Engineering Analysis with Boundary Elements [3 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 0955-7997 Published by Elsevier [2566 journals] [SJR: 1.22] [H-I: 39] |
- The ACA–BEM approach with a binary-key mosaic partitioning for
modelling multiple bubble dynamics- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Zhiwei Fu , Viktor Popov
The fast algorithm adaptive cross approximation (ACA) is applied to accelerate the solution of the boundary element method (BEM). A new method for mosaic partitioning is proposed as part of the implementation of the ACA algorithm. It is based on a binary key system, which represents a hierarchical cluster tree and helps to identify the hierarchy within the ℋ -matrix generated by the BEM. The employed ACA approach proves efficient even for relatively small problems with the degree of freedom of O(103). As the problem size grows, the superior performance of the fast approach becomes more notable by comparison with that of the conventional boundary element method (CBEM). Modelling of bubble dynamics belongs to the moving boundary problems and can be efficiently analysed by using the BEM. By applying the ACA approach, the dense matrices via the collocation scheme are successfully compressed, and the developed model is capable of investigating the time-dependent evolution process of a relatively large number of bubbles (>100) in an efficient way.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- Numerical solution of three-dimensional Laplacian problems using the
multiple scale Trefftz method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Cheng-Yu Ku , Chung-Lun Kuo , Chia-Ming Fan , Chein-Shan Liu , Pai-Chen Guan
This paper proposes the numerical solution of three-dimensional Laplacian problems based on the multiple scale Trefftz method with the incorporation of the dynamical Jacobian-inverse free method. A numerical solution for three-dimensional Laplacian problems was approximated by superpositioning T-complete functions formulated from 18 independent functions satisfying the governing equation in the cylindrical coordinate system. To mitigate a severely ill-conditioned system of linear equations, this study adopted the newly developed multiple scale Trefftz method and the dynamical Jacobian-inverse free method. Numerical solutions were conducted for problems involving three-dimensional groundwater flow problems enclosed by a cuboid-type domain, a peanut-type domain, a sphere domain, and a cylindrical domain. The results revealed that the proposed method can obtain accurate numerical solutions for three-dimensional Laplacian problems, yielding a superior convergence in numerical stability to that of the conventional Trefftz method.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- An ultra-accurate hybrid smoothed finite element method for piezoelectric
problem- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Eric Li , Z.C. He , L. Chen , Bing Li , Xu Xu , G.R. Liu
An ultra-accurate hybrid smoothed finite element method (HS-FEM) is presented for the analysis of piezoelectric structures, in which the electrostatic equations governing piezoelectric problem are solved numerically with simplest triangular elements in 2D and tetrahedral elements in 3D. In the present method, the strain field is assumed to be the weighted average between compatible strains from finite element method (FEM) and smoothed strains from node-based smoothed finite element method (NS-FEM). Numerical results demonstrate that the proposed method possesses a novel bound solution in terms of strain energy and eigenfrequencies, which is very important for safety and reliability assessments of piezoelectric structural properties. In addition, the numerical results obtained from HS-FEM are much more accurate than the standard finite element method using the same of nodes. Furthermore, the computational efficiency of HS-FEM is much better than the FEM.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- Free vibration analysis of stepped rectangular plates resting on
non-homogeneous elastic foundations- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): M. Huang , T. Sakiyama , H. Matsuda , C. Morita
A Half Boundary Method (HBM) is proposed for analyzing the free vibration problem of rectangular plates with stepped thickness resting on non-homogeneous elastic foundations. The unknown quantities of the method exist only on half of the boundary. The non-homogeneous elastic foundation discussed here consists of two-segment elastic Winkler foundation. The fundamental differential equations are established for the bending problem of the plate on elastic foundations. The Green function, which is obtained by transforming these differential equations into integral equations and using numerical integration, is used to establish the characteristic equation of the free vibration. The effects of the modulus of the foundation, the stepped thickness and aspect ratio on the frequency parameters are considered. By comparing the present numerical results with those previously published, the efficiency and accuracy of the present method are investigated.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- Finding unknown heat source in a nonlinear Cauchy problem by the Lie-group
differential algebraic equations method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Chein-Shan Liu
We consider an inverse heat source problem of a nonlinear heat conduction equation, for recovering an unknown space-dependent heat source under the Cauchy type boundary conditions. With the aid of measured initial temperature and initial heat flux, which are disturbanced by random noise causing measurement error, we develop a Lie-group differential algebraic equations (LGDAE) method to solve the resultant differential algebraic equations. The Lie-group numerical method has a stabilizing effect to retain the solution on the associated manifold, which thus naturally has a regularization effect to overcome the ill-posed property of the nonlinear inverse heat source problem. As a consequence, we can quickly recover the unknown heat source under noisy input data only through a few iterations. The initial data used in the recovery of heat source are assumed to be the analytic continuation ones which are not given arbitrarily. Certainly, the measured initial data belong to this type data.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- A Laplace transform DRBEM with a predictor–corrector scheme for
- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Imam Solekhudin , Keng-Cheng Ang
A problem involving time-dependent infiltration from periodic channels with root-water uptake is governed by Richards equation. To study the problem numerically, the governing equation is transformed into a modified Helmholtz equation using the Kirchhoff transformation, dimensionless variables, and Laplace transforms. The modified Helmholtz equation is then solved numerically using a dual reciprocity boundary element method (DRBEM) and a predictor–corrector scheme simultaneously. A numerical inverse Laplace transform is employed to obtain numerical solutions of the problem.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- Application of complex SIE method for the prediction of hydrofracture path
- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): A.A. Andreev , A.N. Galybin , O.Y. Izvekov
This study is aimed at application of the method of complex singular integral equation (SIE) to the problem of crack propagation in non-uniform stress field. The paper examines one actual problem of oil and gas production: modeling of the hydrofracture trajectories in a reservoir subjected to non-uniform distributions of pore pressure. A modification of the method of mechanical quadratures is used to solve the SIE to simulate the hydro-fracture trajectory. The modification addresses discontinuities in the loads acting on the hydrofracture and provides quite accurate and fast solutions for the stress intensity factors. The crack path is modeled by a polygonal line such that the orientation of every subsequent leg is chosen by the criterion of maximum tensile stresses at the crack tip calculated for the current configuration. Different interposition the hydrofracture and the injection wells are examined.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- Stochastic sensitivity of the electromagnetic distributions inside a human
eye modeled with a 3D hybrid BEM/FEM edge element method- Abstract: Publication date: Available online 15 September 2014
Source:Engineering Analysis with Boundary Elements
Author(s): H. Dodig , S. Lalléchère , P. Bonnet , D. Poljak , K. El Khamlichi Drissi
This contribution was dedicated to the assessment of the electromagnetic (EM) distributions inside a 3D modeled human eye. Since the use of accurate and efficient electromagnetic tools is crucial to obtain such results, an original hybrid boundary element method (BEM)/finite element method (FEM) is presented through the example of an EM wave impinging on the eye corneal region. Due to the variability inherent to the characterizing of living parameters (regarding our frequency range of interest about a few GHz), an accurate modeling of those mostly electrical data is necessary. A simple formalism based upon a “philosophy” close to Monte Carlo requirements is proposed in this paper in order to integrate efficiently and precisely uncertainties in the proposed results. The analysis of the sensitivity of different electrical parameters aims to increase a better knowledge of the EM fields distribution inside an eye. Obviously, both the deterministic EM modeling and the stochastic theoretical basis will be presented. The whole model will be illustrated on numerical examples including different random variables.
