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 [2800 journals] |
- 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
- Editorial Board
- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
PubDate: 2015-07-24T12:15:50Z
- Abstract: Publication date: October 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
- Incompressible smoothed particle hydrodynamics-moving IRBFN method for
viscous flow problems- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): D. Ngo-Cong , C.-D. Tran , N. Mai-Duy , T. Tran-Cong
We propose a novel numerical approach based on incompressible smoothed particle hydrodynamics and moving integrated radial basis function networks method, namely ISPH-MIRBFN, for solving incompressible viscous flow problems. In the ISPH method, the pressure is acquired from solving Poisson equation. In the present approach, the pressure Poisson equation is solved on a set of MIRBFN nodal points and the obtained results are then transferred to the SPH particles. The performance of the present method is investigated through several numerical examples including spin-down vortex, flows in a lid-driven closed-cavity and a lid-driven open-cavity with a prescribed bottom wall motion. Numerical results show that the proposed method reduces the spurious pressure fluctuations, yields a smoother pressure-field solution and maintains the computational efficiency when compared to the ISPH.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: October 2015
- Simulation of bubble dynamics near a plate with an aperture in a vertical
cylinder using a combined boundary element-finite difference method- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Mazyar Dawoodian , Abdolrahman Dadvand , Ali Nematollahi
Bubble dynamics near a perforated plate in a vertical cylinder is investigated using a combined boundary element-finite difference method. First, we determined the critical cylinder diameter for which the cylinder wall would not affect the bubble dynamics. Then for the case without cylinder wall effect, the effects of plate hole size and the bubble–hole distance were studied. Finally, the simultaneous effect of plate hole and cylinder diameter on the bubble behavior was evaluated. It was found that, for normalized bubble–hole distances H ′ ≤ 0.8 , there is only a liquid jet from the bottom surface of the bubble directing away from the hole, which becomes stronger as the normalized hole size d ′ is decreased. For H ′ ≥ 1.8 , there is only a liquid jet from the top surface of the bubble directing toward the hole, which becomes stronger as the hole size d ′ is decreased. For 0.8 < H ′ < 1.8 , there are two liquid jets from both the top and the bottom surface of the bubble, which depending on the bubble–hole distance, one of these jets becomes stronger as the hole size is decreased. In addition, smaller cylinder diameter would prolong the lifetime of the bubble.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: October 2015
- Modeling of fluid flow through fractured porous media by a single boundary
integral equation- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): M.N. Vu , S.T. Nguyen , M.H. Vu
The objective of this work is to provide theoretical materials for modelling two-dimensional fluid flow through an anisotropic porous medium containing intersecting curved fractures. These theoretical developments are suitable for numerical simulations using boundary element method and thus present a great advantage in mesh generation term comparing to finite volume discretization approaches when dealing with high fracture density and infinite configuration. The flow is modelled by Darcy’s law in matrix and Poiseuille’s law in fractures. The mass conservation equations, at a point on the fracture and an intersection point between fractures in the presence of a source or a sink, are derived explicitly. A single boundary integral equation is developed to describe the fluid flow through both porous media and fractures, i.e. the whole domain, which includes particularly the mass balance condition at intersection between fractures. Numerical simulations are performed to show the efficiency of this proposed theoretical formulation for high crack density.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: October 2015
- A direct BEM to model the temperature of gradient coils
- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Clemente Cobos Sánchez , Jose María Guerrero Rodriguez , Ángel Quirós Olozábal , Michael Poole
