Boundary Finite Element Method Research Articles

Behavior analysis of energy piles in layered transversely isotropic saturated soils

This paper conducts theoretical research on energy piles in layered saturated transversely isotropic soils under different load forms. Firstly, the Timoshenko beam coupled axial force rod elements is used to simulate the pile elements, and the finite element equilibrium equation for energy single piles is derived accordingly. Then, the extended precise integration method (EPIM) is applied to obtain the fundamental solution of soil, which is regarded as the kernel function of the boundary element method to construct the boundary integral equation. Based on the theory of the coupled finite element method - boundary element method (FEM-BEM), and combined with the equilibrium conditions of force and displacement coordination at the pile-soil interface, the boundary integral equation of soil is coupled with the finite element equilibrium equation of the pile to establish the interaction equation. The calculation results of this method are compared with theoretical solutions and in-site field tests to verify the correctness of this theory. Finally, numerical examples are designed to explore the influence of the parameters of energy piles and soils on the behavior of energy piles in layered saturated transversely isotropic soils under vertical and horizontal loadings.

A Coupled Finite-Boundary Element Method for Efficient Dynamic Structure-Soil-Structure Interaction Modeling

This paper introduces an innovative approach to numerically model Structure–Soil-Structure Interaction (SSSI) by integrating the Boundary Element Method (BEM) and the Finite Element Method (FEM) in a coupled manner. To assess the accuracy of the proposed method, a comparative study is undertaken, comparing its outcomes with those generated by the conventional FEM technique. Alongside accuracy, the computational efficiency aspect is crucial for the analysis of large-scale SSSI problems. Hence, the computational performance of the coupled BEM–FEM method undergoes a thorough examination and is compared with that of the standalone FEM method. The results from these comparisons illustrate the superior capabilities of the proposed method in comparison to the FEM method. The novel approach provides more reliable results compared to traditional FEM methods, serving as a valuable tool for engineers and researchers involved in structural analysis and design.

The mechanical response of energy pile groups in layered cross-anisotropic soils under vertical loadings

The mechanical response of energy pile groups in layered cross-anisotropic soils under vertical loadings is studied with the aid of the coupled finite element method - boundary element method (FEM-BEM). The single energy pile is simulated based on the finite element theory, which then is extended to energy pile groups. The global flexibility matrix for soils is obtained by considering the coupling effects of vertical and thermal loadings. The coupled FEM-BEM equation for the interaction between energy pile groups and soils is derived based on the displacement compatibility condition at the pile-soil interface. According to the displacement coordination condition and force balance in the rigid cap, the displacement of the cap and axial forces of pile groups can be solved. The presented theory is validated by comparing the calculated results with numerical simulations and field test results in existing literature. Finally, effects of the thermal loading, pile-soil stiffness ratio, pile spacing, cross-anisotropy of Young's modulus and the stratification are discussed.

A pile–soil interaction model for ground-borne vibration problems based on the singular boundary method

An efficient three-dimensional approach for solving pile–soil interaction problems is proposed. In the approach, the soil is modelled as an elastic half-space, and its response in the presence of the pile’s corresponding cavity is computed by employing the singular boundary method. The pile is modelled analytically using the classic rod and Euler–Bernoulli beam theories. For the coupling with the soil, the pile is divided in a set of rigid segments that interact along their circumference with the soil. The methodology allows the rotational motions and reaction torques at these segments to be accounted for and their contribution in the accuracy of the scheme is assessed. A criterion to define the minimum number of collocation points that offers an acceptable trade-off between accuracy and numerical performance is also proposed. The method is validated against well-established methodologies and using the reciprocity principle that relates the wave radiation from the pile to the ground field with the incident wave problem due to a load on the ground surface. Results are shown for different soil stiffnesses and different pile length to diameter ratios. The employment of the singular boundary method is shown to provide strong computational advantages to detailed modelling approaches such as the three-dimensional finite element-boundary element method, as well as overcoming the fundamental limitations of plane-strain and axisymmetric methods.

