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 [2801 journals] |
- Shape design optimization of road acoustic barriers featuring top-edge
devices by using genetic algorithms and boundary elements- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): R. Toledo, J.J. Aznárez, D. Greiner, O. Maeso
This paper presents a Boundary Elements (BE) approach for the efficiency improvement of road acoustic barriers, more specifically, for the shape design optimization of top-edge devices in the search for the best designs in terms of screening performance, usually represented by the insertion loss (IL). With this aim, a procedure coupling BE with Evolutionary Algorithm is proposed in pursuing barrier configurations with ever higher IL. The complexity normally associated with such designs raises the need to consider some geometric simplifications in order to ease the shape optimization processes. In this way, the overall barrier configuration is modeled as both thickness and null-thickness bodies (the boundary thickness is neglected), as representatives of very thin elements. Such an idealization requires a Dual Boundary Element formulation that allows the problem to be solved. The procedure is applied to 2D problems and numerical results are presented on the basis of simulations on noise barriers with three different top designs. It is a quite simple process that makes use of well-known both formulations and procedures. The improvements observed in the designs obtained invite to further studies in the same line on devices with similar applications.
PubDate: 2015-11-25T04:27:32Z
- Abstract: Publication date: February 2016
- Boundary face method for 3D contact problems with non-conforming contact
discretization- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Xingshuai Zheng, Jianming Zhang, Kai Xiong, Xiaomin Shu, Lei Han
Three-dimensional contact problems without friction have been studied using the boundary face method (BFM). In this paper, a non-conforming contact discretization approach is used to enforce the contact conditions between the two contact surfaces. This method is based on node-to-surface (NTS), and there is no need that the identical discretization is performed along the contact surfaces of both bodies. The contact equations are written explicitly with both tractions and displacements which are retained as unknowns in boundary integral equation (BIE). An iterative procedure is presented to determine the correct contact zone by obtaining a solution compatible with the contact conditions (no interpenetrations between the domains and no tensile on the final contact zone). Several numerical examples have been presented to illustrate the applicability of the method.
PubDate: 2015-11-25T04:27:32Z
- Abstract: Publication date: February 2016
- Editorial Board
- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
PubDate: 2015-11-25T04:27:32Z
- Abstract: Publication date: January 2016
- The natural boundary integral equation of the orthotropic potential
problem- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Huan-Lin Zhou, Yu Tian, Bo Yu, Zhong-Rong Niu
The governing equation of two-dimensional orthotropic potential problem is transformed into standard Laplace equation by the coordinate transformation method. Then a novel potential derivative boundary integral equation termed natural boundary integral equation (NBIE) is established for the two-dimensional orthotropic potential problem. The NBIE reduces the singularity by one order when compared with the conventional potential derivative boundary integral equation (CDBIE). Thus the potential derivative of the two-dimensional orthotropic potential problem can be computed more accurately by using the NBIE at the same boundary mesh. Furthermore, after using the analytical integral regularization algorithm of nearly singular integrals, the NBIE can obtain more accurate potential derivatives of interior points which are very close to the boundary than the CDBIE. Numerical examples verify the accuracy and efficiency of the present method.
PubDate: 2015-11-25T04:27:32Z
- Abstract: Publication date: January 2016
- The electromagnetic-thermal dosimetry for the homogeneous human brain
model- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Mario Cvetković, Dragan Poljak, Akimasa Hirata
The electromagnetic-thermal dosimetry model of the human brain exposed to electromagnetic (EM) radiation is developed. The EM model based on the surface integral equation (SIE) formulation is derived using the equivalence theorem for the case of a lossy homogeneous dielectric body. The thermal dosimetry model of the brain is based on the form of Pennes׳ equation for heat transfer in biological tissue. The numerical solution of the EM model is carried out using the Method of Moments (MoM) while the bioheat equation is solved using the finite element method (FEM). Developed EM-thermal model has been applied for the internal dosimetry of the human brain to assess the absorbed EM energy and the consequent temperature rise due to the exposure of 900MHz plane wave. Due to the variability of various parameters, the sensitivity of the maximum, minimum and the average steady-state temperature, on the various thermal parameters have been examined, as well as the influence of the parameters variation on the temperature distribution in case of EM exposure. The proposed model may be found useful in the rapid assessment of the temperature distribution in the human brain, prior to having to deal with a tedious development of a more complex models.
PubDate: 2015-11-25T04:27:32Z
- Abstract: Publication date: February 2016
- A new semi-analytic algorithm of nearly singular integrals on higher order
element in 3D potential BEM- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Zongjun Hu, Zhongrong Niu, Changzheng Cheng
By analyzing the geometric characteristics of 8-noded quadrilateral surface elements in three dimensional boundary element method (3D BEM), the relative distance from a source point to the integral element is defined. For the nearly singular integrals on higher order elements in 3D potential BEM, the equivalent integral kernels are constructed by the geometric analysis between the source point and the element in ρ θ system. Subtracting the equivalent kernels from and adding them back to the nearly singular kernels, the nearly singular surface integrals are transformed into the sum of both the non-singular integrals and the singular integrals. So the leading singular parts are separated. The former are computed efficiently by the Gaussian quadrature and the latter are performed with respect to the integral variables ρ and θ , respectively, in which the integrations with respect to ρ are expressed by analytical formulations. Consequently, a new semi-analytic algorithm is established to calculate the nearly strongly singular and hyper-singular surface integrals on higher order element in 3D BEM. Several examples about 3D heat conduction are given to demonstrate the efficiency and accuracy of the present semi-analytic algorithm in BE analysis. Moreover, the present algorithm is used to analyze very thin structures in 3D BEM.
PubDate: 2015-11-25T04:27:32Z
- Abstract: Publication date: February 2016
- A three-dimensional vortex method for the hydrodynamic solution of planing
cambered dihedral surfaces- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Stefano Brizzolara, Giuliano Vernengo
A new numerical approach based on the Vortex Lattice Method (VLM) for the solution of the hydrodynamic performances of cambered hulls in steady planing is formulated and validated. Due to its fully 3D formulation, the method can be applied to both cambered and un-cambered dihedral planing surfaces of any shape without any further approximation. The exact three-dimensional wetted surface of the hull is where the body boundary condition is fulfilled. The sprays region detaching both in front of the stagnation root line and from the wet portion of the chine are modeled in the numerical scheme by means of additional vortex lattice regions. The dynamic boundary condition at the stern of the hull is non-linear with respect to the perturbation potential. Results show the dynamic pressure consistently accounts for the 3D features of the flow especially in the case of cambered planing surfaces. The numerical method is verified by a systematic analysis against semi-empirical methods and it is finally validated with experimental results on prismatic as well as cambered dihedral planing surfaces. Excellent correlations are found for both types of planing surfaces that range in the same confidence interval of higher fidelity numerical models, such as RANSE solvers.
