Boundary Element Method Analysis Research Articles

Dynamic BEM analysis of elastic anisotropic nano‐sheet with surface imperfections and cavities

AbstractThe paper considers elastic anisotropic nano‐sheet with nanotopography and containing embedded nanocavities under time‐harmonic in‐plane wave motion. The mechanical model is based on the classical elastodynamic theory for the anisotropic bulk solid and the nonclassical boundary conditions along its boundary derived by Gurtin and Murdoch. A localized constitutive equation for the half‐plane boundary is considered in the frame of surface elasticity theory. The computational tool is an efficient direct displacement boundary element method (BEM) based on the frequency‐dependent elastodynamic fundamental solution for elastic generally anisotropic material. To show the versatility of the proposed methodology, wave propagation in an elastic anisotropic heterogeneous nano‐sheet with nanorelief presented by hill‐canyon nanotopography is studied. The simulations illustrate the dependence of the wave field on the material anisotropy, on the surface elasticity properties, on the nanorelief peculiarities, on the nanocavities existence and their dynamic interaction, and on the incident wave characteristics. The obtained results reveal the potential of the developed mechanical model based on the boundary integral equations in the frame of surface elasticity theory to produce highly accurate results by using strongly reduced discretization mesh in comparison with the domain‐based methods.

Boundary Element Method Analysis of 3D Effects and Free-Surface Proximity on Hydrofoil Lift and Drag Coefficients in Varied Operating Conditions

_ The use of hydrofoils to enhance ship performance raises the scientific issue of free-surface proximity, which is important to consider during the design stage, to feed velocity prediction programs, for instance. Typically, the flow over a shallowly submerged hydrofoil is characterized by the Froude number, the submergence depth-to-chord ratio, the angle of attack, and geometric parameters of the lifting surface. Among these parameters, the present paper investigates the influence of the wing aspect ratio on the lift and drag coefficients of hydrofoils operating near a free surface. For this purpose, rectangular wings with an H105 profile at 2° angle of attack and aspect ratios ranging from 4 to 20 are systematically analyzed using a 3D boundary element method. The free surface is modeled using a linearized Neumann-Kelvin boundary condition. Chord-based Froude numbers of 0.5, 1.1, and 6.3 are studied. The submersion depth is swept between 0.1 and 30 times the foil chord length. The evolution of the normalized lift and drag coefficients with respect to the foil submersion and the aspect ratio is discussed in detail. Flow velocity is shown to play a significant role in the evolution of the lift and drag coefficients with submersion depth, close to the free surface, for all the aspect ratios. Its influence gets reduced by moving away from the free surface. The critical submersion depth, where the free-surface effects cease, is found to increase with higher flow velocity and aspect ratio. Furthermore, both positive and negative correlations between the force coefficients and the aspect ratio are identified, depending on the operating conditions. It is found that when the proximity to the free surface either enhances or impairs a force coefficient relative to its value in unbounded flow, increasing the aspect ratio amplifies this effect. Overall, this study confirms the effectiveness of steady boundary element methods for simulating the flow around hydrofoil wings in the vicinity of a free surface and contributes to further understanding the influence of geometric parameters on hydrofoil performance. Keywords hydrofoil; free surface; aspect ratio; potential flow; boundary element method (BEM)

A Fast Multi-Frequency Iterative Acoustic Boundary Element Method Solver Based on a Preconditioned Accelerated Recycling Strategy

Common multi-frequency solution strategies for acoustic systems are either associated with high computational costs or resort to model reduction strategies, which potentially induce considerable approximation errors. In that context, this work proposes a fast multi-frequency solver for acoustic Boundary Element Method (BEM) analyses that combines conventional preconditioners with an accelerated recycling strategy, achieving in that way a fast and accurate iterative solution. Specifically, by approximating both the system and the related preconditioner by individual affine expressions, an upfront Galerkin projection on a global deflation basis is facilitated, therefore enabling the deployment of the accelerated recycling scheme. The latter acts by accelerating the construction of the related deflation projectors, therefore leading to a significantly faster recycling procedure. Finally, the efficiency of the global deflation basis is guaranteed through an Automatic Krylov subspaces Recycling for Deflation (AKR-D) [D. Panagiotopoulos, W. Desmet and E. Deckers, An accelerated subspaces recycling strategy for the deflation of parametric linear systems based on model order reduction, Comput. Methods Appl. Mech. Eng. 403 (2023) 115765] algorithm and thus, the cumulative number of iterations required by an iterative solver within a frequency sweep is drastically decreased. The proposed multi-frequency solver is tested on two industrially relevant examples of an interior and an exterior scattering problem, benchmarked against the traditional solution strategies.