The temperature of the gradient coils is an important issue in the development of MRI scanners. Gradient coil performance must be maximised within temperature limits imposed by safety and system requirements. Here we present a model that determines the temperature distribution in gradient coils designed using an inverse boundary element method (IBEM). This forward approach is derived by applying a constant boundary element method (BEM) on a steady-state approximation of the heat equation and combined with the stream function associated to an electric current density. It can be used to estimate the temperature distribution, as well as, the location and temperature of hot spots in gradient coils of arbitrary shape. Several examples of the applicability of the proposed BEM model on different coil geometries and thermal characteristics are presented. In order to validate the method, a small prototype X-gradient coil was built and tested, and the temperature distribution experimentally measured. It was found to be in a good agreement to the temperature distribution simulated by the proposed numerical approach with a suitable choice of the thermal properties.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: October 2015
- Crack path prediction using the natural neighbour radial point
interpolation method- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): J.M.C. Azevedo , J. Belinha , L.M.J.S. Dinis , R.M. Natal Jorge
One of the most challenging problems in computational mechanics is the prediction of the crack propagation path. In this work, the Natural Neighbour Radial Point Interpolation Method (NNRPIM), an efficient meshless method, is extended to the field of fracture mechanics. Since the NNRPIM relies on the Natural Neighbour mathematical concept to obtain the integration mesh and establish the nodal connectivity, the NNRPIM only requires a computational nodal distribution to fully discretise the problem domain. The Radial Point Interpolators (RPI) are used to construct the NNRPIM interpolation functions. Taking advantage of the unique features of the NNRPIM, in this work, the crack propagation path is numerically simulated using an adapted crack path opening algorithm, in which the crack is iteratively extended in line segments. In each iteration, using the obtained stress field, the crack propagation direction is determined using the maximum circumferential stress criterion. Due to the flexibility of the natural neighbour concept, the increase of the domain discontinuities do not represent a numerical difficulty. In the end, several crack opening path benchmark examples are solved in order to show the efficiency of the proposed numerical approach.
PubDate: 2015-07-12T19:10:26Z
- Abstract: Publication date: October 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
- MPM simulations of high-speed and ultra high-speed machining of titanium
alloy (Ti–6Al–4V) based on fracture energy approach- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): X.Y. Gu , C.Y. Dong , J.L. Li , Z.Y. Liu , J.Y. Xu
Based on material point method (MPM), two dimensional (2D) orthogonal chip model on titanium alloy is established. Unlike finite element method (FEM) with seriously distorted meshes during the simulation of large strains such as the formation of shear band, the MPM is especially suitable for the numerical simulation of large deformation and high strain rate of metal material at high temperature. The generalized interpolation material point (GIMP) contact algorithm, Johnson–Cook model and Hillerborg׳s fracture energy criterion are used to simulate the cutting process on Ti–6Al–4V alloy. The parameters option and simulation process are first discussed, then the corresponding chip force and temperature field etc. are analyzed and compared with experimental data available. A good agreement has been found between them. Finally, the evolution of the temperature and cutting force are studied, and the effects of cutting speed and cutting feed rate on the chip morphology and cutting force are also investigated. It was the first time to simulate the serrated and discontinuous chips with the MPM and obtain relatively satisfactory results. The transition from serrated to discontinuous chips has been well captured in this paper.
PubDate: 2015-06-26T16:23:24Z
- Abstract: Publication date: October 2015
- Editorial Board
- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
PubDate: 2015-06-26T16:23:24Z
- Abstract: Publication date: September 2015
- Recovery of the temperature and the heat flux by a novel meshless method
from the measured noisy data- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Yao Sun , Fuming Ma
In this paper, we give an invariant method of fundamental solutions (MFS) for recovering the temperature and the heat flux. The invariant MFS is to keep a very basic natural property, which is called the invariance property under trivial coordinate changes in the problem description. The optimal regularization parameter is chosen by Morozov discrepancy principle. Then the reason for introducing the regularization is explained clearly by using the potential function. Three kinds of boundary value problems are investigated to show the effectiveness of this method with some examples. In especial, when the classical MFS does not give accurate results for some problems, it is shown that the proposed method is effective and stable. For each example, the numerical convergence, accuracy, and stability with respect to the number of source points, the distance between the pseudo and real boundary, and decreasing the amount of noise added into the input data, respectively, are also analyzed.
