Engineering Analysis with Boundary Elements [SJR: 1.216] [H-I: 42] [1 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 0955-7997 Published by Elsevier [2811 journals] |
- Corrigendum to “Yield design of reinforced concrete slabs using a
rotation-free meshfree method” [Eng. Anal. Bound. Elem. 50 (2015)
231–238]- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Canh V. Le , Phuc L.H. Ho , Phuong H. Nguyen , Thang Q. Chu
PubDate: 2015-06-26T16:23:24Z
- Abstract: Publication date: September 2015
- MPM simulations of high-speed and ultra high-speed machining of titanium
alloy (Ti–6Al–4V) based on fracture energy approach- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): X.Y. Gu , C.Y. Dong , J.L. Li , Z.Y. Liu , J.Y. Xu
Based on material point method (MPM), two dimensional (2D) orthogonal chip model on titanium alloy is established. Unlike finite element method (FEM) with seriously distorted meshes during the simulation of large strains such as the formation of shear band, the MPM is especially suitable for the numerical simulation of large deformation and high strain rate of metal material at high temperature. The generalized interpolation material point (GIMP) contact algorithm, Johnson–Cook model and Hillerborg׳s fracture energy criterion are used to simulate the cutting process on Ti–6Al–4V alloy. The parameters option and simulation process are first discussed, then the corresponding chip force and temperature field etc. are analyzed and compared with experimental data available. A good agreement has been found between them. Finally, the evolution of the temperature and cutting force are studied, and the effects of cutting speed and cutting feed rate on the chip morphology and cutting force are also investigated. It was the first time to simulate the serrated and discontinuous chips with the MPM and obtain relatively satisfactory results. The transition from serrated to discontinuous chips has been well captured in this paper.
PubDate: 2015-06-26T16:23:24Z
- Abstract: Publication date: October 2015
- Editorial Board
- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
PubDate: 2015-06-26T16:23:24Z
- Abstract: Publication date: September 2015
- Recovery of the temperature and the heat flux by a novel meshless method
from the measured noisy data- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Yao Sun , Fuming Ma
In this paper, we give an invariant method of fundamental solutions (MFS) for recovering the temperature and the heat flux. The invariant MFS is to keep a very basic natural property, which is called the invariance property under trivial coordinate changes in the problem description. The optimal regularization parameter is chosen by Morozov discrepancy principle. Then the reason for introducing the regularization is explained clearly by using the potential function. Three kinds of boundary value problems are investigated to show the effectiveness of this method with some examples. In especial, when the classical MFS does not give accurate results for some problems, it is shown that the proposed method is effective and stable. For each example, the numerical convergence, accuracy, and stability with respect to the number of source points, the distance between the pseudo and real boundary, and decreasing the amount of noise added into the input data, respectively, are also analyzed.
PubDate: 2015-06-18T14:53:37Z
- Abstract: Publication date: October 2015
- On the free terms of the dual BIE for N-dimensional Laplace problems
- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Jeng-Tzong Chen , Wen-Sheng Huang , Jia-Wei Lee , Hong-Ki Hong
Dual boundary integral equations for the N-dimensional Laplace problems with a smooth boundary are derived by using the contour approach surrounding the singularity. The potentials resulted from the four kernel functions in the dual formulation have different properties across the smooth boundary. For the generalization, we focus on the N-dimensional Laplace equation. The Hadamard principal value (H.P.V.) is derived naturally and is composed of two parts, the Cauchy principal value (C.P.V.) and an unbounded boundary term. The hypersingular integral is not a divergent integral since we can collect the C.P.V. and the unbounded term together. Besides, the weighting of the free term contributed by different kernels is also examined. Finally, a special case of the four-dimensional Laplace equation is implemented and the free term, for any dimension are obtained. The contributions of the free terms for the boundary normal derivative of potential due to the single (L kernel) and the double (M kernel) layer potentials are 1 / N and ( N − 1 ) / N , respectively. It is an interesting phenomenon that the hypersingular kernel contributes more than the singular kernel, and, in addition, the former also yields an unbounded boundary term.
PubDate: 2015-06-18T14:53:37Z
- Abstract: Publication date: October 2015
- The use of the constant vector basis functions for the magnetic field
integral equation- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Ali Deng , Liming Zhang , Minghong Wang
The magnetic field integral equation (MFIE) is widely used in the analysis of electromagnetic scattering problems for conducting objects. Usually, the MFIE is solved by the method of moments (MoM) using the Rao–Wilton–Glisson (RWG) basis functions. In this paper, a new kind of basis function which is named the piece-wise constant vector basis function is proposed and used to solve the MFIE by MoM. Definition of this kind of basis function is given. The calculation of the impedance matrix entries is presented in detail. This kind of basis function is then used for the solution of the MFIE for electromagnetic scattering problems. The radar cross section (RCS) results and the iterative property of both kinds of basis functions are presented. It is shown that the piece-wise constant vector basis functions give similar RCS results as those of the RWG basis functions. Particularly, when iterative solver is used to solve the resultant linear system, the solution scheme using the piece-wise constant vector basis functions iterates much faster than that using the RWG basis functions.