D Fast Multipole Boundary Element Method Analysis of Heat Exchange Performance of Buried Pipe Groups

D Fast Multipole Boundary Element Method Analysis of Heat Exchange Performance of Buried Pipe Groups

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.

An isogeometric boundary element method for transient heat transfer problems in inhomogeneous materials and the non-iterative inversion of loads

• An isogeometric boundary element of multi-patch model is established. • A non-iterative inversion method is proposed. • A very complex model of fighter is discussed in detail. In this paper, the transient thermal analysis theory of isogeometric dual reciprocity boundary element method (IG-DRBEM) of the multi-patch inhomogeneous complex model is established and the non-iterative inversion method of load identification is proposed based on the IG-DRBEM. The establishment of the multi-patch analysis theory framework extended the ability of IG-DRBEM to analyze complex geometry to some extent. The multi-patch analysis method adopted herein is simple and operable, and still retains the advantages of seamless connection between CAD generated geometry and response analysis of isogeometric boundary element method (IGBEM), which is very beneficial to expand IG-DRBEM to practical engineering application fields in the future. The inversion method based on IG-DRBEM makes full use of the good geometrical and field representation ability of NURBS, and further expands the application scope of IG-DRBEM. Furthermore, the introduction of the precision integration method for both forward and inverse problems improves the accuracy and stability of calculation to a certain extent. The numerical results show that the proposed method has good stability and accuracy even when solving complex geometric problems such as a fighter model. Moreover, the implementation of basis function expansion and regularization scheme further improves the accuracy and noise resistance of boundary condition inversion.

A Detailed FEM Study on the Vibro-acoustic Behaviour of Crash and Splash Musical Cymbals

Advanced numerical simulations, that include modal and frequency response function finite element analysis, frequency domain and time domain finite element method – boundary element method analysis, are performed to study the vibro-acoustic behaviour of crash and splash musical cymbals. The results of the modal analysis agree well with experimental measurements found in literature. The frequency domain and time domain coupled finite – boundary element method simulations, despite their high computational resources and time demands, are used for the crucial comparison of the velocity spectrograms on the cymbal to the radiated sound pressure spectrograms in the air. The computational analysis results show that the splash cymbal is characterized by a faster decay and a higher frequency content compared to the crash cymbal. The advanced multiphysics vibro-acoustic simulations that correlate the displacements and velocities of the vibrated structure with the radiated sound pressure results demonstrate the future capability to synthesize the sounds of cymbal music instruments.

Experimental and numerical study on vibration and structure-borne noise of high-speed railway composite bridge

In order to investigate the characteristics of train-induced vibration and structure-borne noise of high-speed railway steel–concrete composite bridge, a 5 × 50 m continuous steel–concrete composite bridge is adopted and tested in this paper. The vibration acceleration response and radiated noise of the bridge are measured during the test. The prediction model of vibration and structure-borne noise is further established to explore the radiation spectrum characteristics of the composite bridge. Firstly, the train-track-bridge dynamic interaction theory is applied to calculate the vibration response of the bridge under high-speed train loading. The boundary element method (BEM) and Statistical Energy Analysis (SEA) are subsequently combined to predict the full-frequency band noise of the structure. The accuracy of the model is verified through comparison with the measured data. Based on the field test and numerical study, it is found that the dominant frequency range of vibration and structure-borne noise is 20 ∼ 1000 Hz. The root mean square (RMS) accelerations of vertical and transverse vibration are lower than 0.5 m/s2, while local vibration of the steel web can reach 1.0 ∼ 2.5 m/s2. As a result, the acoustical contribution of the web at far-field site can reach 80% of the structure-borne noise. In addition, the setting of the bottom concrete reduces the acceleration level of the bottom plate by 10.75 dB and the radiated noise by 7.16 dB, showing a good effect of vibration and noise reduction.

Evaluation of Liner Cavitation Potential through Piston Slap and BEM Acoustics Coupled Analysis

Internal combustion engines take up the major position in the power facility market and still encounter some challenges; one key issue is liner cavitation erosion. The impact vibration between piston and cylinder generates pressure fluctuation on the wet liner surface and leads to the occurrence of cavitation in the case that coolant pressure falls below its vapor pressure. Piston slap methodology has been improved by considering the dynamic characteristics of the piston. Water coolant passage acoustic features were investigated and the Helmholtz effect between cylinders was confirmed. In order to address the cavitation erosion potential of the engine cylinder, acoustic pressure in the cooling water passage was investigated by boundary element method analysis with the acceleration of the cylinder liner which was obtained from the piston slap program. This study revealed that a certain acoustic mode of the cooling water passage had a dominant effect on the amplitude of water coolant dynamic pressure induced by liner vibration. Measures of eliminating the acoustic mode are believed to be able to suspend pressure fluctuation and furthermore the potential of cavitation.

