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 [2812 journals] |
- Editorial Board
- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
PubDate: 2015-07-24T12:15:50Z
- Abstract: Publication date: October 2015
- Level set-based topology optimization for 2D heat conduction problems
using BEM with objective function defined on design-dependent boundary
with heat transfer boundary condition- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Guoxian Jing, Hiroshi Isakari, Toshiro Matsumoto, Takayuki Yamada, Toru Takahashi
This paper proposes an optimum design method for two-dimensional heat conduction problem with heat transfer boundary condition based on the boundary element method (BEM) and the topology optimization method. The level set method is used to represent the structural boundaries and the boundary mesh is generated based on iso-surface of the level set function. A major novel aspect of this paper is that the governing equation is solved without ersatz material approach and approximated heat convection boundary condition by using the mesh generation. Additionally, the objective functional is defined also on the design boundaries. First, the topology optimization method and the level set method are briefly discussed. Using the level set based boundary expression, the topology optimization problem for the heat transfer problem with heat transfer boundary condition is formulated. Next, the topological derivative of the objective functional is derived. Finally, several numerical examples are provided to confirm the validity of the derived topological derivative and the proposed optimum design method.
PubDate: 2015-07-20T11:47:11Z
- Abstract: Publication date: December 2015
- Angular basis functions formulation for 2D potential flows with non-smooth
boundaries- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): D.L. Young , Y.J. Huang , C.S. Wu , V. Sladek , J. Sladek
In this paper a new angular basis functions (ABFs) formulation which is different from the radial basis functions (RBFs) among the meshless methods is proposed to solve potential flow problems with non-smooth or discontinuous boundaries. The unique property of the ABFs formulation is first investigated in this study. In contrast to the method of fundamental solutions (MFS) using the RBFs, we adopt this ABFs collocation method to deal with the non-smooth or discontinuous boundaries more feasibly and accurately. Both the interior and exterior potential flow problems governed by the 2D Laplace equation are explored by both ABFs and RBFs schemes for comparison purposes. A square cavity, a cusp cavity, a uniform flow past a circular cylinder and the NACA 2418 airfoil are examined to test the merits or demerits of both the ABFs and RBFs formulations. From those four numerical experiments, the complementary ABFs formulation is found to be more effective to simulate domains with non-smooth or discontinuous boundaries such as acute, corner and cusp geometries. Furthermore, the basic aerodynamic problems of airfoils modeling are also discussed in the present study. From these numerical experiments, the angular basis function is found to be favorable of simulating the domains with acute, narrow regions and exterior problems.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015
- Incompressible smoothed particle hydrodynamics-moving IRBFN method for
viscous flow problems- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): D. Ngo-Cong , C.-D. Tran , N. Mai-Duy , T. Tran-Cong
We propose a novel numerical approach based on incompressible smoothed particle hydrodynamics and moving integrated radial basis function networks method, namely ISPH-MIRBFN, for solving incompressible viscous flow problems. In the ISPH method, the pressure is acquired from solving Poisson equation. In the present approach, the pressure Poisson equation is solved on a set of MIRBFN nodal points and the obtained results are then transferred to the SPH particles. The performance of the present method is investigated through several numerical examples including spin-down vortex, flows in a lid-driven closed-cavity and a lid-driven open-cavity with a prescribed bottom wall motion. Numerical results show that the proposed method reduces the spurious pressure fluctuations, yields a smoother pressure-field solution and maintains the computational efficiency when compared to the ISPH.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: October 2015
- Simulation of bubble dynamics near a plate with an aperture in a vertical
cylinder using a combined boundary element-finite difference method- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Mazyar Dawoodian , Abdolrahman Dadvand , Ali Nematollahi
Bubble dynamics near a perforated plate in a vertical cylinder is investigated using a combined boundary element-finite difference method. First, we determined the critical cylinder diameter for which the cylinder wall would not affect the bubble dynamics. Then for the case without cylinder wall effect, the effects of plate hole size and the bubble–hole distance were studied. Finally, the simultaneous effect of plate hole and cylinder diameter on the bubble behavior was evaluated. It was found that, for normalized bubble–hole distances H ′ ≤ 0.8 , there is only a liquid jet from the bottom surface of the bubble directing away from the hole, which becomes stronger as the normalized hole size d ′ is decreased. For H ′ ≥ 1.8 , there is only a liquid jet from the top surface of the bubble directing toward the hole, which becomes stronger as the hole size d ′ is decreased. For 0.8 < H ′ < 1.8 , there are two liquid jets from both the top and the bottom surface of the bubble, which depending on the bubble–hole distance, one of these jets becomes stronger as the hole size is decreased. In addition, smaller cylinder diameter would prolong the lifetime of the bubble.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: October 2015