PubDate: 2015-06-11T07:14:38Z
- Abstract: Publication date: October 2015
- Solving inhomogeneous magnetohydrodynamic flow equations in an infinite
region using boundary element method- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Vahid Morovati , Alaeddin Malek
In this paper, the inhomogeneous magnetohydrodynamic (MHD) flow equations are solved in an infinite region (upper half plane). Change of variables is done to find homogeneous equations equivalent to inhomogeneous MHD flow equations, and then these homogeneous equations are solved using boundary element method (BEM) for three types of boundary conditions. The proposed boundary element method provides the solution of MHD flow equations in the infinite region for arbitrary angles of magnetic field radiation on the fluid surface and high Hartmann numbers. This demonstrates the effectiveness, efficiency, and robustness of the proposed boundary element method. Finally, by providing some numerical examples, the effect of radiation angle changing of the magnetic field on the fluid surface and high Hartmann numbers have been shown for solving the intended problem in three types of boundary conditions.
PubDate: 2015-06-06T21:47:15Z
- Abstract: Publication date: September 2015
- Effectiveness of nonsingular solutions of the boundary problems based on
Trefftz methods- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Adam Brański , Dorota Borkowska
The paper describes the application of the Trefftz complete and Kupradze functions in two variational formulations, i.e. the original formulation and inverse one, to the solution of the boundary value problems of the two-dimensional Laplace’s equation. In both formulations the solutions and weighting functions are assumed as the series or the separate function of Trefftz complete functions or Kupradze ones. One way or another all methods are named Trefftz methods. They all are nonsingular and, at the same time, they lead to the BEM. The relationship between the groups of Trefftz methods of the original and inverse formulations is perceived. Numerical experiments are conducted for several Laplace problems. The accuracy and simplicity of the methods are discussed. All methods gave comparable results, therefore they may be interchangeably applied to the solution of boundary problems. However the best method group is pointed out.
PubDate: 2015-06-06T21:47:15Z
- Abstract: Publication date: October 2015
- Editorial Board
- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- Preface
- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
Author(s): C.S. Chen , Ming Li , C.C. Tsai
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- Local radial basis function collocation method for solving thermo-driven
fluid-flow problems with free surface- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
Author(s): Yiu-Chung Hon , Božidar Šarler , Dong-fang Yun
This paper explores the application of the meshless Local Radial Basis Function Collocation Method (LRBFCM) for the solution of coupled heat transfer and fluid flow problems with a free surface. The method employs the representation of temperature, velocity and pressure fields on overlapping five-noded sub-domains through collocation by using Radial Basis Functions (RBFs). This simple representation is then used to compute the first and second derivatives of the fields from the respective derivatives of the RBFs. The energy and momentum equations are solved through explicit time integration scheme. For numerical efficiency, the Artificial Compressibility Method (ACM) with Characteristic Based Split (CBS) technique is firstly adopted to solve the pressure–velocity coupled equations. The performance of the method is assessed based on solving the classical two-dimensional De Vahl Davis steady natural convection benchmark problem with an upper free surface for Rayleigh number ranged from 103 to 105 and Prandtl number equals to 0.71.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- 2D capacitance extraction with direct boundary methods
- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): M. Borkowski
The paper presents the algorithm of hierarchical capacitance extraction based on direct boundary methods. Three selected methods, i.e. Boundary Element Method, direct Trefftz method (based on TH-complete functions) and regular direct Boundary Element Method (direct Trefftz–Kupradze method), are compared for their effectiveness. The algorithm employs binary tree decomposition of the problem domain. Coupling capacitance matrix is calculated in hierarchical process with simultaneous dynamical updating library with basic element matrices. Numerical examples presented in the paper concern 2D planar transmission line structures composed of isotropic dielectric layers.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: September 2015
- Construct ‘FE-Meshfree’ Quad4 using mean value coordinates
- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Yongtao Yang , Xuhai Tang , Hong Zheng
The present work uses mean value coordinates to construct the shape functions of a hybrid ‘FE-Meshfree’ quadrilateral element, which is named as Quad4-MVC. This Quad4-MVC can be regarded as the development of the ‘FE-Meshfree’ quadrilateral element with radial-polynomial point interpolation (Quad4-RPIM). Similar to Quad4-RPIM, Quad4-MVC has Kronecker delta property on the boundaries of computational domain, so essential boundary conditions can be enforced as conveniently as in the finite element method (FEM). The novelty of the present work is to construct nodal approximations using mean value coordinates, instead of radial basis functions which are used in Quad4-RPIM. Compared to the radial basis functions, mean value coordinates does not utilize any uncertain parameters, which enhances stability of numerical results. Numerical tests in this paper show that the performance of Quad4-RPIM becomes even worse than four-node iso-parametric element (Quad4) when the parameters of radial basis functions are not chosen properly. However, the performance of Quad4-MVC is stably better than Quad4.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: October 2015
- A novel linear triangular element of a three-dimensional displacement
discontinuity method- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Wan Cheng , Yan Jin , Hong Li , Mian Chen
Since only the boundary of the domain requires discretization, the boundary element method (BEM) is very efficient for the semi-infinite or infinite rock-related engineering problems, e.g., hydraulic fracturing in reservoir stimulation and rock cutting during excavation. A real fracture in the solid is usually of an arbitrary geometry in three dimensions, which usually requires a three-dimensional displacement discontinuity method (3D DDM) to determine the deformation and stress field in order to achieve reliable results. However, the use of 3D DDM with triangular elements is limited by the singularities of the integral either within or nearby the domain. In this paper, a novel linear triangular element with three nodes on its vertices is proposed. The analytical integral expressions of this linear triangular element are also theoretically derived. A solution procedure is also described which can be applied to determine the displacement and stress field around a three-dimensional fracture inside the infinite solid. The accuracy of these results are compared with the analytical solutions of the displacements and stresses induced by a pressurized penny-shaped. This procedure takes a shorter time and requires less elements than the usual constant DDM when achieving the same accuracy.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: October 2015