PubDate: 2015-06-18T14:53:37Z
- Abstract: Publication date: October 2015
- On the free terms of the dual BIE for N-dimensional Laplace problems
- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Jeng-Tzong Chen , Wen-Sheng Huang , Jia-Wei Lee , Hong-Ki Hong
Dual boundary integral equations for the N-dimensional Laplace problems with a smooth boundary are derived by using the contour approach surrounding the singularity. The potentials resulted from the four kernel functions in the dual formulation have different properties across the smooth boundary. For the generalization, we focus on the N-dimensional Laplace equation. The Hadamard principal value (H.P.V.) is derived naturally and is composed of two parts, the Cauchy principal value (C.P.V.) and an unbounded boundary term. The hypersingular integral is not a divergent integral since we can collect the C.P.V. and the unbounded term together. Besides, the weighting of the free term contributed by different kernels is also examined. Finally, a special case of the four-dimensional Laplace equation is implemented and the free term, for any dimension are obtained. The contributions of the free terms for the boundary normal derivative of potential due to the single (L kernel) and the double (M kernel) layer potentials are 1 / N and ( N − 1 ) / N , respectively. It is an interesting phenomenon that the hypersingular kernel contributes more than the singular kernel, and, in addition, the former also yields an unbounded boundary term.
PubDate: 2015-06-18T14:53:37Z
- Abstract: Publication date: October 2015
- The use of the constant vector basis functions for the magnetic field
integral equation- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Ali Deng , Liming Zhang , Minghong Wang
The magnetic field integral equation (MFIE) is widely used in the analysis of electromagnetic scattering problems for conducting objects. Usually, the MFIE is solved by the method of moments (MoM) using the Rao–Wilton–Glisson (RWG) basis functions. In this paper, a new kind of basis function which is named the piece-wise constant vector basis function is proposed and used to solve the MFIE by MoM. Definition of this kind of basis function is given. The calculation of the impedance matrix entries is presented in detail. This kind of basis function is then used for the solution of the MFIE for electromagnetic scattering problems. The radar cross section (RCS) results and the iterative property of both kinds of basis functions are presented. It is shown that the piece-wise constant vector basis functions give similar RCS results as those of the RWG basis functions. Particularly, when iterative solver is used to solve the resultant linear system, the solution scheme using the piece-wise constant vector basis functions iterates much faster than that using the RWG basis functions.
PubDate: 2015-06-11T07:14:38Z
- Abstract: Publication date: October 2015
- Effectiveness of nonsingular solutions of the boundary problems based on
Trefftz methods- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Adam Brański , Dorota Borkowska
The paper describes the application of the Trefftz complete and Kupradze functions in two variational formulations, i.e. the original formulation and inverse one, to the solution of the boundary value problems of the two-dimensional Laplace’s equation. In both formulations the solutions and weighting functions are assumed as the series or the separate function of Trefftz complete functions or Kupradze ones. One way or another all methods are named Trefftz methods. They all are nonsingular and, at the same time, they lead to the BEM. The relationship between the groups of Trefftz methods of the original and inverse formulations is perceived. Numerical experiments are conducted for several Laplace problems. The accuracy and simplicity of the methods are discussed. All methods gave comparable results, therefore they may be interchangeably applied to the solution of boundary problems. However the best method group is pointed out.
