Engineering Analysis with Boundary Elements [SJR: 1.216] [H-I: 42] [1 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 0955-7997 Published by Elsevier [2801 journals] |
- Meshless method based on Shepard function and partition of unity for
two-dimensional crack problems- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Yongchang Cai, Lin Han, Longgang Tian, Lianyang Zhang
A new Meshless method based on Shepard function and Partition of Unity (MSPU) is proposed for calculating crack SIFs (Stress Intensity Factors) and simulating crack propagation. Link elements are employed to connect the adjacent block elements inside and around the circle of a crack tip, and to solve the challenging problem of imposing essential boundary conditions for meshless methods. The proposed MSPU possesses the merits of concise interpolation formulation and simple numerical implementation, and shows many advantages over existing meshless methods. In this work, the virtual crack closure technique (VCCT) is used to capture the crack tip SIFs, and the crack propagation is determined based on the maximum circumferential stress criterion. Numerical examples of representative cracking problems indicate that the MSPU is of high accuracy, good stability and sufficient convergence rate in fracture analyses, and has a wide application prospective.
PubDate: 2016-02-10T10:20:03Z
- Abstract: Publication date: April 2016
- A comparative analysis of local meshless formulation for multi-asset
option models- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Siraj-ul-Islam, Imtiaz Ahmad
A local meshless radial basis function collocation differential quadrature (LMRBFCDQ) is proposed for the numerical solution of a single and multi-asset option pricing PDE models arising in computational finance. Spatial discretization is performed by both local and a standard global meshless collocation procedures coupled with a set of different time integrators based on the forward Euler difference formula (FEDF), the fully Implicit method (FIM), the Crank–Nicolson method (CNM), the explicit Runge–Kutta method of order two (ERK2), the Crank–Nicolson Runge–Kutta method of order two (CNRK2), the fully Implicit Runge–Kutta method of order two (IRK2), the Runge–Kutta method of order four (RK4), the Embedded Runge–Kutta method (RK23). Operator splitting techniques like the ordinary operator splitting (OOS), the Lie–Trotter splitting, the additive splitting and the Strang splitting are also tested for time integration. The proposed hybrid schemes are the amalgamation of the meshless differential quadrature procedure and the finite difference approximations. Different types of radial basis functions (RBFs) i.e. the multiquadric (MQ), the inverse quadric (IQ) and the Gaussian (GA) are utilized for the spatial discretization of the PDE models. Numerical analysis of a range of computational finance related models are shown to demonstrate accuracy, efficiency and ease of implementation of the proposed meshless-finite difference procedure.
PubDate: 2016-02-10T10:20:03Z
- Abstract: Publication date: April 2016
- Automatic coupling of ABAQUS and a boundary element code for dynamic
elastoplastic problems- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Z.Y. Liu, C.Y. Dong
Based on a FE–BE coupling algorithm, an automatic implementation procedure for the coupling of the ABAQUS with a self-written linear elastic BE code is introduced for dynamic elastoplastic problems. User subroutine (UEL) is developed to enable the incorporation of the BE capabilities within the ABAQUS. Each closed BE domain in the mixed FEM/BEM model is defined as a finite super-element for which the effective stiffness and effective forces are generated by the BE code and hence can be assembled to the global FE formulation. The user can not only benefit from the powerful pre- and post-disposal functions of the ABAQUS, but also deal with systems with infinite extension by using the BEM as a supplement. Basic steps of the automatic coupling procedure are explained and necessary background information is provided. The analysis is conducted through several examples regarding 2D time domain responses. The results of the analysis document a very good agreement between the present solutions and analytical and other numerical results, confirming thus a successful implementation of the developed automatic coupling procedure.
