Engineering Analysis with Boundary Elements [SJR: 1.216] [H-I: 42] [1 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 0955-7997 Published by Elsevier [2805 journals] |
- Singular boundary method using time-dependent fundamental solution for
transient diffusion problems- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): Wen Chen, Fajie Wang
This paper documents the first attempt to apply the singular boundary method (SBM) with time-dependent fundamental solution to transient diffusion equations. An inverse interpolation technique is introduced to determine the origin intensity factor of the SBM. The scheme is mathematically simple, easy-to-program, truly boundary-only, free of integration and mesh. Several examples, especially three-dimensional (3D) cases, are provided to verify time-dependent SBM strategy. The numerical results clearly demonstrate its great potential.
PubDate: 2016-04-25T15:45:15Z
- Abstract: Publication date: July 2016
- Solutions for the magneto-electro-elastic plate using the scaled boundary
finite element method- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): Jun Liu, Pengchong Zhang, Gao Lin, Wenyuan Wang, Shan Lu
A semi-analytical technique based on the elastic theory is employed to study the deformation of a magneto-electro-elastic plate. Solutions are acquired by applying the scaled boundary finite element method (SBFEM), which requires the discretization of the boundary as in the boundary element method but does not need a fundamental solution. In the whole process, the detailed derivation is based on the three-dimensional governing equation. With the aid of the scaled boundary coordinates, the 3D key partial differential equation is converted into the ordinary differential equation. Only the in-plane dimensions are needed to be discretized, which contributes to reducing the computational effort. Furthermore, utilizing the high order spectral element can do good to obtain high accuracy and efficiency. The components of the magneto-electro-elastic field are solved numerically in the in-plane direction and analytically in the thickness direction. Solutions along the vertical direction are formulated as a matrix exponent which is solved by the Padé series expansion of order ( 2 , 2 ) . Comparisons with the numerical examples are provided to validate the proposed solutions. Meanwhile, other examples are carried out to demonstrate the versatility of the present method.
PubDate: 2016-04-25T15:45:15Z
- Abstract: Publication date: July 2016
- A coupled finite element-element-free Galerkin method for simulating
viscous pressure forming- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): Binxian Yuan, Wa Fang, Jiguang Li, Yujun Cai, Zhoude Qu, Zhongjin Wang
Viscous pressure forming (VPF) is a kind of sheet flexible-die forming process which uses a semisolid, flowable and viscous material as the pressure-transmitting medium. Unlike the conventional rigid die punching or hydroforming process, there are strong nonlinear features between the sheet metal and viscous medium in VPF. In this paper, a numerical analysis method for coupling sheet metal deformation and bulk deformation of viscous medium is presented. A static explicit approach based on the Updated Lagrangian (U.L.) formulation is adopted. The elastoplastic deformation of sheet metal is analyzed with finite element method (FEM), and the visco-elastoplastic bulk deformation of viscous medium is analyzed with the element-free Galerkin method (EFGM), which can eliminate mesh distortion unavoidable during the deformation of viscous medium in FEM. The contact and friction between the sheet metal and viscous medium are treated by the penalty function method. An FEM–EFGM program for coupled deformation between sheet metal and viscous medium is developed, called CDSB–FEM–EFGM for short. Several numerical examples of coupled deformation between viscous mediums with different viscosities and sheet metal are presented to demonstrate the effectiveness of the proposed method. Compared the numerical simulation results with experimental measurements, the validity of the CDSB–FEM–EFGM program is obtained.
PubDate: 2016-04-25T15:45:15Z
- Abstract: Publication date: July 2016
- Modeling free-surface flow in porous media with modified incompressible
SPH- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): Gourabananda Pahar, Anirban Dhar
This paper presents a modified incompressible smoothed particle hydrodynamics (MISPH) method for fluid-porous media interaction problems. Navier–Stokes and Brinkman Equations are considered for modeling the fluid flow outside and inside porous media. The MISPH method utilizes a truly incompressible divergence free velocity formulation. The equations are solved by using a robust two-step semi-implicit exact projection method. Turbulence stresses are evaluated by using an semi-analytical Smagorinsky model. The representative volume of the particles changes with the porosity. Interface conditions are imposed implicitly by using Darcy velocity and modified Pressure Poisson Equation (PPE) with porosity in the source/sink term. Impermeable boundary conditions are simulated with fixed ghost particles. The model is validated by using existing experimental results of dambreak flow through a homogeneous porous block in a wet bed. Simulation results show good agreement with experimental data. An application to heterogeneous porous media demonstrates the applicability and adaptability of the proposed framework. The numerical model is capable of efficiently capturing the interaction of fluid in porous and nonporous media.
PubDate: 2016-04-25T15:45:15Z
- Abstract: Publication date: July 2016
- Simulation on the interaction between multiple bubbles and free surface
with viscous effects- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): S. Li, B.Y. Ni
Based on the boundary layer theory, a general Bernoulli equation involving normal and tangential stresses has been derived and the weak viscous effects have been considered. Three-dimensional boundary element method and Green's function have been adopted to solve the interaction between bubbles and free surface. Numerical results have been validated by convergence study and comparison with published results. On this basis, two in-phase and out-phase bubbles in the vicinity of free surface are chosen as cases at different Froude number. Influence of fluid viscosity or Reynolds number is mainly investigated. Physical relevance of numerical computation and the range of validity of numerical simulation are further discussed. It is found that viscous effects depress the interaction between bubbles and free surface, which hinders the formation of the downward jet on the upper bubble surface and declines bubble volume and the height of free-surface spike.
PubDate: 2016-04-25T15:45:15Z
- Abstract: Publication date: July 2016
- Modeling of fluid flow in periodic cell with porous cylinder using a
boundary element method- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): R.F. Mardanov, S.J. Dunnett, S.K. Zaripov
The problem of viscous incompressible flow past a periodic array of porous cylinders (a model of flow in an aerosol filter) is solved. The approximate periodic cell model of Kuwabara is used to formulate the fluid flow problem. The Stokes flow model is then adopted to model the flow outside the cylinder and the Darcy law of drag is applied to find the filtration velocity field inside the porous cylinder. The boundary value problems for biharmonic and Laplace equations for stream functions outside and inside the porous cylinder are solved using a boundary elements method. A good agreement of numerical and analytical models is shown. The analytical formulas for the integrals in the expressions for the stream function, vorticity and Cartesian velocity components are obtained. It is shown that the use of analytical integration gives considerable advantage in computing time.
