Two-dimensional Boundary Element Method Research Articles

A Two-dimensional Boundary Element Method for Calculating Elastic Gravitational Stresses in Slopes

—Elastic stresses arising from gravitational loads in a two-dimensional slope of arbitrary shape are calculated easily using a displacement-discontinuity boundary element method (BEM). A long stress-free crack simulates the topographic surface. Gravity-induced stresses (i.e., body forces) in a laterally confined body are simulated by vertical and horizontal “far-field” stresses equal to ρgy and [ν/(1-ν)]ρgy, respectively. Here ρ is material density, ν is Poisson’s ratio, g is gravitational acceleration, and y is elevation, with y = 0 along the surface far from a ridge top or valley floor. BEM stress solutions compare well with analytical solutions for symmetric topography based on conformal mapping. Our analyses indicate that slope failures are likely to initiate near the bases of bedrock ridges and to be widespread along the slopes of gentle valleys cut in bedrock. The BEM method can be applied to the slopes of arbitrary shape and steepness, and it is well suited for evaluating the near-surface propagation of fractures or fracture-like structures, such as dikes and landslide failure surfaces. Our analysis also highlights the critical importance of properly accounting for the boundary conditions in a boundary value problem.

Elastodynamic direct boundary element methods with enhanced numerical stability properties

Evidence of numerical instabilities in two-dimensional time domain direct boundary element methods is presented. The e!ects of numerical versus analytical integration of spatial integrals on stability are shown, and two new time-stepping algorithms are introduced and compared to existing formulations. The so-called new &direct half-step' scheme and the &epsilon' scheme are shown to improve the numerical stability of direct boundary element methods. Copyright ( 1999 John Wiley & Sons, Ltd.

THE IMPORTANCE OF SOURCE TYPE ON THE ASSESSMENT OF NOISE BARRIERS

A two-dimensional (2-D) boundary element method is used to compute the efficiency of noise barriers in attenuating traffic noise. Different types of source are considered. Point sources and incoherent line sources can be introduced as results of a post-treatment of the 2-D pressure field. The insertion loss of barriers is significantly reduced in the case of more realistic incoherent line sources, as compared to that of coherent line sources. However, the relative efficiency of tops added to a straight barrier is higher.

A new singular boundary element for crack problems: Application to bolted joints

The present paper is concerned with the effective numerical implementation of the two-dimensional Dual Boundary Element Method to analyse the mixed-mode crack growth in bolted joints. All the boundaries are discretized with discontinuous quadratic boundary elements and the crack-tip is modeled by singular elements that exactly represent the strain field singularity 1/ r . The Stress Identity Factors can be computed very accurately from the crack opening displacement at collocation points extremely close to the crack tip. Furthermore, the analysis of two-dimensional elastic contact problems is developed, with an iterative procedure. The contact equations are written explicitly with both transactions and displacements retained as unknowns. The computed results show that the proposed approach for Stress Intensity Factors evaluation is simple, produces very accurate solutions and has little dependence on the size of the elements near the crack tip. The algorithm is applied to several two-dimensional examples and the results obtained are in very good agreement with analytical solutions and experimental results carried out at the AEROSPATIALE Research Centre.

Stresses around pin-loaded hole in composite laminates using direct boundary element method

This study is concerned with stresses around a pin-loaded hole in symmetrically stacked composite laminates of finite size using a two-dimensional direct boundary element method. Effects of friction and clearance between the pin and hole edge on the stresses are accounted for. Also geometric compatibility and force constraint between the pin and the plate are enforced. A new relation for geometric compatibility is proposed. Stress distributions and the contact angle with slip and no-slip regions around the pin-loaded hole corresponding to various parameters are investigated. Some interesting results are obtained. The present method is effective and simple to use which can be implemented with a personal computer.

A simple error indicator for adaptive boundary element method

A posteriori error estimator for two-dimensional adaptive boundary element method is developed. The nodal errors of the state variables—displacements and tractions, are estimated based on the difference of two solutions, one from the original boundary elements solution, and the other from interpolation of the original solution. The L 2 norm is employed to compute local and global percentage errors. The proposed error estimator is simple in implementation, and does not require extensive computation. An h-version adaptive boundary element method has been implemented, and three numerical examples are used to verify the effectiveness of the error indicator proposed in the paper.

