Discontinuity Boundary Element Method Research Articles

Simulating pillar reinforcement using a displacement discontinuity boundary element code

In this study we explore the use of a novel numerical modelling approach to study the effect of pillar reinforcement on pillar stability. Case studies in the literature indicate that tendons, strapping of the pillars, and shotcrete or thin spray-on liners are commonly used to reinforce pillars. No clear methodology exists to select the type of support or to design the capacity of the support required, however. This has led to ongoing collapses in some mines in spite of heavy support being used to reinforce unstable pillars. A limit equilibrium model with confinement on the edge of the pillar was used to simulate the interaction of the support with the failing pillar. The model correctly predicts that an increase in confinement will lead to a decrease in the extent of pillar failure. As the displacement discontinuity boundary element method allows for the efficient solution of large-scale bord-and-pillar layouts, the effect of pillar confinement can now be studied on a mine-wide scale. Accurate calibration of the limit equilibrium model is, however, required before this method can be used for the design of effective pillar support.

Impedance Sensitivity Analysis Based on Discontinuous Isogeometric Boundary Element Method in Automotive Acoustics

Abstract Acoustic sensitivity analysis is an essential technique to determine the direction of structural-acoustic optimization by evaluating the gradient of the objective functions with respect to the design variables. However, acoustic sensitivity analysis with respect to acoustic impedance, which is an important parameter representing the interior absorbent material in automotive acoustics, is lacking in the study. Moreover, acoustic sensitivity analysis implemented with conventional numerical methods is time and effort-consuming in automotive acoustics, due to the large-scale mesh generation. In this work, the impedance sensitivity analysis for automotive acoustics based on the discontinuous isogeometric boundary element method is presented. The regularized boundary integral equation with impedance boundary conditions is established, then the sensitivity is derived by differentiating the boundary integral equation. The efficiency of the proposed method is improved by employing the parallel technique and generalized minimal residual solver. A long duct example with an analytical solution validates the accuracy of the proposed method, and an automotive passenger compartment subjecting to impedance boundary conditions illustrates that the computing time of the proposed method is one order of magnitude less than the conventional method. This work presents an easily implementable and efficient tool to investigate acoustic sensitivity with respect to impedance, showing great potential in the application of automotive acoustics.

Three-dimensional interfacial mechanical-thermal fracture analysis of a two-dimensional hexagonal quasicrystal coating structure

Based on the displacement and temperature discontinuity boundary element method, three-dimensional thermal fracture behaviors of two-dimensional hexagonal quasicrystal (QC) coating with an arbitrary interface crack are studied. First, fundamental solutions of discontinuities are derived using the general solution and Hankel transform technique, and boundary integral-differential equations are constructed at interface. Then, taken a penny-shaped interface crack dispersed by ring elements as an example, Green’s functions with discontinuities are derived on these elements. After that, stress intensity factors (SIFs) and the energy release rate (ERR) are expressed with discontinuities. Finally, effects on fracture were discussed, including coating thickness, applied loads, and material mismatch.

Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements

Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements

Panel Acoustic Contribution Analysis in Automotive Acoustics Using Discontinuous Isogeometric Boundary Element Method

In automotive industries, panel acoustic contribution analysis (PACA) is used to investigate the contributions of the body panels to the acoustic pressure at a certain point of interest. Currently, PACA is implemented mostly by either experiment-based methods or traditional numerical methods. However, these schemes are effort-consuming and inefficient in solving engineering problems, thereby restraining the further development of PACA in automotive acoustics. In this work, we propose a PACA scheme using discontinuous isogeometric boundary element method (IGABEM) to build an easily implementable and efficient method to identify the relative acoustic contributions of each automotive body panel. Discontinuous IGABEM is more accurate and converges faster than continuous BEM and IGABEM in the interior sound pressure evaluation of automotive compartments. In this work, a contribution ratio is defined to estimate the relative acoustic contribution of the structure panels; it can be calculated by reusing the coefficient matrix that has already been generated in the sound pressure evaluation process. The utilization of the parallel technique enables the proposed method to be more efficient than conventional methods; it is validated in two numerical examples, including a car passenger compartment subjected to realistic boundary conditions. A sound pressure response experiment based on a steel box is conducted to verify the accuracy of the interior sound pressure calculation using discontinuous IGABEM. This work is expected to promote the practical process of IGABEM for application in automotive acoustic problems.