Noise Prediction Study of Traction Arc Tooth Cylindrical Gears for New Generation High-Speed Electric Multiple Units

As the speed of the new generation of high-speed electric multiple units (EMU) increases, the requirements for vibration and noise reduction in traction gear trains are becoming higher and higher. Although most researchers have focused on the vibration mechanics analysis of gears, the actual noise has the most direct impact on passenger experience and safety. To address this problem, a new type of curved cylindrical gear is proposed to analyze the dynamic characteristics of the gear pair and predict its radiated noise based on the acoustic-vibration coupling theory using the finite element-boundary element method. Parametric modeling of the gear pair using CREO and assembly motion analysis were performed. ANSYS was used to analyze the stress distribution, inherent frequency, and inherent vibration pattern of the gear pair, and harmonic response analysis was performed using the modal superposition method to solve the displacement frequency response curve and vibration characteristics. ACTRAN was used to construct the free-field model, create acoustic excitation based on the acoustic-vibration coupling equation, set the field points, and predict radiated noise. The research results show that the noise is mainly concentrated in the tooth meshing area, and the root mean square RMS range of its sound pressure level value is 91–100 dB. Its dynamic characteristics and noise values are in line with the traction requirements of high-speed EMU, providing a new idea for improving the noise prediction of traction gears for new generation high-speed EMU, which in turn strongly support the noise control of high-speed EMU stock and thus improve the passenger experience and driving environment.

Artificial neural network framework for prediction of hydroelastic response of very large floating structure

The response of a very large floating structure (VLFS) must take into consideration the elastic deformation of the structure (commonly termed hydroelastic response) under wave action. Conventionally, the hydroelastic response could be computed by using the coupled finite element-boundary element (FE-BE) method, where the mat-like structure is modelled using plate theory and the water modelled using the potential theory. The FE-BE method requires the structure to be discretised into finer elements and the wetted surface boundary to be represented by smaller panels to accurately capture the hydroelastic response of the structure. Thus, the coupled FE-BE method could be computationally expensive when the structure gets larger or when subjected to waves of smaller wavelengths. To accelerate the computational time in predicting the hydroelastic response of the VLFS, a surrogate model trained using the feed-forward neural network is proposed. The hydroelastic responses under different wavelengths, structural stiffnesses and wave directions are first generated where these data are split into three groups for training, validation, and testing (prediction) purposes. The accuracy of the prediction in terms of correlation coefficient R is compared for the different train datasets, the number of neurons and hidden layers as well as the optimisation techniques. The finding shows that an accuracy of close to 99% to the ground truth could be achieved with only 80% of the train dataset. The hydroelastic response under irregular wave conditions predicted using the feed-forward neural network framework is also presented.

A combined iterative complex eigenvalue method and finite element-boundary element method for acoustic analysis of the railway steel bridge deck damped with constrained layer damping

This paper presents a combined method to predict structure-borne noise from the railway steel bridge deck damped with constrained layer damping (CLD), in which the frequency-dependent properties of the viscoelastic material are accurately considered through the iterative complex eigenvalue method (ICEM). Then, a 1:4 steel bridge deck model is designed and manufactured, and a series of hammer tests of the CLD-damped steel bridge deck are carried out in a semi-anechoic chamber to verify the proposed method. Then, the noise reduction effect of CLD is discussed in detail. It shows that the overall SPLs at the near field point S-3 and the far field point S-8 are reduced by 7.5 dB and 11.1 dB, respectively, and the noise attenuation rate along with distance is also improved significantly after damped with CLD. Finally, the influences of the key design parameters of CLD on noise reduction are quantitatively analyzed, so as to provide reference for the research and application of CLD in railway bridge engineering.

Experimental and numerical investigation on the vibro-acoustic characteristics of periodic rib stiffened plate based on band gap theory

This study presents a novel method for analyzing the vibration and noise from the periodic rib stiffened plate (PRSP). For the first time, the band gap theory was combined with hybrid finite element-boundary element method (FE-BEM) to predict the vibro-acoustic characteristics of this structure and guide its vibration and noise reduction design from the perspective of bending wave propagation. The excitation test was carried out simultaneously to verify the rationality and accuracy of the proposed method. Then, the acoustic contribution analysis was conducted and the influence of structural design parameters on bending wave bandgap and noise reduction effect was discussed in detail. The results show that there are alternating passbands and stopbands for bending waves propagating in PRSP, making the vibro-acoustic responses in different frequency bands exhibit distinct differences as well. Increasing the base plate thickness and decreasing the rib spacing are conducive to widen the bandgaps and reduce the noise radiation, which are the decisive factors affecting the vibro-acoustic characteristics of PRSP. While the rib thickness has little effect, this provides a new approach for vibration mitigation and acoustic optimization in steel bridges.