BOUNDARY ELEMENT METHOD FOR ACOUSTIC SCATTERING IN FLUID–FLUIDLIKE AND FLUID–SOLID PROBLEMS

In this paper the application of the two-dimensional boundary element method to the scattering of plane sound waves from an infinite cylinder in a fluid is presented. The acoustic equation of the wave motion in a barotropic, inviscid fluid is deduced from the linearized hydrodynamics equations and the linearized equation of state, while the wave motion inside the solid is described by two different models. Two sets of boundary integral equations are presented for modelling the interaction of fluid–fluidlike and fluid–solid problems. Several test examples are presented to demonstrate the accuracy of the proposed formulations. Comparison with available analytical results, as well as numerical results for different sizes and positions of the internal boundary are given. Farfield coefficients and the results of the scattering cross-section demonstrate the different behaviour of the two models and the influence of the internal boundary.

Dual boundary element analysis of closed cracks

A two-dimensional boundary element method for analysis of closed or partially closed cracks under normal and frictional forces is developed. The single domain dual formulation is used. As a contact problem is non-linear due to the friction phenomena at the crack interface and also because of the boundary conditions which may change during the loading, it is formulated in an incremental and iterative fashion. The stress intensity factors are calculated with the J-integral method. Also crack growth is considered. Several benchmark cases have been analysed to verify the results given by the method. The stress intensity factors and crack paths calculated are similar to those given in the literature. © 1997 John Wiley & Sons, Ltd.

Dual boundary element analysis of closed cracks

A two-dimensional boundary element method for analysis of closed or partially closed cracks under normal and frictional forces is developed. The single domain dual formulation is used. As a contact problem is non-linear due to the friction phenomena at the crack interface and also because of the boundary conditions which may change during the loading, it is formulated in an incremental and iterative fashion. The stress intensity factors are calculated with the J-integral method. Also crack growth is considered. Several benchmark cases have been analysed to verify the results given by the method. The stress intensity factors and crack paths calculated are similar to those given in the literature. ( 1997 by John Wiley & Sons, Ltd.

Explicit Kutta condition for unsteady two-dimensional high-order potential boundary element method

Explicit Kutta condition for unsteady two-dimensional high-order potential boundary element method

Measurement and computation of the acoustic field in a cavitation tunnel

Sound pressure distribution around a monotone sound source was measured inside a marine propeller cavitation tunnel and compared with the calculated result by a two-dimensional boundary element method. The measured sound pressure distribution showed some peaks due to the reflection effect of the tunnel test section boundary. As the frequency increased, the sound pressure distribution became more complicated, showing more peaks. The tunnel reverberant effect should be taken into account when the noise data measured in the tunnel are converted into full-scale values. In the boundary element method calculation, the boundary condition at the acrylic observation window of the tunnel was examined in detail. The calculated sound pressure distribution pattern in the tunnel transverse section agreed well with the measured distribution when a reasonable boundary condition was adopted. The boundary element method is an effective method for theoretically predicting the acoustic field inside the cavitation tunnel if the precise boundary condition is adopted.

Boundary element method for micropolar thermoelasticity

Based on linear micropolar thermoelasticity theory, a two-dimensional boundary element method (BEM) formulation is derived and the corresponding computer programs are developed to solve the problems of micropolar solid. The program is verified by computing the thermal stress in a hollow cylinder. In addition, the new BEM formulation is applied to solve, for the first time, the thermal stress of a square region with a circular hole. The effects of coupling number and characteristic length on the micropolar effects are derived, and the important new findings are summarized.

VLF surface-impedance measurements for ice-depth mapping — an assessment of some commonly encountered interference effects

AbstractThe effects on very low-frequency surface-impedence measurements of lateral variations commonly found in ice environments have been measured and modelled numerically using die quasi-static two-dimensional boundary-element method. Results indicate that surface-impedance measurements made in the vicinity of crevasses oriented perpendicular to the plane Of incidence, and those made in the vicinity of moraines and melt streams, can all show significant changes to the measured apparent resistivity. It is, therefore, misleading to use such measurements in the interpretation of ice depth.

VLF surface-impedance measurements for ice-depth mapping — an assessment of some commonly encountered interference effects

AbstractThe effects on very low-frequency surface-impedence measurements of lateral variations commonly found in ice environments have been measured and modelled numerically using die quasi-static two-dimensional boundary-element method. Results indicate that surface-impedance measurements made in the vicinity of crevasses oriented perpendicular to the plane Of incidence, and those made in the vicinity of moraines and melt streams, can all show significant changes to the measured apparent resistivity. It is, therefore, misleading to use such measurements in the interpretation of ice depth.