PubDate: 2016-02-10T10:20:03Z
- Abstract: Publication date: April 2016
- A combination of the fast multipole boundary element method and Krylov
subspace recycling solvers- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Sören Keuchel, Jan Biermann, Otto von Estorff
The solution of the Helmholtz equation by the Boundary Element Method leads to a sequence of frequency dependent linear systems of equations, where each is typically solved independently. The Krylov Subspace Recycling algorithms, like the GCRO-DR and the GCROT, are based on the idea that the solutions of consecutive systems have similarities and the information of the previous cycle can be reused to accelerate the convergence. These solvers showed very good results for sparse matrices arising in the FEM and are now applied to the fully populated BEM matrices. Additionally, the solution of a single system of equations is accelerated by the Fast Multipole Method, which shows a mostly linear correlation between iterations and calculation time. Hence the newly proposed combination has a high potential of achieving a faster solution process. The 3D Fast Multipole Boundary Element Method additionally incorporates a Burton–Miller formulation and a halfspace formulation to be applicable to a wider range of engineering problems. The method is illustrated and discussed by two different numerical examples. The advantages and critical aspects of the combination are presented.
PubDate: 2016-02-10T10:20:03Z
- Abstract: Publication date: April 2016
- Buckling analysis of functionally graded thin plate with in-plane material
inhomogeneity- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Fuyun Chu, Jianzhang He, Lihua Wang, Zheng Zhong
Buckling analysis of functionally graded material (FGM) thin plates with in-plane material inhomogeneity is investigated based on radial basis functions associated with collocation method. No background mesh is required in the discretization and solution which makes it a truly meshfree method. Two independent problems raised in the buckling analysis are studied according to the procedure. First, radial basis collocation method (RBCM) is employed to yield the non-uniform pre-buckling stresses by solving a 2D plane stress problem. Afterwards, based on Kirchhoff assumption and employing the predetermined non-uniform pre-buckling stresses, Hermite radial basis function collocation method (HRBCM) is proposed to study the buckling loads of FGM thin plates with in-plane material inhomogeneity. Compared to an over-determined system resulting from the conventional RBCM, HRBCM introducing more degrees of freedom on the boundary nodes can lead to a determined system for the eigenvalue problem. Convergence and comparisons studies with analytical solutions demonstrate that the proposed method possesses high accuracy and exponential convergence. Numerical examples illustrate that the material inhomogeneity has considerable effects on the buckling loads and mode shapes of thin plates. As a result, material inhomogeneity can be exploited to optimize the in-plane stress distribution and prevent the buckling of thin plates.
PubDate: 2016-02-10T10:20:03Z
- Abstract: Publication date: April 2016
- Solving a scattering problem in near field optics by a least-squares
method- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Tian Luan, Yao Sun
Motivated by the Trefftz method, a numerical algorithm is proposed based on the least-squares technique for a scattering problem in near field optics. Fundamental solutions and plane wave functions are used to approximate the scattering field toward infinity and the local properties, respectively. Whilst evanescent wave functions are introduced to enrich the plane wave functions to capture the sub-wavelength feature of the field. The continuity across the element boundaries is enforced by minimizing a simple quadratic functional. The method needs not truncate the domain and could obtain high accuracy with even coarse mesh by increasing the number of basis functions. Numerical experiments are also presented to show the effectiveness of the approach.
PubDate: 2016-02-10T10:20:03Z
- Abstract: Publication date: April 2016
- Editorial Board
- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
PubDate: 2016-01-31T09:21:56Z
- Abstract: Publication date: March 2016
- A study concerning the solution of advection–diffusion problems by
the Boundary Element Method- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): C.L.N. Cunha, J.A.M. Carrer, M.F. Oliveira, V.L. Costa
This work is concerned with the development of two Boundary Element Method formulations for the solution of the advection–diffusion problem in two-dimensions. Beside the discussion concerning the development of the BEM formulations, it is important to point out that the problem to be solved has become very important nowadays: if one bears in mind that the advection–diffusion equation describes problems such as pollutants dispersion, then the development of formulations capable of dealing with this social and environmental problem is welcome. In order to verify the accuracy of the proposed formulations, two examples are presented. The numerical results are compared with the analytical solution, when available, and with the results from the Finite Element Method.