- A local meshless collocation method for solving certain inverse problems
- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
Author(s): Wen Li , Xiaoyan Liu , Guangming Yao
In this paper, we propose a meshless scheme based on compactly supported radial basis functions (CS-RBFs) for solving the Cauchy problem of Poisson׳s equation and the inverse heat conduction problems in 2D. By assuming the unknown boundary condition to be a polynomial function, the inverse problems can be solved using a procedure similar to the process for solving forward problems. We employ Tikhonov regularization technique under L-curve regularization parameter to obtain a stable numerical solution. Numerical results verify the effectiveness and stability of this method.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- The local Kansa׳s method for solving Berger equation
- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
Author(s): Jingyu Yang , Xiaofeng Liu , P.H. Wen
In this paper, we present the local Kansa׳s method using radial basis functions (RBFs) to solve Berger equation which is a fourth order partial differential equation. To overcome the difficulty of solving higher order differential equations using localized RBF methods, we split the given equation into two second order partial differential equations. Furthermore, we use Matern function and normalized MQ as basis functions and make a comparison between the two radial basis functions in terms of accuracy and stability. LOOCV (Leave-One-Out-Cross-Validation) is used to find a good shape parameter of MQ and Matern function. To demonstrate the effectiveness of the local Kansa׳s method for solving Berger equation, three examples are given.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- The localized method of approximated particular solutions for solving
two-dimensional incompressible viscous flow field- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
Author(s): C.Y. Lin , M.H. Gu , D.L. Young , J. Sladek , V. Sladek
The purpose of this paper is to demonstrate that the localized method of approximated particular solutions (LMAPS) is a stable, accurate tool for simulating two-dimensional incompressible viscous flow fields with Chorin׳s projection method. Totally there are two numerical experiments conducted: the two-dimensional lid-driven cavity flow problem, and the two-dimensional backward facing step problem. Throughout this study, the LMAPS has been tested by non-uniform point distribution, extremely narrow rectangular domain, internal flow, velocity or pressure driven flow and high velocity or pressure gradient, etc. All results are similar to results of finite element method (FEM) or other literature, and it is concluded that the LMAPS has high potential to be applied to more complicated engineering applications.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- Method of approximate particular solutions for constant- and
variable-order fractional diffusion models- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
Author(s): Zhuo-Jia Fu , Wen Chen , Leevan Ling
The method of approximate particular solutions (MAPS) is an alternative radial basis function (RBF) meshless method, which is defined in terms of a linear combination of the particular solutions of the inhomogeneous governing equations with traditional RBFs as the source term. In this paper, we apply the MAPS to both constant- and variable-order time fractional diffusion models. In the discretization formulation, a finite difference scheme and the MAPS are used respectively to discretize time fractional derivative and spatial derivative terms. Numerical investigation examples show the present meshless scheme has highly accuracy and computationally efficiency for various fractional diffusion models.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- Numerical solutions of two-dimensional flow fields by using the localized
method of approximate particular solutions- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
Author(s): Chia-Ming Fan , Chi-Hung Yang , Wei-Shiang Lai
A combination of the localized method of approximate particular solutions (LMAPS), the implicit Euler method and the Newton’s method is adopted in this paper for transient solutions of two-dimensional velocity–vorticity formulation of the Navier–Stokes equations. The LMAPS, which is truly free from time-consuming mesh generation and numerical quadrature, and the implicit Euler method are, respectively, used for spatial and temporal discretizations of the velocity–vorticity formulation. Using the approximations of particular solutions in every local domain, the derivatives at nodes with respect to space coordinates via the LMAPS can be approximated by linear summations of nearby function values. After the discretizations for space and time derivatives, a system of nonlinear algebraic equations will be yielded at every time step and then the Newton’s method is used for efficiently analyzing these systems. Three numerical examples are provided to validate the accuracy and the simplicity of the proposed scheme and the numerical results are compared well with other numerical and analytical solutions. Besides, the numerical solutions, acquired by using different numbers of total nodes, different numbers of nodes in sub-domain, different shape parameters and different Reynolds numbers, are provided to show the merits of the proposed meshless scheme.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- Application of the method of fundamental solutions and the radial basis
functions for viscous laminar flow in wavy channel- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
Author(s): Jan Adam Kołodziej , Jakub Krzysztof Grabski
This paper deals with the problem of viscous laminar flow in a wavy channel using the method of fundamental solutions and the radial basis functions. First approximation was obtained when the Reynolds number equals zero, in which the considered problem is homogeneous problem which can be easily solved using the method of fundamental solutions. In order to obtain subsequent approximations of the solution, the nonlinear problem was transformed into a sequence of inhomogeneous problems using the Picard iteration method. Applying the method of particular solutions on each iteration step the solution consists of the general solution and the particular solution. The right-hand side of the governing equation in subsequent iteration steps was interpolated using the radial basis functions. Simultaneously the particular solution was obtained and the general solution was obtained by means of the method of fundamental solutions. The unknown coefficients of the solution were obtained using the boundary collocation technique. The main advantage of the proposed procedure is its simplicity and analytical form of the approximate solution. Such meshless approach was never applied previously for the problem of viscous laminar flow in the wavy channel.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- A regularized multi-level technique for solving potential problems by the
method of fundamental solutions- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
Author(s): Csaba Gáspár
