Engineering Analysis with Boundary Elements [3 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 0955-7997 Published by Elsevier [2563 journals] [SJR: 1.22] [H-I: 39] |
- 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
- The method of fundamental solutions for complex electrical impedance
tomography- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): Marjan Asadzadeh Heravi , Liviu Marin , Cristiana Sebu
The forward problem for complex electrical impedance tomography (EIT) is solved by means of a meshless method, namely the method of fundamental solutions (MFS). The MFS for the complex EIT direct problem is numerically implemented, and its efficiency and accuracy as well as the numerical convergence of the MFS solution are analysed when assuming the presence in the medium (i.e. background) of one or two inclusions with the physical properties different from those corresponding to the background. Four numerical examples with inclusion(s) of various convex and non-convex smooth shapes (e.g. circular, elliptic, peanut-shaped and acorn-shaped) and sizes are presented and thoroughly investigated.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: September 2014
- Finite Block Method in elasticity
- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): P.H. Wen , P. Cao , T. Korakianitis
A new point collocation algorithm named Finite Block Method (FBM), which is based on the one-dimensional differential matrix is developed for 2D and 3D elasticity problems in this paper. The main idea is to construct the first order one-dimensional differential matrix for one block by using Lagrange series with uniformly distributed nodes. The higher order derivative matrix for one-dimensional problem is obtained. By introducing the mapping technique, a block of quadratic type is transformed from Cartesian coordinate ( x y z ) to normalised coordinate ( ξ η ς ) with 8 seeds or 20 seeds for two or three dimensions. The differential matrices in physical domain are determined from that in the normalised transformed system. Several 2D and 3D examples are given and comparisons have been made with either analytical solutions or the boundary element method to demonstrate the accuracy and convergence of this method.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: September 2014
- A semi-analytical approach to Green׳s functions for heat equation in
regions of irregular shape- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): Yu. A. Melnikov , V. Reshniak
Initial-boundary-value problems are considered for the classical two-dimensional heat equation in regions of irregular configuration. A semi-analytical algorithm is proposed to accurately compute profiles of Green׳s function for such problems. The algorithm is based on a modification of the standard boundary integral equation method. To make the modification efficient, analytical representations of Green׳s functions are required for relevant regularly shaped regions. These are obtained in a closed form and employed then as kernels of the corresponding heat potentials, reducing the problem to a regular integral equation on a part of a boundary of the considered region.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: September 2014
- Formulation of the MFS for the two-dimensional Laplace equation with an
added constant and constraint- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): Jeng-Tzong Chen , Jheng-Lin Yang , Ying-Te Lee , Yu-Lung Chang
Motivated by the incompleteness of single-layer potential approach for the interior problem with a degenerate-scale domain and the exterior problem with bounded potential at infinity, we revisit the method of fundamental solutions (MFS). Although the MFS is an easy method to implement, it is not complete for solving not only the interior 2D problem in case of a degenerate scale but also the exterior problem with bounded potential at infinity for any scale. Following Fichera׳s idea for the boundary integral equation, we add a free constant and an extra constraint to the traditional MFS. The reason why the free constant and extra constraints are both required is clearly explained by using the degenerate kernel for the closed-form fundamental solution. Since the range of the single-layer integral operator lacks the constant term in the case of a degenerate scale for a two dimensional problem, we add a constant to provide a complete base. Due to the rank deficiency of the influence matrix in the case of a degenerate scale, we can promote the rank by simultaneously introducing a constant term and adding an extra constraint to enrich the MFS. For an exterior problem, the fundamental solution does not contain a constant field in the degenerate kernel expression. To satisfy the bounded potential at infinity, the sum of all source strengths must be zero. The formulation of the enriched MFS can solve not only the degenerate-scale problem for the interior problem but also the exterior problem with bounded potential at infinity. Finally, three examples, a circular domain, an infinite domain with two circular holes and an eccentric annulus were demonstrated to see the validity of the enriched MFS.
PubDate: 2014-07-27T22:15:52Z
- Abstract: Publication date: September 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
- An adaptive expansion technique in the fast multipole method for 3D
acoustics problems at low frequencies- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): Xianhui Wang , Xiaoming Zhang , Jianming Zhang , Xing Shuai Zheng
An adaptive expansion technique is introduced to the implement fast multipole method (FMM) for acoustics problems at low frequencies in this work. This technique determines the number of expansion terms in multipole to local (M2L) translations according to the distance between the two interaction boxes. As a consequence, the computational efficiency of the fast multipole method is improved significantly. In addition, the numerical examples demonstrate the adaptive algorithm is valid for the hyper-singular boundary face method (HBFM) with FMM and the dual boundary face method (CHBFM) with FMM, although it is obtained by the conventional boundary face method (CBFM) with FMM.