PubDate: 2016-01-31T09:21:56Z
- Abstract: Publication date: April 2016
- Effect of surface slip on the relative motion and collision efficiency of
slippery spherical particles- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): C. Pozrikidis
The motion of a pair of spherical particles suspended in a viscous fluid is considered under conditions of Stokes flow. The particle surfaces allow the fluid to slip according to the Navier–Maxwell–Basset law. Batchelor and Green׳s mobility functions determining the relative particle motion during interception are computed with high accuracy using a boundary-integral method, and their dependence on the slip coefficient is discussed. The numerical results confirm that particle collision in the presence of surface slip occurs with a finite impact velocity. As the slip coefficient decreases, and thereby the particle surfaces become increasingly slippery, the collision efficiency in uniaxial elongational and simple shear flow increases monotonically from zero for no-slip surfaces to a finite limit for perfectly slippery surfaces.
PubDate: 2016-01-31T09:21:56Z
- Abstract: Publication date: April 2016
- A new type of high-order elements based on the mesh-free interpolations
- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Dean Hu, Yigang Wang, Haifei Zhan, Shuyao Long
We propose a new type of high-order elements that incorporates the mesh-free Galerkin formulations into the framework of Finite Element Method. Traditional polynomial interpolation is replaced by mesh-free interpolations in the present high-order elements, and the strain smoothing technique is used for integration of the governing equations based on smoothing cells. The properties of high-order elements, which are influenced by the basis function of mesh-free interpolations and boundary nodes, are discussed through numerical examples. It can be found that the basis function has significant influence on the computational accuracy and upper–lower bounds of energy norm, when the strain smoothing technique retains the softening phenomenon. This new type of high-order elements shows good performance when quadratic basis functions are used in the mesh-free interpolations and present elements prove advantageous in adaptive mesh and nodes refinement schemes. Furthermore, it shows less sensitive to the quality of element because it uses the mesh-free interpolations and obeys the Weakened Weak (W2) formulation as introduced in Liu (2010) [3,5].
PubDate: 2016-01-25T08:48:46Z
- Abstract: Publication date: April 2016
- Complex variable moving Kriging interpolation for boundary meshless method
- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Sanshan Tu, Leilei Dong, Hongqi Yang, Yi Huang
In this paper, we proposed the complex variable moving Kriging interpolation (CVMKI) to approximate functions on two-dimensional (2D) boundaries. The CVMKI is based on complex variable theory and the moving Kriging interpolation (MKI). It requires no curvilinear coordinate, and can construct shape functions possessing Kronecker delta function property and partition of unity property. Further, the complex variable boundary node method (CVBNM) is proposed for potential problems based on CVMKI and boundary integration equation (BIE). CVBNM is an efficient and accurate method that can directly impose the boundary conditions. Three 2D example problems are presented to verify the accuracy and efficiency of CVBNM.
PubDate: 2016-01-25T08:48:46Z
- Abstract: Publication date: April 2016
- A dual reciprocity multiwavelet Galerkin method for the numerical solution
of Poisson׳s equation- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Jianxin Luo, Rui Qiao, Jing Li
A dual reciprocity multiwavelet Galerkin method is developed for the solution of Poisson׳s equation in this paper, which combines the dual reciprocity boundary element method (DRBEM) and the multiwavelet Galerkin method (MGM). The DRBEM is used to transform the domain integral in the boundary element formulation of Poisson׳s equation into the boundary of the domain, which is based on compactly supported positive definite radial basis function. Then, the MGM is employed for solving the resulting boundary integral equation, in which Alpert multiwavelets are employed to construct the trial and test functions of Galerkin variational formulation. Because of the use of multiwavelets, the resulting system matrix can be approximated by a sparse matrix. Compared to the DRBEM based on radial basis functions, the present method reduces the memory spaces and computational costs of the system matrix significantly. Numerical results show the efficiency of the present method.
PubDate: 2016-01-21T08:42:09Z
- Abstract: Publication date: April 2016
- Electromagnetic scattering analysis using nonconformal meshes and
monopolar curl-conforming basis functions- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Liming Zhang, Ali Deng, Yiqing Zhang, Xianzhu Meng, Zengtao Lv
A scheme for electromagnetic scattering analysis of perfect electric conducting (PEC) objects using nonconformal meshes is developed in this paper. The difference of the integral operators for the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) are analyzed in detail. It is shown theoretically that basis functions used to expand the surface currents for the MFIE may not necessarily be divergence-conforming. The nonconformal meshes and monopolar n × RWG basis functions are used together to solve the MFIE. Details for the implementation of the proposed method are presented. The method is verified through the numerical results for electromagnetic scattering analysis from several PEC objects. It is shown that this method is a suitable choice for using nonconformal meshes when solving electromagnetic scattering problems with the MFIE.