PubDate: 2015-06-06T21:47:15Z
- Abstract: Publication date: October 2015
- Construct ‘FE-Meshfree’ Quad4 using mean value coordinates
- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Yongtao Yang , Xuhai Tang , Hong Zheng
The present work uses mean value coordinates to construct the shape functions of a hybrid ‘FE-Meshfree’ quadrilateral element, which is named as Quad4-MVC. This Quad4-MVC can be regarded as the development of the ‘FE-Meshfree’ quadrilateral element with radial-polynomial point interpolation (Quad4-RPIM). Similar to Quad4-RPIM, Quad4-MVC has Kronecker delta property on the boundaries of computational domain, so essential boundary conditions can be enforced as conveniently as in the finite element method (FEM). The novelty of the present work is to construct nodal approximations using mean value coordinates, instead of radial basis functions which are used in Quad4-RPIM. Compared to the radial basis functions, mean value coordinates does not utilize any uncertain parameters, which enhances stability of numerical results. Numerical tests in this paper show that the performance of Quad4-RPIM becomes even worse than four-node iso-parametric element (Quad4) when the parameters of radial basis functions are not chosen properly. However, the performance of Quad4-MVC is stably better than Quad4.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: October 2015
- A novel linear triangular element of a three-dimensional displacement
discontinuity method- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Wan Cheng , Yan Jin , Hong Li , Mian Chen
Since only the boundary of the domain requires discretization, the boundary element method (BEM) is very efficient for the semi-infinite or infinite rock-related engineering problems, e.g., hydraulic fracturing in reservoir stimulation and rock cutting during excavation. A real fracture in the solid is usually of an arbitrary geometry in three dimensions, which usually requires a three-dimensional displacement discontinuity method (3D DDM) to determine the deformation and stress field in order to achieve reliable results. However, the use of 3D DDM with triangular elements is limited by the singularities of the integral either within or nearby the domain. In this paper, a novel linear triangular element with three nodes on its vertices is proposed. The analytical integral expressions of this linear triangular element are also theoretically derived. A solution procedure is also described which can be applied to determine the displacement and stress field around a three-dimensional fracture inside the infinite solid. The accuracy of these results are compared with the analytical solutions of the displacements and stresses induced by a pressurized penny-shaped. This procedure takes a shorter time and requires less elements than the usual constant DDM when achieving the same accuracy.
PubDate: 2015-05-31T21:12:53Z
- Abstract: Publication date: October 2015
- Fully nonlinear wave interaction with an array of truncated barriers in
three dimensional numerical wave tank- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Arash Abbasnia , Mahmoud Ghiasi
Wave transition due to coinciding with an array of truncated barrier is simulated by a fully nonlinear three dimensional potential Numerical Wave Tank (NWT). The potential theory is used to describe kinematics of the flow field and the isoparametric Boundary Element Method (BEM) is employed to solve the boundary value problem. The Mixed Eulerian–Lagrangian (MEL) approach and fourth order Runge–Kutta time integration applied for time-marching scheme to model the temporary and fully nonlinear free surface. At each time step, solution of Laplace equation in the Eulerian frame is applied to the fully nonlinear free surface conditions in the Lagrangian manner to achieve the new positions and the boundary value of fluid particles for the next time step. Normal flux of potential wave theory is specified on the inflow boundary to stimulate fluid field and to propagate the nonlinear wave along the tank. To minimize the reflected wave energy into the computational domain, two artificial sponger layers are adopted on the free surface at the both ends of the numerical wave tank. Accuracy and convergence of the present numerical procedure is conducted. Also, interaction between a near trapped mode array of truncated barriers and nonlinear input wave is simulated.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- Wave transmission by partial porous structures in two-layer fluid
- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): H. Behera , S. Koley , T. Sahoo
The present study deals with oblique surface gravity wave scattering and trapping by bottom-standing and surface-piercing porous structures of finite width in two-layer fluid. The problems are analyzed based on the linearized water wave theory in water of uniform depth. Both the cases of interface piercing and non-piercing structures are considered to analyze the effect of porosity in attenuating waves in surface and internal modes. Eigenfunction expansion method is used to deal with wave past porous structures in two-layer fluid assuming that the associated eigenvalues are distinct. Further, the problems are analyzed using boundary element method and results are compared with the analytic solution derived based on the eigenfunction expansion method. Efficiency of the structures of various configuration and geometry on scattering and trapping of surface waves are studied by analyzing the reflection and transmission coefficients for waves in surface and internal modes, free surface and interface elevations, wave loads on the structure and rigid wall. The present study will be of significant importance in the design of various types of coastal structures used in the marine environment for reflection and dissipation of wave energy at continental shelves dominated by stratified fluid which is modeled here as a two-layer fluid.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- Application of the method of fundamental solutions to 2D and 3D Signorini