PubDate: 2016-04-25T15:45:15Z
- Abstract: Publication date: July 2016
- Improved non-singular method of fundamental solutions for two-dimensional
isotropic elasticity problems with elastic/rigid inclusions or voids- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): Q.G. Liu, B. Šarler
In this work, an Improved Non-singular Method of Fundamental Solutions (INMFS) is developed for the solution of two-dimensional linear elasticity problems. The source points and field points are collocated on the physical boundary, while the conventional MFS requires a troublesome fictitious boundary outside the physical domain. In INMFS, the desingularization is, for complying with the displacement boundary conditions, achieved by replacement of the concentrated point sources by distributed sources over circular discs around the singularity, and for complying with the traction boundary conditions by assuming the balance of the forces. This procedure is much more efficient than the previously proposed procedure that involves two reference solutions and at the same time enables INMFS for solving problems with internal voids and inclusions. The method has been assessed by comparison with MFS, analytical solutions and previous desingularization technique. The method is easy to code, accurate, efficient, and straightforwardly extendable to three dimensions.
PubDate: 2016-04-09T13:48:44Z
- Abstract: Publication date: July 2016
- Inverse contact problem for an elastic half-space
- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): A.N. Galybin
This paper presents a system of integral equations for the determination of contact stresses on a part of the boundary of elastic half-space by measured data of displacements on the rest of the stress-free boundary. Inverse problems like this are refereed to as conditionally ill-posed with pronounced dependence of the solution from small perturbations in measured data. The 3D problem formulation is based on spatial harmonic functions. It is proposed to use a Trefftz-type method for the sought harmonic functions based on the radial basis functions to solve the system of integral equations. A synthetic example is presented to illustrate the proposed approach.
PubDate: 2016-04-09T13:48:44Z
- Abstract: Publication date: July 2016
- Periodic band structure calculation by the Sakurai–Sugiura method
with a fast direct solver for the boundary element method with the fast
multipole representation- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): Hiroshi Isakari, Toru Takahashi, Toshiro Matsumoto
In this paper, we present a numerical method for periodic band structure calculation, which is associated with eigenvalue problems for periodic problems, using the boundary element method (BEM). In the BEM, the eigenvalue problems are converted into non-linear eigenvalue problems, which are not tractable with conventional eigensolvers. In the present study, to solve non-linear eigenvalue problems, the block Sakurai–Sugiura (SS) method, which can convert non-linear eigenvalue problems into generalised eigenvalue problems, is utilised. A fast direct solver for the BEM with a fast multipole representation is employed in the algorithm of the block SS method since algebraic equations need to be solved for multiple right-hand sides in the block SS method. We conduct several numerical experiments related to phononic structures to confirm the validity and efficiency of the proposed method. We confirm that the proposed method can calculate the band structure of the phononic structures, and the computational time with the proposed method is less than that with a conventional FEM-based eigensolvers with triangular linear elements even for relatively small problems.
PubDate: 2016-04-09T13:48:44Z
- Abstract: Publication date: July 2016
- Numerical solution of Eshelby's elastic inclusion problem in plane
elasticity by using boundary integral equation- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): Y.Z. Chen
This paper provides a numerical solution for Eshelby's elastic inclusions in an plane elasticity based on the complex variable boundary integral equation (CVBIE) method. An inclusion with arbitrary shape is embedded in the infinite matrix. In the inclusion, the constant eigenstains are assumed. No remote loading is applied to the matrix. The displacements from the assumed eigenstrains are evaluated exactly, which in turn are the generalized loading in the problem. The proposed problem is reduced to solve interior and exterior boundary value problems simultaneously. For the elliptical inclusion case, the computed stresses along the interface of the inclusion side are nearly uniform. One more numerical example is devoted to a square-type inclusion with round corner.
PubDate: 2016-04-06T13:39:35Z
- Abstract: Publication date: July 2016
- The interior field method for Laplace׳s equation in circular domains
with circular holes- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): Zi-Cai Li, John Y. Chiang, Hung-Tsai Huang, Ming-Gong Lee
The null field method (NFM) was proposed by Chen and his co-researchers, and has been discussed in numerous papers, see Chen et al. (2007 [11]), Chen et al. (2002 [12]), Chen et al. (2001 [13]), and Chen and Shen (2009 [14]). The further developments of the NFM have been made in our recent papers (Huang et al., 2013 [21]; Lee et al., 2013 [23]; Lee et al., 2014 [25]; Li et al., 2012 [29]). In this paper, the interior field method (IFM) is proposed, which offers the best performance of the NFM when the field nodes are located exactly on the domain boundary. The algorithms of the IFM are much simpler than those of the NFM, because only one formula of the interior solutions is needed, compared with multiple formulas in the NFM. Since the IFM can be classified into the family of the Trefftz method (Li et al., 2008 [31]), a new error analysis of the IFM and the collocation IFM (CIFM) can be explored, to achieve the optimal convergence rates. Moreover, new proof techniques for aliasing errors in this paper are straightforward, heuristic and much easier to follow, because of direct derivations from trigonometric functions, which are distinct from Canuto and Quarteroni (1982 [8]), Canuto et al. (2006 [9]), and Kreiss and Oliger (1979 [22]). Based on this paper, the IFM and the CIFM may be recommended for those problems solvable by the NFM before.
PubDate: 2016-04-06T13:39:35Z
- Abstract: Publication date: June 2016
- Radial basis function collocation method for an elliptic problem with
nonlocal multipoint boundary condition- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): Svajūnas Sajavičius
Radial basis function domain-type collocation method is applied for an elliptic partial differential equation with nonlocal multipoint boundary condition. A geometrically flexible meshless framework is suitable for imposing nonclassical boundary conditions which relate the values of unknown function on the boundary to its values at a discrete set of interior points. Some properties of the method are investigated by a numerical study of a test problem with the manufactured solution. Attention is mainly focused on the influence of nonlocal boundary condition. The standard collocation and least squares approaches are compared. In addition to its geometrical flexibility, the examined method seems to be less restrictive with respect to parameters of nonlocal conditions than, for example, methods based on finite differences.