PubDate: 2016-01-21T08:42:09Z
- Abstract: Publication date: April 2016
- An extended exponential transformation for evaluating nearly singular
integrals in general anisotropic boundary element method- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Yan Gu, Houqi Dong, Hongwei Gao, Wen Chen, Yaoming Zhang
The exponential transformation is an efficient technique for the accurate numerical evaluation of nearly singular integrals which arise in the boundary element method (BEM). It was shown that this transformation could improve the accuracy of evaluating such integrals by several orders of magnitude. Here, this transformation is extended in a more flexible fashion to allow the evaluation of nearly singular integrals which arise in general anisotropic BEM formulation, with a high degree of accuracy. A major advantage of the new method is its ease of implementation and applicability to a wide class of integrals. Three benchmark test integrals, ranging from nearly weakly, nearly strongly and nearly hyper-strongly singular integrals, are well studied to demonstrate the accuracy and efficiency of the proposed method.
PubDate: 2016-01-21T08:42:09Z
- Abstract: Publication date: April 2016
- A solution strategy for non-linear implicit BEM formulation using a
unified constitutive modelling framework- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): R.G. Peixoto, F.E.S. Anacleto, G.O. Ribeiro, R.L.S. Pitangueira, S.S. Penna
A new solution strategy for the non-linear Implicit Formulation of the Boundary Element Method is presented. Such strategy is based on a decomposition of the strain increment variation vector in two parts: one associated to the cumulative external loads and another associated to the current unbalanced vector, obtained from the difference of the first part and the calculated internal strain field distribution, during the iterative process. This approach makes the algorithm generic enough to deal with different control methods that governs the progression of the non-linear analysis. Also, a unified constitutive modelling framework for a single loading function is used to provide the material constitutive informations required by the solution strategy, which permits the implementation of a very comprehensive series of models in an independent way. However, only local models were treated. To demonstrate the efficiency and versatility of the methodology, some numerical examples are presented.
PubDate: 2016-01-17T14:04:48Z
- Abstract: Publication date: March 2016
- Fast method of approximate particular solutions using Chebyshev
interpolation- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): A.R. Lamichhane, D.L. Young, C.S. Chen
The fast method of approximate particular solutions (FMAPS) is based on the global version of the method of approximate particular solutions (MAPS). In this method, given partial differential equations are discretized by the usual MAPS and the determination of the unknown coefficients is accelerated using a fast technique. Numerical results confirm the efficiency of the proposed technique for the PDEs with a large number of computational points in both two and three dimensions.
PubDate: 2016-01-17T14:04:48Z
- Abstract: Publication date: March 2016
- A new approximate method for an inverse time-dependent heat source problem
using fundamental solutions and RBFs- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): M. Amirfakhrian, M. Arghand, E.J. Kansa
This paper presents a meshless numerical scheme to solve the inverse heat source time dependent problem. Fundamental solutions of heat equations and radial basis functions (RBFs) are used to obtain a numerical solution. Since the coefficient matrix may be ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulting system of linear equations. Therefore, the generalized cross-validation (GCV) criterion is applied to choose a regularization parameter. The accuracy and efficiency of the proposed method is illustrated by some numerical examples.
PubDate: 2016-01-17T14:04:48Z
- Abstract: Publication date: March 2016
- A partition-of-unity based ‘FE-Meshfree’ triangular element
with radial-polynomial basis functions for static and free vibration
analysis- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Yongtao Yang, Dongdong Xu, Hong Zheng
A new ‘FE-Meshfree’ three-node triangular element (Trig3-RPIM) is developed based on the partition of unity (PU) concept. The Trig3-RPIM element employs the shape function of classical three-node triangular element (Trig3) to construct the PU and the radial-polynomial basis function which is free from the possible singularity of the moment matrix to construct the nodal approximation. The Trig3-RPIM element synergizes the individual strengths of finite element method and meshfree method. Moreover, it is free from the linear dependence problem which otherwise cripples many of the PU based finite elements. Several linear, nonlinear and free vibration test problems are solved and the performance of the element is compared with those of the well-known three-node triangular element (Trig3) and four-node iso-parametric quadrilateral element (Quad4). The results show that, for regular meshes, the performance of the element is superior to those of Trig3 and Quad4 elements. For distorted meshes, the present element has better mesh-distortion tolerance than Trig3 and Quad4 elements.