problems- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Hongyan Zheng , Xiaolin Li
This paper presents an application of the method of fundamental solutions (MFS) for the numerical solution of 2D and 3D Signorini problems. In our application, by using a projection technique to tackle the nonlinear Signorini boundary inequality conditions, the original Signorini problem is transformed into a sequence of linear elliptic boundary value problems and then solved by the MFS. Convergence and efficiency of the present MFS is proved theoretically and verified numerically.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- The topology optimization design for cracked structures
- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Vahid Shobeiri
In this paper, the element free Galerkin method (EFG) is proposed for topology optimization of cracked structures using the bi-directional evolutionary structural optimization method (BESO). The mathematical formulation of the topology optimization is developed considering the nodal strain energy as the design variable and the minimization of compliance as the objective function. The element free Galerkin method is enriched by the crack-tip enrichment functions to increase the approximation accuracy near the crack-tip. The Lagrange multiplier method is employed to enforce the essential boundary conditions. Several numerical examples are presented to show the effectiveness of the proposed method. Many issues related to topology optimization of cracked structures such as the effects of crack size and location on the optimal topology are addressed in the examples. The common numerical instabilities do not exist in the results.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- One-stage Method of Fundamental and Particular Solutions (MFS-MPS) for the
steady Navier–Stokes equations in a lid-driven cavity- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): D. Nath , M.S. Kalra , P. Munshi
The coupled nonlinear steady state Navier–Stokes (N–S) equations in the stream function–vorticity form for a lid-driven cavity are solved by a one-stage Method of Fundamental Solutions (MFS) and the Method of Particular Solutions (MPS). This method has been earlier used for linear Poisson-type problems and has not been applied to coupled nonlinear equations. In this method the steady state N–S equations are first put in the form of two nonlinearly coupled Poisson equations and the solution is sought as the sum of their respective homogeneous and particular solutions. The homogeneous solution is obtained using the MFS and the particular solution is found with the help of Radial Basis Functions (RBFs). Both the operations are accomplished in a single stage. The nonlinear coupling of the N–S equations is tackled by iteration and successive relaxation. We find that the method is easy and effective when compared with the boundary element method (BEM) or the two-stage MFS-MPS, due to its meshless, singular integration free qualities and the single stage operation. The results are obtained for the moderate Reynolds numbers by varying the relaxation parameter. The convergence of MFS-MPS scheme for the present nonlinear problem is numerically demonstrated.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- An efficient FEM–BEM coupling method in wave radiation problem
analysis of oil platforms with complicated geometry- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Ke Wang , Zhi Chen
Real body model meshing and data preparation on body surface are two critical steps for the sea load calculation using boundary element method. In this study, an efficient procedure to solve these two issues is developed. The FEM type meshing model is used to construct real 3D platforms. Basic parameters such as mass and volume of platform are directly calculated from FEM model. A data extracting algorithm is developed to obtain the necessary data block on body surface of FEM model for the use of BEM method. A Double and Multiple Nodes Relocation Method (D&MNRM) is employed along sharp edges of FEM model to remove geometrical singularity. Based on the newly rearranged boundary information, shallow water Green function and higher-order boundary element method are used to solve the integral equations. A simple example for floating cylinder and a complex example for ETLP are used to validate the added mass and damping. The results show that the proposed method is efficient and can be extended to wave load analysis of any type of platforms with arbitrary shape.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- Efficient visibility criterion for discontinuities discretised by