PubDate: 2016-04-02T13:19:42Z
- Abstract: Publication date: June 2016
- An edge/face-based smoothed radial point interpolation method for static
analysis of structures- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): S.Z. Feng, X.Y. Cui, F. Chen, S.Z. Liu, D.Y. Meng
This paper formulates an edge/face-based smoothed radial point interpolation method (ES/FS-RPIM) for the 2D and 3D static analysis of structures. In present method, the problem domain is discretized using triangular or tetrahedron cells and the edge-based or face-based smoothing domains are then constructed based on these background meshes. Field functions are approximated using RPIM shape functions which have Kronecker delta function property. An efficient T2L-scheme is employed for the RPIM shape function construction. The system equations are derived using the generalized smoothed Galerkin (GS-Galerkin) weak form and essential boundary conditions can be imposed directly as in the finite element method (FEM). Several numerical examples with different material models are investigated to verify the proposed method in terms of accuracy, stability, efficiency and convergence.
PubDate: 2016-04-02T13:19:42Z
- Abstract: Publication date: July 2016
- A multiple-scale MQ-RBF for solving the inverse Cauchy problems in
arbitrary plane domain- Abstract: Publication date: July 2016
Source:Engineering Analysis with Boundary Elements, Volume 68
Author(s): Chein-Shan Liu, Wen Chen, Zhuojia Fu
The method of radial basis function (RBF) is popularly used in the solution of partial differential equations (PDEs). We propose a multiple-scale MQ-RBF method to solve the linear elliptic PDEs and the corresponding inverse Cauchy problems in simply- and doubly-connected domains, where the multiple scales are automatically determined a priori by the collocation points and source points, which play a role of post-conditioner of linear system to determine the unknown expansion coefficients. In the solution of inverse Cauchy problems the multiple-scale MQ-RBF is quite accurate and stable against large noise level up to 10–30%. Even for a case with only a quarter of boundary being imposed over-specified data, the multiple-scale MQ-RBF can still recover 75% unknown data very well.
PubDate: 2016-04-02T13:19:42Z
- Abstract: Publication date: July 2016
- Numerical solution of ideal MHD equilibrium via radial basis functions
collocation and moving least squares approximation methods- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): Maryam Ghasemi, Reza Amrollahi
In this study, two different meshfree methods consisting of the Radial Basis Functions (RBFs) and the Moving Least Square Method (MLS) are applied to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibrium of plasma in the tokamak. The validity and the effectiveness of the proposed schemes are studied by several test problems through absolute and Root Mean Squared (RMS) errors. Although, during the past few years, a meshfree method is normally applied in magnetohydrodynamic (MHD) studies to the numerical solution of partial differential equations (PDEs) but to the best of our knowledge, its application in MHD equilibrium of the tokamak plasma investigations is rare. The future more extensive studies regarding this numerical method would definitely have a significant impact on improving tokamak numerical tools.
PubDate: 2016-03-28T12:44:02Z
- Abstract: Publication date: June 2016
- Space–time localized radial basis function collocation method for
solving parabolic and hyperbolic equations- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): Mohammed Hamaidi, Ahmed Naji, Abdellatif Charafi
A radial basis collocation method, to solve parabolic and hyperbolic equations, based on the local space–time domain formulation is developed and presented in this paper. The method is different from those that approximate the time derivative using different formulas such as the implicit, explicit, method of lines, or other numerical methods. Considering a partial differential equation with d spatial dimensions, our technique solves the problem as a ( d + 1 ) -dimensional one without distinguishing between space and time variables, and the collocation points have both space and time coordinates. The parabolic equation is solved using the governing domain equation as a condition on the boundary characterized by the final time T. The hyperbolic equation is solved using two different methods. The first one is based on adapting the technique used for solving parabolic equations. The second one is a new technique that looks at the problem as an ill-posed one with incomplete boundary condition data at the final time T of the space–time domain. The accuracy of our proposed method is demonstrated through different examples in one-, two- and three-dimensional spaces on regular and irregular domains.
PubDate: 2016-03-28T12:44:02Z
- Abstract: Publication date: June 2016
- The treatment of BEM for porodynamic problems subjected to a force source
in time-domain- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): Boyang Ding, Jiaqi Jiang, Jing Hu
Based on the Biot׳s dynamic equations, the BEM in time-domain for the dynamic analysis of the poroelastic material subjected to a force source is described in this paper. Some methodologies treated to integral of the Somigliana׳s representative are revealed by authors, using the Green׳s functions in U-P formulation in time-domain, which fast and slow compressional waves has been decoupled. The treatment procedure which the integral variables regarding the fluid phase are transformed appropriately is described. The discretization treatment of the boundary integral equations is expounded in detail. The relevant numerical examples for BEM of the poroelastic material are performed by authors, the results are shown in the form of charts. The reasonable comparisons of the current and the previous solutions are also made in this paper. The treatment approach of stability and convergence as well as their dependence on time step are explained also. The pertinent descriptions may have certain effect to analysis on dynamic issues of other source, such as dislocation, dipole for the poroelastic material. Since the numerical investigation of porodynamic problems in time-domain has been rarely, further researches on the dynamic numerical analysis for the poroelastic material may benefit from the approach of this paper in future.
PubDate: 2016-03-28T12:44:02Z
- Abstract: Publication date: June 2016
- A necessary and sufficient BEM/BIEM for two-dimensional elasticity
problems- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): Jeng-Tzong Chen, Wen-Sheng Huang, Ying-Te Lee, Shing-Kai Kao
It is well known that the patch test is required for the finite element method (FEM). We may wonder whether we need any special test for the boundary element method (BEM). A sufficient and necessary boundary integral equation method (BIEM) to ensure a unique solution is our concern. In this paper, we revisit this issue for the interior two-dimensional (2-D) elasticity problem and investigate the equivalence of the solution space between the integral equation and the partial differential equation. Based on the degenerate kernel and the eigenfunction expansion, the range deficiency of the integral operator for the solution space in the degenerate-scale problem for the 2-D elasticity in the BIEM is analytically studied. According to the Fichera׳s idea, we enrich the conventional BIEM by adding constants and corresponding constraints. In addition, we introduce the concept of modal participation factor (MPF) to examine whether the adding term of rotation is required for interior simply-connected problems. Finally, two simple examples of degenerate-scale problems containing circular and elliptical boundaries subjected to various boundary conditions of the rigid body translation and rotation for 2-D elasticity problems are demonstrated by using the necessary and sufficient BIEM.