BEM analysis of protection of rock caverns from cracking by water infilling and rock softening

This paper studies the elastic behavior of near ground cavern infilled with water in a layered rock mass by applying axisymmetric boundary element method (BEM). The results of two case studies are presented to quantitatively show the effect of water infilling on the elastic stress and deformation of layered isotropic halfspaces with a spherical cavern. The cavern water pressure has a significant effect to the normal and shear stress distributions on the cavern surface. Moreover, the effect of water softening on the elastic modulus of the rock mass is considerable to the displacements on both the ground and cavern surfaces. However, this effect is insignificant for all induced stresses on the cavern surface. Hence, the full infilling of water in the rock cavern can protect the surrounding rock from cracking or fracturing because water softening can also increase the rock mass toughness.

Axisymmetric BEM analysis of layered elastic halfspace with volcano-shaped mantle and cavity under internal gas pressure

This paper presents an axisymmetric BEM analysis of layered elastic halfspace with volcano-shaped mantle and cavity under internal gas pressure. The problem is of interest to understand the behavior of volcanoes, tectonic earthquakes and other oil and gas reservoirs. The volcano-shaped mantle ground topography and the internal spherical or ellipsoidal cavity are added to the conventional model of layered halfspace. The analysis uses the axisymmetric boundary element method (BEM) associated with the fundamental solution of a multilayered elastic fullspace subject to the concentrated ring-body force. The BEM is further verified for its high efficiency and accuracy by comparing its result with the analytical and FEM solutions for the problem of a homogeneous elastic halfspace whose spherical cavity is under internal pressure. The BEM is used to examine the effect of the volcano-shaped mantle, the cavity shape, the layered material properties and the internal pressure on the elastic behavior of the halfspace under the internal pressure loading within the cavity. The displacements and stresses at the external and internal boundaries and within the layered halfspace are presented and analyzed in detail. The presence of the volcano-shaped mantle can reduce significantly the swelling ground movement induced by the expansive pressure in the cavity in the layered halfspace. The cavity shape can have significant effect to the location and magnitude of the maximum tensile principal hoop stress on the cavity surface induced by its internal pressure.

Debonding development in cracked steel plates strengthened by CFRP laminates under fatigue loading: Experimental and boundary element method analysis

Carbon fiber reinforced polymer (CFRP) laminates can effectively enhance the fatigue life of steel structures. However, few studies have investigated the influence of crack-induced debonding in the CFRP-steel interface on the CFRP strengthening efficiency and the relationship of crack propagation and debonding development. This study experimentally and numerically – with the boundary element method (BEM) – investigated crack propagation and debonding development in CFRP-strengthened cracked steel (Q345, Q460, and Q690) plates. The fatigue test specimens were subjected to a maximum stress of 50% steel yield stress and a stress ratio of 0.1, during which real-time changes in CFRP strain distribution were recorded by digital image correlation (DIC). The CFRP strain gradient calculations showed that crack-induced debonding was crack length-dependent. The numerical fatigue life results were in good agreement with the experimental data when considering debonding and overestimated the experimental data without considering debonding, demonstrating the necessity of considering crack-induced debonding in calculation and design. Furthermore, a relationship was obtained between crack propagation and debonding development.

Convergence analysis of a Galerkin boundary element method for electromagnetic resonance problems

In this paper a convergence analysis of a Galerkin boundary element method for resonance problems arising from the time harmonic Maxwell’s equations is presented. The cavity resonance problem with perfect conducting boundary conditions and the scattering resonance problem for impenetrable and penetrable scatterers are treated. The considered boundary integral formulations of the resonance problems are eigenvalue problems for holomorphic Fredholm operator-valued functions, where the occurring operators satisfy a so-called generalized Gårding’s inequality. The convergence of a conforming Galerkin approximation of this kind of eigenvalue problems is in general only guaranteed if the approximation spaces fulfill special requirements. We use recent abstract results for the convergence of the Galerkin approximation of this kind of eigenvalue problems in order to show that two classical boundary element spaces for Maxwell’s equations, the Raviart–Thomas and the Brezzi–Douglas–Marini boundary element spaces, satisfy these requirements. Numerical examples are presented, which confirm the theoretical results.