Preliminary results of the modelling of the Mexico City valley with a two-dimensional boundary element method for the scattering of SH waves : E. Reinoso, L.C. Wrobel & H. Power, Soil Dynamics & Earthquake Engineering, 12(8), 1993, pp 457–468

Preliminary results of the modelling of the Mexico City valley with a two-dimensional boundary element method for the scattering of SH waves : E. Reinoso, L.C. Wrobel & H. Power, Soil Dynamics & Earthquake Engineering, 12(8), 1993, pp 457–468

Predicting the scattering from reflectors and diffusers using two-dimensional boundary element methods

This paper demonstrates that two-dimensional boundary element methods are fast and efficient techniques for predicting the scattering from reflectors and diffusers. Of particular interest in this study were diffusers used in auditoria. The scattered pressure distributions were closely predicted by the boundary element methods, which is often sufficient for acousticians. The absolute scattering magnitude was not always well predicted. Consequently, two different techniques have been developed which compensate for predicting the inherently three-dimensional problems using two-dimensional methods. The compensations work very well for mid to high frequencies. They also work better for scattering near the geometric scattering angle.

Contact Stress between Circular Plate and Limestone Powder in Compression.

This paper is concerned with the estimation of contact stress between a rolling circular plate and powder. Uniaxial compression tests of limestone powder are carried out to investigate the effect of particle size on the compressive stress. During the compression of powder by a rolling circular plate, the inner stress of the plate is analyzed using the two-dimensional boundary element method and photoelastic analysis. Calculated values, which are evaluated under the assumption that shearing deformation of the powder does not take place under compression, display good agreement with the experimental resusts on the inner stress of the rolling circular plate.

Automatic grid generation for two-dimensional viscoplastic boundary element methods by the transfinite mapping method

A scheme of automatic grid generation for viscoplastic boundary element method (BEM) analysis using the transfinite mapping method which has been developed in the finite element method is presented. The advanced techniques for the mesh spacing of transfinite mapping method in BEM are studied. The applications demonstrate that the method in BEM has high computational efficiency and precise modelling of boundaries. This reduces the time and effort required by the analyst to set up a nonlinear model; the amount of input data required are reduced by as much as possible.

Preliminary results of the modelling of the Mexico City valley with a two-dimensional boundary element method for the scattering of SH waves

A numerical method is used for calculating the two-dimensional scattering of incident SH waves to try to explain some of the amplification patterns observed from recent data of the Mexico City's accelerometric array. The method is briefly presented and its efficiency is tested against analytical and other numerical solutions for canyons and alluvial valleys. Spectral ratios computed for transition and lake-bed zones of the Mexico City valley with respect to the average motion at hill-zone sites are also presented. The one-dimensional model is used to explain the amplifications observed at a site where the valley is relatively shallow, while the two-dimensional approach is employed at another site at the centre of the valley where irregular amplification patterns have been observed. Results in the time domain are also shown.

Mechanics of curved slip surfaces in rock

Curved slip surfaces are common structures in geologic and geotechnical situations. Important examples include geologic faults and the basal slip surfaces of landslides. The author analyses these structures by using two-dimensional boundary element and fracture mechanics methods to study the influence of curvature on displacements and related deformation of surrounding rock. Although analytical solutions for stresses and displacements associated with a curved crack exist in the literature, solutions for a curved slip surface with friction are not available. Curved slip surfaces are idealized as curviplanar cuts in a linearly elastic plate and a Coulomb frictional slip criterion, tensile failure (crack-like opening) provision, and constraint on slip surface wall interpenetration are included in the model. Remote principal stresses produce sliding displacements along favorably oriented slip surface segments, and stresses in the surrounding plate are calculated from these displacements. Mechanical modeling of ideal circular-arc slip surfaces shows that Mode-II displacements can in general vary in distribution and sense along curved slip surfaces as a function of curvature and remote stress orientation. Because regions of decreased and increased mean normal stress depend on the occurrence and positions of slipping segments, the locations of extensional and contractional deformation structures need not be located only near the terminations of curved slip surfaces. This result contrasts with predictions and observations of rock fracture near terminations of straight slip surfaces. In the latter case, the ends of slipping segments usually coincide with the slip surface terminations.