triangular surface meshes- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): Nicholas Holgate , Grand Roman Joldes , Karol Miller
This study proposes a computationally efficient algorithm for determining which pairs of points among many predetermined pairs in three dimensions will maintain straight line visibility between one another in the presence of an arbitrary surface mesh of triangles. This is carried out in the context of meshless numerical methods with the goal of implementing near-real-time discontinuity propagation simulation. A brief overview is given of existing discontinuity modelling techniques for meshless methods. Such techniques necessitate determination of which key pairs of points (nodes and quadrature points) lack straight line visibility due to the discontinuity, which is proposed to be modelled with a surface mesh of triangles. The efficiency of this algorithm is achieved by allocating all quadrature points and surface mesh triangles to the cells of an overlayed three-dimensional grid in order to rapidly identify for each triangle an approximately minimal set of quadrature points whose nodal connectivities may be interrupted due to the presence of the triangle, hence eliminating most redundant visibility checking computations. Triangles are automatically split such that any size of overlayed cubic grid cells can be employed, and the parameters governing triangle splitting and binning have been examined experimentally in order to optimise the visibility algorithm.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- An element-free IMLS-Ritz framework for buckling analysis of FG–CNT
reinforced composite thick plates resting on Winkler foundations- Abstract: Publication date: September 2015
Source:Engineering Analysis with Boundary Elements, Volume 58
Author(s): L.W. Zhang , Z.X. Lei , K.M. Liew
An element-free based improved moving least squares-Ritz (IMLS-Ritz) method is proposed to study the buckling behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) resting on Winkler foundations. The first-order shear deformation theory (FSDT) is employed to account for the effect of shear deformation of plates. The IMLS is used for construction of the two-dimensional displacement field. We derive the energy functional for moderately thick plates. By minimizing the energy functional via the Ritz method, solutions for the critical buckling load of the functionally graded carbon nanotube (FG–CNT) reinforced composite plates on elastic matrix are obtained. Numerical experiments are carried out to examine the effect of the Winkler modulus parameter on the critical buckling loads. The influences of boundary condition, plate thickness-to-width ratio, plate aspect ratio on the critical buckling loads are also investigated. It is found that FG–CNT reinforced composite plates with top and bottom surfaces of CNT-rich have the highest critical buckling loads.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: September 2015
- An edge-based/node-based selective smoothed finite element method using
tetrahedrons for cardiovascular tissues- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Chen Jiang , Zhi-Qian Zhang , G.R. Liu , X. Han , W. Zeng
This paper presents a three-dimensional selective smoothed finite element method with edge-based and node-based strain smoothing techniques (3D-ES/NS-FEM) for nonlinear anisotropic large deformation analyses of nearly incompressible cardiovascular tissues. 3D-ES/NS-FEM owns several superior advantages, such as the robustness against the element distortions and superior computational efficiency, etc. To simulate the large deformation experienced by cardiovascular tissues, the static and explicit dynamic 3D-ES/NS-FEMs are derived correspondingly. Performance contest results show that 3D-ES/NS-FEM-T4 outperforms the standard FEM and other S-FEMs. Furthermore, this 3D-ES/NS-FEM-T4 is applied to analyze intact common carotid artery undergo mean blood pressure and passive inflation of anatomical rabbit bi-ventricles. The results are validated with the reference solutions, and also demonstrate that present 3D-ES/NS-FEM-T4 is a powerful and efficient numerical tool to simulate the large deformation of anisotropic tissues in cardiovascular systems.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- A 3D FEM/BEM code for ground–structure interaction: Implementation
strategy including the multi-traction problem- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Philippe Jean
The purpose of this paper is to describe the development of a 3D BEM–FEM code for ground–structure interaction. The technical choices and difficulties are reported. In particular, the multitraction problem has been implemented in 3D following a technique recently published in 2D for elastodynamics. It is showed that the separation of tractions is mandatory at corners but not at edges. The free surface and infinite interlayers are meshed by means of finite planes of varying dimensions. The paper also focuses on the validity of 2.5 approaches suggesting that in many situations the 2.5D model is well adapted. Reference situations are used for validation. The case of a pile joining a free surface and an interlayer between two different soils is described in detail. Finally computations are validated against measurements.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- Is the Burton–Miller formulation really free of fictitious