The method of fundamental solutions is investigated in the case when the source points are located along the boundary of the domain of the original problem and coincide with the collocation points. The appearing singularities are eliminated by several techniques: by using approximate but continuous fundamental solutions (regularization) and via auxiliary subproblems to avoid the stronger singularities that appear in the normal derivatives of the fundamental solution (desingularization). Both monopole and dipole formulations are investigated. A special iterative solution algorithm is presented, which converts the original (mixed) problem to a sequence of pure Dirichlet and pure Neumann subproblems. The pure subproblems can be handled efficiently by using conjugate gradients. The efficiency is significantly increased by embedding the resulting method in a natural multi-level context. At the same time, the problem of the use of highly ill-conditioned matrices is also avoided.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- The MFS as a basis for the PIM or the HAM – comparison of numerical
methods- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
Author(s): Anita Uscilowska
The aim of this paper is to present implementation of the Method of Fundamental Solutions. Using the MFS the fundamental solution of the operators appearing in the governing equations should be known. For many engineering problems the governing equations are linear with unknown fundamental solutions or nonlinear. The purpose of this paper is implementation of the Picard Iterations Method or Homotopy Analysis Method in such case. Both methods are supported by the MFS. Some engineering problems described by linear equation with unknown fundamental solution and system of nonlinear equations are considered. The numerical experiment, solving these engineering problems, is performed using both methods. The correctness of the results obtained by both methods is checked. The conditions of the convergence of both methods are described.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- Simulation of elastic wave propagation in layered materials by the method
of fundamental solutions- Abstract: Publication date: August 2015
Source:Engineering Analysis with Boundary Elements, Volume 57
Author(s): Ji Lin , Wen Chen , Linlin Sun
In this paper, the method of fundamental solutions (MFS) is applied in combination with the domain decomposition method to the simulation of elastic wave propagation in layered materials. The domain of the problem under consideration is decomposed into several sub-domains. In each sub-domain, the solution is approximated separately by the MFS formulation. At the sub-domain interfaces, continuity of the displacement and traction is imposed as the boundary conditions. The validity of this approach is demonstrated through a series of two- and three-dimensional numerical experiments.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: August 2015
- Analyzing the load distribution of four-row tapered roller bearing with
Boundary Element Method- Abstract: Publication date: July 2015
Source:Engineering Analysis with Boundary Elements, Volume 56
Author(s): Xia Yang , Qingxue Huang , Chuang Yan
A Boundary Element Method (BEM) is used to study the roller bearing contact problem due to its high non-linearity. The plate units are used to simulate the rollers, the bearing boundary elements are used to realize the discontinuous nature of the traction on the contact area, and the Hertz contact theory is used to revise contact widths between rollers and the inner and outer races. According to assembly and fit characteristics of rolling mill tapered roller bearings, in which both clearance fits are adopted to the inner race with the mill roll and the outer race with the shaft block, the four-objects elastic frictional contact program of bearing BEM is compiled, with which a rolling mill four-row tapered roller bearing is simulated. The shaft block direct measure method is used to measure the load distribution of the four-row tapered roller bearing. The experimental data and the result of simulation are compared, and the load distribution laws of simulation identify with the test result, which proves the validity and effectiveness of using elastic frictional contact BEM to analyze the load distribution of bearing.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: July 2015
- Editorial Board
- Abstract: Publication date: July 2015
Source:Engineering Analysis with Boundary Elements, Volume 56
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: July 2015
- High performance of the scaled boundary finite element method applied to
the inclined soil field in time domain- Abstract: Publication date: July 2015
Source:Engineering Analysis with Boundary Elements, Volume 56
Author(s): Shan Lu , Jun Liu , Gao Lin
An efficient method for modelling the wave propagation in semi-infinite domain is proposed. It is applicable to soil–structure interaction problems for complex inclined soil field. The scaled boundary finite element method is modified through the original scaling center substituting by a scaling line. Based on this scaling line, the dynamic stiffness equation is derived. Then, an accurate and efficient continued fraction method is firstly introduced for solving equation for the model with rigid bedrock. By using the continued fraction solution and introducing auxiliary variables, the equation of motion of unbounded domain is built. Coupling the far field modelling by modified scaled boundary finite element method with the near field modelling by the finite element method, the global time-domain equation is obtained, which is a standard equation of motion for the whole domain. As a key point, the precise time-integration method is firstly employed to solve global equation of motion. The advantages of this integration method are that the integral interval is divided into quite small piece. It makes sure the precision achieve to computer precision. Owning to adopting five terms Taylor expansion for each small integral interval, the computational precision is increased greatly. Applying precise time-integration method in this paper, it greatly improves the accuracy and computing speed of proposed method. By using the sub-structure method, the inclined soil field is modelled. Numerical examples demonstrate accuracy and high efficiency of the new method, especially for complex dip mediums.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: July 2015
- A combined conformal and sinh–sigmoidal transformations method for
nearly singular boundary element integrals- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Jia-He Lv , Xia-Ting Feng , Fei Yan , Peng-Zhi Pan , Gui-Zhong Xie
Accurate and efficient evaluation of nearly singular integrals is a major concern in 3D BEM. Most existing widely-used non-linear transformations are only performed in radial direction. Actually, the near singularity may derive from three aspects: element shape, radial direction and angular direction. In this paper, a combined conformal and sinh–sigmoidal transformations method is proposed to evaluate nearly singular integrals arising in 3D BEM. The method can be decomposed into three steps: firstly, a conformal transformation is introduced to eliminate the shape effect caused by large aspect ratios and peak/big obtuse angles; secondly, the classical sinh transformation is applied in radial direction to cluster more Gaussian points towards the nearly singular point; finally, an improved sigmoidal transformation is utilized to rearrange Gaussian points in angular direction more reasonably. Extensive numerical examples including unit triangular element, elements with different aspect ratios, elements with different angles and curved triangular element are given to verify the robustness and competitiveness of presented method.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- A three-dimensional implementation of the boundary element and level set