PubDate: 2015-11-21T04:07:37Z
- Abstract: Publication date: February 2016
- A BEM formulation in conjunction with parametric equation approach for
three-dimensional Cauchy problems of steady heat conduction- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Fajie Wang, Wen Chen, Wenzhen Qu, Yan Gu
This study documents the first attempt to apply a nonsingular indirect boundary element method (BEM) for the solution of three-dimensional (3D) inverse heat conduction problems. The present BEM formulation avoids the calculation of hyper-singular integrals. Furthermore, the exact geometrical representation of computational domain is adopted by parametric equations to eliminate the errors in traditional approaches of polynomial shape functions. Due to its boundary-only discretizations and semi-analytical nature, the proposed method can be viewed as a competitive candidate for the solution of inverse problems. Four benchmark numerical examples indicate that the proposed method, in conjunction with proper regularization techniques, is accurate, computationally efficient and numerically stable for the solution of 3D inverse problems subjected to various levels of noise in input data.
PubDate: 2015-11-21T04:07:37Z
- Abstract: Publication date: February 2016
- A BIEM using the Trefftz test functions for solving the inverse Cauchy and
source recovery problems- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Chein-Shan Liu
In this paper we develop a global domain/boundary integral equation method for the Laplace and Poisson equations, which is based on the Green׳s second identity. A derived global relation links the source term to the Dirichlet and Neumann boundary conditions into a single integral equation in terms of the Trefftz test functions. By suitably choosing the Trefftz test functions, which are not the usual Green functions as that used in the conventional boundary integral method, the present boundary integral equation method (BIEM) can find the unknown boundary conditions for the inverse Cauchy problems very well. Even under a large noise to 10% and the data over-specified in a 25% portion of the whole boundary, the recovered result is still accurate. The inverse source problems of the Poisson equation are resolved numerically by using the BIEM which is stable and effective for strongly ill-posed case with a large noise being imposed on the supplementary data.
PubDate: 2015-11-08T16:21:26Z
- Abstract: Publication date: January 2016
- Boundary element method based vibration analysis of elastic bottom plates
of fluid storage tanks resting on Pasternak foundation- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): B. Uğurlu
A higher-order boundary element procedure is presented for the free vibration analysis of flexible base plates of rigid fluid storage tanks resting on elastic foundation. The main principles of the procedure are replacing the biharmonic operator of the thin plate vibration problem by two successive harmonic operators, and representing the forcing terms (plate inertia, fluid loading and foundation influence) by applying the dual reciprocity boundary element formulation. The fluid effect on the plate dynamics is incorporated into the analysis by invoking another boundary element solution, which expresses the fluid pressure over the plate surface in terms of plate deflection. The performance of the method is thoroughly investigated and the nature of dynamic plate–foundation–fluid interaction is studied from several perspectives. The method provides excellent predictions, within the limits of Kirchhoff plate, potential flow, and Pasternak foundation models.
PubDate: 2015-11-08T16:21:26Z
- Abstract: Publication date: January 2016
- Boundary element method applied to ultrasound elastography
- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Anderson Gabriel Santiago, Luiz Cezar Trintinalia, Marco Antonio Gutierrez
This paper presents a new methodology for computational elastography applied to simulated ultrasound images using numerical and computer vision methods. The aim is to estimate the elastic moduli of different tissues using images of the same cross section of mathematical phantoms acquired at different pressure conditions. The method uses Optical Flow techniques to evaluate displacement field and an inverse analysis based on the Boundary Element Method (BEM) for structural analysis. In order to evaluate the displacement field, two distinct formulations for Optical Flow are used: Lucas–Kanade and Brox. The methodology was validated in terms of error measurements, number of iterations and computational cost considering two ultrasound mathematical phantoms. A comparison between simulations using BEM and Finite Element Method (FEM) have shown that the association of BEM with Lucas–Kanade method can estimate the elastic moduli of the mathematical phantoms with similar accuracy, when compared to FEM (9.79±8.58%). However, if a dense mesh is considered in the contour discretization, the BEM method converges in a fraction of the computational cost, when compared to FEM, 60s and ~6h, respectively. Considering the observed results, the proposed method may be a useful tool for other quantitative methods in elastography.
PubDate: 2015-11-08T16:21:26Z
- Abstract: Publication date: January 2016
- Adaptive 2D IGA boundary element methods
- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Michael Feischl, Gregor Gantner, Alexander Haberl, Dirk Praetorius
We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error estimator for Galerkin IGA boundary element methods, the present work focuses more on collocation and weighted-residual error estimators, which provide reliable upper bounds for the energy error. Our analysis allows piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS. We formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots. Numerical experiments show that the proposed adaptive strategy leads to optimal convergence, and related IGA boundary element methods are superior to standard boundary element methods with piecewise polynomials.
PubDate: 2015-11-08T16:21:26Z
- Abstract: Publication date: January 2016
- The use of element free Galerkin method based on moving Kriging and radial
point interpolation techniques for solving some types of Turing models- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Mehdi Dehghan, Mostafa Abbaszadeh, Akbar Mohebbi
In this paper two numerical procedures are presented for solving a class of Turing system. Firstly, we obtain a time discrete scheme by approximating time derivative via finite difference technique. Then we introduce the moving Kriging interpolation and radial point interpolation and also obtain their shape functions. We use the element free Galerkin method for approximating the spatial derivatives. This method uses a weak form of the considered equation that is similar to the finite element method with the difference that in the classical element free Galerkin method test and trial functions are moving least squares (MLS) approximation shape functions. Since the shape functions of moving least squares (MLS) approximation do not have Kronecker delta property, we cannot implement the essential boundary condition, directly. Thus we employ the shape functions of moving Kriging interpolation and radial point interpolation technique which have the mentioned property. Also, in the element free Galerkin method, we do not use any triangular, quadrangular or other type of meshes. The element free Galerkin method is a global method while finite elements method is a local one. This technique employs a background mesh for integration which makes it different from the truly mesh procedures. The coefficient matrix of the element free Galerkin is symmetric. Also, using numerical algorithms, we can conclude that the eigenvalues of the coefficient matrix are positive. Thus, for solving the obtained linear system of equations from the discretization, we use the conjugant gradient method. To keep away from solving a nonlinear algebraic system of equations and obtaining the acceptable numerical results, we use a predictor–corrector algorithm. Several test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed schemes.