Reduction of Train-Induced Vibrations—Calculations of Different Railway Lines and Mitigation Measures in the Transmission Path

The reduction of train-induced ground vibrations by different railway lines and by mitigation measures in the propagation path is analysed in a unified approach by two-dimensional finite element calculations where the reduction is expressed as the amplitude ratio between a specific and the reference situation (the surface track without a mitigation measure). In general, there is no reduction at low frequencies, and the reduction becomes stronger with increasing frequency. A maximum reduction ratio of 0.1 at high frequencies is established with an open trench. Reduction ratios between 0.7 and 0.2 have been found for the other situations, filled trenches, walls, plates, and blocks, as well as for railway lines on embankment, in cuts and in a tunnel. Bridges can produce amplifications due to their resonance frequencies, but also strong reductions due to the massive bridge piers. The influence of some parameters has been analysed, the length of the bridge span, the inclination of the embankment and the cut, and the stiffness of the soil and of the tunnel structure. The dynamic track stiffnesses of a surface, bridge and tunnel track have been calculated by the 3D finite-element boundary-element method for comparison with corresponding measurements.

Modeling of Magnetoelectric Effects in Composite Structures by FEM–BEM Coupling

In this paper, a coupling of the Finite Element Method (FEM) and the Boundary Element Method (BEM) is used to model the behavior of magnetoelectric effects in composite structures. This coupling of numerical methods makes it possible not to have to consider a free space domain, and thus to use a single mesh for the magnetic, mechanical and electrical problems. This results in a consequent reduction of the number of unknowns which is accompanied by shorter computation times compared to a classical FEM approach. A mixed magnetic vector potential, reduced magnetic scalar potential formulation is used for the magnetic problem, and classical FEM formulations are used for electrical and mechanical problems. The resulting global algebraic system is solved by a block Gauss-Seidel solver.

A Method for Ranging and Positioning Casing with High-Intensity Magnets: Simulations and Experimental Studies

Summary Wellbores in the upper vertical section of cluster wells are typically positioned close together, resulting in a high possibility of wellbore collision accidents. In the drilling process, accurately determining the distance and bearing of the casings of adjacent production wells is key to controlling the wellbore trajectory to avoid collision accidents. In this study, a method is proposed that uses a high-intensity magnet to magnetize a close-range casing and subsequently measures the axial forces on the magnet to determine the casing distance and positioning. Based on the theoretical analysis of the magnet’s force, the boundary finite element method is used to numerically analyze the influence of the casing position on the magnet. The force on the magnet decreases exponentially with the increase in casing distance and decreases nonlinearly and rapidly as the angle increases. A method to determine the position of a casing by analyzing the forces on two adjacent magnets is proposed. Based on the fitting of the simulation results, a mathematical model that calculates the casing distance and azimuth is established. A simple experimental device was designed to verify the reliability of the numerical simulations and casing ranging and positioning of the models. The maximal calculation error of the casing distance is determined at 5 mm, and the angle error is less than 2°. Moreover, the actual measured distance is less than 1 m. The angle between the axes of the high-intensity magnets has an important influence on the distance measurement range. The following steps are suggested to improve the detection range of the casing: Improve the remanence of the high-intensity magnet; extend the length of the force arm of the force measuring mechanism; apply a high-resolution torque sensor; and set a smaller angle between the axes of the high-intensity magnets. The proposed method can achieve high-efficiency measurements and calculations of the casing distance and bearing based on a simple measurement structure and low-cost manufacturing. It also has the potential to be applied to multiple short-range casing ranging and positioning scenarios.