PubDate: 2016-03-28T12:44:02Z
- Abstract: Publication date: June 2016
- Singularity analysis of planar cracks in three-dimensional piezoelectric
semiconductors via extended displacement discontinuity boundary integral
equation method- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): MingHao Zhao, Yuan Li, Yang Yan, CuiYing Fan
The displacement discontinuity boundary integral equation method is extended to analyze the singularity of near-border fields of the planar crack of arbitrary shape in the isotropic plane of a three-dimensional transversely isotropic piezoelectric semiconductor. The hyper-singular boundary integral equations are derived in terms of the displacement, electric potential and carrier density discontinuities across the crack faces, in which body integrals for the carrier density are introduced. Based on the finite-part integrals, singularity exponents and asymptotic expressions of the crack border fields are obtained. The stress, electric displacement and electric current intensity factors are given in terms of the displacement, electric potential and carrier density discontinuities. Finite element results for penny-shaped and line cracks based on the piezoelectric-conductor iterative method are used to verify the derivations of the intensity factors.
PubDate: 2016-03-28T12:44:02Z
- Abstract: Publication date: June 2016
- Editorial Board
- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
PubDate: 2016-03-24T03:10:09Z
- Abstract: Publication date: May 2016
- Numerical simulation of time-dependent Navier–Stokes and MHD
equations using a meshless method based on fundamental and particular
solutions- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): D. Nath, M.S. Kalra, P. Munshi
In this paper a meshless method based on fundamental and particular solution (MFS–MPS) is implemented to numerically solve the time-dependent Navier–Stokes equations in stream function–vorticity form for lid-driven cavity flows. Further, the method is applied to natural convection problem in a cavity where an additional temperature equation and mixed boundary conditions are involved. Finally the MHD equations in stream function–vorticity–magnetic field-current density form are solved for MHD flows in a lid-driven cavity. A semi-implicit approach is used for the time advancing in which the time derivative is discretized using first order forward-difference approximation, the Laplace operator is taken in next time level, and rest of the terms are taken in the current time level. We take the number of boundary collocation points more than the source points and solve the overdetermined system of equation in a least squares sense at each time step. The least squares approach alleviates the problem of ill-conditioning to a certain extent. The results obtained are in good agreement with the previous numerical works where available. We find that the meshless method based on MFS–MPS is simple and effective, and can easily be applied to the coupled time-dependent nonlinear system of equations.
PubDate: 2016-03-24T03:10:09Z
- Abstract: Publication date: June 2016
- Dynamic 2.5-D green׳s function for a poroelastic half-space
- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): Shunhua Zhou, Chao He, HongGui Di
The dynamic two-and-a-half-dimensional (2.5-D) Green׳s function for a poroelastic half-space subject to a point load and dilatation source is derived based on Biot׳s theory, with the consideration of both a permeable surface and an impermeable surface. The governing differential equations for the 2.5-D Green׳s function are established by applying the Fourier transform to the governing equations of the three-dimensional (3-D) Green׳s function. The dynamic 2.5-D Green׳s function is derived in a full-space using the potential decomposition and discrete wavenumber methods. The surface terms are introduced to fulfil the free-surface boundary conditions and thereby obtain the dynamic 2.5-D Green׳s function for a poroelastic half-space with the permeable and impermeable surfaces. The half-space 2.5-D Green׳s function is verified through comparison with the 2.5-D Green׳s function regarding an elastodynamic half-space and the 3-D Green׳s function for a poroelastic half-space. A numerical case is provided to compare between the full-space solutions and the half-space solutions with two different sets of free-surface boundary conditions. In addition, a case study of efficient calculation of vibration from a tunnel embedded in a poroelastic half-space is presented to show the application of the 2.5-D Green׳s function in engineering problems.
PubDate: 2016-03-24T03:10:09Z
- Abstract: Publication date: June 2016
- The CPCT based CBIE and HBIE for potential problems in three dimensions
- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): Jia-He Lv, Xia-Ting Feng, Bing-Rui Chen, Quan Jiang, Hao-Sen Guo
In this paper, the authors present a more efficient and robust implementation of conventional and hypersingular BIEs for potential problems in three dimensions under the framework of boundary face method (BFM). The focus is laid on the accurate evaluation of singular curved surface integrals, and three aspects related are considered simultaneously: (a) the near singularity caused by distorted element shape; (b) the near singularity derived from the angular direction; (c) the singularity in the radial direction. A conformal polar coordinate transformation (CPCT) is employed to eliminate the shape effect of distorted integration cells, which can retain the shape characteristic. Besides, an improved sigmoidal transformation is introduced to alleviate the near singularity in the angular direction. By combination of the two strategies with previous singularity subtraction method, an efficient numerical integration scheme has been obtained for various orders of singularities. Some numerical examples including parallelogram plate, sphere and hollow cylinder examples with coarse meshes are presented to demonstrate the accuracy and flexibility of the proposed method.
PubDate: 2016-03-24T03:10:09Z
- Abstract: Publication date: June 2016
- Improved localized radial basis function collocation method for
multi-dimensional convection-dominated problems- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): D.F. Yun, Y.C. Hon
In this paper, the localized radial basis function collocation method (LRBFCM) is combined with the partial upwind scheme for solving convection-dominated fluid flow problems. The localization technique adopted in LRBFCM has shown to be effective in avoiding the well known ill-conditioning problem of traditional meshless collocation method with globally defined radial basis functions (RBFs). For convection–diffusion problems with dominated convection, stiffness in the form of boundary/interior layers and shock waves emerge as convection overwhelms diffusion. We show in this paper that these kinds of stiff problems can be well tackled by combining the LRBFCM with partial upwind scheme. For verification, several numerical examples are given to demonstrate that this scheme improves the LRBFCM in providing stable, accurate, and oscillation-free solutions to one- and two-dimensional Burgers׳ equations with shock waves and singular perturbation problems with turning points and boundary layers.
PubDate: 2016-03-24T03:10:09Z
- Abstract: Publication date: June 2016
- A fast multipole method accelerated adaptive background cell-based domain
integration method for evaluation of domain integrals in 3D boundary
element method- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): Wei Zhou, Qiao Wang, Yonggang Cheng, Gang Ma
A background cell-based domain integration method is proposed in this paper for evaluating domain integrals in 3D problems. The cells are created by an adaptive oct-tree structure based on the information of boundary elements, and no other discretization is needed. Cells that contain boundary elements can be subdivided into smaller sub-cells adaptively to obtain the desired accuracy according to the sizes and levels of the boundary elements. Applying the method directly in the boundary element method is time-consuming since the time complexity is O(NM), where N and M are the numbers of nodes and cells, respectively. The fast multipole method is coupled with the cell-based domain integration method to further accelerate the computational efficiency, and the main formulations are introduced in this paper. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.