Displacement discontinuity method for interfacial cracks in one-dimensional hexagonal quasi-crystal coating under thermal-mechanical loading

This study derived Green’s functions of the concentrated interfacial displacement and temperature discontinuities. Green’s functions and the displacement and temperature discontinuity method were used to analyze interfacial cracks in a one-dimensional (1D) hexagonal quasi-crystal (QC) coating under thermal-mechanical loading. The boundary integral-differential equations were established for an interfacial crack, the fundamental solutions were obtained for uniformly distributed temperature, and the displacement discontinuities were applied over a line element. The near-crack-tip oscillatory singularity of stresses was eliminated by introducing the Gaussian distribution function to approximate the delta function. After this treatment, the expressions of the stress and heat flux intensity factors without oscillatory singularity, and the energy release rate (ERR) at the crack tips were obtained. The displacement and temperature discontinuity boundary element method for numerical simulation is proposed, and the influence of relevant factors is briefly discussed.

Analysis of a penny-shaped crack with semi-permeable boundary conditions across crack face in a 3D thermal piezoelectric semiconductor

In this paper, we study a penny-shaped crack model with electrically and thermally semi-permeable boundary conditions in a three-dimensional transversely isotropic piezoelectric semiconductor. An extended displacement discontinuity boundary element method together with an iterative process is proposed to analyze the penny-shaped crack model. The extended displacement discontinuities across crack face, electric displacement and heat flux along an inner crack cavity, as well as extended stress intensity factors near crack front are obtained via the proposed method. The effects on extended intensity factors near crack front are discussed, including boundary conditions across crack face, applied loads and initial electron concentration. It is shown that boundary conditions across crack face significantly affect extended stress intensity factors near crack front. This implies that a larger initial electron concentration can lead to electrical failure.

Effect of Elevated Temperature on Concrete Structures by Discontinuous Boundary Element Method

Changes in the thermomechanical properties of fiber-reinforced concrete (FRC) exposed to fire are fundamentally affected by the type and volume fraction of fibers. Because the loss of FRC load-bearing capacity is mainly caused by structural damage, a new numerical procedure based on a modified method of discontinuous boundary elements (DBEM) is proposed, which is modified to include thermomechanical processes in concrete together with the effect of fibers. DBEM allows the reader to visually track the location and extent of material damage.

A Preconditioned Krylov Subspace Iterative Methods for Inverse Source Problem by Virtue of a Regularizing LM-DRBEM

In this paper, we investigate an effectual methodology to solve the problem of identifying the source term standing on a combined discontinuous dual reciprocity boundary element method with a regularized Levenberg–Marquardt algorithm. The mathematical model is described by optimizing the variation between the measured potential in some points within the problem domain and the estimated one by the discontinuous dual reciprocity boundary element approximation. To provide a qualitative evaluation, the derived dense and non symmetric matrix system of the forward problem is solved by virtue of the LU factorization and using some preconditioned Krylov subspace iterative algorithms, expressly the biconjugate gradient stabilized, the generalized minimum residual and the squared conjugate gradient method. Due to noise interference, a regularized Levenberg–Marquardt algorithm is adopted to retrieve the unknown source term. Extensive experiments evince greater effectiveness and stability criteria of the proposed approach.

A Discontinuous Dual Reciprocity Method in Conjunction with a Regularized Levenberg–Marquardt Method for Source Term Recovery in Inhomogeneous Anisotropic Materials

This paper outlines a new approach to identify a source term of a [Formula: see text]D elliptic equation for anisotropic nonhomogenous media. The proposed methodology is based on the minimization of an objective function representing differences between the measured potential and those calculated by using the discontinuous dual reciprocity boundary element method, the measurements are required to render a unique solution and supposed to be pointwise in the problem domain. Since the additional data may be contaminated by measurement noises or the numerical computing errors, we adopt a regularizing Levenberg–Marquardt method to solve the nonlinear least-squares problem attained from the inverse source problem. The numerical performance of the proposed approach is studied at the end for both geometries: smooth and piecewise smooth one. The results show a very good agreement with the analytical solutions under exact and noisy data.