PubDate: 2016-01-17T14:04:48Z
- Abstract: Publication date: April 2016
- A new type of high-accuracy BEM and local stress analysis of real beam,
plate and shell structures- Abstract: Publication date: April 2016
Source:Engineering Analysis with Boundary Elements, Volume 65
Author(s): Zhenhan Yao
A high-accuracy BEM (HABEM) presented by the author is briefly summarized, and then applied to the local stress analysis (LSA) of real clamped thin-plate beam, in 2D and 3D models. The simple examples in 2D have shown the process of discretization error reduction via mesh refinement under guidance of error indicator. The numerical results have shown the feasibility and high accuracy of the presented HABEM. On the other hand the results obtained are valuable for the strength evaluation in engineering. The corresponding 3D HABEA has also been presented. The results agree with the corresponding 2D analysis. But the complexity of the 3D HABEA is much higher than 2D one. The advantage of dimension reduction is also the major advantage of BEM over FEM. For 3D HABEM an improved equal-accuracy Gaussian quadrature for regular including nearly singular integrals, and that for weakly singular integrals is presented and numerically verified in detail. For the local stress analysis of real beam, plate and shell structures the 3D HABEA is necessary, in such case it is encountered with a large-scale BEA problem, and fast algorithm should be introduced. Such approach is defined as high-performance BEM, which will be a new research field in future.
PubDate: 2016-01-17T14:04:48Z
- Abstract: Publication date: April 2016
- PDE centres enhancement in the Localized Regular Dual Reciprocity Method
- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): N. Caruso, M. Portapila, H. Power
In this work we present an improvement of the Localized Regular Dual Reciprocity Method (LRDRM). LRDRM is an integral domain decomposition method with two distinguishing features, the boundary conditions are imposed at the local interpolation level and all the calculated integrals are regular. In this work we present an enhancement of this method where the interpolation functions themselves satisfy the partial differential equation to be solved. Results for 1D and 2D convection‐diffusion, 2D Helmholtz and 2D Poisson equations are presented, attaining accuracies two to three orders of magnitude higher than the original version of the LRDRM.
PubDate: 2016-01-13T13:51:46Z
- Abstract: Publication date: March 2016
- Analysis of landslide-generated impulsive waves using a coupled DDA-SPH
method- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Wei Wang, Guang-qi Chen, Hong Zhang, Su-hua Zhou, Shu-guang Liu, Yan-qiang Wu, Fu-song Fana
Large impulsive waves generated by slope failures and a subsequent landslide in a reservoir area may lead to serious damage to the dam, shoreline properties and lives. Therefore, analysis of landslide-generated impulsive waves is of significant importance for hazard prevention and reduction. There are three key points for analyzing this problem: (i) the landslide run-out, (ii) the free surface flow and (iii) the landslide-water interaction process. The Discontinuous Deformation Analysis (DDA) method was previously developed to investigate discontinuous block movements, while the Smoothed Particle Hydrodynamics (SPH) method was used mostly to model free surface flow. However, the solid–fluid interaction is seldom considered in the respective fields, which greatly restricts their applications. For this reason, the coupled DDA-SPH method was proposed in this study to solve the solid–fluid interaction problem. To validate this approach, this study considered a wedge sliding along an inclined plane and interacting with the water body. The corresponding Heinrich’s experimental results were adopted to evaluate the accuracy of the coupled method in modeling the landslide movement and wave profile, proving that the landslide motion and wave profiles could be captured accurately by the coupled method. Finally, the effect of the governing parameters on the wave amplitude was discussed.