PubDate: 2015-11-04T15:59:06Z
- Abstract: Publication date: January 2016
- A quasi-static interface damage model with cohesive cracks:
SQP–SGBEM implementation- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Roman Vodička
A quasi-static model for crack-mode sensitive interface damage with linearly elastic bodies at small strains is developed. It invokes a cohesive type response of the interface interpreted as a thin layer of an adhesive. The damage model is defined with the aim to obtain stress–strain relations in the cohesive zone typically employed in engineering interface-models. The weak solution of the problem is sought numerically by a semi-implicit time-stepping procedure which uses recursive double minimization in displacements and damage separately. The spatial discretization is performed by the symmetric Galerkin boundary-element method. Quadratic and sequential quadratic programming are implemented to resolve each partial minimization of the recursive scheme in the computation of the time-discretized solutions. Sample 2D numerical examples demonstrate applicability of the model as well as efficiency of the SGBEM and convex programming numerical implementations.
PubDate: 2015-11-04T15:59:06Z
- Abstract: Publication date: January 2016
- Efficient SPH simulation of time-domain acoustic wave propagation
- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Y.O. Zhang, T. Zhang, H. Ouyang, T.Y. Li
As a Lagrangian meshfree method, smoothed particle hydrodynamics (SPH) can eliminate much of the difficulty in solving acoustic problems in the time domain with deformable boundaries, complex topologies, or those that consist of multiphase systems. However, the optimal value of the computational parameters used in the SPH simulation of acoustics remains unknown. In this paper, acoustic wave equations in Lagrangian form are proposed and solved with the SPH method to compute the two-dimensional sound propagation model of an ideal gas in the time domain. We then assess how the numerical error is influenced by the time step, the smoothing length, and the particle spacing by investigating the interaction effects among the three parameters using Taguchi method with orthogonal array design (OAD) and analysis of variance (ANOVA). On the basis of this assessment, appropriate values for these computational parameters are discussed separately and validated with a two-dimensional computational aeroacoustic (CAA) model. The results demonstrate that the Courant number for the meshless SPH simulation of two-dimensional acoustic waves is proposed to be under 0.4, whereas the ratio of the smoothing length to the particle spacing is between 1.0 and 2.5.
PubDate: 2015-11-04T15:59:06Z
- Abstract: Publication date: January 2016
- Dynamics of an air bubble induced by an adjacent oscillating bubble
- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Rui Han, Shiping Wang, Xiongliang Yao
This study is concerned with the collapse of an air bubble induced by its adjacent oscillating bubble, including the splitting of the air bubble and the subsequent transitions of the two split sub-bubbles from singly-connected to doubly-connected. The numerical modeling is based on the potential flow theory coupled with the boundary integral method. A two-vortex-rings model is put forward to further simulate the interaction between two toroidal bubbles and a singly-connected one, which is rarely seen in previous studies. To validate the numerical model, experiments are carried out for the dynamics of an air bubble induced by a spark generated bubble captured by a high speed camera. Our numerical results agree qualitatively with the experimental data. It is found that the strength parameter ε of the oscillating bubble greatly affects the jet velocity of air bubble and the length ratio l′ of air bubble determines its collapsing pattern.
PubDate: 2015-10-23T05:20:04Z
- Abstract: Publication date: January 2016
- A stable nodal integration method with strain gradient for static and
dynamic analysis of solid mechanics- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): H. Feng, X.Y. Cui, G.Y. Li
A stable nodal integration method with strain gradient (SNIM-SG) for curing the temporal instability of node-based smoothed finite element method (NS-FEM) is proposed for dynamic problems using linear triangular and tetrahedron element. In each smoothing domain, except for considering the smoothed strain into the calculation of potential energy functional as NS-FEM, a term related to strain gradient is taken into account as a stabilization term. The proposed SNIM-SG can achieve appropriate system stiffness in strain energy between FEM and NS-FEM solutions and obtains quite favorable results in elastic and dynamic analysis. The accuracy and stability of SNIM-SG solution are studied through detailed analyzes of benchmark cases and practical engineering problems. In elastic-static analysis, it is found that SNIM-SG can provide higher accuracy in displacement field than the reference approaches do. In free vibration analysis, the spurious non-zero energy modes can be eliminated effectively owing to the fact that SNIM-SG solution strengths the original relatively soft NS-FEM, and SNIM-SG is confirmed to obtain fairly accurate natural frequency values in various examples. All in all, SNIM-SG cures the flaws of NS-FEM and enhances the dominant of nodal integration. Thus, the efficacy of the presented formulation in solving solid mechanics problems is well represented and clarified.
PubDate: 2015-10-23T05:20:04Z
- Abstract: Publication date: January 2016
- Meshless analyses for time-fractional heat diffusion in functionally
graded materials- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Slavomir Krahulec, Jan Sladek, Vladimir Sladek, Yiu-Chung Hon
The meshless local radial basis function method is applied to solve stationary and transient heat conduction problems in 2-D and 3-D bodies with functionally graded material properties. Time fractional derivative using Caputo definition is considered to describe anomalous diffusion phenomena. For temporal discretization, the Caputo time fractional derivative is approximated within each time interval 〈 t k , t k + 1 〉 by series of derivatives of integer order. The spatial discretization is performed by using the local radial basis collocation method. Numerical analyses are given on square (2D) and cubic (3D) domains to show the influence of the temporal fractional derivative parameter and gradation material parameter on the temperature distribution and temperature evolution in transient heat conduction problem.