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
- A domain renumbering algorithm for multi-domain boundary face method
- Abstract: Publication date: July 2014
Source:Engineering Analysis with Boundary Elements, Volume 44
Author(s): Jianming Zhang , Chenjun Lu , Yuan Li , Lei Han , Pan Wang , Guangyao Li
In this paper, a domain number optimization algorithm for the multi-domain boundary face method is proposed. The advantage of the algorithm is to make nonzero blocks of the overall assembled matrix are as close to the main diagonal as possible. This will minimize the block fill-in effect that occurs during the solution process. Consequently, the time used for LU-decomposition and the memory requirement of the matrix will be reduced significantly. In this algorithm, one or more level structures are generated by considering the freedom degrees and the connectivity of the domains. Then we renumber the domains according to the level structure of the smallest bandwidth. Four steady-state heat conduction problems of multi-domain are solved to test the algorithm, and high efficiency is observed.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: July 2014
- Simulation of plant cell shrinkage during drying – A SPH–DEM
approach- Abstract: Publication date: July 2014
Source:Engineering Analysis with Boundary Elements, Volume 44
Author(s): H.C.P. Karunasena , W. Senadeera , R.J. Brown , Y.T. Gu
Plant based dried food products are popular commodities in global market where much research is focused to improve the products and processing techniques. In this regard, numerical modeling is highly applicable and in this work, a coupled meshfree particle-based two-dimensional (2-D) model was developed to simulate microscale deformations of plant cells during drying. Smoothed Particle Hydrodynamics (SPH) was used to model the viscous cell protoplasm (cell fluid) by approximating it to an incompressible Newtonian fluid. The visco-elastic characteristic of the cell wall was approximated to a Neo-Hookean solid material augmented with a viscous term and modeled with a Discrete Element Method (DEM). Compared to a previous work [44], this study proposes three model improvements: linearly decreasing positive cell turgor pressure during drying, cell wall contraction forces and cell wall drying. The improvements made the model more comparable with experimental findings on dried cell morphology and geometric properties such as cell area, diameter, perimeter, roundness, elongation and compactness. This single cell model could be used as a building block for advanced tissue models which are highly applicable for product and process optimizations in Food Engineering.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: July 2014
- Editorial Board
- Abstract: Publication date: July 2014
Source:Engineering Analysis with Boundary Elements, Volume 44
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: July 2014
- Non-singular Method of Fundamental Solutions for anisotropic elasticity
- Abstract: Publication date: August 2014
Source:Engineering Analysis with Boundary Elements, Volume 45
Author(s): Q.G. Liu , B. Šarler
The purpose of the present paper is to develop a Non-singular Method of Fundamental Solutions (NMFS) for two-dimensional anisotropic linear elasticity problems. The NMFS is based on the classical Method of Fundamental Solutions (MFS) with regularization of the singularities. This is achieved by replacing the concentrated point sources with distributed sources over disks around the singularity, as recently developed for isotropic elasticity problem. In case of the displacement boundary conditions, the values of distributed sources are calculated by a simple numerical procedure, since the closed form solution is not available. In case of traction boundary conditions, the respective desingularized values of the derivatives of the fundamental solution in the coordinate directions, as required in the calculations, are calculated indirectly by considering two reference solutions of the linearly varying simple displacement fields. The feasibility and accuracy of the newly developed method are demonstrated through comparison with MFS solutions and analytical solutions for a spectra of anisotropic plane strain elasticity problems, including bi-material arrangements. NMFS turns out to give similar results as the MFS in all spectra of performed tests. The lack of artificial boundary is particularly advantageous for using NMFS in multi-body problems.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: August 2014
- Transient 3D heat conduction in functionally graded materials by the
method of fundamental solutions- Abstract: Publication date: August 2014
Source:Engineering Analysis with Boundary Elements, Volume 45
Author(s): Ming Li , C.S. Chen , C.C. Chu , D.L. Young
In this paper, the three-dimensional transient heat conduction problems in functionally graded materials (FGMs) have been solved using the method of fundamental solutions (MFS). To be more specific, we consider the FGMs with thermal conductivity and specific heat vary exponentially in z-direction. In the numerical simulation, we coupled the fundamental solution of diffusion equation with the method of time–space unification which provides a simple and direct approach for solving time-dependent problems. The parameter transformation technique is also utilized to obtain the fundamental solutions which contain the thermal conductivity and the specific heat conditions. The MFS is very attractive in handling problems with irregular domain due to the simplicity of the method. The numerical results are in good agreement comparing with analytical solution and results obtained from the finite element method.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: August 2014