PubDate: 2016-01-13T13:51:46Z
- Abstract: Publication date: March 2016
- Elastoplastic analysis of Reissner׳s plates by the boundary element
method- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): S.R.C. Oliveira, V.J. Karam
A new formulation for plate bending elastoplastic analysis by the Boundary Element Method (BEM) using Reissner׳s theory is presented in this work. The classical theory of plasticity is considered, with an initial strain formulation and using von Mises׳s yield criterion. The basic governing equations are first presented, in which plastic strains due to bending are included. Integral equations are presented for displacements at internal and boundary points and also for stress resultants at internal points, including the expressions for the new tensors and free terms. Numerical implementation is performed by employing quadratic boundary elements and constant triangular internal cells, both with linear geometry. An incremental–iterative process is used in order to solve the elastoplastic equations. Some numerical examples are presented at the end of the work and the corresponding results are validated by comparing them with results of other works, obtained from numerical or analytical methods.
PubDate: 2016-01-13T13:51:46Z
- Abstract: Publication date: March 2016
- Grid-based volume integration for elasticity
- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Dmitry Petrov, Y. Deng, L.J. Gray, Wenjing Ye
A regular grid direct volume integral method has recently been proposed for domain integrals stemming from Poisson or nonlinear Laplace problems. The volume integral is exactly decomposed into a non-singular boundary integral, plus a remainder volume integral that can be accurately evaluated using a regular grid overlaying the problem domain. For elasticity, achieving the analogous decomposition requires the ‘Galerkin vector’ H that satisfies E ( H ) = U , where E is the elasticity equation and U the Kelvin fundamental solution. Herein, Fourier transforms are employed to derive formulas for H and the corresponding traction kernel T H , for both two and three dimensional isotropic elasticity. The three dimensional formulas, and their numerical implementation, are validated by solving relatively simple body force elasticity problems with known solutions. Results for a fast (P-FFT) boundary integral formulation are also presented.
PubDate: 2016-01-09T13:33:33Z
- Abstract: Publication date: March 2016
- Improved finite integration method for partial differential equations
- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): M. Li, Z.L. Tian, Y.C. Hon, C.S. Chen, P.H. Wen
Based on the recently developed finite integration method (FIM) for solving one-dimensional partial differential equations by using the trapezoidal rule for numerical quadrature, we improve in this paper the FIM with an alternative extended Simpson׳s rule in which the Cotes and Lagrange formulas are used to determine the first order integral matrix. The improved one-dimensional FIM is then further extended to solve two-dimensional problems. Numerical comparison with the finite difference method and the FIM (Trapezoidal rule) are performed by several one- and two-dimensional real application including the Poisson type differential equations and plate bending problems. It has been shown that the newly revised FIM has made significant improvement in terms of accuracy compare without much sacrifice on the stability and efficiency.
PubDate: 2016-01-09T13:33:33Z
- Abstract: Publication date: March 2016
- A comprehensive study on Green׳s functions and boundary integral
equations for 3D anisotropic thermomagnetoelectroelasticity- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Iaroslav Pasternak, Roman Pasternak, Heorhiy Sulym
The paper derives Somigliana type boundary integral equations for 3D thermomagnetoelectroelasticity of anisotropic solids. In the absence of distributed volume heat and body forces these equations contain only boundary integrals. Besides all of the obtained terms of integral equations are to be calculated in the real domain, which is advantageous to the known equations that can contain volume integrals or whose terms should be calculated in the mapped temperature domain. All kernels of the derived integral equations and the 3D thermomagnetoelectroelastic Green׳s function for a point heat are obtained explicitly based on the Radon transform technique. Verification of the obtained equations and fundamental solutions is provided.
PubDate: 2016-01-09T13:33:33Z
- Abstract: Publication date: March 2016
- Analysis of two methods based on Galerkin weak form for fractional
diffusion-wave: Meshless interpolating element free Galerkin (IEFG) and
finite element methods- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Mehdi Dehghan, Mostafa Abbaszadeh, Akbar Mohebbi
In this paper we apply a finite element scheme and interpolating element free Galerkin technique for the numerical solution of the two-dimensional time fractional diffusion-wave equation on the irregular domains. The time fractional derivative which has been described in the Caputo׳s sense is approximated by a scheme of order O ( τ 3 − α ) , 1 < α < 2 , and the space derivatives are discretized with finite element and interpolating element free Galerkin techniques. We prove the unconditional stability and obtain an error bound for the two new schemes using the energy method. However we would like to emphasize that the main aim of the current paper is to implement the Galerkin finite element method and interpolating element free Galerkin method on complex domains. Also we present error estimate for both schemes proposed for solving the time fractional diffusion-wave equation. Numerical examples demonstrate the theoretical results and the efficiency of the proposed scheme.
