Three-dimensional Boundary Element Method Research Articles

Accuracy Improvement of Inner-Point Formula in Three-Dimensional BEM

Three approaches have been proposed for improving the accuracy of the inner-point formula of the three-dimensional boundary element method and their performances have been estimated as compared with the regularized inner-point formula. The results of computations show that the proposed approaches are suitable for accurate computations of the numerical solution in the vicinity of the boundary

3D BEM for general anisotropic elasticity

A new method for computing the system matrices G and H of the three-dimensional boundary element method is presented for the elastostatic problems of general anisotropy. Green’s functions, expressed by the line integrals over a semi-circle, have a simple structure that allows analytical integration over the boundary elements. The computation for the system matrices G and H is reduced to numerical integration of regular line integrals over the unit semi-circle. The proposed method has been implemented and tested with numerical examples.

Application of a three-dimensional poroelastic BEM to modeling the biphasic mechanics of cell–matrix interactions in articular cartilage

Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three-dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain.

Boundary Element Modeling of the Realistic Human Body Exposed to Extremely-Low-Frequency (ELF) Electric Fields: Computational and Geometrical Aspects

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents the human exposure assessment to high-voltage extremely-low-frequency (ELF) fields by the three-dimensional (3-D) boundary element method (BEM). The formulation is based on a realistic, anatomically based representation of the human body. The main objective is to analyze the influence of the relative position of the arms with respect to the body on the axial distribution of current density along the body and to determine the most vulnerable regions. Numerical results along head, neck, torso, abdomen, arms, legs, and ankles are presented and discussed in the case of grounded subject standing under power-distribution lines and in the vicinity of power transformer substations. </para>

3-D Electrical Impedance Tomography for Piecewise Constant Domains With Known Internal Boundaries

Electrical impedance tomography (EIT) is a badly posed inverse problem, but can be stabilized if one assumes that the conductivity is piecewise constant, with a relatively small number of distinct regions, and that the region boundaries are known, for example from prior anatomical imaging. With this assumption, we introduce a three-dimensional (3-D) boundary element method (BEM) model for the forward EIT map from injected currents to measured voltages, and 3-D inverse solutions for both BEM and the finite element method (FEM) which explicitly take into account the parameterization implied by the known boundary locations. We develop expressions for the Jacobians for both methods, since they are nonlinear, to more rapidly solve the inverse problem. We show simulation results in a torso geometry with the heart and lungs as inhomogeneities. In a simulation study, we could reconstruct the conductive values of some internal organs of a human torso with more than 92% accuracy even with inaccurate internal boundary locations, a randomized rather than constant conductivity profile (with the standard deviation of the Gaussian-distributed conductivities set to 20% of their mean values), signal to measurement noise of 50 dB, and with different meshes used for the forward and inverse problems. BEM and FEM perform similarly, leading to the conclusion that the choice between them should be based on secondary considerations such as computational efficiency or the need to model conductivity anisotropies.

A Numerical Tool for the Design/Analysis of Dual-Cavitating Propellers

The motivation of this work is to develop a numerical tool to explore a new propeller design with dual-cavitating characteristics, i.e., one that is capable of operating efficiently at low speeds in subcavitating (fully wetted) mode and at high speeds in the supercavitating mode. To compute the hydrodynamic performance, a three-dimensional (3D) potential-based boundary element method (BEM) is presented. The BEM is able to predict complex cavitation patterns and blade forces on fully submerged and partially submerged propellers in subcavitating, partially cavitating, fully cavitating, and ventilated conditions. To study the hydroelastic characteristic of potential designs, the 3D BEM is coupled with a 3D finite element method (FEM) to compute the blade stresses, deflections, and dynamic characteristics. An overview of the formulation for both the BEM and FEM is presented. The numerical predictions are compared to experimental measurements for the well-known Newton Rader (NR) three-bladed propeller series with varying pitch and blade area ratios. Comparison of the performance of the Newton Rader blade section to conventional blade sections is presented.

Three-Dimensional Indirect Boundary Element Method Formulation for Dynamic Analysis of Frames Buried in Semiinfinite Elastic Media

This paper presents a formulation of the indirect boundary element method based on the principle of virtual work for the dynamic analysis of frame structures buried in semi-infinite elastic media. The present formulation, which falls in the category of symmetric Galerkin boundary element methods, leads to symmetric stiffness matrices for the continuum that may be defined in terms of conventional structural analysis variables (i.e., generalized displacements and lumped forces). It is shown that, in the context of the present formulation, rotation degrees of freedom may readily be introduced in the interpolation scheme with very little additional computational effort. The consistency of the present formulation with well-established results is assessed by comparing the predictions for the static and dynamic stiffness of single piles with other results from the literature. Finally, the dynamic stiffness of a single buried frame under vertical and horizontal loading is studied. The analysis shows that the stiffness of the full frame may not always be accurately estimated by means of results for single piles, even when dynamic interaction factors are used.