PubDate: 2016-03-19T02:43:01Z
- Abstract: Publication date: June 2016
- BEM and FEM analysis of fluid–structure interaction in a double tank
- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): J. Ravnik, E. Strelnikova, V. Gnitko, K. Degtyarev, U. Ogorodnyk
In this paper we present a fluid–structure interaction analysis of shell structures with compartments partially filled with a liquid. The compound shell was a simplified model of a fuel tank. The shell is considered to be thin and Kirghoff–Lave linear theory hypotheses are applied. The liquid is ideal and incompressible. Its properties and the filling levels may be different in each compartment. The shell vibrations coupled with liquid sloshing under the force of gravity were considered. The shell and sloshing modes were analysed simultaneously. The coupled problem is solved using a coupled BEM and FEM in-house solver. The tank structure is modeled by FEM and the liquid sloshing in the fluid domain is described by BEM. The method relies on determining the fluid pressure from the system of singular integral equations. For its numerical solution, the boundary element method was applied. The boundary of the liquid computational domain is discretized by nine-node boundary elements. The quadratic interpolation of functions and linear interpolation of flux are involved. The natural frequencies were obtained for the cylindrical double tank with two compartments.
PubDate: 2016-03-19T02:43:01Z
- Abstract: Publication date: June 2016
- A combination of EFG-SBM and a temporally-piecewise adaptive algorithm to
solve viscoelastic problems- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): X.F. Guo, H.T. Yang
This paper combines Element-Free Galerkin Scaled Boundary Method (EFG-SBM) with a temporally-piecewise adaptive algorithm to solve viscoelastic problems. By expanding variables at a discretized time interval, the variations of variables can be described more precisely, and a space-time domain coupled problem can be converted into a series of recurrent boundary value problems which are solved by EFG-SBM via an adaptive computing process. Numerical tests including creep and relaxation are given to verify the proposed algorithm.
PubDate: 2016-03-19T02:43:01Z
- Abstract: Publication date: June 2016
- Improving accuracy and efficiency of stress analysis using scaled boundary
finite elements- Abstract: Publication date: June 2016
Source:Engineering Analysis with Boundary Elements, Volume 67
Author(s): Gao Lin, Lin Pang, Zhiqiang Hu, Yong Zhang
The scaled boundary finite element method (SBFEM) is a fundamental-solution-less boundary element method, which leads to semi-analytical solutions for stress fields. As only the boundary is discretized, the spatial dimension is reduced by one. In this paper, the SBFEM based polygon elements are utilized to improve the accuracy and efficiency of stress analysis. It retains the attractive feature of the SBFEM in solving problems with unbounded media and singularities. In addition, polygon elements are more flexible in meshing and mesh transition. Various measures which help improving accuracy or efficiency of the stress analysis, i.e. refining polygon mesh, nodal enrichment, appropriate placing of the scaling center, merging polygon elements and NURBS enhanced curved boundaries are discussed and compared. As a result, further insight into the refinement and improvement strategies for stress analysis is provided.
PubDate: 2016-03-19T02:43:01Z
- Abstract: Publication date: June 2016
- Acceleration of isogeometric boundary element analysis through a black-box
fast multipole method- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): R.N. Simpson, Z. Liu
This work outlines the use of a black-box fast multipole method to accelerate the far-field computations in an isogeometric boundary element method. The present approach makes use of T-splines to discretise both the geometry and analysis fields allowing a direct integration of CAD and analysis technologies. A black-box fast multipole method of O(N) complexity is adopted that minimises refactoring of existing boundary element codes and facilitates the use of different kernels. This paper outlines an algorithm for implementing the open-source black-box fast multipole method BBFMM3D 1 1 https://github.com/ruoxi-wang/BBFMM3D within an existing isogeometric boundary element solver, but the approach is general in nature and can be applied to any boundary element surface discretisation. The O(N) behaviour of the approach is validated and compared against a standard direct solver. Finally, the ability to model large models of arbitrary geometric complexity directly from CAD models is demonstrated for potential problems.
PubDate: 2016-03-15T02:04:47Z
- Abstract: Publication date: May 2016
- The transient heat conduction MPM and GIMP applied to isotropic materials
- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): X.Y. Gu, C.Y. Dong, T. Cheng, Y. Zhang, Y. Bai
In the material point method (MPM)/generalized interpolation material point (GIMP), the material domain is discretized into a set of Lagrangian particles. The interaction between these particles will be confirmed using the Eulerian background grid. In each time step, the momentum equations and the spatial derivatives are integrated using the background grid. Thus, the MPM/GIMP take the advantages of both the Eulerian and Lagrangian methods and avoid their respective defects. Especially, the MPM/GIMP have the advantage in the numerical simulation of extreme large deformation, fracture and impact problems in which the heat flow appears. Compared with other meshless methods, the MPM/GIMP applied to the transient heat transfer problems obtain much less attention. In order to extend the applied fields of the MPM and GIMP, this paper will present two- and three-dimensional MPM/GIMP to carry out and discuss the transient heat conduction analysis in the isotropic materials. The availability and accuracy of the present method are tested through three numerical examples, i.e. the transient heat conductions in a square plate and a complex shaped plate, and a high conductive cuboidal copper block with complex shape. The results from the MPM/GIMP are compared with those from the analytical solution or finite element method.
PubDate: 2016-03-15T02:04:47Z
- Abstract: Publication date: May 2016
- Element-subdivision method for evaluation of singular integrals over
narrow strip boundary elements of super thin and slender structures- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): Xiao-Wei Gao, Jin-Bo Zhang, Bao-Jing Zheng, Ch. Zhang
In this paper, based on the numerical investigation of singular integrals over narrow strip boundary elements stemming from BEM analysis of thin and slender structures with different numbers of Gauss points, an efficient method is proposed for evaluating the narrow strip singular boundary integrals using an adaptive unequal interval element-subdivision method in the intrinsic parameter plane. In this method, the size of the sub-element closest to the singular point is determined first in terms of the orders of the shape functions along two intrinsic coordinate directions. Then, the sizes of other sub-elements are computed by employing a criterion proposed by Gao and Davies [1,2] for evaluating nearly singular integrals in terms of an allowed number of Gauss points and the distance from the source point to the sub-element. The features of the proposed method are that the computational accuracy of various orders of singular integrals is controlled by the upper bound of the error of Gauss quadrature, rather than through artificially giving the size of the sub-elements and number of Gauss points, and because of using the unequal interval element-subdivision method, the number of required sub-elements is not large even for an element with high aspect ratio, usually less than 10 for a plate with aspect ratio of 100:1. A number of numerical examples for plates and shells with different aspect ratios are analyzed for various orders of integrals to demonstrate the efficiency of the proposed method.