Numerical analysis and experimental measurement on segmented ring transducer acoustic fields

In order to overcome the shortcomings of the two traditional methods of finite element method (FEM) and direct coupling of mechanical FEM and acoustic boundary element method (BEM) in the comprehensive simulation of acoustic characteristics of non-two-dimensional axisymmetrical transducers, the acoustic FEM and acoustic BEM coupling method is adopted in this study to model, calculate and analyze the three-dimensional (3D) model of the segmented ring transducer. Firstly, the basic theory of FEM, BEM and FEM-BEM coupling calculation of the transducer is introduced. Secondly, a 1/8 3D model of the segmented ring transducer is built to simulate the underwater electro-acoustic characteristics of the transducer. Finally, a transducer prototype is manufactured according to the numerical model, and the electro-acoustic performance of the transducer is measured in the anechoic tank. The numerical results of transmission voltage response (TVR), admittance and radiation directivity curves are in good agreement with the experimentally measured results, which indicate that the proposed method is correct and effective. Therefore, the method could be used to comprehensively calculate the acoustic characteristics of the segmented ring transducer. In addition, the method could be used not only to study the acoustic problems of other transducers or transducers arrays with complex structures that are non-two-dimensional axisymmetrical, but also to comprehensively analyze and predict the near-field and far-field acoustic characteristics of any transducers including two-dimensional (2D) axisymmetrical transducers.

Efficient Numerical Solution of Coupled Axisymmetric Plasma Equilibrium and Eddy Current Problems

This paper presents an efficient numerical tool for solving the problem of transient nonlinear evolution of plasma equilibrium in presence of eddy currents. The code, named FRIDA-TD (FRIDA-Time Domain), and based on the existing FRIDA (FRee-boundary Integro-Differential Axisymmetric) code, exploits two different approaches for solving the elated nonlinear system of Partial Differential Equations (PDE): (i) Finite Element Method - Boundary Element Method (FEM-BEM) for plasma equilibrium, and (ii) Axisymmetric Volume Integral (AVI) formulation for eddy currents. The resulting FRIDA-TD is a fast and flexible tool suitable for engineering-oriented purposes, such as the design of Tokamak devices, set up of plasma operations, prediction of performance scenarios, and design of feedback control systems. FRIDA-TD is successfully validated at first with the well-established CarMa0NL code, and then against experimental data of the RFX-mod device.

A Computational Method for Acoustic Interaction with Large Complicated Underwater Structures Based on the Physical Mechanism of Structural Acoustics

A numerical coupling approach is proposed to fast predict the acoustic radiation from a vibrating large-complicated underwater structure. In this study, the physical mechanism of sound radiation from underwater large target is used for the first time to improve the efficiency and keep the accuracy of the numerical algorithm. Although the traditional coupled finite element method/boundary element method (FEM-BEM) is accurate, it contains a large number of boundary elements and thus requires a long computation time for large-complicated structures. The research on the physical mechanism of structural acoustics shows that when BEM is applied on the near-field artificial boundary at a proper distance away from the wet structural surface, large-size boundary elements are acceptable and the number of boundary elements and computation time are remarkably reduced. Thus, the fluid outside the structure is divided into the interior domain and the exterior domain by the artificial boundary. Then, the numerical method is realized by coupling structural finite element modelling with interior fluid finite element modelling and with exterior fluid boundary element modelling. Compared with the theoretical value, the experimental value and the results of the traditional FEM-BEM, the correctness of the proposed algorithm and its advantage of computational efficiency are verified. The computation time of the proposed method is over 99% shorter than that of FEM-BEM in the calculation example of a large-complicated structure. The proposed method can be further applied to multidomain acoustic and multibody acoustic calculations.

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.

Sound transmission through baffled multilayered curved shells using a transfer matrix method

The present work describes the use of a transfer matrix method to define the acoustic behavior of multilayered and periodic baffled curved shells consisting of a generic arrangement of homogeneous and heterogeneous periodic layers of various nature (fluid, solid, and poroelastic). The dynamic stiffness matrix of a unit cell is manipulated in order to derive the through-radius transfer matrix of a cylindrical periodic layer. Thus, the acoustic radiation or transmission of multilayered shells can be assessed. The blocked pressure field due to an incident plane wave is defined by taking into account the infinite rigid baffle by means of a two-dimensional boundary element model. Analytical expressions for the cylindrical acoustic impedances are utilized to define the coupling with the bounding fluid media. Furthermore, a one-dimensional windowing technique is adopted to account for the finite length of the shells. The proposed approach is validated by systematic comparison with a full finite-boundary element method.