PubDate: 2015-10-23T05:20:04Z
- Abstract: Publication date: January 2016
- Three efficient numerical models to analyse the step problem in shallow
water- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): E.G.A. Costa, J.A.F. Santiago, L.M.C. Godinho, L.C. Wrobel, W.J. Mansur
In this paper, the problem of acoustic wave propagation in a waveguide of infinite extent is modelled, taking into account constant depth in each section of the sea. Efficient numerical strategies in the frequency domain are addressed to investigate two-dimensional acoustic wave propagation in a shallow water configuration, considering a step in the rigid bottom and a flat free surface. The time domain responses are obtained by means of an inverse Fast Fourier Transform (FFT) of results computed in the frequency domain. The numerical approaches used here are based on the Boundary Element Method (BEM) and the Method of Fundamental Solutions (MFS). In the numerical models only the inclined or vertical interface between the sub-regions of different depth are discretized, as Green׳s functions that take into account the presence of free and rigid surfaces are used. These Green׳s functions are obtained either by eigenfunction expansion or by Ewald׳s method. A detailed discussion on the performance of these formulations is carried out, with the aim of finding an efficient numerical formulation to solve the step problem in shallow water.
PubDate: 2015-10-23T05:20:04Z
- Abstract: Publication date: January 2016
- A multiple-scale Pascal polynomial triangle solving elliptic equations and
inverse Cauchy problems- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Chein-Shan Liu, Chung-Lun Kuo
The polynomial expansion method is a useful tool to solve partial differential equations (PDEs). However, the researchers seldom use it as a major medium to solve PDEs due to its highly ill-conditioned behavior. We propose a single-scale and a multiple-scale Pascal triangle formulations to solve the linear elliptic PDEs in a simply connected domain equipped with complex boundary shape. For the former method a constant parameter R 0 is required, while in the latter one all introduced scales are automatically determined by the collocation points. Then we use the multiple-scale method to solve the inverse Cauchy problems, which is very accurate and very stable against large noise to 20%. Numerical results confirm the validity of the present multiple-scale Pascal polynomial expansion method.
PubDate: 2015-10-23T05:20:04Z
- Abstract: Publication date: January 2016
- Boundary element formulation of the Mild-Slope equation for harmonic water
waves propagating over unidirectional variable bathymetries- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Antonio Cerrato, José A. González, Luis Rodríguez-Tembleque
This paper presents a boundary element formulation for the solution of the Mild-Slope equation in wave propagation problems with variable water depth in one direction. Based on Green׳s function approximation proposed by Belibassakis [1], a complete fundamental-solution kernel is developed and combined with a boundary element scheme for the solution of water wave propagation problems in closed and open domains where the bathymetry changes arbitrarily and smoothly in a preferential direction. The ability of the proposed formulation to accurately represent wave phenomena like refraction, reflection, diffraction and shoaling, is demonstrated with the solution of some example problems, in which arbitrary geometries and variable seabed profiles with slopes up to 1:3 are considered. The obtained results are also compared with theoretical solutions, showing an excellent agreement that demonstrates its potential.
PubDate: 2015-10-23T05:20:04Z
- Abstract: Publication date: January 2016
- Estimation of effective elastic moduli of random structure composites by
the method of fundamental solutions- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Valeriy A. Buryachenko
One considers linearly elastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of aligned homogeneous heterogeneities of non-canonical shape. Effective elastic moduli as well as the first statistical moments of stresses in the phases are estimated through the averaged boundary integrals over the inclusion boundaries. The modified popular micromechanical models are based on the numerical solution for one inhomogeneity inside the infinite matrix loaded by remote homogeneous effective field. This solution is obtained by a meshfree method based on fundamental solutions basis functions for a transmission problem in linear elasticity. The problem here addressed, consists in computing the displacement and traction fields of an elastic object, which has piecewise constant Lamé coefficients, from a given displacement (or stress) field on the infinity. The main properties of the method are analyzed and illustrated with several numerical simulations in 2D domains.
PubDate: 2015-10-10T19:49:26Z
- Abstract: Publication date: January 2016
- Editorial Board
- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
PubDate: 2015-09-29T14:57:34Z
- Abstract: Publication date: December 2015
- A weighting-iteration method in the time domain for solving the scattering
problem of a complex-shaped scatterer- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Jui-Hsiang Kao
A weighting-iteration method in the time domain is developed to calculate the scattered waves from a complex-shaped scatterer. The incident waves can be mono-frequency or multi-frequency, and the complex object includes sharp edges and dramatic variations in geometry. The solid angles on the boundary elements of a complex-shaped scatterer are generally reduced to below the standard value of 0.5 for points on a smooth part of the boundary. These reduced solid angles destroy the convergence history during the iteration process in the time domain. A weighting function associated with the variation of solid angles is introduced to robust and rapid convergence in the time domain. The new method is used to calculate the scattering from a cube with sharp edges and an indented surface. The weighting function speeds up the convergence history to reach a robust convergence for both mono- and multiple-frequency incident waves.
PubDate: 2015-09-29T14:57:34Z
- Abstract: Publication date: January 2016
- Numerical solution for the degenerate scale problem in plane elasticity
using null field CVBIE- Abstract: Publication date: January 2016
Source:Engineering Analysis with Boundary Elements, Volume 62
Author(s): Y.Z. Chen
This paper provides a numerical solution for the degenerate scale problem in plane elasticity using the null field complex variable boundary integral equation (CVBIE). After performing the coordinate transformation, the CVBIE can be formulated in the normal scale. After making discretization, a linear algebraic equation is obtained. The influence matrix in the normal scale is invertible. By introducing two basic solutions, the degenerate scale problem is finally solved. Several numerical examples are given.
PubDate: 2015-09-13T13:04:42Z
- Abstract: Publication date: January 2016
- A traction-recovery method for evaluating boundary stresses on thermal
elasticity problems of FGMs- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Jian Liu, Hai-Feng Peng, Xiao-Wei Gao, Miao Cui
A new approach is presented to calculate boundary stresses in thermal stress analysis of structures consisting of functionally grades materials (FGMs) based on the traction-recovery method. In this approach, the in-plane strains are calculated first using the computed nodal displacements by simply differentiating shape functions at the point of interest, and then the boundary stresses are recovered by Hooke׳s law together with the known tractions on the boundary. This approach has the advantage of without need to evaluate strongly singular boundary integrals. With the comparison to the FEM software ANSYS, two numerical examples for plane stress and 3D problems are presented to verify the correctness of the proposed method in evaluating boundary thermal-stresses of FGMs.
