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 [2799 journals] |
- Retraction notice to “An alternative BEM formulation, based on
dipoles of stresses and tangent operator technique, applied to cohesive
crack growth modelling” [Eng. Anal. Bound. Elem. 41 (2014)
74–82]- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Hugo Luiz Oliveira, Edson Denner Leonel
PubDate: 2015-09-29T14:57:34Z
- Abstract: Publication date: December 2015
- 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
- Calculation of 2D nearly singular integrals over high-order geometry
elements using the sinh transformation- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Yaoming Zhang, Yanpeng Gong, Xiaowei Gao
The accurate evaluation of nearly singular integrals plays an important role in the implementation of BEM. In general, these include evaluating the solution near the boundary or treating problems with thin domains, which are respectively named the boundary layer effect and the thin-body effect in BEM. Although many methods of evaluating two-dimensional (2D) nearly singular integrals have been developed in recent years with varying degrees of success, questions still remain. In this paper, we present an efficient strategy for numerical evaluation of 2D nearly singular integrals that arise in the solution of 3D BEM using eight-node second-order quadrilateral surface elements. The strategy is an extension of the sinh transformation, which is used to evaluate the 1D or 2D nearly singular integrals on simple geometry elements, such as usual linear or planar elements. Several numerical examples involving boundary layer effect and thin body problems in 3D potential problems are investigated to verify the proposed scheme, yielding very promising results.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- An isogeometric enriched quasi-convex meshfree formulation with
application to material interface modeling- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Hanjie Zhang, Dongdong Wang
An isogeometric enriched quasi-convex meshfree method is presented with particular application to the material interface modeling. The current quasi-convexity of the meshfree approximation is achieved by introducing the mixed reproducing points of isogeometric B-spline basis functions into the meshfree consistency conditions. The resulting new meshfree shape functions have a similar form as the standard reproducing kernel meshfree shape functions, while the negative portions of the shape functions are significantly reduced. It is shown that this quasi-convex meshfree scheme yields better accuracy compared with the conventional meshfree method. Furthermore, in order to accurately model the material interface where the strain jump needs to be properly treated, a coupled isogeometric–meshfree approximation with a unified format of reproducing conditions is devised. The problem geometry and strain jump for the material interface are described by the isogeometric basis functions with repeated knots in the interface normal direction, while the rest regions are discretized by the isogeometric enriched quasi-convex meshfree approximation. This approach encompasses the geometry exactness of isogeometric analysis as well as the model refinement robustness of meshfree formulation. The effectiveness of the proposed method is thoroughly demonstrated by several typical numerical examples.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Evaluating hypersingular integrals of 3D acoustic problems on curved
surfaces- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Jinlong Feng, Zhenhan Yao, Yinghua Liu, Xiaoping Zheng
In this paper two numerical methods are developed to calculate hypersingular integrals of 3D acoustic problems on curved surfaces. When Burton–Miller method is used to solve acoustic problems, the occurrence of hypersingular integrals will be unavoidable. In this case, the hypersingular integrals need to be treated carefully to reach high accuracy. Two different methods are investigated to compute hypersingular integrals for different types of elements. Numerical examples, dealing with the problems of sound radiation and scattering respectively, are presented for examining the efficiency and accuracy of present algorithm.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Dynamic Green׳s function for a three-dimensional concentrated load
in the interior of a poroelastic layered half-space using a modified
stiffness matrix method- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Zhongxian Liu, Jianwen Liang, Chengqing Wu
This paper presents a new modified stiffness matrix method for the dynamic response analysis of a three-dimensional poroelastic layered half space subject to internal concentrated loads. This three-dimensional problem can be simplified as two two-dimensional problems consisting of the in-plane response and the anti-plane response. Similar to the principle of displacement method in structural mechanics, firstly, the top and bottom surfaces of a loaded layer are fixed, and the reaction forces at two “fixed ends” can be obtained using the superposition of the particular and homogeneous solution. Secondly, the displacement at the layer interface can be obtained using a direct stiffness method. In the loaded layer, the Green׳s function is decomposed into the particular solution, the homogeneous solution and the reaction solution, and the particular solution can be replaced by the analytical solution for the poroelastic full space. With this technique, the convergence problem due to the improper integral can be addressed with sources and receivers at similar or at the same depth, and a fictitious surface does not need to be introduced as in the traditional method. Finally, the results of the dynamic response of a poroelastic layered half space are presented both in the frequency and time domain.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Shape optimizations of inhomogeneities of two dimensional (2D) and three