PubDate: 2016-01-01T11:51:06Z
- Abstract: Publication date: March 2016
- Dual boundary element analysis of fatigue crack growth, interaction and
linkup- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): E. Santana, A. Portela
Multiple-site and widespread fatigue damage have been an issue to the aircraft and construction industry for a long period. Structural components develop cracks at several locations which grow with crack paths that are difficult to predict. When two cracks approach one another, their stress fields influence each other leading to an enhancing or shielding effect which depends on the position and orientation of the cracks. Since there are no generalized analytical methods for predicting crack stress fields, simulation of multiple-crack growth is an important and challenging task which is still an evolving area of research. This paper describes a two-dimensional application of the dual boundary element method (DBEM) to the analysis of mixed-mode multiple-crack growth in linear elastic fracture mechanics, under fatigue loading. The crack-growth process is simulated with an incremental multiple-crack extension analysis based on the maximum principal stress criterion. For each increment of the analysis, in which crack extensions are modelled with new straight boundary elements, the DBEM is applied to perform a single-region stress analysis of the cracked structure and the J-integral is used to compute the stress intensity factors. The incremental analysis is based on a prediction–correction technique that defines, in each increment of the analysis, the direction and the extension of the multiple interacting cracks, thus taking into account the discreteness of the analysis and ensuring that the requirement of the path uniqueness is satisfied. Based on the ligament yield criterion which assumes that when the plastic zones of two adjacent cracks touch each other, the ligament between the cracks fails and the cracks coalesce, plates with multiple-site damage can be analysed. The fatigue life and residual strength of the structure are introduced as a post-processing procedure on the results of the multiple-crack growth. Results of this incremental analysis are presented for several geometries with multiple-site damage, demonstrating the accuracy and efficiency of the strategies adopted in the analysis.
PubDate: 2016-01-01T11:51:06Z
- Abstract: Publication date: March 2016
- A multiple scale Trefftz method for the Laplace equation subjected to
large noisy boundary data- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Yung-Wei Chen
In this paper, we develop an equal norm based multiple scale Trefftz method (MSTM) to solve the Laplace equation subjected to large noisy boundary data. When the complicated geometry with noisy perturbation and ill-conditioned system by using higher-order T-complete functions are encountered, numerical convergence is hard to reach. To tackle these complicated problems, we adopt the MSTM combined with the vector regularization method (VRM) to eliminate the higher-order numerical oscillation phenomena. Due to the inclusion of the characteristic length in the scheme, the ill-posed problem of the constructed Vandermonde matrix is reduced, and the number of terms in the T-complete functions can be increased to stabilize the numerical calculations. More importantly, the proposed approach can successfully overcome the ill-posedness of severely ill-conditioned matrices appearing in linear equations and thus, obtain the accurate numerical solution under a serious noise disturbance. The results reveal that the method presents a simple and stable way to deal with the highly ill-posed problem.
PubDate: 2015-12-28T11:39:09Z
- Abstract: Publication date: March 2016
- An improved Moving Kriging-based meshfree method for static, dynamic and
buckling analyses of functionally graded isotropic and sandwich plates- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Chien H. Thai, Vuong N.V. Do, H. Nguyen-Xuan
A meshfree method with a modified distribution function of Moving Kriging (MK) interpolation is investigated. This method is then combined with a high order shear deformation theory (HSDT) for static, dynamic and buckling analyses of functionally graded material (FGM) isotropic and sandwich plates. A meshfree method uses the normalized form of MK interpolation under a new quartic polynomial correlation to build the basis shape functions in high order approximations. The Galerkin weak form is used to separate the system equations which is numerically solved by meshfree method. A rotation-free technique extracted from isogeometric analysis is introduced to eliminate the degrees of freedom of slopes. Then, the method retains a highly computational effect with a lower number of degrees of freedom. In addition, the requirement of shear correction factors is ignored and the traction free is at the top and bottom surfaces of FGM plates. Various thickness ratios, boundary conditions and material properties are studied to validate the numerical analyses of the rectangular and circular plates. The numerical results show that the present theory is more stable and well accurate prediction as compared to three-dimensional (3D) elasticity solution and other meshfree methods in the literature.