based structural optimisation- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): B. Ullah , J. Trevelyan , I. Ivrissimtzis
This paper presents a three-dimensional structural optimisation approach based on the boundary element and level set methods. The structural geometry is implicitly represented with the level set method, which evolves an initial structural model towards an optimal configuration using an evolutionary structural optimisation approach. The boundary movements in the three-dimensional level set based optimisation method allow automatic hole nucleation through the intersection of two surfaces moving towards each other. This suggests that perturbing only the boundary can give rise to changes not only in shape, but also in topology. At each optimisation iteration, the Marching Cubes algorithm is used to extract the modified geometry (i.e. the zero level set contours) in the form of a triangular mesh. As the boundary element method is based on a boundary discretisation approach, the extracted geometry (in the form of a triangular mesh) can be directly analysed within it. However, some mesh smoothing is required; HC-Laplacian smoothing is a useful algorithm that overcomes the volumetric loss associated with simpler algorithms. This eliminates the need for an additional discretisation tool and provides a natural link between the implicitly represented geometry and its structural model throughout the optimisation process. A complete algorithm is proposed and tested for the boundary element and level set methods based topology optimisation in three-dimensions. Optimal geometries compare well against those in the literature for a range of benchmark examples.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- A simple accurate formula evaluating origin intensity factor in singular
boundary method for two-dimensional potential problems with Dirichlet
boundary- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Xing Wei , Wen Chen , Linlin Sun , Bin Chen
In this work, a simple accurate formula is presented to evaluate the origin intensity factor of the singular boundary method (SBM) for two-dimensional Dirichlet potential problems. The SBM is considered as an improved version of the method of fundamental solutions and remedies the controversial auxiliary boundary outside the computational domain in the latter. The origin intensity factor is a central concept in the SBM to overcome the source singularity of the fundamental solution while placing source points on the physical boundary. In literature, the origin intensity factor for the Dirichlet boundary condition is numerically obtained which may cause numerical instability in large-scale simulations. This work proposes a simple formula to calculate the origin intensity factor for two-dimensional Dirichlet potential problems. Numerical experiments show that it is feasible and perform robustly for problems under various irregular domains.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- Second-order Taylor Expansion Boundary Element Method for the second-order
wave diffraction problem- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Wenyang Duan , Jikang Chen , Binbin Zhao
A new Boundary Element Method (BEM) is developed for the solution of the induced velocity at the sharp corners in the context of potential flow. This method is based on the framework of low-order direct BEM to solve the Boundary Integral Equation (BIE), which mainly applies the Taylor expansion to the dipole strength in the BIE, reserves the first-order, second-order and mixed derivatives, and finally solves the corresponding tangential derivatives with respect to the field point in the BIE to form the closed equations. So the method is named the second-order Taylor Expansion Boundary Element Method (the 2nd order TEBEM), which can accurately solve the induced velocity on the non-smooth boundary, compared with the low-order BEM (Constant panel method), and all of the singular integrals in 2nd order TEBEM can be solved analytically. Its implementation is quite easy compared with high-order BEM. The characteristics of 2nd order TEBEM are studied by various wave diffraction problems, and the results of 2nd order TEBEM are compared with the analytical solutions and other numerical results, which show satisfactory agreements.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- Recursive moving least squares
- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Hamid Mehrabi , Behzad Voosoghi
The meshless moving least squares (MLS) is expanded here based on recursive least squares (RLS) where the outcome is the newly developed recursive moving least squares (RMLS) approximation method. In RMLS method each nodal point has its own size of the support domain; accordingly, the number of field points on the influence domain varies from node to node. This method makes it possible to select the optimal size of the support domain by imposing any arbitrary measures such as precision or convergence of the unknown parameters on the support domain. Moreover, the possibility of applying the statistical test in removing any undesired outliers of function values is provided. Another feature of this newly developed method is providing the possibility of revealing the significant break-lines and faults diagnosis on the surface. In RMLS the radius of the support domain would become extended to a point where the optimal precision of unknown parameters is achieved or reach the discontinuous or high gradient interfaces. The numerical results indicate that this method improves the accuracy of approximated surface more than 50%, especially for rough surfaces or the contaminated particles by random or gross errors, with no significant increase in time.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- Analysis of dynamic stress concentration problems employing spline-based
wavelet Galerkin method- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Satoyuki Tanaka , Shogo Sannomaru , Michiya Imachi , Seiya Hagihara , Shigenobu Okazawa , Hiroshi Okada
Two-dimensional (2D) dynamic stress concentration problems are analyzed using the wavelet Galerkin method (WGM). Linear B-spline scaling/wavelet functions are employed. We introduce enrichment functions for the X-FEM to represent a crack geometry. In the WGM, low-resolution scaling functions are periodically located across the entire analysis domain to approximate deformations of a body. High-resolution wavelet functions and enrichment functions including crack tip singular fields are superposed on the scaling functions to represent the severe stress concentration around holes or crack tips. Heaviside functions are also enriched to treat the displacement discontinuity of the crack face. Multiresolution analysis of the wavelet basis functions plays an important role in the WGM. To simulate the transients, the wavelet Galerkin formulation is discretized using a Newmark-β time integration scheme. A path independent J-integral is adopted to evaluate the dynamic stress intensity factor (DSIF). We solve dynamic stress concentration problems and evaluate DSIF of 2D cracked solids. The accuracy and effectiveness of the proposed method are discussed through the numerical examples.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- The evaluation of compound options based on RBF approximation methods
- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Ali Safdari-Vaighani , Ali Mahzarnia
Recently, real options have gained more importance in computational finance studies. It has already been shown that the compound option pricing can be formulated as a two-pass boundary PDE arising from Black–Scholes model. Radial basis function (RBF) as a meshfree approximation method is widely used for numerical study of the time dependent PDEs. In this paper, the aim is to introduce the robust numerical approach based on RBF-QR to compute the price of European compound options such as the popular put on put options. We also extend the proposed approach to American compound option pricing. The numerical experiments will show the efficiency of the performance for European and American compound option with single asset and multi-asset cases.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- The modified dual reciprocity boundary elements method and its application
for solving stochastic partial differential equations- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Mehdi Dehghan , Mohammad Shirzadi
This paper proposes a numerical method based on the dual reciprocity boundary elements method (DRBEM) to solve the stochastic partial differential equations (SPDEs). The concept of dual reciprocity method is used to convert the domain integral to the boundary. The conventional DRBEM starts with approximation of the source term of the original PDEs with radial basis functions (RBFs). Due to the fact that the nonhomogeneous term of SPDEs considered in this paper involves Wiener process, the traditional DRBEM cannot be applied. So a modification of it is suggested that has some advantages in comparison with the traditional DRBEM and can be developed for solving the SPDEs. The time evolution is discretized by using the finite difference method, while the modified DRBEM is proposed for spatial variations of field variables. The noise term is approximated at the collocation points at each time step. We employ the generalized inverse multiquadrics (GIMQ) RBFs to approximate functions in the presented technique. To confirm the accuracy of the new approach, several examples are employed and simulation results are reported. Also the convergence of the new technique is studied numerically.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- Stochastic spline fictitious boundary element method for analysis of thin
plate bending problems with random fields- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Cheng Su , Jia Xu
Mathematical formulation and computational implementation of the stochastic spline fictitious boundary element method (SFBEM) are presented for stochastic analysis of thin plate bending problems with loadings and structural parameters modeled with random fields. Two sets of governing differential equations with respect to the mean and deviation of deflection are derived by including the first order terms of deviations. These equations are in similar forms to those of deterministic thin plate bending problems, and can be solved using deterministic fundamental solutions. The calculation is conducted with SFBEM, a modified indirect boundary element method (IBEM), resulting in the means and covariances of responses. The proposed method is validated by comparing the solutions obtained with Monte Carlo simulation for a number of example problems and a good agreement of results is observed.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- Fully nonlinear wave interaction with an array of truncated barriers in
three dimensional numerical wave tank- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Arash Abbasnia , Mahmoud Ghiasi
Wave transition due to coinciding with an array of truncated barrier is simulated by a fully nonlinear three dimensional potential Numerical Wave Tank (NWT). The potential theory is used to describe kinematics of the flow field and the isoparametric Boundary Element Method (BEM) is employed to solve the boundary value problem. The Mixed Eulerian–Lagrangian (MEL) approach and fourth order Runge–Kutta time integration applied for time-marching scheme to model the temporary and fully nonlinear free surface. At each time step, solution of Laplace equation in the Eulerian frame is applied to the fully nonlinear free surface conditions in the Lagrangian manner to achieve the new positions and the boundary value of fluid particles for the next time step. Normal flux of potential wave theory is specified on the inflow boundary to stimulate fluid field and to propagate the nonlinear wave along the tank. To minimize the reflected wave energy into the computational domain, two artificial sponger layers are adopted on the free surface at the both ends of the numerical wave tank. Accuracy and convergence of the present numerical procedure is conducted. Also, interaction between a near trapped mode array of truncated barriers and nonlinear input wave is simulated.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- Wave transmission by partial porous structures in two-layer fluid
- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): H. Behera , S. Koley , T. Sahoo
The present study deals with oblique surface gravity wave scattering and trapping by bottom-standing and surface-piercing porous structures of finite width in two-layer fluid. The problems are analyzed based on the linearized water wave theory in water of uniform depth. Both the cases of interface piercing and non-piercing structures are considered to analyze the effect of porosity in attenuating waves in surface and internal modes. Eigenfunction expansion method is used to deal with wave past porous structures in two-layer fluid assuming that the associated eigenvalues are distinct. Further, the problems are analyzed using boundary element method and results are compared with the analytic solution derived based on the eigenfunction expansion method. Efficiency of the structures of various configuration and geometry on scattering and trapping of surface waves are studied by analyzing the reflection and transmission coefficients for waves in surface and internal modes, free surface and interface elevations, wave loads on the structure and rigid wall. The present study will be of significant importance in the design of various types of coastal structures used in the marine environment for reflection and dissipation of wave energy at continental shelves dominated by stratified fluid which is modeled here as a two-layer fluid.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- Application of the method of fundamental solutions to 2D and 3D Signorini
problems- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Hongyan Zheng , Xiaolin Li