PubDate: 2016-03-15T02:04:47Z
- Abstract: Publication date: May 2016
- Numerical study on local steady flow effects on hydrodynamic interaction
between two parallel ships advancing in waves- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): C.B. Yao, W.C. Dong
Underway replenishment is an essential component of long-term naval operations. During underway replenishment, two ships travel in close proximity at a moderate forward speed. For this issue, frequency domain analysis methods with and without incorporation of local steady flow effects are developed to investigate wave loads and free motions of two parallel ships advancing in waves, which are based on analytical quadrature of the Bessho form translating-pulsating source Green function over a panel or a waterline segment and a direct velocity potential approach. The local steady flow effects were taken into consideration through m-terms in the boundary conditions; meanwhile, the Neumann-Kelvin linear free surface condition was combined. By comparing present added mass, damping coefficient and motion results of Wigley I to those of experiments and other numerical solutions; it is found that present computational results show good agreement. In order to verify these methods for hydrodynamic interaction between two parallel ships, two experiments are carried out respectively to measure the wave loads and free motions for adjacent parallel ship models advancing with an identical speed in head regular waves. Results obtained by the present solution are in favorable agreement with the model tests, meanwhile, results of methods taking the local steady flow effects into consideration show better agreement. Further, the component of wave loads and the interaction effects of speeds and different clearances are deeply investigated. It is found that the effect of clearance and the speed are important factors relating to the interaction effect.
PubDate: 2016-03-07T13:47:27Z
- Abstract: Publication date: May 2016
- A BEM based methodology to solve inverse problems considering fictitious
background media- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): Markcilei Lima Dan, Webe João Mansur, Franciane Conceição Peters
This paper proposes a new BEM based inversion methodology named Fictitious Background Media Inverse Formulation (FBMIF) to solve inverse problems described in terms of the Helmholtz equation for inhomogeneous media. The BEM based approach considers a Green’s function related to a homogeneous background medium, a fictitious medium, which works as a transfer function. Thereafter, considering a nonrestrictive linearization scheme, the FBMIF is completely defined. Three examples are used to test the efficacy of the proposed model of inversion, which can be extended to other mathematical models different from those governed by the Helmholtz equation.
PubDate: 2016-03-07T13:47:27Z
- Abstract: Publication date: May 2016
- Isogeometric shape design sensitivity analysis of elasticity problems
using boundary integral equations- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): Minho Yoon, Seonho Cho
Using boundary integral equations and isogeometric approach, a shape design sensitivity analysis (DSA) method is developed for two dimensional elastic structures. In the isogeometric approach, NURBS basis functions in CAD systems are directly utilized in response analysis, which enables a seamless incorporation of exact geometry and higher continuity into computational framework. To enhance the accuracy of shape design sensitivity, the CAD-based higher-order geometric information such as curvature, normal, and tangential vector is exactly embedded in the sensitivity expressions. In boundary integral formulation, shape design velocity field is decomposed into normal and tangential components, which significantly affect the accuracy of shape design sensitivity. Also, the proposed boundary-based method does not require the tedious design parameterization of internal domain. Through the numerical examples, the developed shape DSA method turns out to be more accurate than conventional finite element based one.
PubDate: 2016-03-07T13:47:27Z
- Abstract: Publication date: May 2016
- An indirect boundary element method to model the 3-D scattering of elastic
waves in a fluid-saturated poroelastic half-space- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): Zhongxian Liu, Lei Liu, Jianwen Liang, Yadong Zhou
The indirect boundary element method (IBEM) is extended to solve the scattering of elastic waves by three-dimensional (3-D) subsurface irregularities in a fluid-saturated poroelastic half-space. The Green׳s functions of inclined circular loads and fluid source in a poroelastic full space are deduced based on Biot’s theory. According to the single-layered potential theory, the scattered waves are constructed by using fictitious uniform loads and fluid source distributed on the boundary elements on the scatterer surface, and their magnitudes are determined by the continuity or traction-free boundary conditions. Accuracy verification illustrates that this proposed method can deal with 3-D wave scattering problems in an infinite poroelastic medium conveniently and accurately. Then, the scattering of plane waves by a 3-D canyon is investigated. Numerical results indicate that: the scattering of waves in a poroelastic half-space strongly depends on the incident frequency and incident angle; the 3-D amplification effects both on the displacement and pore pressure appear to be more significant than the corresponding 2-D case; medium porosity of the half space also plays a key role on the wave scattering, especially for obliquely incident waves at the critical angle, and the influence of drainage condition seems to be more considerable for high porosities.
PubDate: 2016-03-07T13:47:27Z
- Abstract: Publication date: May 2016
- Band structure computation of in-plane elastic waves in 2D phononic
crystals by a meshfree local RBF collocation method- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): Hui Zheng, Chuanzeng Zhang, Yuesheng Wang, Jan Sladek, Vladimir Sladek
In this paper, the band structures of in-plane elastic waves in two-dimensional (2D) phononic crystals are calculated by using a meshfree local radial basis functions (RBF) collocation method. In order to improve the stability of the local RBF collocation method, special techniques suggested in our previous work for anti-plane waves are further improved and extended for calculating the primary field quantities and their normal derivatives required by the treatment of the boundary conditions in the local RBF collocation method for computing the band structures of the in-plane elastic waves in 2D phononic crystals. The developed meshfree local RBF collocation method for the band structure calculations of in-plane elastic waves propagating in 2D phononic crystals is validated by using the corresponding numerical results obtained with the finite element method (FEM). The band structures of different material combinations or acoustic impedance ratios, different filling fractions, various lattice forms and scatterer shapes are computed numerically to show the accuracy and the efficiency of the meshfree local RBF collocation method for computing the band structures of in-plane elastic waves in 2D phononic crystals.
PubDate: 2016-03-07T13:47:27Z
- Abstract: Publication date: May 2016
- Slope limiters for radial basis functions applied to conservation laws
with discontinuous flux function- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): Fayssal Benkhaldoun, A. Halassi, Driss Ouazar, Mohammed Seaid, Ahmed Taik
We present slope limiters in meshless radial basis functions for solving nonlinear equations of conservation laws with flux function that depends on discontinuous coefficients. The method is based on the local collocation formulation and does not require either generation of a grid or evaluation of an integral. Upwind techniques are used to allocate collocation points within the characteristic solutions and different slope limiter functions are investigated. The main advantages of this approach are neither mesh generations nor Riemann problem solvers are required during the solution process. Numerical results are shown for several test examples including models on vehicular traffic and two-phase flows. The main focus is to examine the performance of the proposed meshless method for shock-capturing property in conservation laws with discontinuous flux function. The obtained results demonstrate its ability to capture the main solution features.
