuration of damping properties of the space’s boundaries

Improvement of squeezing ground prediction and monitoring capabilities for Mount Isa Mines Northern 3500 orebody

This paper investigates readily incorporable improvements to the identification of squeezing ground conditions and the determination of the depth of movement for Mount Isa Copper Operations’ Northern 3500 (MICO N3500) orebody. Numerical modelling using the boundary element method (BEM) indicated that the current use of elastic material properties to calculate the rockwall condition factor and predict tunnel squeezing is appropriate, as no apparent benefit was gained by employing elastoplastic material properties or including the tunnel void geometry. Further analysis using the finite element method indicated that complex, large-scale models would be required to make meaningful improvement on the elastic BEM model. However, due to large time and computational overheads such models are not practical within the site’s engineering workflow. In conjunction with numerical modelling, a prototype monitoring device was also developed to address the problem of rigid instrument shear and inspection camera obstruction when determining the depth of movement in a squeezing rockmass. The reverse downhole probe device will allow distance measurement and a live video feed to be returned to the excavation surface by taking advantage of stable ground beyond the excavation zone of influence and using a thin, flexible cable to transmit power and data.

Incorporating fault mechanics into inversions of aftershock data for the regional remote stress, with application to the 1992 Landers, California earthquake

We present a new stress inversion algorithm that accounts for the physics relating the remote stress, slip along complex faults, and aftershock focal mechanisms, in a linear-elastic, heterogeneous, isotropic whole- or half-space. For each new remote stress, the solution of the simulation is obtained by the superposition of three pre-calculated solutions, leading to a constant time evaluation. Consequently, the full three-dimensional boundary element method model need not be recomputed and is independent of the structural complexity of the underlying model. Using a synthetic model, we evaluate several different measures of fit, or cost functions, between aftershocks and model results. Cost functions that account for aftershock slip direction provide good constraint on the remote stress, while functions that evaluate only nodal plane orientations do not. Inversion results are stable for values of friction ≤0.5 on mainshock faults. We demonstrate the technique by recovering the remote stress regime at the time of the 1992M 7.3 Landers, California earthquake from its aftershocks and find that the algorithm performs well relative to methods that invert earthquakes occurring prior to the Landers mainshock. In the mechanical inversion, incorporating fault structures is necessary, but small differences in fault geometries do not impact these inversion results. Each inversion provides a complete solution for an earthquake as output, including fault slip and the stress and deformation fields around the fault(s). This allows for many additional datasets to be used as input, including fault surface slip, GPS data, InSAR data, and/or secondary fracture orientations.

Experimental and Numerical Validation of an Automotive Subsystem through the Employment of FEM/BEM Approaches

In this paper a deep numerical analysis on an internal combustion engine cover is carried out. A hybrid numerical model has been used to evaluate the acoustic performance of engine cover. The Hybrid model is composed of two numerical models: FE (Finite Element) and BEM (Boundary Element Method) models. The FE model patterns structural system, whilst BEM model patterns fluid environment. The main aim of the present work is to characterize, through the employment of numerical simulation, the acoustic performance of the engine cover by using the NR (Noise Reduction) parameter. The numerical frequency response analysis has been implemented using acoustic impedance experimental data, measured for four different thicknesses of sound proof material forming the cover system. The spectrum of acoustic impedance has been evaluated in near field with a sophisticated probe, pressure-velocity probe (p-v probe).The analysis of the obtained results have highlighted the weaknesses as regards sound attenuation of the cover system and possible further improvements of cover system acoustic performance.

Solving the hypersingular boundary integral equation for the Burton and Miller formulation.

This paper presents an easy numerical implementation of the Burton and Miller (BM) formulation, where the hypersingular Helmholtz integral is regularized by identities from the associated Laplace equation and thus needing only the evaluation of weakly singular integrals. The Helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes not used when the surface is not smooth. The hypersingular operators arising in this process are regularized and then evaluated by an indirect procedure based on discretized versions of the Calderón identities linking the integral operators for associated Laplace problems. The method is valid for acoustic radiation and scattering problems involving arbitrarily shaped three-dimensional bodies. Unlike other approaches using direct evaluation of hypersingular integrals, collocation points still coincide with mesh nodes, as is usual when using conforming elements. Using higher-order shape functions (with the boundary element method model size kept fixed) reduces the overall numerical integration effort while increasing the solution accuracy. To reduce the condition number of the resulting BM formulation at low frequencies, a regularized version α = ik/(k(2 )+ λ) of the classical BM coupling factor α = i/k is proposed. Comparisons with the combined Helmholtz integral equation Formulation method of Schenck are made for four example configurations, two of them featuring non-smooth surfaces.