PubDate: 2015-08-30T08:12:55Z
- Abstract: Publication date: December 2015
- Displacement discontinuity analysis of a nonlinear interfacial crack in
three-dimensional transversely isotropic magneto-electro-elastic
bi-materials- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): YanFei Zhao, MingHao Zhao, Ernian Pan
The displacement discontinuity method is introduced and extended to study the electric and magnetic nonlinear effect of an interfacial crack in three-dimensional magneto-electro-elastic bi-materials under combined loadings. Green’s functions due to uniformly distributed extended displacement discontinuities over a ring element are derived via the extended displacement discontinuity integro-differential equation method. The electric−magnetic polarization saturation model is adopted for the electric and magnetic nonlinearities at the vicinity of the crack front where the perfect electric displacement and magnetic induction saturations are assumed. The final formulation is discretized as a system of linear equations and an iterative approach is introduced to solve the unknown sizes of the two saturation zones by requiring that the electric displacement and magnetic induction intensity factors vanish at ends of their corresponding zones. The effect of the electric and magnetic fields on the saturation zones and the influence of the saturation zones on the stress intensity factor are illustrated with numerical examples.
PubDate: 2015-08-30T08:12:55Z
- Abstract: Publication date: December 2015
- Acoustic simulation using α-FEM with a general approach for reducing
dispersion error- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Z.C. He, Eric Li, G.Y. Li, F. Wu, G.R. Liu, X. Nie
The alpha finite element method (α-FEM) developed recently has showed outstanding features in solving solid mechanics and acoustic problems. In the α-FEM, a parameter alpha has been introduced to make the best use of “over-stiffness” of the FEM model and “over-softness” of the NS-FEM model to achieve the ultimate performance. Because the parameter alpha varies with the problems and the mesh size, it is difficult to find a general approach to determine, which holds back the application of the α-FEM method. In this paper, acoustic simulation using α-FEM with a general approach for reducing dispersion error is proposed. We first carry out a theoretical analysis of dispersion error, leading to a very important relation between the dispersion error and the parameter alpha. Next, the parameter of alpha is then determined by minimizing the dispersion error. The determined parameter alpha enables a proper gradient smoothing operation in the α-FEM, and provides a perfect balance between the stiffness and mass in the discrete system matrix, which dramatically reduces the dispersion error. The properties of the present α-FEM have been confirmed numerically via examples of 1D, 2D and 3D acoustic problems with various boundary conditions.
PubDate: 2015-08-30T08:12:55Z
- Abstract: Publication date: December 2015
- Shock-induced two dimensional coupled non-Fickian
diffusion–elasticity analysis using meshless generalized finite
difference (GFD) method- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Seyed Mahmoud Hosseini
In this work, the application of a meshfree method based on the generalized finite differences (GFD) method is developed for two dimensional analysis of coupled non-Fickian diffusion–elasticity. The two dimensional analyzed domain is subjected to shock loading in the problem. The equations of motion are transferred to Laplace domain by Laplace-transform technique and descritized using the presented meshfree method. The obtained results in Laplace domain are transferred to time domain using Talbot Laplace inversion technique for studying on the dynamic behaviors of displacements and molar concentration. It is found that the molar concentration diffuses through 2D domain with a finite speed similar to elastic wave. The propagation of mass diffusion and elastic waves are obtained and discussed at various time intervals. The distribution of molar concentration and displacements along “x” and “y” directions are illustrated at various time intervals for certain points on both axes.
PubDate: 2015-08-30T08:12:55Z
- Abstract: Publication date: December 2015
- Solving Helmholtz problems with the boundary element method using direct
radial basis function interpolation- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Carlos Friedrich Loeffler, Webe João Mansur, Hércules de Melo Barcelos, André Bulcão
In the present study, a direct interpolation technique that uses radial basis functions is applied to the boundary element method integral term, which refers to inertia, in the Helmholtz equation; consequently, free vibration frequencies and corresponding amplitudes can be determined from an eigenvalue problem solution. The proposed method, which has already been successfully applied to scalar problems governed by the Poisson equation, does not require standard domain integration procedures, which employ cell discretisation, and is more robust than the dual-reciprocity technique. Although similar to the latter in some aspects, because it uses radial basis functions and their primitives for interpolation, the proposed methodology is more general. It allows the immediate use of interpolation functions of any type, and there are no convergence or monotonicity problems as the number of basis points is increased.
PubDate: 2015-08-26T07:11:41Z
- Abstract: Publication date: December 2015
- A coupled smoothed finite element method (S-FEM) for structural-acoustic
analysis of shells- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): G. Wang, X.Y. Cui, Z.M. Liang, G.Y. Li
In this paper, a coupled smoothed finite element method (S-FEM) is developed to deal with the structural-acoustic problems consisting of a shell configuration interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements that can be generated automatically for any complicated geometries are adopted to discretize the problem domain. A gradient smoothing technique (GST) is introduced to perform the strain smoothing operation. The discretized system equations are obtained using the smoothed Galerkin weakform, and the numerical integration is applied over the further formed edge-based and face-based smoothing domains, respectively. To extend the edge-based smoothing operation from plate structure to shell structure, an edge coordinate system is defined local on the edges of the triangular element. Numerical examples of a cylinder cavity attached to a flexible shell and an automobile passenger compartment have been conducted to illustrate the effectiveness and accuracy of the coupled S-FEM for structural-acoustic problems.
PubDate: 2015-08-18T05:46:33Z
- Abstract: Publication date: December 2015
- 2D boundary element analysis of defective thermoelectroelastic bimaterial
with thermally imperfect but mechanically and electrically perfect
interface- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Iaroslav Pasternak, Roman Pasternak, Heorhiy Sulym
This paper utilizes the Stroh formalism and the complex variable approach to derive the integral formulae and boundary integral equations of anisotropic thermoelectroelasticity for a bimaterial solid with Kapitza-type interface. Obtained integral formulae and boundary integral equations do not contain domain integrals, thus, the boundary element approach based on them does not require any additional procedures accounting for the stationary temperature field acting in the solid. All kernels of the boundary integral equations are written explicitly in a closed form. Verification for limiting values of thermal resistance of the interface is provided. Obtained boundary integral equations are incorporated into the boundary element analysis procedure. Several problems are considered, which shows the influence of thermal resistance of the bimaterial interface on fields’ intensity at the tips of electrically permeable and impermeable cracks.