PubDate: 2016-03-07T13:47:27Z
- Abstract: Publication date: May 2016
- Stochastic spline fictitious boundary element method for modal analysis of
plane elastic problems with random fields- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): Cheng Su, Zhongshan Qin, Xueming Fan
Mathematical formulation and computational implementation of the stochastic spline fictitious boundary element method (SFBEM) are presented for modal analysis of plane elastic problems with structural parameters modeled as random fields. Two sets of governing differential equations with respect to the means and deviations of displacement modes are derived by including the first order terms of deviations. These equations are in similar forms to those of deterministic plane elastostatic problems, and can be solved using deterministic elastostatic fundamental solutions, resulting in the means and covariances of the eigenvalues and mode shapes. For the effective treatment of the domain integrals involved in the deviation solution, the random fields considered are represented by Karhunen–Loeve (KL) expansion in conjunction with the Galerkin projection. Numerical examples indicate that the results of the present method are in good agreement with those from the Monte Carlo simulation (MCS) with small variations, and the present approach is more efficient than the perturbation stochastic finite element method (FEM) with the same KL expansion technique.
PubDate: 2016-03-07T13:47:27Z
- Abstract: Publication date: May 2016
- Computing eigenmodes of elliptic operators using increasingly flat radial
basis functions- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): C.-S. Huang, C.-H. Hung, S. Wang
Solving multi-dimensional eigenmodes problem for elliptic operator using radial basis functions (RBFs) was proposed by Platte and Driscoll (2004) [14]. They convert the eigenmodes problem to an eigenpairs problem of a finite dimensional matrix. We formulate an approach based on using finite order interpolating polynomials as eigenfunctions for eigenmodes problem. We prove that, under some simple conditions on the RBFs, two approaches converge when increasingly flat BRFs are being used. These results are supported by numerical examples.
PubDate: 2016-02-24T11:00:53Z
- Abstract: Publication date: May 2016
- A domain decomposition based method for two-dimensional linear elastic
fractures- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): Zhijun Liu, Hong Zheng, Cong Sun
In this study, the two-dimensional physical domain containing cracks is divided into several non-overlapping parts: rectangular crack-tip regions around crack tips and the outer region without any crack tip. In each crack-tip region the displacement is approximated with Williams׳ series; while in the outer region it is approximated with numerical manifold interpolation. In order to balance accuracy and efficiency in solution, a transitional zone encompassing each crack-tip region is locally refined with a structured mesh. To avoid singular integration over a crack-tip region, the potential energy over every crack-tip region is transformed into the boundary integration. Three different methods to enforce compatibility on interfaces are compared, concluding the Lagrange multiplier method is superior over the other two.
PubDate: 2016-02-24T11:00:53Z
- Abstract: Publication date: May 2016
- Coupled groundwater flow and contaminant transport simulation in a
confined aquifer using meshfree radial point collocation method (RPCM)- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): L. Guneshwor Singh, T.I. Eldho, A. Vinod Kumar
In this study, a meshfree radial point collocation method is used to model the contaminant transport through confined aquifer. The discretization of the governing equations is done by a point collocation method and radial basis functions (RBF) are used as the interpolation function. For comparative study, two widely used radial basis functions namely multi-quadrics and exponential RBF are used. A local circular support domain is employed to construct the shape functions. In the model, no information on nodal inter-relationship is required for shape function construction except the nodal coordinates, unlike in finite-difference (FDM) or finite-element (FEM) based methods. The developed model is validated through benchmark problems in one and two dimensions. Further, application of the model for advective transport with high Peclet number has been studied and the model has been found to be effective in handling the instability of high Peclet problems. For the field problem considered, the results obtained from the model have been compared with the FEM solution and was found to be satisfactory. This method is relatively easy to implement and offers better accuracy with acceptable computational time. Considering the significant advantages offered by this method, it can serve as a good alternative to the conventional methods.
PubDate: 2016-02-24T11:00:53Z
- Abstract: Publication date: May 2016
- A meshless radial basis function method for 2D steady-state heat
conduction problems in anisotropic and inhomogeneous media- Abstract: Publication date: May 2016
Source:Engineering Analysis with Boundary Elements, Volume 66
Author(s): S.Y. Reutskiy
The paper presents a new meshless numerical method for solving 2D steady-state heat conduction problems in anisotropic and inhomogeneous media. The coefficients of the governing PDEs are spatially dependent functions including the main operator part. The boundary conditions of a most general form for the temperature and the heat flux are considered. The key idea of the method is the use of the basis functions which satisfy the homogeneous boundary conditions of the problem. Each basis function used in the algorithm is a sum of a RBF and a special correcting function which is chosen to satisfy the homogeneous BC of the problem. The conical radial basis functions, the Duchon splines and the multiquadric RBFs are used in approximation of the PDE. This allows us to seek an approximate solution in the form which satisfies the boundary conditions of the initial problem with any choice of the free parameters. As a result we separate the approximation of the boundary conditions and the approximation of the PDE inside the solution domain. The numerical experiments are carried out for accuracy and convergence investigations. The comparison of the numerical results obtained in the paper with the exact solutions and with the data obtained with the use of other numerical techniques is performed. The numerical examples demonstrate that the present method is accurate, convergent, stable, and computationally efficient in solving this kind of problems.
PubDate: 2016-02-19T10:44:40Z
- Abstract: Publication date: May 2016
- Editorial Board
- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
PubDate: 2016-02-19T10:44:40Z
- Abstract: Publication date: April 2016
- A new type of high-order elements based on the mesh-free interpolations
- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Dean Hu, Yigang Wang, Haifei Zhan, Shuyao Long
We propose a new type of high-order elements that incorporates the mesh-free Galerkin formulations into the framework of Finite Element Method. Traditional polynomial interpolation is replaced by mesh-free interpolations in the present high-order elements, and the strain smoothing technique is used for integration of the governing equations based on smoothing cells. The properties of high-order elements, which are influenced by the basis function of mesh-free interpolations and boundary nodes, are discussed through numerical examples. It can be found that the basis function has significant influence on the computational accuracy and upper–lower bounds of energy norm, when the strain smoothing technique retains the softening phenomenon. This new type of high-order elements shows good performance when quadratic basis functions are used in the mesh-free interpolations and present elements prove advantageous in adaptive mesh and nodes refinement schemes. Furthermore, it shows less sensitive to the quality of element because it uses the mesh-free interpolations and obeys the Weakened Weak (W2) formulation as introduced in Liu (2010) [3,5].