- Modeling of fluid flow through fractured porous media by a single boundary
integral equation- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): M.N. Vu , S.T. Nguyen , M.H. Vu
The objective of this work is to provide theoretical materials for modelling two-dimensional fluid flow through an anisotropic porous medium containing intersecting curved fractures. These theoretical developments are suitable for numerical simulations using boundary element method and thus present a great advantage in mesh generation term comparing to finite volume discretization approaches when dealing with high fracture density and infinite configuration. The flow is modelled by Darcy’s law in matrix and Poiseuille’s law in fractures. The mass conservation equations, at a point on the fracture and an intersection point between fractures in the presence of a source or a sink, are derived explicitly. A single boundary integral equation is developed to describe the fluid flow through both porous media and fractures, i.e. the whole domain, which includes particularly the mass balance condition at intersection between fractures. Numerical simulations are performed to show the efficiency of this proposed theoretical formulation for high crack density.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: October 2015
- A direct BEM to model the temperature of gradient coils
- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Clemente Cobos Sánchez , Jose María Guerrero Rodriguez , Ángel Quirós Olozábal , Michael Poole
The temperature of the gradient coils is an important issue in the development of MRI scanners. Gradient coil performance must be maximised within temperature limits imposed by safety and system requirements. Here we present a model that determines the temperature distribution in gradient coils designed using an inverse boundary element method (IBEM). This forward approach is derived by applying a constant boundary element method (BEM) on a steady-state approximation of the heat equation and combined with the stream function associated to an electric current density. It can be used to estimate the temperature distribution, as well as, the location and temperature of hot spots in gradient coils of arbitrary shape. Several examples of the applicability of the proposed BEM model on different coil geometries and thermal characteristics are presented. In order to validate the method, a small prototype X-gradient coil was built and tested, and the temperature distribution experimentally measured. It was found to be in a good agreement to the temperature distribution simulated by the proposed numerical approach with a suitable choice of the thermal properties.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: October 2015
- Crack path prediction using the natural neighbour radial point
interpolation method- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): J.M.C. Azevedo , J. Belinha , L.M.J.S. Dinis , R.M. Natal Jorge
One of the most challenging problems in computational mechanics is the prediction of the crack propagation path. In this work, the Natural Neighbour Radial Point Interpolation Method (NNRPIM), an efficient meshless method, is extended to the field of fracture mechanics. Since the NNRPIM relies on the Natural Neighbour mathematical concept to obtain the integration mesh and establish the nodal connectivity, the NNRPIM only requires a computational nodal distribution to fully discretise the problem domain. The Radial Point Interpolators (RPI) are used to construct the NNRPIM interpolation functions. Taking advantage of the unique features of the NNRPIM, in this work, the crack propagation path is numerically simulated using an adapted crack path opening algorithm, in which the crack is iteratively extended in line segments. In each iteration, using the obtained stress field, the crack propagation direction is determined using the maximum circumferential stress criterion. Due to the flexibility of the natural neighbour concept, the increase of the domain discontinuities do not represent a numerical difficulty. In the end, several crack opening path benchmark examples are solved in order to show the efficiency of the proposed numerical approach.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: October 2015
- A meshfree method based on the radial basis functions for solution of
two-dimensional fractional evolution equation- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Hadi Roohani Ghehsareh , Sayna Heydari Bateni , Ali Zaghian
In the current work, numerical solution of a two-dimensional fractional evolution equation has been investigated by using two different aspects of strong form meshless methods. In the first method a time discretization approach and a numerical technique based on the convolution sum are employed to approximate the appearing time derivative and fractional integral operator, respectively. It has been proven analytically that the time discretization scheme is unconditionally stable. Then a meshfree collocation method based on the radial basis functions is used for solving resulting time-independent discretization problem. As the second approach, a fully Kansa׳s meshfree method based on the Gaussian radial basis function is formulated and well-used directly for solving the governing problem. In this technique an explicit formula to approximate the fractional integral operator is computed. The given techniques are used to solve two examples of problem. The computed approximate solutions are reported through the tables and figures, also these results are compared together and with the other available results. The presented results demonstrate the validity, efficiency and accuracy of the formulated techniques.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015
- A novel semi-analytical algorithm of nearly singular integrals on higher