Influence of scour on the vertical response of rock‐socketed piles in layered saturated rock–soil mass

AbstractThe influence of scour on the vertical response of rock‐socketed piles in a layered saturated rock–soil mass is studied through the finite element‐boundary element coupling method. By utilizing the theoretical solution of layered saturated media as the kernel function, the boundary element method (BEM) is used to deduce the boundary integral equations of rock–soil mass. Meanwhile, the pile is modelled with the three‐node bar element and the global stiffness matrix of the pile is assembled by the finite element method (FEM). Then according to the scour type, the flexibility matrix of the foundation is recombined and extended, which is consistent with the stiffness matrix dimension of the pile. In consideration of the force balance and continuity conditions at the pile‐soil‐rock interface, the FEM–BEM coupling equation is established to solve the interaction between layered rock–soil mass and rock‐socketed pile that considers different scour types. A corresponding MATLAB program is compiled to verify the correctness of the present theory by comparisons with the existing literature solutions, field tests and the finite element solutions. The influences of the scour type, scour depth, socketed length as well as pile‐rock mass modulus ratio and rock mass stratification on the vertical response of a rock‐socketed single pile are further discussed through several numerical examples.

Efficient FEM-BEM Coupling Based on Argyris Element for Axi-Symmetric Open Boundary Magnetostatic Problems

This article describes a novel and accurate implementation of finite element method-boundary element method (FEM-BEM) coupling based on Argyris element (AE), for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C^{1}$ </tex-math></inline-formula> solution of axi-symmetric magnetostatic problems in open boundary domains. The aim of the work is twofold: 1) to provide novel, easy, and accurate way to compute the basis functions that is strongly not affected by accuracy errors and 2) to give a clear mathematical and numerical description of the FEM-BEM coupling based on AE. The first goal is achieved by shifting to the origin the physical triangular elements and computing the basis function in the shifted coordinate system. Second, AE-based FEM-BEM coupling relies on the boundary integral equations (BIEs) for poloidal flux and its partial derivatives of both first and second order, accurately computed by combining the analytical formula based on elliptic integrals together with high degree Gaussian cubature. The application of the proposed method to an advanced plasma equilibrium magnetic configuration, typical of magnetic confinement fusion (MCF) (i.e., <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">snowflake configuration</i> ), highlights that, even in case of coarse triangulation, satisfactory results can be achieved, and the error on the boundary conditions (BCs) is well below machine working precision.

A Study on Plate Bending Analysis Using Boundary Element Method

This study presents a method for level ice-structure interaction analysis to estimate the fatigue damage of arctic structures by applying plate theory to the behavior of level ice. The boundary element method (BEM), which incurs a lower computational cost than the finite element method (FEM), was introduced to solve the plate bending problem. The BEM formulation was performed by applying the BEM to plate theory. Finally, to check the validity of the proposed method, the BEM results and FEM results obtained using the ABAQUS commercial software were compared. The response results of the BEM analysis agreed well with those of the FEM analysis. Based on the results of the analysis, the BEM approach is considered to be very powerful in level ice-structure interaction analysis for estimating level ice-induced fatigue damage. Further work is being conducted to perform level ice fracture analysis based on the stress field calculated using the boundary element method.

Acceleration effects in slamming and transition stages for the water entry of curved wedges with a varying speed

Water entry of wedges with curvature, including slamming and transition stages, differs from the linear wedge cases that were fully investigated and formulated. The transition stage is a successive stage of the slamming stage, where the spray root has exceeded the top of the wedge. In this paper, the slamming and transition stages of a two-dimensional (2D) normal water entry of curved wedges with a varying speed are numerically studied by a hybrid boundary-finite element method (HBF), which solves the fully nonlinear, 2D incompressible potential flow without considering the effects of gravity and the surface tension of water. For the slamming stage, an approximate solution based on the similitude of flow characteristics between the constant and varying speed impacts is proposed, and the expressions of the pressure coefficient and the hydrodynamic force formulated by the acceleration effects are derived. The approximate solution provides fast predictions of pressure distribution and the hydrodynamic force acting on the wedge surface for the varying speed impact. For the transition stage, the acceleration effect is addressed by extending the correction of the added mass coefficient from the linear wedge cases to curved wedge cases. The formula of hydrodynamic force for water entry in varying speeds is given by the slamming coefficient of constant-speed impact and the correction of the added mass coefficient. The predictions by the new formula are in good agreement with the HBF results and experimental results for varying speed impact cases of various curved wedges.