PubDate: 2014-09-18T03:07:01Z
- Abstract: Publication date: Available online 15 September 2014
- Multiobjective optimization for node adaptation in the analysis of
composite plates using a meshless collocation method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): C.M.C. Roque , J.F.A. Madeira , A.J.M. Ferreira
The bending of simply supported composite plates is analyzed using a direct collocation meshless numerical method. In order to optimize node distribution the Direct MultiSearch (DMS) for multiobjective optimization method is applied. In addition, the method optimizes the shape parameter in radial basis functions. The optimization algorithm was able to find good solutions for a large variety of nodes distribution.
PubDate: 2014-09-18T03:07:01Z
- Abstract: Publication date: January 2015
- Fully nonlinear wave interaction with freely floating non-wall-sided
structures- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): B.Z. Zhou , G.X. Wu , B. Teng
A fully nonlinear numerical model for a floating body in the open sea has been developed based on velocity potential together with a higher-order boundary element method (BEM). The total wave elevation and the total velocity potential are separated into two parts, based on the incoming wave from infinity and the disturbed potential by the body. The mesh is generated only once at the initial time and the element nodes are rearranged subsequently without changing their connectivity by using a spring analogy method. Through some auxiliary functions, the mutual dependence of fluid/structure motions are decoupled, which allows the body acceleration to be obtained without the knowledge of the pressure distribution. Numerical results are provided for forces and run-ups of a fixed cylinder with flare and the comparison is made with the second order theory in the frequency domain. Simulations are also made for a freely floating body responding to wave excitation. Resonance related to ringing excited by the high order force at the triple wave frequency is discussed. Further results are provided for motions, forces and run-ups of a floating cylinder with flare. Comparison with the results for the fixed body and body in single degree of freedom is made.
PubDate: 2014-09-18T03:07:01Z
- Abstract: Publication date: January 2015
- The general boundary element method for 3D dual-phase lag model of bioheat
transfer- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Ewa Majchrzak , Lukasz Turchan
Heat transfer processes proceeding in the 3D domain of heating tissue are discussed. The problem is described by dual-phase lag equation supplemented by adequate boundary and initial conditions. To solve the problem the general boundary element method is proposed. The examples of computations are presented in the final part of the paper. The efficiency and exactness of the algorithm proposed are discussed and the conclusions are also formulated.
PubDate: 2014-09-10T01:48:39Z
- Abstract: Publication date: January 2015
- Geometrically nonlinear elastodynamic analysis of hyper-elastic neo-Hooken
FG cylinder subjected to shock loading using MLPG method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Mohammad Hossein Ghadiri Rad , Farzad Shahabian , Seyed Mahmoud Hosseini
In this paper, geometrically nonlinear dynamic behavior of FG thick hollow cylinder under axisymmetric mechanical shock loading is investigated using meshless local Petrov–Galerkin (MLPG) method. The FG cylinder is assumed to be made of large deformable materials such as carbon-based polymers. Thus, the neo-Hooken hyper-elastic constitutive model is employed for the problem. The material properties of FG cylinder are varied as nonlinear function of radius in volume fraction forms. Radial point interpolation method is used to approximate the field variables in the local integral equations. Weak formulation on local sub-domains using a Heaviside test function is adopted to get the system of equations. It should be emphasized that the formulations are derived using total Lagrangian approach, which refers all variables to the initial configuration. The iterative Newmark/Newton–Raphson technique is used to solve the equilibrium equations. In order to verify the feasibility and accuracy of the presented method, a thick hollow FG cylinder is linearly analyzed and compared with published data. The dynamic behaviors of displacements and stresses are obtained using nonlinear analysis and discussed in details for various kinds of neo-Hooken FGMs.
PubDate: 2014-09-10T01:48:39Z
- Abstract: Publication date: January 2015
- Direct use of radial basis interpolation functions for modelling source
terms with the boundary element method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Carlos F. Loeffler , Átila L. Cruz , André Bulcão
In this paper a new technique is presented for transforming the domain integral related to the source term that characterizes the Poisson Equation, within the scope of the boundary element method, for two-dimensional problems. Similarly to the Dual Reciprocity Technique, the proposed scheme avoids domain discretization using primitive radial basis functions; however, it transforms the domain integral into a single boundary integral directly. The proposed procedure is simpler, more versatile and some useful and modern techniques related to radial basis function theory can be applied. Numerical tests show the accuracy of the proposed technique for a simple class of complete radial interpolation functions, pointing out the importance of internal poles and the potential of applying fitting interpolation schemes to minimize the computational storage, particularly considering more complex future approaches, in which a mass matrix may be generated. For the analysis of the accuracy and convergence of the proposed method, results are compared with those obtained using Dual Reciprocity, using known analytical solutions for reference.