Field Tests and Three-Dimensional Semi-Analytical Boundary Element Method Analysis of a Row of Holes as Active Barrier in Saturated Soil

Abstract The adverse effects of ground vibrations can be eliminated or prevented by installation of various types of wave barriers, such as a row of holes. The analysis is accomplished with the aid of a series of field experiments and numerical simulation. Three-dimensional semi-analytical boundary element models are established to use a row of holes as active wave barrier to isolate the ground vibrations generated by the machine foundation laid on the surface of saturated soil foundation, and the effects of the model parameters on isolation effectiveness are investigated and discussed in detail. A simple single program multiple data parallel algorithm is developed with the aid of Matlab software to increase calculating efficiency. The results show that a row of holes can isolate the ground vibrations successfully. Increasing the radius and the depth and decreasing the net spacing between two successive holes can all result in an increase in the screening effectiveness. According to the results, it is suggested in the design that the hole radius should take the value of 0.1∼0.15λR (λR is the Rayleigh wave length), and the hole depth and the net spacing should take the value no more than 1.0λR and 0.1λR, respectively. Moreover, the distance between the machine foundation and barrier can affect the screening effectiveness, and the larger the distance is, the poorer the screening effectiveness is. The number of holes in a row has less effect on the screening effectiveness. However, the bigger the number of holes in a row is, the larger the screening zone behind the barriers is.

Three dimensional modified BEM analysis of forward scattering problems in elastic solids

In this paper, a three-dimensional modified boundary element method (BEM) is proposed to solve the guided wave scattering problem by cavity-type flaws in an infinite plate. The aim of modification is to correct the artificial scattering introduced by inevitable modal truncation at far-field in the traditional BEM model. The far-field wave displacement fields beyond the BEM model are assumed to be the summation of orthogonal propagating guided wave patterns, and are finally incorporated into BEM equation sets as the modified items to account for the contribution of infinite boundaries traditionally omitted. With this improvement, the spurious reflected waves are eliminated. The method is formulated for a three-dimensional homogeneous, isotropic, elastic plate and its implementation is discussed in details. The formulation is finally validated for several benchmark problems.

The Dual-Reciprocity Boundary Element Method Solution for Gas Recovery from Unconventional Reservoirs with Discrete Fracture Networks

SummaryIn this paper, we present a novel application of the dual-reciprocity boundary-element formulation (DRBEM) to model compressible (gas) fluid flow in tight and shale-gas reservoirs containing arbitrary distributed finite- or infinite-conductivity discrete fractures. Compared with the standard boundary-element method (BEM), the DRBEM transforms the nonlinear domain integrals at the righthand side (RHS) of BEM formulations for nonlinear partial differential equations into equivalent boundary integrals. This transformation allows retention of the domain-integral-free, boundary-integral-only character of standard BEM approaches. The proposed approach is based on coupling DRBEM with the finite-volume method (FVM) in which a multidimensional system is solved by integrating over a line with random fractures. The resulting system of equations is solved simultaneously for fracture and matrix boundary conditions by combining DRBEM and FVM without invoking any approximation for pressure-dependent nonlinear terms such as gas viscosity and compressibility. Numerical examples and field cases are presented to test the validity and showcase the capabilities of the proposed approach. The proposed model provides a general framework that can be applied to a variety of well and fracture geometries and operating schedules, and it is used to analyze production behavior for these complex systems. To the best of the authors’ knowledge, this is the first successful application of the dual-reciprocity principle to the BEM analysis of massively fractured horizontal wells (MFHWs) performance in natural-gas formations in which nonlinear, pressure-dependent gas properties are captured without approximation.

Efficient isogeometric boundary element method for analysis of acoustic scattering from rigid bodies.

Boundary integral analysis of scattering from rigid bodies is well known. Analysis often proceeds along the following lines: representation of the geometry using a collection of triangles, representation of physics using low order ansatz functions defined on each triangle, and then solving the resulting discrete system. This prescription for the common solution stands out in terms of the low-order approximation of both geometry and representation of physics; specifically, both are C0. Taking inspiration from computer graphics literature, a framework wherein continuity of representation (both geometry and physics) can be as high as C2 is developed. In this paper, the steps necessary to develop such a iso-geometric (i.e., using the same basis functions for representing both geometry and physics) boundary integral solver are elucidated. In doing so, an efficient method based on a wideband fast multipole method to evaluate the required inner products and matrix vector products is proposed and demonstrated. Numerous examples are presented to highlight the benefits of the proposed approach.