3D Electromagnetic Analysis of Levitating Transporter Using Bulk Superconductor

We have constructed and demonstrated levitating transporter models composed of the superconductor bulks (HTS bulks) and permanent magnets. The dynamic characteristics of lift force, lateral force and magnetic stiffness are very important for the design of superconducting devices such as a levitation system. The electromagnetic phenomenon should be clarified through the accurate analyses of the magnetic field and shielding current distributions within HTS bulks. In this study, we developed a new simulation program based on the three-dimensional hybrid finite element and boundary element (3D hybrid FE-BE) method, which combines with the fast multipole method (FMM). By using the FMM, it is possible to solve the large-scale problem with a reduction of the required memory size and improvement of the accuracy. This simulation program can consider the anisotropic and nonlinear <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$E-J$</tex> characteristics of HTS bulks. The results of experiment and numerical simulation are in good agreement.

Conjugate gradient methods for three-dimensional BEM systems of equations

A fundamental advantage of the boundary element method (BEM) is that the dimensionality of the problems is reduced by one. However, this advantage has to be weighted against the difficulty in solving the resulting systems of algebraic linear equations whose matrices are dense, non-symmetric and sometimes ill conditioned. For large three-dimensional problems the application of the classical direct methods becomes too expensive. This paper studies the comparative performance of iterative techniques based on conjugate gradient solvers as bi-conjugate gradient (Bi-CG), generalized minimal residual (GMRES), conjugate gradient squared (CGS), quasi-minimal residuals (QMR) and bi-conjugate gradient stabilized (Bi-CGStab) for potential and exterior problems. Preconditioning is also considered and assessed. Two examples, one from electrostatics and other from fluid mechanics, were employed to test these methods, which proved to be effective and competitive as solvers for BEM linear algebraic systems of equations.

A fast method for nonlinear three-dimensional free-surface waves

An efficient numerical model for solving fully nonlinear potential flow equations with a free surface is presented. Like the code that was developed by Grilli et al . (Grilli et al . 2001 Int. J. Numer. Methods Fluids 35 , 829–867), it uses a high-order three-dimensional boundary-element method combined with mixed Eulerian–Lagrangian time updating, based on second-order explicit Taylor expansions with adaptive time-steps. Such methods are known to be accurate but expensive. The efficiency of the code has been greatly improved by introducing the fast multipole algorithm. By replacing every matrix–vector product of the iterative solver and avoiding the building of the influence matrix, this algorithm reduces the computing complexity from to nearly , where N is the number of nodes on the boundary. The performance of the method is illustrated by the example of the overturning of a solitary wave over a three-dimensional sloping bottom. For this test case, the accelerated method is indeed much faster than the former one, even for quite coarse grids. For instance, a reduction of the complexity by a factor six is obtained for N =6022, for the same global accuracy. The acceleration of the code allows the study of more complex physical problems and several examples are presented.

露天資源開発の現状と新たな展開を支える技術 高感度傾斜計による岩盤斜面モニタリングと挙動分析

A high-resolution borehole tilt-meter is introduced to measure the inclination of rock slope at an open pit limestone mine, and the movement of rock slope is analyzed based on the measured results from the tilt-meter and numerical results by a three-dimensional boundary element method (3D-BEM). Firstly, the applicability of tile-meter to monitor the movement of rock slope due to a bench-cut excavation is investigated by 3D-BEM and the required accuracy of a tilt-meter is made clear. Then a high-resolution borehole tilt-meter is introduced and explained. Secondly, based on the measured results for nine months in a limestone mine, the mechanical behavior of rock slope is analyzed. The general mechanical behavior of rock slope due to excavation of a bench is then analyzed by 3D-BEM. Finally, using the results of measurement and numerical analysis, the mechanical behavior of rock slope is made clear. It is concluded that a high-resolution borehole tilt-meter is applicable to monitor the movement of rock slope in a short period.

101 三次元境界要素法による三次元接着構造体の熱応力における特異応力場解析(OS2-1 計算固体力学の最新応用(1),オーガナイズドセッション:2 計算固体力学の最新応用)

101 三次元境界要素法による三次元接着構造体の熱応力における特異応力場解析(OS2-1 計算固体力学の最新応用(1),オーガナイズドセッション:2 計算固体力学の最新応用)

Extrapolation expansions for Hanging-Chad-Type Galerkin integrals with plane triangular elements

Applications of three-dimensional Galerkin boundary element methods requirethe numerical evaluation of many four-dimensional integrals.In this paper we explore the possibility of using extrapolation quadrature.To do so, one needs appropriate error functional expansions.The treatment here is limited tointegration over a region $\mathcal T_1 \times \mathcal T_2$,where $\mathcal T_1$ and $\mathcal T_2$ are planar triangularelements in a hanging-chadconfiguration; that is, they have one vertex in common but are otherwise disjoint.We derive error expansions for product trapezoidal rulesvalid for integrands having an $|r_{12}|^{-1}$ factor. This factor gives riseto a weak singularity at the common vertex.