PubDate: 2014-09-10T01:48:39Z
- Abstract: Publication date: January 2015
- Simulation of semiconductor devices with a local numerical approach
- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): G. Kosec , R. Trobec
A numerical solution of the Drift-Diffusion Model for simulation of semiconductor devices based on the local meshless numerical method is presented. Numerical difficulties inherited from convection-dominated processes and high gradients near junctions typically results in oscillations within the solution. The difficulties can be alleviated by artificial dissipation schemes or by other stabilization approaches that often require a complex computation to improve the solution convergence. We applied a simple numerical approach with a local coupling and without special treatments of nonlinearities. The proposed approach is straightforward to implement and is suitable for parallel execution. We demonstrate the efficiency of the proposed methodology on a simulation of PN junction. The results are compared against previously published data with a good agreement achieved. The applicability of the proposed methodology is confirmed with the simulation of extended tests with more complicated geometries and more intense dynamics. The computational efficiency is demonstrated through the measurement of execution time and speedup on shared memory computer architecture.
PubDate: 2014-09-10T01:48:39Z
- Abstract: Publication date: January 2015
- Editorial Board
- Abstract: Publication date: November 2014
Source:Engineering Analysis with Boundary Elements, Volume 48
PubDate: 2014-09-05T00:42:39Z
- Abstract: Publication date: November 2014
- A least squares based meshfree technique for the numerical solution of the
flow of viscoelastic fluids: A node enrichment strategy- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Mohsen Lashkarbolok , Ebrahim Jabbari , Jerry Westerweel
A fully implicit least-squares-based meshfree method is used to solve the governing equations of viscoelastic fluid flow. Here, pressure is connected to the continuity equation by an artificial compressibility technique. A radial point interpolation method is used to construct the meshfree shape functions. The method is used to solve two benchmark problems. Thanks to the flexibility of meshfree methods in domain discretization, a simple node enrichment strategy is used to discrete the problem domain more purposefully. It is shown that the introduced enrichment process have a positive effect on the accuracy of the results.
PubDate: 2014-09-05T00:42:39Z
- Abstract: Publication date: January 2015
- Stress distribution of mine roof with the boundary element method
- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): R. Wu , J.H. Xu , C. Li , Z.L. Wang , S. Qin
Mine roof, is a stiff rock strata, located on the top of coal seam, which can prevent the deformation and control the stability of coal roadway after the coal roadway is tunneled, so mine roof is one of the most important structures in coal mining engineering. In this paper, mine roof is treated as elastic plate, which is studied thoroughly at the theoretical level. Based on the mechanical models of plane and stress analysis for elastic roof, using the boundary integral equation which is obtained by the natural boundary reduction, this paper obtains stress functions of elastic half roof, as well as the analytical and numerical solutions to the each stress field functions. We also analyze the rules of different stress distributions for roof under a concentrated force and a uniform distribution load, the results of calculation show uniformity of the stress distribution. In order to research the mine roof deformation law, Mohr–Coulomb model is established to describe the deformation behavior of roof surrounding rock, FLAC3D is also used to simulate the deformation of roof after the coal roadway is tunneled under different length of coal roadway excavation. The comparison result between BEM solution and FLAC3D simulation shows advantages to solve the problem by boundary element method, and numerical simulation proves the deformation behavior of roof is influenced by the length of coal roadway excavation.
PubDate: 2014-09-05T00:42:39Z
- Abstract: Publication date: January 2015
- A fast directional BEM for large-scale acoustic problems based on the
Burton–Miller formulation- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Yanchuang Cao , Lihua Wen , Jinyou Xiao , Yijun Liu
In this paper, a highly efficient fast boundary element method (BEM) for solving large-scale engineering acoustic problems in a broad frequency range is developed and implemented. The acoustic problems are modeled by the Burton–Miller boundary integral equation (BIE), thus the fictitious frequency issue is completely avoided. The BIE is discretized by using the Nyström method based on the curved quadratic elements, leading to simple numerical implementation (no edge or corner problems) and high accuracy in the BEM analysis. The linear systems are solved iteratively and accelerated by using a newly developed kernel-independent wideband fast directional algorithm (FDA) for fast summation of oscillatory kernels. In addition, the computational efficiency of the FDA is further promoted by exploiting the low-rank features of the translation matrices, resulting in two- to three-fold reduction in the computational time of the multipole-to-local translations. The high accuracy and nearly linear computational complexity of the present method are clearly demonstrated by typical examples. An acoustic scattering problem with dimensionless wave number kD (where k is the wave number and D is the typical length of the obstacle) up to 1000 and the degrees of freedom up to 4 million is successfully solved within 10h on a computer with one core and the memory usage is 24GB.
PubDate: 2014-09-05T00:42:39Z
- Abstract: Publication date: January 2015
- A modified scaled boundary approach in frequency domain with diagonal
coefficient matrices- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Masoud Hajialilue-Bonab , Hamid Reza Tohidvand
In order to solve the scaled boundary differential equation in dynamic stiffness, an initial value is needed. This initial value can be obtained using high frequency asymptotic expansion of dynamic stiffness matrix. Expanded dynamic stiffness matrix of unbounded mediums at high frequency was presented by previous researchers based on the fully populated coefficient matrices. In this paper, lumped coefficient matrices are used to modify the scaled boundary procedure. Some extra computational efforts of the original scaled boundary method can be eliminated using the proposed approach. The scaled boundary spectral element method (SBSEM) is used to achieve lumped coefficient matrices. It is shown that the proposed method leads to correct dynamic stiffness matrix. Therefore, it can be applied to solve scaled boundary differential equation of unbounded mediums, efficiently. A comparison between the results of the modified and the original methods is presented and accuracy of the modified method is investigated.