dimensional (3D) steady state heat conduction problems by the boundary
element method- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): C.Y. Dong
The shape optimizations of inhomogeneities for 2D and 3D steady state heat conductions in an infinite medium are respectively studied by the boundary element method (BEM). Interest in the shape optimization by the BEM is mainly due to its high computation accuracy and simplicity in meshing. The boundary integral equations and the heat energy formulations in this paper only contain the temperature on each inhomogeneity–matrix interface. The heat energy increment in the inhomogeneous medium is taken as the objective function. The method of moving asymptotes (MMA) is adopted to carry out numerical implementation of the shape optimizations of 2D and 3D inhomogeneities.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Transient heat conduction analysis of functionally graded materials by a
multiple reciprocity boundary face method- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Guangyao Li, Shuaiping Guo, Jianming Zhang, Yuan Li, Lei Han
This paper applies the multiple reciprocity boundary face method to solve transient heat conduction problems of functionally graded materials. It is assumed that the material properties vary in z-direction exponentially or quadratically. Several variable substitutions are employed to convert this problem to standard diffusion equations. After those substitutions, however, the initial condition and the heat source density function, which lead the domain integral of the boundary integral equation, become more complicated. In this application, the Laplace transformation is used to remove the time dependence of the problem. A multiple reciprocity formulation with the modified Helmholtz fundamental solutions is used to convert the domain integral into boundary integrals and several non-integral terms. Numerical examples show that the results of our method are in good agreement with the analytical solutions or finite element method solutions at both internal and boundary points.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Accurate numerical evaluation of domain integrals in 3D boundary element
method for transient heat conduction problem- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Yunqiao Dong, Chenjun Lu, Yuan Li, Jianming Zhang, Guizhong Xie, Yudong Zhong
This paper presents an improved approach for the numerical evaluation of domain integrals that appear in the solution of transient heat conduction problems when using a time-dependent boundary integral equation method. An implementation of this method requires the accurate evaluation of the domain integrals. As the time step value is very small, the integrand in the domain integral is close to singular, thus rendering accurate evaluation of the integral difficult. First a closest point is introduced when the source point is close to, but not on the cell in the present method. Then a coordinate transformation coupled with a cell subdivision technique is proposed considering the position of the source point or the closest point and the relations between the size of the cell and the time step value. With the new method, accurate evaluation of domain integrals can be obtained. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- The multi-domain FMM-IBEM to model elastic wave scattering by
three-dimensional inclusions in infinite domain- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Zhongxian Liu, Fengjiao Wu, Dong Wang
The scattering of elastic wave by three-dimensional (3-D) inclusions embedded in solid infinite domain is solved by a Fast Multipole accelerated multi-domain Indirect Boundary Element Method (FMM-IBEM). Based on the single-layer potential theory, the scattered field is constructed by virtual uniform loads acted on circular elements covering the boundary surface, and then the analytic integration of the exact Green’s function for infinite space can be applied. By using the Taylor series expansion of compressional and shear waves potential function, the multipole expansion and local expansion coefficients of Green’s function are deduced. The detailed procedure of multi-domain FMM-IBEM for such problem is presented. It is verified that this method substantially improves the computing efficiency and reduces the memory storage, then the elastic wave scattering problems involving millions of degrees of freedom (DOFs) can be solved accurately and efficiently on an ordinary workstations. Finally, the scattering problems of P, SV waves by spherical inclusions group and 3-D random inclusions in elastic infinite domain are solved, and some important characteristics of plane P and SV waves scattering by inclusions group are discussed through typical numerical results.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Finite block Petrov–Galerkin method in transient heat conduction
- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): M. Li, A Monjiza, Y.G. Xu, P.H. Wen
Based on the two-dimensional Lagrange series interpolation, the formulation of the Finite Block Petrov–Galerkin (FBPG) in the weak form is presented in this paper. In this case, the first order of partial differentials are only needed in the weak form governing equations and in the Neumann boundary condition. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate ( x o y ) to the normalized coordinate ( ξ o η ) with 8 seeds. Time dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin׳s inversion method is used to determine all the physical values in the time domain. Illustrative numerical examples are given and comparisons have been made with either analytical solutions or other numerical solutions including meshless method and the Finite Element Method (ABAQUS).