PubDate: 2015-08-18T05:46:33Z
- Abstract: Publication date: December 2015
- On two accurate methods for computing 3D Green׳s function and its
first and second derivatives in piezoelectricity- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Longtao Xie, Chuanzeng Zhang, Chyanbin Hwu, Jan Sladek, Vladimir Sladek
In this paper, we present two accurate methods for the calculation of the Green׳s function and its derivatives for three-dimensional anisotropic piezoelectric solids. In the first method, the Stroh formalism is used. The Green׳s function is expressed explicitly in terms of the Stroh eigenvectors, which are eigenvectors of the fundamental piezoelectricity matrix. The explicit derivatives of the 3D Green׳s function in terms of the derivatives of the Stroh eigenvalues and Stroh eigenvectors are derived for generally anisotropic piezoelectric materials. In the second method, we first express the Green׳s function and its derivatives in terms of novel infinite line integrals. Then the explicit expressions are obtained by the application of the Cauchy׳s residue theorem. The accuracies of both methods are verified by the numerical results compared with analytical solutions. Both explicit expressions are only applicable when the Stroh eigenvalues are distinct, which can be ensured by a small perturbation on some material constants in the case of degenerated eigenvalues.
PubDate: 2015-08-14T05:15:35Z
- Abstract: Publication date: December 2015
- A high-order numerical manifold method with nine-node triangular meshes
- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Huo Fan, Siming He, Zhongming Jiang
The numerical manifold method (NMM) is a unified framework that is used to describe continuous and discontinuous problems. The NMM is derived based on the finite cover approximation theory and gains its name after the mathematical notion of manifold. It is also a method based on the partition of unity (PU) and it introduces two cover systems: the mathematical cover (MC) and the physical cover (PC). There are two approaches for constructing high-order approximations. The first approach involves a non-constant PU function and non-constant local approximations. This results in the linear dependence (LD) problem and leads to the singularity in a global matrix. The second approach involves a higher PU function and constant local approximations. The increase in the order of approximations should go along with the increase in star but the LD problem can be avoided completely in theory. In this paper, a new high-order NMM with nine-node triangular meshes is proposed. The upgrade from first-order NMM to high-order NMM is illustrated in detail. Moreover, the initial stress matrix is analyzed in detail. The effectiveness and accuracy of the proposed high-order NMM are validated using several typical examples. The proposed high-order NMM supplements the existing family of non-LD high- and low-order NMM under MC with triangular meshes.
PubDate: 2015-08-14T05:15:35Z
- Abstract: Publication date: December 2015
- Augmented Numerical Manifold Method with implementation of flat-top
partition of unity- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Lei He, Xinmei An, Xiaoying Liu, Zhiye Zhao, Shengqi Yang
This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency.
PubDate: 2015-08-14T05:15:35Z
- Abstract: Publication date: December 2015
- Solving Helmholtz equation with high wave number and ill-posed inverse
problem using the multiple scales Trefftz collocation method- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Chung-Lun Kuo, Weichung Yeih, Chein-Shan Liu, Jiang-Ren Chang
In this article, the solutions for the Helmholtz equation for forward problems with high wave number and ill-posed inverse problems using the multiple scales Trefftz collocation method are investigated. The resulting linear algebraic systems for these problems are ill-posed and therefore require special treatments. The equilibrated matrix concept is adopted to determine the scales and to construct an equivalent linear algebraic problem with a leading matrix less ill-posed such that standard solver like the conjugate gradient method (CGM) can be adopted. Five examples, including two forward problems with the high wave number and three inverse Cauchy problems, are given to show the validity for the approach. Results show that the equilibrated matrix concept can yield a less ill-posed leading matrix such that the conventional linear algebraic solver like CGM can be successfully adopted. This approach has a very good noise resistance.
PubDate: 2015-08-14T05:15:35Z
- Abstract: Publication date: December 2015
- Free vibration of moderately thick functionally graded plates by a
meshless local natural neighbor interpolation method- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): S.S. Chen, C.J. Xu, G.S. Tong, X. Wei
Using a meshless local natural neighbor interpolation (MLNNI) method, natural frequencies of moderately thick plates made of functionally graded materials (FGMs) are analyzed in this paper based on the first-order shear deformation theory (FSDT), which is employed to take into account the transverse shear strain and rotary inertia. The material properties of the plates are assumed to vary across the thickness direction by a simple power rule of the volume fractions of the constituents. In the present method, a set of distinct nodes are randomly distributed over the middle plane of the considered plate and each node is surrounded by a polygonal sub-domain. The trial functions are constructed by the natural neighbor interpolation, which makes the constructed shape functions possess Kronecker delta property and thus no special techniques are required to enforce the essential boundary conditions. The order of integrands involved in domain integrals is reduced due to the use of three-node triangular FEM shape functions as test functions. The natural frequencies computed by the present method are found to agree well with those reported in the literature, which demonstrates the versatility of the present method for free vibration analysis of moderately thick functionally graded plates.
PubDate: 2015-08-09T04:22:05Z
- Abstract: Publication date: December 2015
- A new BEM for solving 2D and 3D elastoplastic problems without initial
stresses/strains- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Wei-Zhe Feng, Xiao-Wei Gao, Jian Liu, Kai Yang
In this paper, new boundary-domain integral equations are derived for solving two- and three-dimensional elastoplastic problems. In the derived formulations, domain integrals associated with initial stresses (strains) are avoided to use, and material nonlinearities are implicitly embodied in the integrand kernels associated with the constitutive tensor. As a result, only displacements and tractions are explicitly involved in the ultimate integral equations which are easily solved by employing a mature efficient non-linear equation solver. When materials yield in response to applied forces, the constitutive tensor (slope of the stress–strain curve for a uniaxial stress state) becomes discontinuous between the elastic and plastic states, and the effect of this non-homogeneity of constitutive tensor is embodied by an additional interface integral appearing in the integral equations which include the differences of elastic and plastic constitutive tensors. The domain is discretized into internal cells to evaluate the resulted domain integrals. An incremental variable stiffness iterative algorithm is developed for solving the system of equations. Numerical examples are given to verify the correctness of the proposed BEM formulations.