- Solution of a continuous casting of steel benchmark test by a meshless
method- Abstract: Publication date: August 2014
Source:Engineering Analysis with Boundary Elements, Volume 45
Author(s): R. Vertnik , B. Šarler
This paper solves a recently proposed industrial benchmark test (Šarler et al., 2012 [1]) by a meshless method. The physical model is established on a set of macroscopic equations for mass, energy, momentum, turbulent kinetic energy, and dissipation rate in two dimensions. The mixture continuum model is used to treat the solidification system. The mushy zone is modeled as a Darcy porous media with Kozeny–Karman permeability relation, where the morphology of the porous media is modeled by a constant value. The incompressible turbulent flow of the molten steel is described by the Low-Reynolds-Number (LRN) k–ε turbulence model, closed by the Abe–Kondoh–Nagano closure coefficients and damping functions. The numerical method is established on explicit time-stepping, collocation with multiquadrics radial basis functions on non-uniform five-nodded influence domains, and adaptive upwinding technique. The velocity–pressure coupling of the incompressible flow is resolved by the explicit Chorin’s fractional step method. The advantages of the method are its simplicity and efficiency, since no polygonisation is involved, easy adaptation of the nodal points in areas with high gradients, almost the same formulation in two and three dimensions, high accuracy and low numerical diffusion. The results are carefully presented and tabulated, together with the results obtained by ANSYS-Fluent, which would in the future permit straightforward comparison with other numerical approaches as well.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: August 2014
- Simulation of macrosegregation with mesosegregates in binary metallic
casts by a meshless method- Abstract: Publication date: August 2014
Source:Engineering Analysis with Boundary Elements, Volume 45
Author(s): G. Kosec , B. Šarler
Simulation of macrosegregation with mesosegregates as a consequence of solidification of a binary Sn–10%Pb alloy in a 2-dimensional rectangular cast is tackled in the present paper. Coupled volume averaged governing equations for mass, energy, momentum and species transfer are considered by incorporating Lever solidification rule and incompressible Newtonian fluid with Darcy limit in the mushy zone. Solid phase is assumed stationary. Double diffusive effects in the melt are modeled by the thermal and solutal Boussinesq hypothesis. The physical model is solved by the meshless Local Radial Basis Function Collocation Method (LRBFCM) by using 5-noded influence domains, multiquadrics radial basis functions and explicit time stepping. Pressure–velocity coupling is based on local pressure correction. Adaptive upwinding has to be used for stabilization of the convective terms. The numerical simulations reveal instabilities during solidification process that introduce anomalies in the final segregation map that scale with the typical cast as well as sub-cast dimensions. The main advantages of choosing the represented meshless approach for solving the problem are in its simplicity and similar coding in 2D and 3D, as well as straightforward applicability in non-uniform node arrangements. The locality of the proposed numerical approach is also convenient for parallel execution. It is demonstrated that LRBFCM can be advantageously used in casting simulations where the chemical segregation exhibits industrially relevant multi-scale patterns.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: August 2014
- 3D Lattice Boltzmann flow simulations through dendritic mushy zones
- Abstract: Publication date: August 2014
Source:Engineering Analysis with Boundary Elements, Volume 45
Author(s): A. Ludwig , A. Kharicha , C. Hölzl , J. Domitner , M. Wu , T. Pusztai
Literature data on permeability of dendritic microstructures show a wide scatter. For a given solid fraction the permeability may vary easily by two orders of magnitude. This might be caused by some unavoidable technical problems in doing the corresponding experiments. However, even numerical results may vary greatly depending on the source of the input microstructure and/or the dimension of flow simulation (2D vs. 3D) and/or the applied boundary conditions. In the present work we have used the Lattice Boltzmann technique to perform flow simulations through 2D and 3D dendritic microstructures coming from (i) simplified geometrical approximations, (ii) phase field simulations of binary alloys and (iii) computer tomographs on AlCu alloys. The discussion of the results shows that for low solid fraction, simple geometries can be used as substitute for dendritic structures. However, once the secondary arms are more prominent, large deviations and scattering occur. These deviations are caused by the strong variation of the dendrites geometry along the growth direction, making simplified structures insufficient to derive a reasonable value for the permeability.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: August 2014