PubDate: 2014-08-14T23:16:10Z
- Abstract: Publication date: January 2015
- The collocation multipole method for solving multiple scattering problems
with circular boundaries- Abstract: Publication date: November 2014
Source:Engineering Analysis with Boundary Elements, Volume 48
Author(s): W.M. Lee , J.T. Chen
This paper presents a semi-analytical approach to solving the multiple scattering problems with circular boundaries. To satisfy the Helmholtz equation in polar coordinates, the multipole expansion for the scattered acoustic field is formulated in terms of the Hankel functions which also satisfy the radiation condition at infinity. Rather than using the addition theorem, the multipole method and directional derivative are both combined to propose a collocation multipole method in which the acoustic field and its normal derivative with respect to non-local polar coordinates can be calculated without any truncated error. The boundary conditions are satisfied by uniformly collocating points on the boundaries. By truncating the multipole expansion, a finite linear algebraic system is acquired and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one circular cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and five circular–cylindrical scatterers are critically compared with those provided by the boundary element method and ones reported in the literature to validate the present method. Finally, the effects of the separation between scatterers and the incident wave number on the near and far field of acoustic scattering are investigated.
PubDate: 2014-08-14T23:16:10Z
- Abstract: Publication date: November 2014
- Boundary integral equations and Green׳s functions for 2D
thermoelectroelastic bimaterial- Abstract: Publication date: November 2014
Source:Engineering Analysis with Boundary Elements, Volume 48
Author(s): Iaroslav Pasternak , Roman Pasternak , Heorhiy Sulym
This paper presents a comprehensive study on the 2D boundary integral equations, Green׳s functions and boundary element method for thermoelectroelastic bimaterials containing cracks and thin inclusions. Based on the extended Stroh formalism, complex variable approach and the Cauchy integral formula, the paper derives integral formulae for the Stroh complex functions, and Somigliana type integral identities for 2D thermoelectroelastic bimaterial. The kernels arising in the integral formulae are obtained explicitly and in a closed-form. It is proved that these kernels are fundamental solutions for a line extended force and a line heat. The far-field mechanical, electric and thermal load and internal volume load are accounted for in the obtained integral formulae. The latter allow to derive boundary integral equations for a bimaterial containing holes, cracks and thin inclusions, and to develop the corresponding boundary element approach. Special tip boundary elements used in the analysis allow accurate determination of the stress and electric displacement intensity factors for cracks and thin deformable inclusions. Several numerical examples are considered that show the validity and efficiency of the developed boundary element approach in the analysis of defective thermoelectroelastic anisotropic bimaterials.
PubDate: 2014-08-14T23:16:10Z
- Abstract: Publication date: November 2014
- PROMETHEE technique to select the best radial basis functions for solving
the 2-dimensional heat equations based on Hermite interpolation- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Saeed Kazem , Farhad Hadinejad
In this work, we have decided to select the best radial basis functions for solving the 2-dimensional heat equations by applying the multiple criteria decision making (MCDM) techniques. Radial basis functions (RBFs) based on the Hermite interpolation have been utilized to approximate the solution of heat equation by using the collocation method. Seven RBFs, Gaussian (GA), Multiquadrics (MQ), Inverse multiquadrics (IMQ), Inverse quadrics (IQ), third power of Multiquadrics (MQ3), Conical splines (CS) and Thin plate Splines (TPS), have been applied as basis functions as well. In addition, by choosing these functions as alternatives and calculating the error, condition number of interpolation matrix, RAM memory and CPU time, obtained by Maple software, as criteria, rating of cases with the help of PROMETHEE technique has been investigated. In the end, the best function has been selected according to the rankings.
PubDate: 2014-08-14T23:16:10Z
- Abstract: Publication date: January 2015
- On the use of the vertical straight wire model in electromagnetics and
related boundary element solution- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Dragan Poljak , Silvestar Šesnić , Damir Cavka , Khalil El Khamlichi Drissi
The paper deals with an analysis of various EMC problems related to radiation and scattering from wires using a vertical straight wire model based on the corresponding Pocklington integro-differential equation. The rigorous solution of the Pocklington type equation is undertaken via the Galerkin–Bubnov Indirect Boundary Element Method (GB-IBEM). Many illustrative computational examples presented throughout the paper are related to dipole antenna above a lossy half-space, metal rods penetrating the ground, lightning channel and vertical grounding electrode. Obtained numerical results are somewhere compared to NEC or analytical results, respectively.
PubDate: 2014-08-14T23:16:10Z
- Abstract: Publication date: January 2015
- A numerical study of Asian option with radial basis functions based finite
differences method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Alpesh Kumar , Lok Pati Tripathi , Mohan K. Kadalbajoo
The purpose of this paper is to design and describe the valuation of Asian option by radial basis function approximation. A one state variable partial differential equation which characterizes the price of European type Asian option is discussed. The governing equation is discretized by the θ-method and the option price is approximated by radial basis function based finite difference method. Numerical experiments are performed with European option and Asian option and results are compared with theoretical and numerical results available in the literature. We show numerically that the scheme is second order accurate. Stability of the scheme is also discussed.
PubDate: 2014-08-14T23:16:10Z
- Abstract: Publication date: January 2015
- An explicit time integration scheme of numerical manifold method
- Abstract: Publication date: November 2014
Source:Engineering Analysis with Boundary Elements, Volume 48
Author(s): X.L. Qu , G.Y. Fu , G.W. Ma
The traditional numerical manifold method (NMM) has the advantage of simulating a continuum and a discontinuum in a unified framework based on a dual cover system. However, since an implicit time integration algorithm is used, the computational efficiency of the original NMM is very low, especially when more contacts are involved. The present study proposes an explicit version of the NMM. Since a lumped mass matrix is used for the manifold element, the accelerations by the corresponding physical covers can be solved explicitly without forming a global stiffness matrix. The open–close iteration is still applied to ensure computational accuracy. The developed method is first validated by two examples, and a highly fractured rock slope is subsequently simulated. Results show that the computational efficiency of the proposed explicit NMM has been significantly improved without losing the accuracy. The explicit NMM is more suitable for large-scale rock mass stability analysis and it deserves to be further developed for engineering computations in rock engineering.