A direct BEM to model the temperature of gradient coils

The temperature of the gradient coils is an important issue in the development of MRI scanners. Gradient coil performance must be maximised within temperature limits imposed by safety and system requirements. Here we present a model that determines the temperature distribution in gradient coils designed using an inverse boundary element method (IBEM). This forward approach is derived by applying a constant boundary element method (BEM) on a steady-state approximation of the heat equation and combined with the stream function associated to an electric current density. It can be used to estimate the temperature distribution, as well as, the location and temperature of hot spots in gradient coils of arbitrary shape. Several examples of the applicability of the proposed BEM model on different coil geometries and thermal characteristics are presented. In order to validate the method, a small prototype X-gradient coil was built and tested, and the temperature distribution experimentally measured. It was found to be in a good agreement to the temperature distribution simulated by the proposed numerical approach with a suitable choice of the thermal properties.

Dynamic response of a periodic viaduct to a moving loading with consideration of the pile–soil–structure interaction

In this paper, the dynamic response of a periodic pile-supported viaduct to a moving loading when considering the pile–soil–structure interaction is investigated. By using the Duhamel integral, the Fourier and Floquet transform methods, the frequency domain response of the viaduct to the moving loading is represented by an integral of the frequency–wavenumber domain response function over the representative span of the viaduct. The time domain response of the viaduct can be retrieved by the inversion of the Fourier transform. By means of the wavenumber domain boundary element method model for the periodic pile row supporting the viaduct, the compliances of the pile row are obtained. Employing the compliances of the pile row and coupling the superstructure of the viaduct with the pile row, the frequency–wavenumber domain response function of the viaduct is determined. With the proposed model, the dynamic responses of the pile-supported viaduct to the moving loading in both the frequency and time domains are presented. It is found that resonance peaks of the frequency domain response of the viaduct are more likely to occur in the passbands of the viaduct, and the number of the resonance peaks decreases with increasing velocity. When the velocity of the loading is small, the time domain response of the viaduct is almost symmetrical about the loading. However, as the velocity increases, the response of the viaduct becomes asymmetric. Further, when the velocity of the loading is large enough, shockwave-like vibration occurs in the periodic viaduct.

Modeling of sound scattering by an obstacle located below a hardbacked rigid porous medium

The boundary integral equation (BIE) formulation takes advantage of the well-known Green’s function for the sound fields above a plane interface. It can then lead to a simplified numerical solution known as the boundary element method (BEM) that enables an accurate computation of sound fields above the plane interface with the presence of obstacles of complex shapes. The current study is motivated by the need to explore the acoustical characteristics of a layer of sound absorption materials embedded with equally spaced rigid inserts. In principle, this problem may be solved by a standard finite element program but it is found more efficient to use the BIE approach by discretizing only the boundary surfaces of the obstacles within the medium. The formulation is facilitated by using accurate Green’s functions for computing the sound fields above and within a layer of rigid porous medium. This paper reports a preliminary study to model the scattering of sound by an obstacle placed within the layered rigid porous medium. The two-dimensional Green’s functions will be derived and used for the development of a BEM model for computing the sound field above and within the rigid porous medium due to the presence of an arbitrarily shaped obstacle.

Satellite radar data reveal short-term pre-explosive displacements and a complex conduit system at Volcán de Colima, Mexico

The geometry of the volcanic conduit is a main parameter controlling the dynamics and the style of volcanic eruptions and their precursors, but also one of the main unknowns. Pre-eruptive signals that originate in the upper conduit region include seismicity and deformation of different types and scales. However, the locality of the source of these signals and thus the conduit geometry often remain unconstrained at steep sloped and explosive volcanoes due to the sparse instrumental coverage in the summit region and difficult access. Here we infer the shallow conduit system geometry of Volcán de Colima, Mexico, based on ground displacements detected in high resolution satellite radar data up to seven hours prior to an explosion in January 2013. We use Boundary Element Method modeling to reproduce the data synthetically and constrain the parameters of the deformation source, in combination with an analysis of photographs of the summit. We favour a two-source model, indicative of distinct regions of pressurization at very shallow levels. The location of the upper pressurization source coincides with that of post-explosive extrusion; we therefore attribute the displacements to transient (elastic) pre-explosive pressurization of the conduit system. Our results highlight the geometrical complexity of shallow conduit systems at explosive volcanoes and its effect on the distribution of pre-eruptive deformation signals. An apparent absence of such signals at many explosive volcanoes may relate to its small temporal and spatial extent, partly controlled by upper conduit structures. Modern satellite radar instruments allow observations at high spatial and temporal resolution that may be the key for detecting and improving our understanding of the generation of precursors at explosive volcanoes.