order elements in two dimensional BEM- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Zhongrong Niu , Zongjun Hu , Changzheng Cheng , Huanlin Zhou
In this paper, a novel semi-analytical algorithm is developed to evaluate the nearly strong and hyper-singular integrals on higher order elements in two dimensional (2-D) BEM. By analyzing the geometrical feature of higher order elements in the intrinsic coordinates, the relative distance from a source point to the element of integration is defined to describe the character of the nearly singular integrals. By a series of deduction, the leading singular part of the integral kernel functions on the higher order elements is separated from each of the nearly singular integrals. Then the nearly singular integrals on the higher order elements close to the source point are transformed to the sum of both the non-singular parts and nearly singular parts by the subtraction, in which the former are calculated by the conventional numerical quadratures and the latter are evaluated by the resulting analytical formulations. Furthermore, the BEM with the quadratic elements was used to analyze the displacements and stresses near the boundary as well as thin-walled structures in 2-D elasticity. The numerical results from three examples demonstrate that the quadratic BE analysis with the semi-analytical algorithm is more accurate and efficient than the Linear BE analysis with the analytical algorithm for the nearly singular integrals. In fact, the Linear BE analysis has been greatly more advantageous compared with the finite element analysis for the thin-walled structures.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015
- Efficient evaluation of integrals with kernel 1/rχ for quadrilateral
elements with irregular shape- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Jia-He Lv , Xia-Ting Feng , Fei Yan , Quan Jiang
In this paper, integrals with kernel 1 / r χ are concerned with the following three aspects: a). the near singularity caused by distorted element shape; b). the near singularity derived from the angular direction; c). the singularity/near singularity in the radial direction. A conformal polar coordinate transformation (CPCT) is proposed to eliminate the shape effect of elements, which can keep the shape characteristic of distorted elements, and an improved sigmoidal transformation is introduced to alleviate the near singularity in the angular direction. By combination of the two strategies with existing methods, such as singularity subtraction method and distance transformation method utilized in this paper, an efficient and robust numerical integration approach can be obtained for various orders of singular/nearly singular integrals, and a distorted curved quadrilateral element extracted from a cylinder surface is provided to demonstrate the efficiency and robustness of the proposed method.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015
- A collocation and least squares p-singular boundary method without
fictitious boundary- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Mehrzad Ghorbani , Daniel Watson
This study proposes a new version, p-SBM, of the numerical singular boundary method (SBM) to solve general classes of elliptic PDEs such as: Laplace, Helmholtz and diffusion equations. In SBM, the fundamental solution (FS) of the problem must be given but unlike the method of fundamental solutions (MFS), a fictitious boundary is not required. Instead, the inverse interpolation technique (IIT) and least squares method for the calculation of the singular diagonal elements of the interpolation matrix allows us to avoid the singularity at origin. In this study, we enrich the traditional SBM by adding a constant parameter or a linear combination to the previous MFS approximation and use various types of internal, external and boundary nodes. The p-SBM is applied to some homogeneous Laplace, Helmholtz and Diffusion problems to show its ability and solution accuracy. The non-homogeneous problems can be handled by using the dual reciprocity method (DRM).
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015
- Hybrid LES/URANS simulation of turbulent natural convection by BEM
- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): P. Kocutar , L. Škerget , J. Ravnik
In this paper we have developed a hybrid LES/URANS turbulent model for a BEM based turbulent fluid flow solver. We employed the unified LES/URANS approach, where the interface between the LES and URANS regions is defined using a physical quantity, which dynamically changes during numerical simulation. The main characteristic of the unified hybrid model is that only one set of governing equations is used for fluid flow simulation in both the LES and URANS regions. Regions where turbulent kinetic energy is calculated by LES and URANS models are determined using a switching criterion. We used the Reynolds number based on turbulent kinetic energy and the Reynolds number based on total turbulent kinetic energy to establish the LES/URANS interface switching criterion. Depending on flow characteristics and with the use of switching criterion, we chose between sub-grid scale viscosity (SGS) and URANS effective viscosity. The SGS or URANS effective viscosity is used in the transport equation for turbulent kinetic energy and in governing equations for fluid flow. The developed numerical algorithm was tested by simulating turbulent natural convection within a square cavity. The hybrid turbulent model was implemented within a numerical algorithm based on the boundary element method, where single domain and sub-domain approaches are used. The governing equations are written in velocity–vorticity formulation. We used the false transient time scheme for the kinematics equation.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015
- 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
- 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 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