Simulation of heat distribution in the human eye using discontinuous dual reciprocity boundary element method and non-overlapping domain decomposition approach

Simulation of heat distribution in the human eye using discontinuous dual reciprocity boundary element method and non-overlapping domain decomposition approach

Analysis of elastic−plastic fracture in two-dimensional decagonal quasicrystals using the displacement discontinuity method

The generalized Dugdale model of cracks in two-dimensional decagonal quasicrystals is studied by developing the extended displacement discontinuity boundary element method. Expressions for the phonon and phason stress intensity factors and energy release rate are given in terms of the phonon and phason displacement discontinuities near the crack front. The extended displacement discontinuity boundary element method, with an iterative approach of determining the size of the yielding zone, is adopted to numerically simulate the nonlinear fracture problem. The effects of phonon and phason loadings, as well as the yield stress on the size of yielding zone and energy release rate, are discussed.

Slip on wavy frictional faults: Is the 3rd dimension a sticking point?

The formulation for the 3D triangular displacement discontinuity boundary element method with frictional constraints is described in detail. Its accuracy in comparison to analytical solutions is then quantified. We show how this can be used to approximate stress intensity factors at the crack tips. Using this method, we go on to quantify how slip is reduced on fault surfaces with topography, where the asperities are approximated as a sinusoidal waveform, i.e. corrugations. We use stress boundary conditions (compressive) orientated such that frictional contacts shear. We show that slip reductions relative to planar faults for 2D line and 3D penny-shaped crack models are comparable within 10% when slip is perpendicular to the corrugations. Using the 3D model, we then show how slip is reduced more when corrugation wavelengths are doubled compared to the reduction due to corrugation misalignment with the slip direction. When slip is parallel with the corrugation alignment we show that reducing the out-of-plane stress, from the normal traction acting on the fault when planar to that resolved on a perpendicular plane, has the same effect as halving the length of the corrugation waveform in terms of slip reduction for a given amplitude.

Extended displacement discontinuity method for analysis of penny-shaped cracks in three-dimensional thermal piezoelectric semiconductors

Abstract In this paper, the extended displacement discontinuity (EDD) boundary element method is developed to analyze a penny-shaped crack in the isotropic plane of a three-dimensional (3D) transversely isotropic thermal piezoelectric semiconductor (PSC). The generalized Almansi's theorem and the operator theory are used to obtain the general solutions under generalized loading. The fundamental solutions for extended displacement discontinuities (EDDs) applied on the penny-shaped crack surface, which include the displacement, electric potential, carrier density, and temperature discontinuities, are derived. By using the EDD boundary element method, the EDD under mechanical, electrical and heat loading near the edge of a penny-shaped crack is calculated. The stress and heat flux intensity factors of the crack are obtained. The influence of uniform and non-uniform heat loadings on the fracture of 3D transversely isotropic thermal PSCs is investigated.

Effects of thermal and electric boundary conditions on fracture of three-dimensional thermopiezoelectric media

An arbitrarily shaped planar crack under different thermal and electric boundary conditions on the crack surfaces is studied in three-dimensional transversely isotropic thermopiezoelectric media subjected to thermal–mechanical–electric coupling fields. Using Hankel transformations, Green functions are derived for unit point extended displacement discontinuities in three-dimensional transversely isotropic thermopiezoelectric media, where the extended displacement discontinuities include the conventional displacement discontinuities, electric potential discontinuity, as well as the temperature discontinuity. On the basis of these Green functions, the extended displacement discontinuity boundary integral equations for arbitrarily shaped planar cracks in the isotropic plane of three-dimensional transversely isotropic thermopiezoelectric media are established under different thermal and electric boundary conditions on the crack surfaces, namely, the thermally and electrically impermeable, permeable, and semi-permeable boundary conditions. The singularities of near-crack border fields are analyzed and the extended stress intensity factors are expressed in terms of the extended displacement discontinuities. The effect of different thermal and electric boundary conditions on the extended stress intensity factors is studied via the extended displacement discontinuity boundary element method. Subsequent numerical results of elliptical cracks subjected to combined thermal–mechanical–electric loadings are obtained.