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Transmission loss prediction of silencers by using combined boundary
element method and point collocation approach- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): L. Yang, Z.L. Ji, T.W. Wu
A technique that combines the boundary element method (BEM) and the point collocation approach is proposed to calculate the transmission loss (TL) of silencers in the absence of mean flow and temperature gradient. A long silencer is first divided into several substructures for analysis purposes. The point collocation approach is applied to produce the impedance matrices of any long substructure that has an axially uniform cross section to produce its impedance matrix. On the other hand, the direct mixed-body BEM is used to produce the impedance matrices of any irregular sections. The point collocation approach employs a modal expansion of the cross-sectional modes extracted by the 2D finite element method (FEM), and then matches the sound pressures and particle velocities at the collocation points on both ends to calculate the impedance matrix. All the substructure impedance matrices are then combined to form the resultant impedance matrix of the whole silencer for TL computation. Several test cases are presented to valid the combined technique and to demonstrate its computational efficiency.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: December 2015
- Radial integration BEM for solving non-Fourier heat conduction problems
- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Wei-An Yao, Hong-Xiao Yao, Bo Yu
The radial integral BEM (RIBEM) with a step-by-step integration method is presented for solving non-Fourier heat conduction problems in this paper. First, the system of second-order ordinary differential equations is obtained by using the RIBEM to discretize the space domain. Then, the Newmark method and the central difference method are adopted to solve the system of ordinary differential equations with respect to time. Finally, several numerical examples with laser heat sources are performed to demonstrate the performance of the present method. The results show that the present approach can obtain accurate and stable numerical results.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Free vibration analysis of two-dimensional functionally graded coated and
undercoated substrate structures- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Y. Yang, K.P. Kou, C.C. Lam, V.P. Iu
In this paper, the free vibration behaviors of the functionally graded (FG) coated and undercoated substrate structures are studied by a meshfree boundary–domain integral equation method. Based on the two-dimensional elasticity theory, the boundary–domain integral equations for each single layer of these coating–substrate structures are derived initially by using elastostatic fundamental solutions. Employ the radial integration method to transform the domain integrals into boundary integrals and achieve a meshfree scheme. By applying the multi-region boundary element method, obtain the generalized eigenvalue system of the whole structure, which involves system matrices with boundary integrals only and the complete solutions for natural frequency and vibration modes are rigidly resolved. A comparative study of FG versus homogeneous coating is conducted. The influences of material composition, material gradient, coating thickness ratio, substrate structure aspect ratio and the boundary conditions on the natural frequencies of the FG coated and undercoated substrate structure are evaluated and discussed.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Editorial Board
- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Boundary element and mesh reduction methods in thermal and nonhomogeneous
problems- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Xiao-Wei Gao
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Solutions of 2D and 3D non-homogeneous potential problems by using a
boundary element-collocation method- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Wenzhen Qu, Wen Chen, Zhuojia Fu
This paper presents the boundary element method for the numerical simulation of 2D and 3D nonhomogeneous potential problems. A novel technique, called recursive composite multiple reciprocity method (RCMRM), is introduced to avoid the domain integral of the non-homogenous equation in the boundary element method (BEM). The proposed method has no requirement of domain discretization, and thus is a truly boundary-type numerical method. Numerical results illustrate that the present method is computationally efficient, accurate, and convergent with an increasing number of boundary elements and collocation points.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Meshless modeling of natural convection problems in non-rectangular cavity
using the variational multiscale element free Galerkin method- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Xiaohua Zhang, Ping Zhang
In this paper, the two-dimensional natural convection problems in complex geometries were solved by using the variational multiscale element free Galerkin (VMEFG) method. The VMEFG method is a meshless method which coupled element free Galerkin method and variational multiscale method, thus it inherits the advantages of variational multiscale and meshless methods. In this method, the field variables are decomposed into coarse and fine scales first, then solved fine scale problem analytically by using bubble functions, in the process, the stabilization parameters had appeared naturally. Moreover, it ensures that the resultant formulations yield a consistent stabilized method. From the viewpoint of application, the presented method can employ equal order basis for pressure and velocity, which is not only easy to implement but also avoid the restriction of the Babuŝka–Brezzi condition and eliminate non-physical oscillations. Several test problems, including natural convection in the semicircular cavity, triangular cavity and triangular cavity with zig-zag shaped bottom wall are considered to investigate the accuracy of the proposed method. The numerical results obtained using VMEFG showed very good agreement with those available in the literature.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: December 2015
- An improved direct method for evaluating hypersingular stress boundary
integral equations in BEM- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Wei-Zhe Feng, Jian Liu, Xiao-Wei Gao