Boundary-element method simulation of the impact of bounding walls on the dynamics of a particle group freely moving in a wide-gap Couette flow

In this study, the impact of the bounding walls on the dynamics of a group of neutrally-buoyant identical rigid spheres freely moving at negligible Reynolds numbers in a wide-gap Couette flow, which is important for understanding the particle migrations presented in concentrated suspensions subjected to inhomogeneous shear flows, is simulated by a three-dimensional boundary-element method (BEM) code. The results show that the particle interactions very close to the bounding walls cause the particle group to migrate away from the walls. As the distance of the bounding walls from the group increases, the migration changes direction and the group then move towards the walls. As this distance continues to increase, the migration of the group decreases and beyond a specific distance from the bounding walls the migration of the group is negligible. In addition, the BEM simulations show that the extent and rate of the migration of the group increase as the inter-particle distance decreases.

Boundary-element simulation of hydrodynamic interaction of two smooth spheres suspended in an unbounded Couette flow

The hydrodynamic interaction between two particles, suspended in shear flows, is fundamental to the macroscopic characterization of suspension flows. Although the understanding of the hydrodynamic interaction between two particles suspended in a quiescent or linear shear flow is mature, studies of the interaction in a non-linear shear field are rare. The current study calculates such interactions between two neutrally-buoyant smooth spheres moving at negligible Reynolds numbers in an unbounded wide-gap Couette flow by three-dimensional boundary-element method (BEM) simulations. Both the identical sphere-pair and the disparate sphere-pair are considered. The numerical results show that there is a preferential cross-streamline migration of the center-of-gravity of the sphere-pair in the plane of shear in the unbounded wide-gap Couette flow that does not arise in simple shear-flow. This migration is always directed towards low-shear regions when the sphere having the larger translational velocity approaches the other sphere, and reverses towards high-shear regions when the faster sphere leads the other sphere in the plane of shear. There is also a cross-streamline migration of the center-of-gravity of the sphere-pair in the plane of vorticity, but this migration does not have a preferential direction. These migrations are symmetric about the point where the spheres are at the minimum separation, and are only significant when the hydrodynamic interaction of the spheres is sufficiently strong. These results show that the migration of the center-of-gravity of the sphere-pair can be attributed to the non-linearity of the shear field. The hydrodynamic interaction between the two spheres has been quantified under various conditions by the BEM simulations for both identical and disparate spheres.

Modeling and simulation of heat transfer for glass bulb mold

Abstract Cooling system design in glass bulb pressing operation can greatly affect the productivity and the quality of the final product. The concept of cyclic-averaged steady temperature field is proposed in modeling. Heat transfer in the mold region is considered to be a cyclic-steady three-dimensional conduction; heat transfer within the glass melt region is treated as a transient, one-dimensional conduction; heat exchange between the cooling system surface and coolant is treated as a steady heat convection. A hybrid model consisting of a three-dimensional boundary element method for the mold region and a finite-difference method with a variable mesh for the melt region is used for numerical simulation. Compared with the experimental data, the numerical model developed here is computationally efficient and sufficiently accurate.

Three-Dimensional Contact Boundary Element Method for Roller Bearing

The analysis of the forces and the rigidity of roller bearings is a multi-body contact problem, so it cannot be solved by contact boundary element method (BEM) for two elastic bodies. Based on the three-dimensional elastic contact BEM, according to the character of roller bearing, the new solution given in this paper replaces the roller body with a plate element and traction subelement. Linear elements are used in non-contact areas and a quadratic element is used in the contact area. The load distribution among the roller bodies and the load status in the inner rolling body can be extracted.