PubDate: 2014-08-10T23:03:20Z
- Abstract: Publication date: November 2014
- A three-dimensional crack growth simulator with displacement discontinuity
method- Abstract: Publication date: November 2014
Source:Engineering Analysis with Boundary Elements, Volume 48
Author(s): Jingyu Shi , Baotang Shen , Ove Stephansson , Mikael Rinne
This paper first outlines the theory of a well established three dimensional boundary element method: displacement discontinuity method (DDM) and proposes to use a crack growth criterion based on maximum normal or shear stress for a three dimensional crack growth simulator, FRACOD3D. Triangular elements are used in the simulator code. A numerical scheme is used to overcome a difficulty associated with the evaluation of the basic solution for DDM in some special situations and another numerical scheme is used to calculate the stresses on the boundary elements where the stresses obtained from the normal DDM scheme have large errors. The crack growth is implemented incrementally in that new front elements are introduced at the crack front; thus no need to re-mesh the old part of the cracks. The effects of neighbouring front elements are taken into account in implementation of the crack growth to overcome severer twisting of the new front elements generated from the growth. The numerical results from FRACOD3D of two simple examples agree very well with analytical solutions, and propagation configuration of a circular disc crack in an infinite body under shear is close to that observed in an experiment in literature under similar loading condition.
PubDate: 2014-08-10T23:03:20Z
- Abstract: Publication date: November 2014
- Approximation schemes of stresses on elements for the three-dimensional
displacement discontinuity method- Abstract: Publication date: November 2014
Source:Engineering Analysis with Boundary Elements, Volume 48
Author(s): Jingyu Shi , Baotang Shen
The displacement discontinuity method is a boundary element method. It uses the analytical expressions for displacements and stresses in an infinite isotropic homogeneous linear elastic body caused by difference (discontinuity) of displacements across small planar crack surfaces. The basic solution of the method is the displacement discontinuities (DDs) across the crack elements. After DDs are obtained, the displacement and stresses at other points in the body can be calculated. It discretises the crack without considering the individual surface of the crack, thus for crack propagation issues, it uses fewer (half) number of elements than normal BEM and therefore less computation time and computer memory requirement. However, it is found that the stresses calculated from the DDs for points on and close to the crack have large errors. Here we present two numerical schemes for approximation of stresses on the crack elements in three-dimensional problems, which are implemented in a code for fracture propagation. The schemes give a reasonably accurate approximation for elements where the crack surface is relatively smooth. It is found that for elements next to sharp kinking or at the corner of a crack, the results from the schemes are not satisfactory. A modification is proposed for these cases.
PubDate: 2014-08-10T23:03:20Z
- Abstract: Publication date: November 2014
- Computation of nearly singular integrals in 3D BEM
- Abstract: Publication date: November 2014
Source:Engineering Analysis with Boundary Elements, Volume 48
Author(s): Yaoming Zhang , Xiaochao Li , Vladimir Sladek , Jan Sladek , Xiaowei Gao
This paper presents a general methodology for numerical evaluation of the nearly singular 2D integrals over the eight-node second-order quadrilateral geometry elements arising in 3D BEM. An accurate formula of distance between the source and the field point is proposed firstly. And then an extended form of the exponential transformation, which was firstly proposed by present author to regularize nearly singular integrals arising in 2D BEM, is developed to smooth out the rapid variation of the aforementioned formula of distance. Finally, several numerical examples involving boundary layer effect and thin body problems in 3D elastostatics are investigated to verify the proposed scheme, yielding very promising results. Moreover, it should be stressed that the proposed scheme is suitable for any high-order surface elements.
PubDate: 2014-08-10T23:03:20Z
- Abstract: Publication date: November 2014
- Groundwater flow simulation in unconfined aquifers using meshless local
Petrov–Galerkin method- Abstract: Publication date: November 2014
Source:Engineering Analysis with Boundary Elements, Volume 48
Author(s): Boddula Swathi , T.I. Eldho
The complex behaviour of the aquifer system is generally studied by solving a set of governing equations using either analytical or numerical methods. Numerical techniques like finite difference method (FDM) and finite element method (FEM) are generally being used to solve such problems, as analytical solutions can be obtained only for simple cases. The Meshless methods are the recently developed numerical technique which can be alternatively used for solving the groundwater problem. A variety of Meshless methods are under intense research for the development of solution for many engineering problems. As no meshing, it can save substantial cost and time on pre-processing, unlike mesh based methods, which require meshing and re-meshing. In this paper, the Galerkin equivalent of Meshless Local Petrov–Galerkin (MLPG) method with Exponential/Gaussian Radial basis function (EXP–RBF) is used for the first time for solving the unconfined groundwater problem. Computer models in MATLAB have been developed in 2D for the solution of unconfined aquifer problems. The developed models are verified with available analytical and numerical solutions. The results are found to be satisfactory. The present study shows that the MLPG based method can be used in the effective simulation of groundwater flow problems.