3D topographic stress perturbations and implications for ground control in underground coal mines

It is well known that the perturbed stress field beneath valleys can result in roof instabilities in shallow underground coal and stone mines. Quantitatively predicting the magnitude of these stress perturbations, particularly beneath complicated three-dimensional (3D) topography, has not become commonplace in mine planning, perhaps due to the complexity and time-consuming nature of the problem. Here we utilize 3D digital elevation models and the 3D boundary element method (BEM) approach to efficiently calculate the pre-mining topographically perturbed stress field in the vicinity of the Carroll Hollow coal mine in eastern Ohio. We find that regions of elevated compressive stress in the mine correspond to areas in which cutter roof failure is a common source of roof instability. Furthermore, both the magnitude and inclination of the principal stresses calculated from the 3D topographic BEM model are found to be consistent with observed failure distributions within the mine. We propose that the approach outlined in this study can be efficiently applied to the mine planning process in order to mitigate or avoid potentially hazardous mining conditions.

A model for the dynamic response of a defected periodic bridge with PSWS coupling

In this study, a numerical model is developed to investigate the dynamic response of a defected periodic bridge (DPB) when considering pile–soil–water–structure (PSWS) interaction. In order to determine the dynamic response of the DPB, the DPB is decomposed into three parts – left and right semi-infinite periodic bridges and the defected span. To account for the coupling between the superstructure of the bridge and the pile foundations, a coupled boundary element method (BEM) model is used to model the pile–soil–water (PSW) interaction. By using the PSW BEM model, the transfer matrices for the pier and beam, the joint condition at the beam–beam–pier (BBP) junction, the response of the DPB to the characteristic wave is obtained. To investigate the relation between the response of the DPB and the defect state of the corresponding super-cell, the super-cell method is developed for the DPB. Numerical results for the energy bands of the super-cell show that the defected span of the DPB may give rise to additional passband frequencies, namely, the defect state frequencies. Moreover, when the DPB is subjected to a characteristic wave with frequency equal to the defect state frequency, resonance may occur and the response of the DPB corresponding to the resonance is localized around the defected span.

Free Vibration Analysis of a Periodic Viaduct Supported by Pile Foundations

In this study, a numerical model is developed for the analysis of the free vibration of an open-type periodic structure, namely, a periodic viaduct supported by pile foundations. The viaduct is supposed to be composed of infinite spans, with each span consisting of a pile foundation, a pier, two longitudinal beams (left and right beams), and three linking springs. The boundary-element method (BEM) is used to solve the pile-soil interaction problem first. Based on the developed BEM model for the pile-soil system, the compliances of the pile foundation are obtained. By using the compliances of the pile foundation, the joint conditions at the beam-beam-pier (BBP) junction and the transfer matrix method, the eigenvalue equation for the periodic viaduct is established. Numerical results for the energy bands of the viaduct show that there are three kinds of characteristic waves propagating in the periodic viaduct. The first and second kinds of waves are highly decaying. The third characteristic wave can propagate in pseudopassbands with a small attenuation. Also, it is found that, unlike a closed periodic structure, because of the energy transmission from the viaduct to the half-space soil, all energy bands for the open viaduct considered in this study are complex bands with nonzero imaginary wave numbers.

A boundary element model for acoustic responses in the ear canal and its statistical validation and updating

A boundary element method (BEM) model for acoustic responses in individual ear canals was developed, and its validity was assessed and updated using a statistical approach. The BEM model was developed using high resolution computed tomography (CT) scanning from a healthy male adult. The BEM model, which was discretized adaptively for a frequency band of up to 22 kHz, included the head, pinna, ear canals, and tympanic membranes. The variability of the BEM model due to the uncertain acoustic boundary conditions and measurement locations was predicted using the eigenvector dimension reduction (EDR) method. Then, the likelihood function estimation approach was introduced in order to measure the agreement between the acoustic responses of the simulation model and experimental results. In order to enhance the simulation model performance, the acoustic boundary conditions of the BEM model were updated using a statistical calibration approach that maximizes the likelihood function value between the calculated probability density functions (PDFs) of the simulation model and the measurement data. The results of the validation and calibration procedures applied to the BEM model demonstrated that the proposed method provides a very effective method of verifying the model validity and enhancing the performance of the simulation model.