PubDate: 2015-08-09T04:22:05Z
- Abstract: Publication date: December 2015
- Boundary augmented Lagrangian method for contact problems in linear
elasticity- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Shougui Zhang, Xiaolin Li
An augmented Lagrangian method, based on the fixed point method and boundary variational formulations, is designed and analysed for frictionless contact problems in linear elasticity. Using the equivalence between the contact boundary condition and a fixed point problem, we develop a new iterative algorithm that formulates the contact problem into a sequence of corresponding linear variational equations with the Steklov–Poincaré operator. Both theoretical results and numerical experiments show that the method presented is efficient.
PubDate: 2015-08-09T04:22:05Z
- Abstract: Publication date: December 2015
- A local meshless collocation method for solving
Landau–Lifschitz–Gilbert equation- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Ahmad Shirzadi, Fariba Takhtabnoos
This paper is concerned with a meshless simulation of the two dimensional Landau–Lifschitz–Gilbert (LLG) equation which describes the dynamics of the magnetization inside a ferromagnetic body. After elimination of the time variable by a suitable finite difference scheme, a combination of the meshless local RBF and the finite collocation method is used for spatial discretizations of the field variables. Three test problems are numerically investigated and the results reveal the effectiveness of the method.
PubDate: 2015-08-05T04:02:12Z
- Abstract: Publication date: December 2015
- Boundary methods for Dirichlet problems of Laplace׳s equation in
elliptic domains with elliptic holes- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Zi-Cai Li, Li-Ping Zhang, Yimin Wei, Ming-Gong Lee, John Y. Chiang
Recently, the null field method (NFM) is proposed by J.T. Chen with his groups. In NFM, the fundamental solutions (FS) with the field nodes Q outside of the solution domains are used in the Green formulas. In this paper, the NFM is developed for the elliptic domains with elliptic holes. First, the FS is expanded by the infinite series in elliptic coordinates. When the Fourier approximations of the boundary conditions on the elliptic boundaries are chosen, the explicit algebraic equations are derived, and the semi-analytic solutions can be found. Next, the interior field method (IFM) is developed, which is equivalent to the NFM when the field nodes approach the domain boundary. Moreover, the collocation Trefftz method (CTM) is also employed by using the particular solutions in elliptic coordinates. The CTM is the simplest algorithm, has no risk of degenerate scales, and can be applied to non-elliptic domains. Numerical experiments are carried out for elliptic domains with one elliptic hole by the IFM, the NFM and the CTM. In summary, for Laplace׳s equation in elliptic domains, a comparative study of algorithms, errors, stability and numerical results is explored in this paper for three boundary methods: the NFM, the IFM and the CTM.
PubDate: 2015-08-05T04:02:12Z
- Abstract: Publication date: December 2015
- Reconstruction of inaccessible boundary value in a sideways parabolic
problem with variable coefficients—Forward collocation with finite
integration method- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Yue Yu, Dinghua Xu, Y.C. Hon
We investigate a sideways problem of reconstructing an inaccessible boundary value for parabolic equation with variable coefficients. Formulating the sideways problem into a sequence of well-posed direct problems (DP) and a system of Ordinary Differential Equations (ODE), we combine the recently developed finite integration method (FIM) with radial basis functions (RBF) to iteratively obtain the solution of each DP by solving an ill-posed linear system. The use of numerical integration instead of finite quotient formula in FIM completely avoids the well known roundoff-discretization errors problem in finite difference method and the use of RBF as forward collocation method (FCM) gives a truly meshless computational scheme. For tackling the ill-posedness of the sideways problem, we adapt the traditional Tikhonov regularization technique to obtain stable solution to the system of ODEs. Convergence analysis is then derived and error estimate shows that the error tends to zero when perturbation δ → 0 . We can then obtain highly accurate and stable solution under some assumptions. Numerical results validate the feasibility and effectiveness of the proposed numerical algorithms.
PubDate: 2015-08-05T04:02:12Z
- Abstract: Publication date: December 2015
- Optimal material distribution for heat conduction of FGM based on meshless
weighted least-square method- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): H.M. Zhou, W.H. Zhou, G. Qin, P.M. Ming
A numerical procedure is presented to determine the optimal material distribution of functionally graded material (FGM) for heat conduction problem. The material volume fractions are used as primary design variables and material properties are assumed to be temperature independent. The purpose is to minimize the difference between the actual values of a field variable and a desired target field with given initial and boundary conditions for transient problem. Examples are solved numerically for given boundary conditions and objective functions using meshless weighted least-square (MWLS) method. A discrete function is employed in the MWLS method to construct a set of linear equation, which avoids the burdensome task of numerical integration and leads to a pure meshless analysis for FGM. The presented optimization method, through the numerical experiments, is found to provide optimal volume fraction distributions that minimize objective function, as well as the rapid and stable convergence.
PubDate: 2015-08-05T04:02:12Z
- Abstract: Publication date: December 2015
- Level set-based topology optimization for 2D heat conduction problems
using BEM with objective function defined on design-dependent boundary
with heat transfer boundary condition- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Guoxian Jing, Hiroshi Isakari, Toshiro Matsumoto, Takayuki Yamada, Toru Takahashi
This paper proposes an optimum design method for two-dimensional heat conduction problem with heat transfer boundary condition based on the boundary element method (BEM) and the topology optimization method. The level set method is used to represent the structural boundaries and the boundary mesh is generated based on iso-surface of the level set function. A major novel aspect of this paper is that the governing equation is solved without ersatz material approach and approximated heat convection boundary condition by using the mesh generation. Additionally, the objective functional is defined also on the design boundaries. First, the topology optimization method and the level set method are briefly discussed. Using the level set based boundary expression, the topology optimization problem for the heat transfer problem with heat transfer boundary condition is formulated. Next, the topological derivative of the objective functional is derived. Finally, several numerical examples are provided to confirm the validity of the derived topological derivative and the proposed optimum design method.