This paper presents an application of the method of fundamental solutions (MFS) for the numerical solution of 2D and 3D Signorini problems. In our application, by using a projection technique to tackle the nonlinear Signorini boundary inequality conditions, the original Signorini problem is transformed into a sequence of linear elliptic boundary value problems and then solved by the MFS. Convergence and efficiency of the present MFS is proved theoretically and verified numerically.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- The topology optimization design for cracked structures
- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Vahid Shobeiri
In this paper, the element free Galerkin method (EFG) is proposed for topology optimization of cracked structures using the bi-directional evolutionary structural optimization method (BESO). The mathematical formulation of the topology optimization is developed considering the nodal strain energy as the design variable and the minimization of compliance as the objective function. The element free Galerkin method is enriched by the crack-tip enrichment functions to increase the approximation accuracy near the crack-tip. The Lagrange multiplier method is employed to enforce the essential boundary conditions. Several numerical examples are presented to show the effectiveness of the proposed method. Many issues related to topology optimization of cracked structures such as the effects of crack size and location on the optimal topology are addressed in the examples. The common numerical instabilities do not exist in the results.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- One-stage Method of Fundamental and Particular Solutions (MFS-MPS) for the
steady Navier–Stokes equations in a lid-driven cavity- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): D. Nath , M.S. Kalra , P. Munshi
The coupled nonlinear steady state Navier–Stokes (N–S) equations in the stream function–vorticity form for a lid-driven cavity are solved by a one-stage Method of Fundamental Solutions (MFS) and the Method of Particular Solutions (MPS). This method has been earlier used for linear Poisson-type problems and has not been applied to coupled nonlinear equations. In this method the steady state N–S equations are first put in the form of two nonlinearly coupled Poisson equations and the solution is sought as the sum of their respective homogeneous and particular solutions. The homogeneous solution is obtained using the MFS and the particular solution is found with the help of Radial Basis Functions (RBFs). Both the operations are accomplished in a single stage. The nonlinear coupling of the N–S equations is tackled by iteration and successive relaxation. We find that the method is easy and effective when compared with the boundary element method (BEM) or the two-stage MFS-MPS, due to its meshless, singular integration free qualities and the single stage operation. The results are obtained for the moderate Reynolds numbers by varying the relaxation parameter. The convergence of MFS-MPS scheme for the present nonlinear problem is numerically demonstrated.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- An efficient FEM–BEM coupling method in wave radiation problem
analysis of oil platforms with complicated geometry- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Ke Wang , Zhi Chen
Real body model meshing and data preparation on body surface are two critical steps for the sea load calculation using boundary element method. In this study, an efficient procedure to solve these two issues is developed. The FEM type meshing model is used to construct real 3D platforms. Basic parameters such as mass and volume of platform are directly calculated from FEM model. A data extracting algorithm is developed to obtain the necessary data block on body surface of FEM model for the use of BEM method. A Double and Multiple Nodes Relocation Method (D&MNRM) is employed along sharp edges of FEM model to remove geometrical singularity. Based on the newly rearranged boundary information, shallow water Green function and higher-order boundary element method are used to solve the integral equations. A simple example for floating cylinder and a complex example for ETLP are used to validate the added mass and damping. The results show that the proposed method is efficient and can be extended to wave load analysis of any type of platforms with arbitrary shape.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- Efficient visibility criterion for discontinuities discretised by
triangular surface meshes- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Nicholas Holgate , Grand Roman Joldes , Karol Miller
This study proposes a computationally efficient algorithm for determining which pairs of points among many predetermined pairs in three dimensions will maintain straight line visibility between one another in the presence of an arbitrary surface mesh of triangles. This is carried out in the context of meshless numerical methods with the goal of implementing near-real-time discontinuity propagation simulation. A brief overview is given of existing discontinuity modelling techniques for meshless methods. Such techniques necessitate determination of which key pairs of points (nodes and quadrature points) lack straight line visibility due to the discontinuity, which is proposed to be modelled with a surface mesh of triangles. The efficiency of this algorithm is achieved by allocating all quadrature points and surface mesh triangles to the cells of an overlayed three-dimensional grid in order to rapidly identify for each triangle an approximately minimal set of quadrature points whose nodal connectivities may be interrupted due to the presence of the triangle, hence eliminating most redundant visibility checking computations. Triangles are automatically split such that any size of overlayed cubic grid cells can be employed, and the parameters governing triangle splitting and binning have been examined experimentally in order to optimise the visibility algorithm.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- An element-free IMLS-Ritz framework for buckling analysis of FG–CNT
reinforced composite thick plates resting on Winkler foundations- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): L.W. Zhang , Z.X. Lei , K.M. Liew
An element-free based improved moving least squares-Ritz (IMLS-Ritz) method is proposed to study the buckling behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) resting on Winkler foundations. The first-order shear deformation theory (FSDT) is employed to account for the effect of shear deformation of plates. The IMLS is used for construction of the two-dimensional displacement field. We derive the energy functional for moderately thick plates. By minimizing the energy functional via the Ritz method, solutions for the critical buckling load of the functionally graded carbon nanotube (FG–CNT) reinforced composite plates on elastic matrix are obtained. Numerical experiments are carried out to examine the effect of the Winkler modulus parameter on the critical buckling loads. The influences of boundary condition, plate thickness-to-width ratio, plate aspect ratio on the critical buckling loads are also investigated. It is found that FG–CNT reinforced composite plates with top and bottom surfaces of CNT-rich have the highest critical buckling loads.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- An edge-based/node-based selective smoothed finite element method using
tetrahedrons for cardiovascular tissues- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Chen Jiang , Zhi-Qian Zhang , G.R. Liu , X. Han , W. Zeng