An efficient numerical method for evaluating all kinds of singular boundary integrals presented in Ref. Gao, 2002 [16] is improved by using a newly derived formulation for computing the spatial derivative of the global distance, which is inevitably used in the finite part of radial integrals. Based on this improvement, more accurate and stable results are obtained in evaluating singular integrals on curved boundary elements. Applying this improved singular integral method to evaluate hypersingular boundary integrals in the stress boundary integral equation, and a high order accuracy of stresses is achieved. Numerical examples are given to illustrate the correctness of the proposed method, and computational results show that the accurate stresses can be obtained even on a coarse mesh, compared with other conventional techniques.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: December 2015
- An efficient boundary integral equation method for multi-frequency
acoustics analysis- Abstract: Publication date: December 2015
Source:Engineering Analysis with Boundary Elements, Volume 61
Author(s): Xianhui Wang, Huitao Chen, Jianming Zhang
In this paper, a multi-frequency calculation technique based on least square approximate is introduced into the boundary integral equation method (BIEM) for 3D acoustics problems. The quadrilateral constant elements are used in multi-frequency calculation technique. In this method, the exponential term is expanded only when the source point and the field point locate in the same element. Thus, all the diagonal entries in system matrices are independent of the wave number. As a result, the integrals for the diagonal entries in all the final matrices (different frequencies) only are calculated once. Comparing with the original BIEM, the storage requirement for the presented method only adds O(n) (n is the total number of the elements). In addition, the presented method can be used to deal with the full frequency acoustic problems. Numerical examples show the accuracy and efficiency of the presented technique.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: December 2015
- Calculation of three-dimensional nearly singular boundary element
integrals for steady-state heat conduction- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Guizhong Xie, Liangwen Wang, Jianming Zhang, Dehai Zhang, Hao Li, Wenliao Du
In this work, a novel approach is presented for three-dimensional nearly singular boundary element integrals for steady-state heat conduction. Accurate evaluation of the nearly singular integrals is an important issue in the implementation of boundary element method (BEM). In this paper, an exponential transformation is introduced to deal with the nearly singular integrals in three-dimensional BEM. First, a triangle polar coordinate system is introduced. Then, the exponential transformation is performed by five steps. For each step, a new transformation is proposed based on the distance from the source point to surface elements which is expressed as r 2 = O ( A k 2 ( θ ) ρ 2 + r 0 2 ) , and all steps can finally be unified into a uniform formation. Moreover, to perform integrations on irregular elements, an adaptive integration scheme considering both the element shape and the projection point associated with the proposed transformation is introduced. Numerical examples are presented to verify the proposed method. Results demonstrate the accuracy and efficiency of our method.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Method of fundamental solutions for 3D elasticity with body forces by
coupling compactly supported radial basis functions- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Cheuk-Yu Lee, Hui Wang, Qing-Hua Qin
In this paper, a meshless computational model by integrating the method of fundamental solutions (MFS) and the method of particular solutions fulfilled with compactly supported radial basis functions (CSRBF) is developed for three-dimensional (3D) linear elasticity with the presence of body forces. The corresponding displacement and stress particular solution kernels across the support radius are firstly derived using Galerkin vectors and then are used to modify the boundary conditions. Subsequently, the classical meshless MFS, in which the homogeneous part of the full solutions are approximated using the linear combination of displacement and stress fundamental solutions in 3D linear elasticity, is formulated for solving the homogeneous 3D linear elastic system. Finally, several examples are presented to demonstrate the accuracy and efficiency of the present meshless method and also the effect of sparseness of interpolation matrix in CSRBF interpolation is discussed.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- Analysis of the temperature field in anisotropic coating-structures by the
boundary element method- Abstract: Publication date: November 2015
Source:Engineering Analysis with Boundary Elements, Volume 60
Author(s): Changzheng Cheng, Zhilin Han, Huanlin Zhou, Zhongrong Niu
The distance r between the source point and the field point is very short when the boundary element method is used to calculate the boundary quantities in the coating domain, which is very thin with respect to the substrate. The nearly singular integrals will occur during the process of numerical calculation of the boundary integral equations when the distance r is approaching to zero. The calculation difficulty of nearly singular integrals has seriously hindered the application of the boundary element method to the analysis of the physical quantities in the coating-structures. Herein, the analytical formulations for the nearly singular integrals in potential boundary integral equations developed by the authors before are generalized to the multi-domain system. This multi-domain boundary element method, in which the nearly singular integrals have been cracked, is introduced to analyze the temperature field in anisotropic coating-structures. The numerical examples demonstrate that the present method can model the temperature field in the coating-structure with much thinner coating in contrast with the conventional boundary element method. For the cases there are no analytical solutions available, the solutions from the finite element method are given out as the referenced ones. The temperature fields obtained by the present method can approach to the finite element solutions perfectly when the coating is very thin. The present method is versatile for the temperature analysis of the isotropic, orthotropic and anisotropic coating-structures.
PubDate: 2015-09-04T23:48:34Z
- Abstract: Publication date: November 2015
- 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