PubDate: 2014-08-10T23:03:20Z
- Abstract: Publication date: November 2014
- Upwind strategies for local RBF scheme to solve convection dominated
problems- Abstract: Publication date: November 2014
Source:Engineering Analysis with Boundary Elements, Volume 48
Author(s): Y.V.S.S. Sanyasiraju , Chirala Satyanarayana
The most common strategy existing in the literature for solving convection dominated Convection–Diffusion Equations (CDE) is using central approximation to the diffusive terms and upwind approximation to the convective terms. In the present work, we propose a multiquadric local RBF based grid-free upwind (LRBF_U) scheme for solving convection dominated CDE. In this method, the entire CDE operator is discretized over the nodes in the upwind local support domain for strongly convection dominant problems. The variable (optimal) shape parameter for LRBF_U scheme has been obtained by using a local optimization algorithm developed by the authors. It has been observed that for highly convection dominated problems, the LRBF_U scheme produces stable and accurate results. The proposed scheme is also been compared with the conventional Central-Upwind combined scheme, to demonstrate its superiority in generating high accurate solutions than the latter.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: November 2014
- Editorial Board
- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: September 2014
- Equivalent mechanical model of liquid sloshing in multi-baffled containers
- Abstract: Publication date: October 2014
Source:Engineering Analysis with Boundary Elements, Volume 47
Author(s): M. Ebrahimian , M.A. Noorian , H. Haddadpour
This study presents a method to determine an equivalent mechanical model (EMM) for multi-baffled containers with arbitrary geometries. The method is implemented for 2D and axisymmetric containers. The Laplace equation and Green׳s theorem are used to develop the fluid model and the boundary element method (BEM) is used to solve the fluid field governing equation. Moreover, a zoning method is utilized to model arbitrary arrangements of baffles in multi-baffled containers and a reduced order model is developed to model the free-surface sloshing. The exerted hydrodynamic pressure distribution, forces and moments on the walls of the container are determined based on the Bernoulli equation and a set of recursive formulation is presented to develop the model for multi-baffled containers. The results are validated in comparison with the literature and very good agreement is achieved. Furthermore, the effects of baffle attributes on the EMM parameters are also investigated and some conclusions are outlined.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: October 2014
- Isogeometric analysis of laminated composite plates based on a
four-variable refined plate theory- Abstract: Publication date: October 2014
Source:Engineering Analysis with Boundary Elements, Volume 47
Author(s): Loc V. Tran , Chien H. Thai , Hien T. Le , Buntara S. Gan , Jaehong Lee , H. Nguyen-Xuan
In this paper, a simple and effective formulation based on isogeometric approach (IGA) and a four variable refined plate theory (RPT) is proposed to investigate the behavior of laminated composite plates. RPT model satisfies the traction-free boundary conditions at plate surfaces and describes the non-linear distribution of shear stresses without requiring shear correction factor (SCF). IGA utilizes basis functions, namely B-splines or non-uniform rational B-splines (NURBS), which reveals easily the smoothness of any arbitrary order. It hence handles easily the C 1 requirement of the RPT model. Approximating the displacement field with four degrees of freedom per each node, the present method retains the computational efficiency while ensuring the reasonable accuracy in solution.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: October 2014
- Revisit of the equivalence of the displacement discontinuity method and
boundary element method for solving crack problems- Abstract: Publication date: October 2014
Source:Engineering Analysis with Boundary Elements, Volume 47
Author(s): Y.J. Liu , Y.X. Li
In this note, it is shown explicitly that the displacement discontinuity method (DDM) is equivalent to the boundary element method (BEM) for solving crack problems. To show this, the direct traction boundary integral equation (BIE) in terms of the displacement jump across crack surfaces is applied to a crack in an infinite 2-D elastic domain. Then, the direct traction BIE is discretized with constant line elements. All the integrals are evaluated analytically. The yielded linear system of equations is found to be exactly the same as the original DDM system of equations in terms of the displacement discontinuities. This proof of the equivalence of the DDM and BEM suggests that the two methods are the same in nature and both are based on the same traction BIE for crack problems.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: October 2014
- The numerical solution of Fokker–Planck equation with radial basis
functions (RBFs) based on the meshless technique of Kansa׳s approach
and Galerkin method- Abstract: Publication date: October 2014
Source:Engineering Analysis with Boundary Elements, Volume 47
Author(s): Mehdi Dehghan , Vahid Mohammadi
This paper describes two numerical methods based on radial basis functions (RBFs) for solving the time-dependent linear and nonlinear Fokker–Planck equations in two dimensions. These methods (RBFs) give a closed form for approximating the solution of partial differential equations. We approximate the linear and nonlinear Fokker–Planck equations with radial basis functions which are based on two techniques, one of them is Kansa׳s approach and another technique is the Galerkin method of Tau type [54]. In this work, we discretize the time variable with Crank–Nicolson method. For the space variable, we apply the radial basis functions which are Multiquadrics (MQ) and Inverse Quadric (IQ). Also, we employ another radial basis function which was introduced in [35]. These basis functions depend on constant (shape) parameter. As is well known, the shape parameter has a strong influence on the accuracy of the numerical solutions and thus we test and compare several different strategies to choose this parameter. Both techniques (Kansa׳s approach and Tau method) yield a linear system of algebraic equations say AX=b. The matrix A is usually very ill-conditioned. We apply QR decomposition technique for solving the linear system arising from our approximations. Finally, some test problems are presented to illustrate the efficiency of the new methods for the numerical solution of linear and nonlinear Fokker–Planck equations. Also, to show the good accuracy of the method of radial basis functions, we compute the errors using L ∞ , root mean square (RMS) and L 2 norms.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: October 2014
- An efficient accurate Local Method of Approximate Particular Solutions for
solving convection–diffusion problems- Abstract: Publication date: October 2014
Source:Engineering Analysis with Boundary Elements, Volume 47
Author(s): C.A. Bustamante , H. Power , W.F. Florez
An efficient accurate Local Method of Approximate Particular Solutions (LMAPS) using Multiquadric Radial Basis Functions (RBFs) for solving convection–diffusion problems is proposed. It consists in adding auxiliary points to the local interpolation stencil at which the governing PDE is enforced, known as PDE points, besides imposing the boundary condition at the stencil in contact with the problem boundary. Two convection–diffusion problems are considered as test problems and solved with two previous local direct RBF collocation schemes (with and without PDE points) and two LMAPS (with and without PDE points), as well as the Global MAPS, in order to compare accuracy, convergence order and their behaviour in terms of the shape parameter. If PDE points are added, the result accuracy is improved as well as the convergence rate when using both local direct and MAPS formulations.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: October 2014
- Regional connectivity in modified finite point method
- Abstract: Publication date: October 2014
Source:Engineering Analysis with Boundary Elements, Volume 47
Author(s): Boe Shiun Chen , Ting-Kuei Tsay , Kuo-Cheng Chiang , Chun-Wen Yang