An indirect boundary element method for analysis of 3D thermoelastic problem with cracks

In this paper, we first consider a combined boundary element method for numerical simulation of effect of temperature change on deformation due to time-varying heat conditions. The numerical simulation uses combination of an indirect boundary element method (IBEM) for temperature field and displacement discontinuity method (DDM) for displacement and stress fields. Time-varying fictitious heat source is employed in the IBEM and is approximated with a series of fictious heat sources with constant strengths that are applied incrementally at different times. Mathematically, the smooth-varying strength function of fictitious heat source is approximated with a stepwise function. The solution schemes previously developed for fictitious heat sources with constant strength are used for each increment. The combined scheme is used to compare the thermal effects caused by constant temperature and time-varying temperature on surface of a spherical cavity in an infinite body. The approximation scheme is verified with analytical solution when the temperature on the spherical cavity surface varies linearly with time. Then thermal fields around a conceptual thermal energy storage tank is simulated. Finally, the effects of temperature change in cracks connected to a vertical borehole on the propagation pattern of the cracks are investigated with the numerical scheme. It is found that cold temperature on the crack surfaces could help to reduce curvature of crack surfaces when multiple cracks are used, compared with fluid flow driven growth.

A NURBS-based isogeometric boundary element method for analysis of liquid sloshing in axisymmetric tanks with various porous baffles

An isogeometric boundary element method (IGA-BEM) based on the non-uniform rational B-splines (NURBS) is firstly performed to investigate the liquid sloshing in axisymmetric tanks with the porous baffles. The proposed method can completely maintain the advantages of the BEM that only the boundary of a domain requires discretization. By applying the NURBS basis functions it can exactly describe the geometry of the boundary. Meanwhile, it can also be obtained better solution field approximation at the domain boundary. Furthermore, as to the axisymmetric geometries of the containers considered in this paper, the 3-D liquid sloshing problems can be effectively reduced to 2-D ones on half of the cross-sections of the containers, which can significantly increase the computational efficiency. Meanwhile, the zoning method is employed in this paper to treat the arbitrary mounted porous baffles, and the Laplace equation is utilized as the governing equation of the potential flow model by assuming the fluid motion to be inviscid, irrotational and incompressible. Additionally, the weighted residual method together with the Green’s theorem is applied to develop the BEM integral equation. The natural sloshing frequencies and dynamic sloshing forces solved by the proposed method are compared with the available literatures and the traditional boundary element method (BEM). Good agreements are observed in the comparisons between numerical results and those of the existing literatures. And higher accuracy and convergence can be achieved by the proposed IGA-BEM method with significantly fewer nodes than the traditional BEM. Moreover, spherical tanks with the coaxial hemispherical, wall-mounted conical or surface-piercing cylindrical porous baffle, ellipsoidal tanks with spheroidal or surface-piercing cylindrical porous baffle, and the toroidal tank with tubular porous baffle are considered to investigate the effects of the porous-effect parameter, radius, length, height, horizontal and vertical semi-axes of the porous baffle on the sloshing characteristics (i.e. dynamic sloshing forces and surface elevations). The results show that the surface-piercing cylindrical porous baffle offers more noticeable suppression on sloshing response than the hemispherical and spheroidal porous baffles. Changing the radius of the tubular porous baffle has almost negligible effect on the sloshing force acting on the toroidal tank. The excitation frequency corresponding to the maximal value of sloshing force can be altered evidently by changing the porous-effect parameter of the porous baffle. In addition, choosing reasonable porous-effect parameter, radius, horizontal semi-axes and relatively larger length, height as well as vertical semi-axes for the porous baffles yields considerable suppression on the sloshing response.

Isogeometric Analysis of the Dual Boundary Element Method for the Laplace Problem With a Degenerate Boundary

ABSTRACTIn this paper, we develop the isogeometric analysis of the dual boundary element method (IGA-DBEM) to solve the potential problem with a degenerate boundary. The non-uniform rational B-Spline (NURBS) based functions are employed to interpolate the geometry and physical function. To deal with the rank-deficiency problem due to the degenerate boundary, the hypersingular integral equation is introduced to promote the full rank for the influence matrix in the dual BEM. Finally, three numerical examples are given to verify the accuracy of our proposed method. Both circular and square domains subjected to the Dirichlet boundary condition are considered. The engineering problem containing a degenerate boundary is considered, e.g., a seepage flow problem with a sheet pile. Numerical results of the IGA-DBEM agree well with these of the exact solution and the original dual boundary element method.