PubDate: 2015-07-20T11:47:11Z
- Abstract: Publication date: December 2015
- Angular basis functions formulation for 2D potential flows with non-smooth
boundaries- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): D.L. Young , Y.J. Huang , C.S. Wu , V. Sladek , J. Sladek
In this paper a new angular basis functions (ABFs) formulation which is different from the radial basis functions (RBFs) among the meshless methods is proposed to solve potential flow problems with non-smooth or discontinuous boundaries. The unique property of the ABFs formulation is first investigated in this study. In contrast to the method of fundamental solutions (MFS) using the RBFs, we adopt this ABFs collocation method to deal with the non-smooth or discontinuous boundaries more feasibly and accurately. Both the interior and exterior potential flow problems governed by the 2D Laplace equation are explored by both ABFs and RBFs schemes for comparison purposes. A square cavity, a cusp cavity, a uniform flow past a circular cylinder and the NACA 2418 airfoil are examined to test the merits or demerits of both the ABFs and RBFs formulations. From those four numerical experiments, the complementary ABFs formulation is found to be more effective to simulate domains with non-smooth or discontinuous boundaries such as acute, corner and cusp geometries. Furthermore, the basic aerodynamic problems of airfoils modeling are also discussed in the present study. From these numerical experiments, the angular basis function is found to be favorable of simulating the domains with acute, narrow regions and exterior problems.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015
- A meshfree method based on the radial basis functions for solution of
two-dimensional fractional evolution equation- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Hadi Roohani Ghehsareh , Sayna Heydari Bateni , Ali Zaghian
In the current work, numerical solution of a two-dimensional fractional evolution equation has been investigated by using two different aspects of strong form meshless methods. In the first method a time discretization approach and a numerical technique based on the convolution sum are employed to approximate the appearing time derivative and fractional integral operator, respectively. It has been proven analytically that the time discretization scheme is unconditionally stable. Then a meshfree collocation method based on the radial basis functions is used for solving resulting time-independent discretization problem. As the second approach, a fully Kansa׳s meshfree method based on the Gaussian radial basis function is formulated and well-used directly for solving the governing problem. In this technique an explicit formula to approximate the fractional integral operator is computed. The given techniques are used to solve two examples of problem. The computed approximate solutions are reported through the tables and figures, also these results are compared together and with the other available results. The presented results demonstrate the validity, efficiency and accuracy of the formulated techniques.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015
- A novel semi-analytical algorithm of nearly singular integrals on higher
order elements in two dimensional BEM- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Zhongrong Niu , Zongjun Hu , Changzheng Cheng , Huanlin Zhou
In this paper, a novel semi-analytical algorithm is developed to evaluate the nearly strong and hyper-singular integrals on higher order elements in two dimensional (2-D) BEM. By analyzing the geometrical feature of higher order elements in the intrinsic coordinates, the relative distance from a source point to the element of integration is defined to describe the character of the nearly singular integrals. By a series of deduction, the leading singular part of the integral kernel functions on the higher order elements is separated from each of the nearly singular integrals. Then the nearly singular integrals on the higher order elements close to the source point are transformed to the sum of both the non-singular parts and nearly singular parts by the subtraction, in which the former are calculated by the conventional numerical quadratures and the latter are evaluated by the resulting analytical formulations. Furthermore, the BEM with the quadratic elements was used to analyze the displacements and stresses near the boundary as well as thin-walled structures in 2-D elasticity. The numerical results from three examples demonstrate that the quadratic BE analysis with the semi-analytical algorithm is more accurate and efficient than the Linear BE analysis with the analytical algorithm for the nearly singular integrals. In fact, the Linear BE analysis has been greatly more advantageous compared with the finite element analysis for the thin-walled structures.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015
- Efficient evaluation of integrals with kernel 1/rχ for quadrilateral
elements with irregular shape- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Jia-He Lv , Xia-Ting Feng , Fei Yan , Quan Jiang
In this paper, integrals with kernel 1 / r χ are concerned with the following three aspects: a). the near singularity caused by distorted element shape; b). the near singularity derived from the angular direction; c). the singularity/near singularity in the radial direction. A conformal polar coordinate transformation (CPCT) is proposed to eliminate the shape effect of elements, which can keep the shape characteristic of distorted elements, and an improved sigmoidal transformation is introduced to alleviate the near singularity in the angular direction. By combination of the two strategies with existing methods, such as singularity subtraction method and distance transformation method utilized in this paper, an efficient and robust numerical integration approach can be obtained for various orders of singular/nearly singular integrals, and a distorted curved quadrilateral element extracted from a cylinder surface is provided to demonstrate the efficiency and robustness of the proposed method.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015
- A collocation and least squares p-singular boundary method without
fictitious boundary- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Mehrzad Ghorbani , Daniel Watson
This study proposes a new version, p-SBM, of the numerical singular boundary method (SBM) to solve general classes of elliptic PDEs such as: Laplace, Helmholtz and diffusion equations. In SBM, the fundamental solution (FS) of the problem must be given but unlike the method of fundamental solutions (MFS), a fictitious boundary is not required. Instead, the inverse interpolation technique (IIT) and least squares method for the calculation of the singular diagonal elements of the interpolation matrix allows us to avoid the singularity at origin. In this study, we enrich the traditional SBM by adding a constant parameter or a linear combination to the previous MFS approximation and use various types of internal, external and boundary nodes. The p-SBM is applied to some homogeneous Laplace, Helmholtz and Diffusion problems to show its ability and solution accuracy. The non-homogeneous problems can be handled by using the dual reciprocity method (DRM).
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015
- Hybrid LES/URANS simulation of turbulent natural convection by BEM
- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): P. Kocutar , L. Škerget , J. Ravnik
In this paper we have developed a hybrid LES/URANS turbulent model for a BEM based turbulent fluid flow solver. We employed the unified LES/URANS approach, where the interface between the LES and URANS regions is defined using a physical quantity, which dynamically changes during numerical simulation. The main characteristic of the unified hybrid model is that only one set of governing equations is used for fluid flow simulation in both the LES and URANS regions. Regions where turbulent kinetic energy is calculated by LES and URANS models are determined using a switching criterion. We used the Reynolds number based on turbulent kinetic energy and the Reynolds number based on total turbulent kinetic energy to establish the LES/URANS interface switching criterion. Depending on flow characteristics and with the use of switching criterion, we chose between sub-grid scale viscosity (SGS) and URANS effective viscosity. The SGS or URANS effective viscosity is used in the transport equation for turbulent kinetic energy and in governing equations for fluid flow. The developed numerical algorithm was tested by simulating turbulent natural convection within a square cavity. The hybrid turbulent model was implemented within a numerical algorithm based on the boundary element method, where single domain and sub-domain approaches are used. The governing equations are written in velocity–vorticity formulation. We used the false transient time scheme for the kinematics equation.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: December 2015