In this paper, a concept of regional connectivity has been integrated into the modified finite point method (MFPM) [33] to solve problems with different physical behaviors in adjacent regions. This approach has been employed to improve accuracy in its applications to harbor resonance of the MFPM, which has searched adjacent nodes by relative distance for local collocation. By identifying regional connectivity, only closer nodes within regions of the same regional connectivity with respect to a base point can be included for correct local collocation. In coastal engineering, phenomenon of resonance of harbors with breakwaters is a crucial consideration in harbor planning and design. Numerical computations of harbor resonance induced by monochromatic water-waves are used to verify the MFPM numerical model integrated with regional connectivity approach. The whole computational domain is divided into several subdomains, based on different physical behaviors. After numbering of each subdomain, regional connectivity is provided to exclude searching the nearest nodes from inappropriate subdomains for local collocation. Harbors of different physical geometries, with and without breakwaters have been examined when analytical solutions [18] are available. Very good agreement between numerical results and analytical solutions has demonstrated that the concept of regional connectivity has improved the performance of MFPM. Application of this regional connectivity concept will be needed in similar problems, such as a crack in a thin plate, and a cutoff of groundwater seepage.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: October 2014
- A comparison study of meshfree techniques for solving the two-dimensional
linear hyperbolic telegraph equation- Abstract: Publication date: October 2014
Source:Engineering Analysis with Boundary Elements, Volume 47
Author(s): S. Abbasbandy , H. Roohani Ghehsareh , I. Hashim , A. Alsaedi
In this paper, a comparison between two common techniques based on the radial basis function (RBFs), direct and indirect approaches and their localized forms is performed to numerical investigation of the two-dimensional linear second-order hyperbolic telegraph equation. Four meshfree methods based on the strong form equation, the nonsymmetric radial basis function collocation method or Kansa׳s method, the method of approximate particular solutions and the localized versions of these methods are formulated and the performances of these methods for solving governing problem are compared. A time stepping approach is employed for the first and second order time derivatives. The multiquadrics (MQ) and inverse multiquadrics (IMQ) functions are used as basis functions for interpolating either unknown function or Laplacian of the unknown function in the proposed techniques. Some numerical results are given to demonstrate the validity and efficiency of these methods. Through the presented results, it can be observed that local versions of the methods have superior stability and efficiency and the global methods are sensitive to the shape parameter and large amount of collocation points.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: October 2014
- A fast multipole boundary element method for modeling 2-D multiple crack
problems with constant elements- Abstract: Publication date: October 2014
Source:Engineering Analysis with Boundary Elements, Volume 47
Author(s): Zhao Guo , Yijun Liu , Hang Ma , Shuo Huang
A fast multipole boundary element method (BEM) for solving 2-D multiple crack problems in linear elastic fracture mechanics is presented in this paper. For multiple crack problems, both the degrees of freedom (DOFs) and the size of system matrices increase quickly as the number of cracks increases, and the conventional BEM cannot support such large systems. Instead of using the singular quarter-point boundary elements at the crack tips, constant line elements are applied to symmetrically discretize the outer boundaries and crack surfaces in the present approach. In order to keep the accuracy within a limited acceptable range, a relatively large number of constant elements are required to discretize the crack surfaces. The crack opening displacement (COD) fields of the multiple crack problems are obtained by the fast multipole BEM. Stress intensity factors (SIFs) are extracted from the obtained displacement fields near the crack tip by using one point COD formula. Comparison of the CODs between the fast multipole BEM and a finite element method using ANSYS are illustrated to show the feasibility of the proposed approach. With the acceleration of fast multipole technique, multi-crack problems can be dealt with desktop PCs. Several numerical examples are presented for computing the SIFs of cracks to study the effectiveness and the efficiency of the proposed approach. The numerical results clearly demonstrate the potentials of the fast multipole BEM for solving 2-D large-scale multi-crack problems by using constant elements.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: October 2014
- Editorial Board
- Abstract: Publication date: October 2014
Source:Engineering Analysis with Boundary Elements, Volume 47
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: October 2014
- The mystery of the shape parameter IV
- Abstract: Publication date: November 2014
Source:Engineering Analysis with Boundary Elements, Volume 48
Author(s): Lin-Tian Luh
This is the fourth paper of our study of the shape parameter c contained in the famous multiquadrics ( − 1 ) ⌈ β ⌉ ( c 2 + ‖ x ‖ 2 ) β , β > 0 , and the inverse multiquadrics ( c 2 + ‖ x ‖ 2 ) β , β < 0 . The theoretical ground is the same as the third paper. However, we extend the space of interpolated functions to a more general one. This leads to a totally different set of criteria of choosing c.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: November 2014
- An efficient transient analysis of realistic grounding systems:
Transmission line versus antenna theory approach- Abstract: Publication date: November 2014
Source:Engineering Analysis with Boundary Elements, Volume 48
Author(s): B. Nekhoul , D. Poljak , D. Sekki , D. Cavka , B. Harrat , K. Kerroum , K. El Khamlichi Drissi
An efficient transmission line (TL) model for the analysis of the transient behavior of realistic grounding system is presented. The model is based on the general solution of the TL equations in the frequency domain expressed in terms of the Φ-matrix, or the direct time domain solution based on the Finite Difference Time Domain (FDTD) method. The presented TL approach provides relatively simple numerical implementation, accurate results and requires rather low computational time. The accuracy of the results obtained via TL approach is in a good agreement with the numerical results computed via the rigorous antenna theory approach based on the integral equation formulation and corresponding boundary element solution.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: November 2014
- Numerical solution of the t-version complex variable boundary integral
equation for the interior region in plane elasticity- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): Y.Z. Chen
This paper suggests the t-version complex variable boundary integral equation (CVBIE) for the interior region in plane elasticity. All the kernels in the t-version CVBIE are expressed explicitly. The property for the operator acting upon the displacement is studied. It is proved that there are three types of rigid mode movement of displacement for the t-version CVBIE, if the boundary is assumed under a traction free condition. Discretization of the t-version CVBIE is suggested. For the hypersingular integral, the integration is carried out exactly in the concept of Hadamard׳s finite part integral. Two particular examples which have known solution beforehand are used to examine the accuracy in computation. The Neumann and the Dirichlet boundary value problems are examined numerically. It is proved that the computation error is acceptable in the examples.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: September 2014
- Optimal positioning of anodes and virtual sources in the design of
cathodic protection systems using the method of fundamental solutions- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): W.J. Santos , J.A.F. Santiago , J.C.F. Telles
The method of fundamental solutions (MFS) is used for the solution of Laplace׳s equation, with nonlinear boundary conditions, aiming at analyzing cathodic protection systems. In the MFS procedure, it is necessary to determine the intensities and the distribution of the virtual sources so that the boundary conditions of the problem are satisfied. The metallic surfaces, in contact with the electrolyte, to be protected, are characterized by a nonlinear relationship between the electrochemical potential and current density, called cathodic polarization curve. Thus, the calculation of the intensities of the virtual sources entails a nonlinear least squares problem. Here, the MINPACK routine LMDIF is adopted to minimize the resulting nonlinear objective function whose design variables are the coefficients of the linear superposition of fundamental solutions and the positions of the virtual sources outside the problem domain. First, examples are presented to validate the standard MFS formulation as applied in the simulation of cathodic protection systems, comparing the results with a direct boundary element (BEM) solution procedure. Second, a MFS methodology is presented, coupled with a genetic algorithm (GA), for the optimization of anode positioning and their respective current intensity values. All simulations are performed considering finite regions in R 2.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: September 2014