- Coupled BEM–FEM analysis of flow and heat transfer over a solar
thermal collector- Abstract: Publication date: August 2014
Source:Engineering Analysis with Boundary Elements, Volume 45
Author(s): J. Ravnik , M. Hriberšek , L. Škerget
A wavelet transform based BEM numerical scheme is used for Large Eddy Simulation of turbulent natural and forced convection of air flowing over a solar thermal collector. The collector is enclosed by vertical fins forming an open shallow cavity. The numerical scheme employs the velocity–vorticity formulation of Navier–Stokes equations using LES turbulence model where boundary element and finite element methods are combined. Grids with up to 2×105 nodes are used in simulations lasting for 6×104 time steps. Three inflow air velocities are considered corresponding to Reynolds number value up to 2 × 10 4 . Temperature difference between air and collector of about 50K is considered. Heat transfer from the thermal solar collector is studied via the average Nusselt number value, its time series and its relationship to the values of Reynolds and Rayleigh numbers. The results show that the largest heat losses occur behind the fin due to shedding of large vortices that transport hot air away from the collector. Heat losses decrease along the central part of the collector and feature another smaller peak just before the air hits the fin on the opposite side of the collector.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: August 2014
- Variational multiscale element free Galerkin method for
convection-diffusion-reaction equation with small diffusion- Abstract: Publication date: September 2014
Source:Engineering Analysis with Boundary Elements, Volume 46
Author(s): Xiaohua Zhang , Hui Xiang
This paper presents the variational multiscale element free Galerkin method to solve convection-diffusion-reaction equation. The equation under consideration involves a small diffusivity and a large reaction coefficient, which leads to reaction-convection dominated problem. The variational multiscale element free Galerkin method is derived based on Hughes׳s variational multiscale formulation and element free Galerkin method, thus it inherits the advantages of variational multiscale and meshless methods, meanwhile, the formulation is free of any user-defined parameters owing to the stabilization parameter arises naturally. In order to investigate the presented method, both steady and unsteady 2D convection-diffusion-reaction problems are considered, and the numerical results illustrate the proposed method has the high accuracy and stability for solving convection-diffusion-reaction equation.
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: September 2014
- Editorial Board
- Abstract: Publication date: August 2014
Source:Engineering Analysis with Boundary Elements, Volume 45
PubDate: 2014-06-14T16:33:59Z
- Abstract: Publication date: August 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
- A model-integrated localized collocation meshless method for large scale
three-dimensional heat transfer problems- Abstract: Publication date: Available online 29 March 2014
Source:Engineering Analysis with Boundary Elements
Author(s): S. Gerace , K. Erhart , A. Kassab , E. Divo
We present a Model Integrated Meshless Solver (MIMS) tailored to solve practical large-scale industrial problems. This is accomplished by developing a robust meshless technique as well as a comprehensive model generation procedure. By closely integrating the model generation process into the overall solution methodology, the presented techniques are able to fully exploit the strengths of the meshless approach to achieve levels of automation, stability, and accuracy currently unseen in the area of engineering analysis. Specifically, MIMS implements a blended meshless solution approach which utilizes a variety of shape functions to obtain a stable and accurate iteration process. This solution approach is then integrated with a newly developed, highly adaptive model generation process which employs a quaternary triangular surface discretization for the boundary, a binary-subdivision discretization for the interior, and a unique shadow layer discretization for near-boundary regions. Together, these discretization techniques are able to achieve directionally independent, automatic refinement of the underlying model, allowing the method to generate accurate solutions without the need for intermediate human involvement. In addition, by coupling the model generation with the solution process, the presented method is able to address the issue of ill-constructed geometric input such as small features, poorly formed faces, and other such pathologies often generated from solid models in the course of design and in the end to provide an intuitive, yet powerful approach to solving modern engineering analysis problems.
PubDate: 2014-04-29T06:47:23Z
- Abstract: Publication date: Available online 29 March 2014
- Mesh reduction methods for industrial applications
- Abstract: Publication date: Available online 3 April 2014
Source:Engineering Analysis with Boundary Elements
Author(s): Božidar Šarler
PubDate: 2014-04-29T06:47:23Z
- Abstract: Publication date: Available online 3 April 2014