PubDate: 2016-01-25T08:48:46Z
- Abstract: Publication date: April 2016
- Complex variable moving Kriging interpolation for boundary meshless method
- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Sanshan Tu, Leilei Dong, Hongqi Yang, Yi Huang
In this paper, we proposed the complex variable moving Kriging interpolation (CVMKI) to approximate functions on two-dimensional (2D) boundaries. The CVMKI is based on complex variable theory and the moving Kriging interpolation (MKI). It requires no curvilinear coordinate, and can construct shape functions possessing Kronecker delta function property and partition of unity property. Further, the complex variable boundary node method (CVBNM) is proposed for potential problems based on CVMKI and boundary integration equation (BIE). CVBNM is an efficient and accurate method that can directly impose the boundary conditions. Three 2D example problems are presented to verify the accuracy and efficiency of CVBNM.
PubDate: 2016-01-25T08:48:46Z
- Abstract: Publication date: April 2016
- A dual reciprocity multiwavelet Galerkin method for the numerical solution
of Poisson׳s equation- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Jianxin Luo, Rui Qiao, Jing Li
A dual reciprocity multiwavelet Galerkin method is developed for the solution of Poisson׳s equation in this paper, which combines the dual reciprocity boundary element method (DRBEM) and the multiwavelet Galerkin method (MGM). The DRBEM is used to transform the domain integral in the boundary element formulation of Poisson׳s equation into the boundary of the domain, which is based on compactly supported positive definite radial basis function. Then, the MGM is employed for solving the resulting boundary integral equation, in which Alpert multiwavelets are employed to construct the trial and test functions of Galerkin variational formulation. Because of the use of multiwavelets, the resulting system matrix can be approximated by a sparse matrix. Compared to the DRBEM based on radial basis functions, the present method reduces the memory spaces and computational costs of the system matrix significantly. Numerical results show the efficiency of the present method.
PubDate: 2016-01-21T08:42:09Z
- Abstract: Publication date: April 2016
- Electromagnetic scattering analysis using nonconformal meshes and
monopolar curl-conforming basis functions- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Liming Zhang, Ali Deng, Yiqing Zhang, Xianzhu Meng, Zengtao Lv
A scheme for electromagnetic scattering analysis of perfect electric conducting (PEC) objects using nonconformal meshes is developed in this paper. The difference of the integral operators for the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) are analyzed in detail. It is shown theoretically that basis functions used to expand the surface currents for the MFIE may not necessarily be divergence-conforming. The nonconformal meshes and monopolar n × RWG basis functions are used together to solve the MFIE. Details for the implementation of the proposed method are presented. The method is verified through the numerical results for electromagnetic scattering analysis from several PEC objects. It is shown that this method is a suitable choice for using nonconformal meshes when solving electromagnetic scattering problems with the MFIE.
PubDate: 2016-01-21T08:42:09Z
- Abstract: Publication date: April 2016
- An extended exponential transformation for evaluating nearly singular
integrals in general anisotropic boundary element method- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Yan Gu, Houqi Dong, Hongwei Gao, Wen Chen, Yaoming Zhang
The exponential transformation is an efficient technique for the accurate numerical evaluation of nearly singular integrals which arise in the boundary element method (BEM). It was shown that this transformation could improve the accuracy of evaluating such integrals by several orders of magnitude. Here, this transformation is extended in a more flexible fashion to allow the evaluation of nearly singular integrals which arise in general anisotropic BEM formulation, with a high degree of accuracy. A major advantage of the new method is its ease of implementation and applicability to a wide class of integrals. Three benchmark test integrals, ranging from nearly weakly, nearly strongly and nearly hyper-strongly singular integrals, are well studied to demonstrate the accuracy and efficiency of the proposed method.
PubDate: 2016-01-21T08:42:09Z
- Abstract: Publication date: April 2016
- A partition-of-unity based ‘FE-Meshfree’ triangular element
with radial-polynomial basis functions for static and free vibration
analysis- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Yongtao Yang, Dongdong Xu, Hong Zheng
A new ‘FE-Meshfree’ three-node triangular element (Trig3-RPIM) is developed based on the partition of unity (PU) concept. The Trig3-RPIM element employs the shape function of classical three-node triangular element (Trig3) to construct the PU and the radial-polynomial basis function which is free from the possible singularity of the moment matrix to construct the nodal approximation. The Trig3-RPIM element synergizes the individual strengths of finite element method and meshfree method. Moreover, it is free from the linear dependence problem which otherwise cripples many of the PU based finite elements. Several linear, nonlinear and free vibration test problems are solved and the performance of the element is compared with those of the well-known three-node triangular element (Trig3) and four-node iso-parametric quadrilateral element (Quad4). The results show that, for regular meshes, the performance of the element is superior to those of Trig3 and Quad4 elements. For distorted meshes, the present element has better mesh-distortion tolerance than Trig3 and Quad4 elements.
PubDate: 2016-01-17T14:04:48Z
- Abstract: Publication date: April 2016
- A new type of high-accuracy BEM and local stress analysis of real beam,
plate and shell structures- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Zhenhan Yao
A high-accuracy BEM (HABEM) presented by the author is briefly summarized, and then applied to the local stress analysis (LSA) of real clamped thin-plate beam, in 2D and 3D models. The simple examples in 2D have shown the process of discretization error reduction via mesh refinement under guidance of error indicator. The numerical results have shown the feasibility and high accuracy of the presented HABEM. On the other hand the results obtained are valuable for the strength evaluation in engineering. The corresponding 3D HABEA has also been presented. The results agree with the corresponding 2D analysis. But the complexity of the 3D HABEA is much higher than 2D one. The advantage of dimension reduction is also the major advantage of BEM over FEM. For 3D HABEM an improved equal-accuracy Gaussian quadrature for regular including nearly singular integrals, and that for weakly singular integrals is presented and numerically verified in detail. For the local stress analysis of real beam, plate and shell structures the 3D HABEA is necessary, in such case it is encountered with a large-scale BEA problem, and fast algorithm should be introduced. Such approach is defined as high-performance BEM, which will be a new research field in future.
PubDate: 2016-01-17T14:04:48Z
- Abstract: Publication date: April 2016