- Transient free-surface seepage in three-dimensional general anisotropic
media by BEM- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): K. Rafiezadeh , B. Ataie-Ashtiani
Kinematic boundary condition is usually used when dealing with transient free-surface flow problems in isotropic media. When dealing with anisotropic problems, a transformation can transform the anisotropic media to an equivalent isotropic media for seepage analysis, but the kinematic boundary condition cannot be used directly in the transformed media. A generalization of the kinematic boundary condition along any arbitrary direction is derived for use in the transformed domain for general three-dimensional anisotropic problems. A boundary element method for solving transient free-surface seepage problems is developed and the treatment of the proposed kinematic boundary condition in the boundary element method is given. Three examples have been solved to show the reliability and flexibility of the model. Examples are verified with some available experimental and numerical cases to show the accuracy of the model for predicting the phreatic surface and it is shown that anisotropy has a very important and non-neglecting effect in the behavior and the shape of phreatic surface.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: September 2014
- The numerical manifold method for elastic wave propagation in rock with
time-dependent absorbing boundary conditions- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): Zhijun Wu , Lifeng Fan
In this study, a modified first-order Higdon׳s absorbing boundary scheme is proposed and incorporated into the numerical manifold method (NMM) to reduce reflections from artificial boundaries induced by truncating infinite media. The modified time-dependent absorbing boundary scheme can not only consider the absorbing boundary and input boundary at the same artificial boundary, but also take the effects of the incident angles into consideration by adjusting the velocities and strains of points at the boundary automatically. For illustrating the efficiency of the proposed time-dependent absorbing boundary scheme, comparisons between the results of the proposed method and the widely used viscous boundary conditions for different incident angles are presented. The developed NMM is then used to investigate wave attenuation and transmission across a joint in an infinitely long rock bar.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: September 2014
- A comparison of the meshless RBF collocation method with finite element
and boundary element methods in neutron diffusion calculations- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): T. Tanbay , B. Ozgener
The multigroup neutron diffusion equation is solved numerically by the meshless radial basis function collocation and mesh-based finite and boundary element methods. For the collocation method, multiquadrics, inverse multiquadrics and Gaussian basis functions are utilized, whereas linear shape functions are the choice for finite and boundary element methods. External and fission source problems are studied. In the context of external source case, constant, trigonometric, and linear sources are considered. The collocation method converges exponentially which is faster than the algebraic rates of finite and boundary element methods for both problems, and it was found that by adjusting the value of the shape parameter, very high accuracies can be achieved even with large fill distances. In the fission source case, multiquadrics is found to be superior to finite and boundary elements for the determination of multiplication factor, while boundary elements gave the best result for group fluxes. A comparison of CPU times shows that, finite element method has outperformed radial basis function collocation and boundary elements. When the stability is considered, finite and boundary element methods have the advantage of being more stable than the collocation technique.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: September 2014
- Nonlinear solution of the PS model for a semi-permeable crack in a 3D
piezoelectric medium- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): CuiYing Fan , HuaYang Dang , MingHao Zhao
By considering the electric field in the crack cavity, the polarization saturation (PS) model of a penny-shaped crack under electrically semi-permeable boundary condition in a three-dimensional piezoelectric medium is studied via both the extended displacement discontinuity boundary integral equation method and the boundary element method. An approximate analytical solution is derived, and the electric displacement in the crack cavity, the electric yielding zone and the local J-integral are obtained. The extended displacement discontinuity boundary element method with double iterative approaches is adapted to numerically simulate the electrically semi-permeable crack and to validate the analytical solution. The effects of different boundary conditions on the electric yielding zone and the local J-integral are also investigated.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: September 2014
- New approximation functions in the meshless finite volume method for 2D
elasticity problems- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): M. Ebrahimnejad , N. Fallah , A.R. Khoei
In this paper, two new approximation functions are introduced. These new techniques, which are referred herein as the multi-triangles method (MTM) and weighted multi-triangles method (WMTM) are applied for the approximation of unknowns and their derivatives at the points of interest. The approximations are performed in terms of the unknowns corresponding to the field nodes which are the vertices of the region surrounding the desired point and determined by Delaunay triangulations. The capability and accuracy of the proposed approximation functions are compared with the other approximating techniques in the meshless finite volume (MFV) frame work for some benchmark problems. Numerical examples reveal the superiority of the WMTM and MTM over the common moving least squares technique (MLS) and radial point interpolation method (RPIM) for the same number of nodes in the support domain. Moreover, the suggested methods need less computational time especially when dense field nodes are applied.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: September 2014
- Analysis of heat flux singularity at 2D notch tip by singularity analysis
method combined with boundary element technique- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): Changzheng Cheng , Zhilin Han , Shanlong Yao , Zhongrong Niu , Naman Recho
It is known that the heat flux becomes infinite near the notch tip due to material or geometric discontinuities. Numerical methods such as boundary element method and finite element method cannot adequately analyze the accurate singular heat flux field since they traditionally employ piecewise polynomials. In this paper, the singularity analysis method coupled with the boundary element technique is proposed for the accurate analysis of two-dimensional singular heat flux field near the notch tip. The V-notched structure is departed into two parts, which are the near tip singular sector and far tip non-singular section. The singularity analysis is executed on the near notch tip sector for searching singularity orders and corresponding characteristic angular functions by introducing the heat flux asymptotic expansions into heat conduction governing equations. The conventional boundary element method is applied to modeling the far notch tip region because there is no heat flux singularity. The asymptotic expansions of the near tip physical field and the boundary integral equations established on the far notch tip region are combined together for solving the expansion coefficients in heat flux asymptotic expansions. Thus, the complete heat flux field near the notch vertex can be accurately determined.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: September 2014