Analysis of arbitrarily shaped planar cracks in two-dimensional hexagonal quasicrystals with thermal effects. Part II: Numerical solutions

• 2D hexagonal quasicrystals planar crack with thermal effects analyzed numerically. • Green's functions are derived for uniform triangular and rectangular elements. • The EDD-BEM is proposed for planar crack analysis in infinite 2D hexagonal QC body. • Elliptical crack with different loadings are investigated and presented graphically. The extended displacement discontinuity (EDD) boundary element method is developed to analyze an arbitrarily shaped planar crack in two-dimensional (2D) hexagonal quasicrystals (QCs) with thermal effects. The EDDs include the phonon and phason displacement discontinuities and the temperature discontinuity on the crack face. Green's functions for uniformly distributed EDDs over triangular and rectangular elements for 2D hexagonal QCs are derived. Employing the proposed EDD boundary element method, a rectangular crack is analyzed to verify the Green's functions by discretizing the crack with rectangular and triangular elements. Furthermore, the elliptical crack problem for 2D hexagonal QCs is investigated. Normal, tangential, and thermal loads are applied on the crack face, and the numerical results are presented graphically.

Extended displacement discontinuity method for analysis of cracks in 2D thermal piezoelectric semiconductors

The extended displacement discontinuities method has previously been used for crack analysis of elastic materials, piezoelectric media, magneto-electro-elastic media and piezoelectric semiconductors. Here, this method is extended to study cracks in two-dimensional n-type thermal piezoelectric semiconductors. The extended displacement discontinuities include the conventional displacement discontinuity, electric potential discontinuity, carrier density discontinuity, as well as temperature discontinuity across crack faces; correspondingly, the extended stresses represent conventional stress, electric displacement, electric current, and heat flux. Employing a Fourier transform, the fundamental solutions for a line crack under uniformly distributed extended displacement discontinuities on the crack faces are derived under mechanical, electrical, and heat loading. Based on the obtained fundamental solutions, an extended displacement discontinuity boundary element method is developed. The stress and heat flux intensity factors at the crack tip are calculated under different combined loadings.

Dynamics of an Underwater Explosion Bubble near a Rigid Wall: Effect of Slenderness Ratio, Installation, and Distance Parameter

ABSTRACT Zhang, Z.; Wang, L.; Yao, X., and Lang, J., 2017. Dynamics of an underwater explosion bubble near a rigid wall: Effect of slenderness ratio, installation, and distance parameter. Structural damage of maritime construction (e.g., dams, warships, etc.) has received considerable international attention in recent years because of underwater explosions from accidental events and terrorist bombing attacks. Therefore, research studies on underwater explosion load characteristics will have a great influence on the future of coastal and maritime engineering. Here, level set–direct ghost fluid–Runge Kutta discontinuous Galerkin method and boundary element method are combined to establish a model of underwater explosion near a rigid wall. First, the hybrid algorithm is used to simulate the process of underwater explosion in free field; the results agree well with experimental data, proving the effectiveness of the algorithm. Second, the process of underwater explosion near a rigid wall is simulated by the p...

Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 2: Numerical method

The extended displacement discontinuity boundary integral equation and boundary element method are extended to analyze a three-dimensional (3D) arbitrarily shaped interface crack in a one-dimensional hexagonal, quasicrystal bi-material with both electric and thermal effects under combined phonon-phason-electric-thermal loadings. Based on the analogy with the analysis method for three-dimensional, transversely isotropic magnetoelectrothermoelastic bi-materials (Dang et al., in press) the numerical method is proposed for one-dimensional quasicrystal bi-materials. Firstly, the fundamental solutions for uniformly distributed, extended displacement discontinuities applied over a constant triangular element are obtained by integrating the fundamental solutions for unit-point extended displacement discontinuities given in Part 1 over the triangular area (Zhao et al., 2017). Secondly, in order to eliminate the oscillatory singularity near the crack front, the Delta function in the integral–differential equations is approximated by the Gaussian distribution function, and the Heaviside step function is replaced by the Error function accordingly. Thirdly, the extended stress intensity factors without oscillatory singularities and the energy release rate are all obtained in terms of the extended displacement discontinuities. At last, the extended displacement discontinuity boundary element method is proposed to validate the analytical solution. In the numerical simulation, the multi-physical behavior of an elliptical, interface crack is numerically simulated. The correctness of the proposed numerical method, the influence of the applied, combined phonon-phason-electric-thermal loadings, the material-mismatch, and the ellipticity ratio are all studied.

Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media

Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media