This paper presents a three-dimensional selective smoothed finite element method with edge-based and node-based strain smoothing techniques (3D-ES/NS-FEM) for nonlinear anisotropic large deformation analyses of nearly incompressible cardiovascular tissues. 3D-ES/NS-FEM owns several superior advantages, such as the robustness against the element distortions and superior computational efficiency, etc. To simulate the large deformation experienced by cardiovascular tissues, the static and explicit dynamic 3D-ES/NS-FEMs are derived correspondingly. Performance contest results show that 3D-ES/NS-FEM-T4 outperforms the standard FEM and other S-FEMs. Furthermore, this 3D-ES/NS-FEM-T4 is applied to analyze intact common carotid artery undergo mean blood pressure and passive inflation of anatomical rabbit bi-ventricles. The results are validated with the reference solutions, and also demonstrate that present 3D-ES/NS-FEM-T4 is a powerful and efficient numerical tool to simulate the large deformation of anisotropic tissues in cardiovascular systems.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- A 3D FEM/BEM code for ground–structure interaction: Implementation
strategy including the multi-traction problem- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Philippe Jean
The purpose of this paper is to describe the development of a 3D BEM–FEM code for ground–structure interaction. The technical choices and difficulties are reported. In particular, the multitraction problem has been implemented in 3D following a technique recently published in 2D for elastodynamics. It is showed that the separation of tractions is mandatory at corners but not at edges. The free surface and infinite interlayers are meshed by means of finite planes of varying dimensions. The paper also focuses on the validity of 2.5 approaches suggesting that in many situations the 2.5D model is well adapted. Reference situations are used for validation. The case of a pile joining a free surface and an interlayer between two different soils is described in detail. Finally computations are validated against measurements.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- Is the Burton–Miller formulation really free of fictitious
eigenfrequencies?- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Chang-Jun Zheng , Hai-Bo Chen , Hai-Feng Gao , Lei Du
This paper is concerned with the fictitious eigenfrequency problem of the boundary integral equation methods when solving exterior acoustic problems. A contour integral method is used to convert the nonlinear eigenproblems caused by the boundary element method into ordinary eigenproblems. Since both real and complex eigenvalues can be extracted by using the contour integral method, it enables us to investigate the fictitious eigenfrequency problem in a new way rather than comparing the accuracy of numerical solutions or the condition numbers of boundary element coefficient matrices. The interior and exterior acoustic fields of a sphere with both Dirichlet and Neumann boundary conditions are taken as numerical examples. The pulsating sphere example is studied and all fictitious eigenfrequencies corresponding to the related interior problem are observed. The reasons are given for the usual absence of many fictitious eigenfrequencies in the literature. Fictitious eigenfrequency phenomena of the Kirchhoff–Helmholtz boundary integral equation, its normal derivative formulation and the Burton–Miller formulation are investigated through the eigenvalue analysis. The actual effect of the Burton–Miller formulation on fictitious eigenfrequencies is revealed and the optimal choice of the coupling parameter is confirmed.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- DMLPG solution of the fractional advection–diffusion problem
- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): M. Ramezani , M. Mojtabaei , D. Mirzaei
The aim of this work is application of the direct meshless local Petrov–Galerkin (DMLPG) method for solving a two-dimensional time fractional advection–diffusion equation. This method is based on the generalized moving least squares (GMLS) approximation, and makes a considerable reduction in the cost of numerical integrations in weak forms. In fact, DMLPG shifts the integrals over the close form polynomials rather than the complicated MLS shape functions. Moreover, the values of integrals on subdomains with the same shapes are equal. Thus DMLPG is a weak-based meshless technique in the cost-level of collocation or integration-free methods. In time domain, a simple and suitable finite difference approximation is employed. Some examples show the advantages of the new method in comparison with the traditional MLPG method.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- Taylor series fast multipole boundary element method for solution of
Reissner׳s shear deformable plate bending problems- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Morcos F. Samaan , Mohammed E. Nassar , Youssef F. Rashed
In this paper, a new fast multipole BEM for the solution of Reissner׳s plates is presented. The suggested formulation is based on expressing the fundamental solutions in forms of potentials. Hence, these potentials and their relevant fundamental solutions are expanded by means of Taylor series expansions. Accordingly, the far field integrations are represented by these series expansions and summed for far clusters, whereas the near field integrations are kept to be computed directly. In the present formulation, equivalent collocations are based on both first and second shift collocations for kernels. By the present implementation of the fast multipole BEM in coupling with iterative solver (GMRES), the computational cost is rapidly reduced from O(N 3) in the conventional BEM to O(N log N) and O(N) for first and second shift respectively. Numerical examples are given to demonstrate the efficiency of the formulation against the conventional direct BEM. The accuracy of the results is traced by truncating Taylor series expansions to certain terms. It was demonstrated via numerical examples that three terms for both first shift and second shift are enough to produce sufficient accuracy with substantial reduction of solution time.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- Stress analysis for two-dimensional thin structural problems using the
meshless singular boundary method- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Yan Gu , Wen Chen , Bo Zhang
This short communication documents the first attempt to apply the singular boundary method (SBM) for the stress analysis of thin structural elastic problems. The troublesome nearly-singular kernels, which are crucial in the applications of the SBM to thin shapes, are dealt with efficiently by using a non-linear transformation technique. Three benchmark numerical examples, ranging from thin films, thin shell-like structures and multi-layer coating systems, are well studied to demonstrate the effectiveness of the proposed method. The advantages, disadvantages and potential applications of the method to thin structural problems, as compared with the boundary element (BEM) and finite element (FEM) methods, are also discussed.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- FEM SUPG stabilisation of mixed isoparametric BEMs: Application to
linearised free surface flows- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Nicola Giuliani , Andrea Mola , Luca Heltai , Luca Formaggia
In finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015