eigenfrequencies?- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Chang-Jun Zheng , Hai-Bo Chen , Hai-Feng Gao , Lei Du
This paper is concerned with the fictitious eigenfrequency problem of the boundary integral equation methods when solving exterior acoustic problems. A contour integral method is used to convert the nonlinear eigenproblems caused by the boundary element method into ordinary eigenproblems. Since both real and complex eigenvalues can be extracted by using the contour integral method, it enables us to investigate the fictitious eigenfrequency problem in a new way rather than comparing the accuracy of numerical solutions or the condition numbers of boundary element coefficient matrices. The interior and exterior acoustic fields of a sphere with both Dirichlet and Neumann boundary conditions are taken as numerical examples. The pulsating sphere example is studied and all fictitious eigenfrequencies corresponding to the related interior problem are observed. The reasons are given for the usual absence of many fictitious eigenfrequencies in the literature. Fictitious eigenfrequency phenomena of the Kirchhoff–Helmholtz boundary integral equation, its normal derivative formulation and the Burton–Miller formulation are investigated through the eigenvalue analysis. The actual effect of the Burton–Miller formulation on fictitious eigenfrequencies is revealed and the optimal choice of the coupling parameter is confirmed.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- DMLPG solution of the fractional advection–diffusion problem
- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): M. Ramezani , M. Mojtabaei , D. Mirzaei
The aim of this work is application of the direct meshless local Petrov–Galerkin (DMLPG) method for solving a two-dimensional time fractional advection–diffusion equation. This method is based on the generalized moving least squares (GMLS) approximation, and makes a considerable reduction in the cost of numerical integrations in weak forms. In fact, DMLPG shifts the integrals over the close form polynomials rather than the complicated MLS shape functions. Moreover, the values of integrals on subdomains with the same shapes are equal. Thus DMLPG is a weak-based meshless technique in the cost-level of collocation or integration-free methods. In time domain, a simple and suitable finite difference approximation is employed. Some examples show the advantages of the new method in comparison with the traditional MLPG method.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- Taylor series fast multipole boundary element method for solution of
Reissner׳s shear deformable plate bending problems- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Morcos F. Samaan , Mohammed E. Nassar , Youssef F. Rashed
In this paper, a new fast multipole BEM for the solution of Reissner׳s plates is presented. The suggested formulation is based on expressing the fundamental solutions in forms of potentials. Hence, these potentials and their relevant fundamental solutions are expanded by means of Taylor series expansions. Accordingly, the far field integrations are represented by these series expansions and summed for far clusters, whereas the near field integrations are kept to be computed directly. In the present formulation, equivalent collocations are based on both first and second shift collocations for kernels. By the present implementation of the fast multipole BEM in coupling with iterative solver (GMRES), the computational cost is rapidly reduced from O(N 3) in the conventional BEM to O(N log N) and O(N) for first and second shift respectively. Numerical examples are given to demonstrate the efficiency of the formulation against the conventional direct BEM. The accuracy of the results is traced by truncating Taylor series expansions to certain terms. It was demonstrated via numerical examples that three terms for both first shift and second shift are enough to produce sufficient accuracy with substantial reduction of solution time.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- Stress analysis for two-dimensional thin structural problems using the
meshless singular boundary method- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Yan Gu , Wen Chen , Bo Zhang
This short communication documents the first attempt to apply the singular boundary method (SBM) for the stress analysis of thin structural elastic problems. The troublesome nearly-singular kernels, which are crucial in the applications of the SBM to thin shapes, are dealt with efficiently by using a non-linear transformation technique. Three benchmark numerical examples, ranging from thin films, thin shell-like structures and multi-layer coating systems, are well studied to demonstrate the effectiveness of the proposed method. The advantages, disadvantages and potential applications of the method to thin structural problems, as compared with the boundary element (BEM) and finite element (FEM) methods, are also discussed.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015
- FEM SUPG stabilisation of mixed isoparametric BEMs: Application to
linearised free surface flows- Abstract: Publication date: October 2015
Source:Engineering Analysis with Boundary Elements, Volume 59
Author(s): Nicola Giuliani , Andrea Mola , Luca Heltai , Luca Formaggia
In finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.
PubDate: 2015-05-27T07:42:40Z
- Abstract: Publication date: October 2015