Numerical 3D BEM Simulation Of ACP System For A Buried Tank Influenced ByA Steel Reinforced Concrete Foundation

An advanced three-dimensional Boundary Element Method (BEM) approach is used to quantify the influence and mitigation of a steel reinforced concrete foundation on the cathodic protection (CP) level of a neighbouring buried tank. Due to the fact that the reinforced concrete is connected to the CP system, this concrete structure attracts a substantial fraction of the current that is injected by far field anodes. As a consequence, the tank wall that is facing the foundation, is under protected (tank/soil potential -600 to –700 mV vs. Cu/CuSO4), while the opposite tank wall (facing the far field) is well protected (-1200 mV vs. Cu/CuSO4). These simulations are in agreement with the measurements. Rather than remediate this situation by an expensive trial and error approach, Gasunie preferred to cooperate with ElSyCa and to simulate first the effects of various possible solutions they had in mind. These simulations predict a significant improvement of the tank wall protection level by about 200 mV at the foundation side when insulating screens are placed between the tank and the foundation (depending on size and position of the screens) while the far field side is hardly influenced. As the solver is fully integrated in the SolidWorks CAD environment, any modification of the dimensions of the entire configuration (e.g. the screens), the surface mesh characteristics (determining the computational accuracy), and the physico-chemical input parameters (polarisation characteristics, soil conductivity, etc.) can be established in a fast and easy manner.

Hydrodynamic interaction of two neutrally-buoyant smooth spheres suspended in plane Poiseuille flow: the BEM simulations versus the MoR approximations

The hydrodynamic interaction between two particles suspended in shear flows is fundamental to the macroscopic characterization of suspension flows. Although such interaction in quiescent or linear shear flow is well understood, studies on that in a nonlinear shear field are rare. In this study, the hydrodynamic interaction between two neutrally-buoyant smooth spheres moving at negligible Reynolds numbers in an unbounded plane Poiseuille flow has been calculated by three-dimensional boundary element method (BEM) simulations. The BEM results have been compared with the analytical results obtained with the method-of-reflection (MoR) approximations. The BEM simulations have been found to provide satisfactory predictions if the number of elements on the spheres are more than 200, whereas the MoR approximations provide satisfactory predictions only when the minimum separation between the spheres is relatively large although this MoR method has the advantage to easily calculate the hydrodynamic interaction between two spheres freely moving at negligible Reynolds numbers in unbounded quadratic flow by solving ordinary differential equations. Furthermore, it is found that there is a preferential cross-streamline migration of the center-of-gravity of the sphere-pair in the plane of shear in plane Poiseuille flow which does not arise in simple shear flow. This migration is always directed towards low shear regions when the sphere having larger translational velocity approaches the other sphere, and reverses towards high shear regions when the faster sphere leads the other sphere in the plane of shear. There is also a cross-streamline migration of the center-of-gravity of the sphere-pair in the plane of vorticity, but this migration does not have a preferential direction. These migrations are symmetric about the point where the spheres are at the minimum separation, and are only significant when the hydrodynamic interaction of the spheres is strong. These results show that the migration of the center-of-gravity of the sphere-pair can be attributed to the nonlinearity of the shear field, which agrees with the MoR approximations. The hydrodynamic interaction between the two spheres has been quantified under various conditions by the BEM simulations for both identical and disparate spheres.

Arbitrary Lagrangian-Eulerian 기법에 의한 원통형 유체저장구조물 내부유체의 비선형 슬러싱 해석

유체자유수면의 동적거동을 합리적으로 예측하기 위해서는 비선형 특성을 보이는 자유수면의 동역학적 경계조건을 고려해야할 뿐만 아니라 시간에 따라 변화하는 자유수면의 위치변화에 따른 운동학적 경계조건을 고려하여야 한다. 이러한 문제는 대상구조물이 3차원이 될 경우 더욱 복잡해지므로 3차원 비선형 유체자유수면의 해석은 이론해의 도출이 어려우며 수치해석 방법을 이용하는 것이 효과적이다. 본 연구에서는 수치해석 안정성이 높고 3차원 문제에서도 하나의 변수로 유체거동을 모사할 수 있는 arbitrary Lagrangian-Eulerian approach 를 경계요소에 적용하여 효율적이며 안정적인 유체 대변형 해석기법을 개발하였다. 개발된 기법은 향후 자유수면의 비선형 효과를 고려한 유체-구조물 상호작용 해석에 효과적으로 적용할 수 있을 것으로 판단된다. The solution to a liquid sloshing problem is challenge to the field of engineering. This is not only because the dynamic boundary condition at the free surface is nonlinear, but also because the position of the free surface varies with time in a manner not known a priori. Therefore, this nonlinear phenomenon, which is characterized by the oscillation of the unrestrained free surface of the fluid, is a difficult mathematical problem to solve numerically and analytically. In this study, three-dimensional boundary element method(BEM), which is based on the so-called an arbitrary Lagrangian-Eulerian(ALE) approach for the fluid flow problems with a free surface, was formulated to solve the behavior of the nonlinear free surface motion. An ALE-BEM has the advantage to track the free surface along any prescribed paths by using only one displacement variable, even for a three-dimensional problem. Also, some numerical examples were presented to demonstrate the validity and the applicability of the developed procedure.