PubDate: 2015-12-24T11:14:54Z
- Abstract: Publication date: March 2016
- DRBEM solutions of Stokes and Navier–Stokes equations in cavities
under point source magnetic field- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): P. Senel, M. Tezer-Sezgin
This paper describes an iterative dual reciprocity boundary element method (DRBEM) for the solutions of Stokes and Navier–Stokes equations in cavities under the effect of an external point source magnetic field placed very close to the bottom. The fluid is viscous, incompressible and electrically non-conducting but magnetizable, and the flow is steady, laminar and fully developed. Both the Stokes and Navier–Stokes equations are solved in terms of velocity and pressure of the fluid by using DRBEM. Pressure boundary conditions are obtained through momentum equations by approximating pressure gradients with finite differences. All the space derivatives are computed by using DRBEM coordinate matrix. The results of Stokes flow under point magnetic source in lid-driven square and circular cavities are presented and compared. The three-dimensional flow of an incompressible fluid is considered in the 2D rectangular cross-section of a long duct with and without a moving top-lid imposed to a point magnetic source. The axial velocity is also computed due to the pressure gradient given in the axial direction. The obtained results for varying magnetic number show that the flow is appreciably influenced by the presence of the magnetic field.
PubDate: 2015-12-24T11:14:54Z
- Abstract: Publication date: March 2016
- Waves induced by a two-dimensional foil advancing in shallow water
- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): G.D. Xu, Q. Meng
The waves generated by a two-dimensional (2D) foil moving in shallow water at subcritical, super-critical and hyper-critical speeds have been investigated. The velocity potential theory is adopted to prescribe the flow with vortex shedding. The fluid-structure interaction, as well as the fully nonlinear free surface movement, is tackled by the mixed-Euler-Lagrangian method through a time stepping scheme. It has been observed that upstream solitary waves emerge when the depth Froude number F H = U ( g H ) − 0.5 approaching the critical value ( ≈ 1.0 ), where U is the speed of the foil, g is the gravitational acceleration and H is the depth of quiescent water. The transition from sub-critical to the super-critical state is studied. As F H keeps increasing to a hyper-critical state, a single upstream soliton is caught up with by the foil. When the foil travels with a negative attack angle at hyper-critical speed, a ‘reversed soliton’ has been found.
PubDate: 2015-12-24T11:14:54Z
- Abstract: Publication date: March 2016
- On the Green’s functions for a two-phase soft electroactive medium
subjected to biasing fields- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Yilan Huang, Guozhan Xia, Weijian Zhou, Weiqiu Chen
We consider the problem of a point force and/or a point charge applied in the interior of an infinite two-phase medium, which consists of two perfectly or smoothly bonded soft electroactive half-spaces. Both two half-spaces are initially subjected to an arbitrary multi-directional stretch and a biasing electric field. A linearized incremental theory is adopted to describe the deformation caused by the point force and/or point charge. A concise general solution to the governing equations of the perturbed infinitesimal elastic and electric fields is employed. By the trial-and-error method, the analytical expressions for the quasi-harmonic functions in the general solution are constructed explicitly, but with several undetermined constants. These constants can be easily determined from the conditions on the perfect or smooth interface as well as some other considerations. As special cases of the present two-phase Green’s functions, the generalized Mindlin solution and Lorentz solution for an electroactive half-space subjected to an initial biasing field are discussed. The more specified generalized Boussinesq solution and Cerruti solution are also given in the appendix.
PubDate: 2015-12-24T11:14:54Z
- Abstract: Publication date: March 2016
- Editorial Board
- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
PubDate: 2015-12-20T10:59:30Z
- Abstract: Publication date: February 2016
- Cohesive crack propagation modelling in wood structures using BEM and the
Tangent Operator Technique- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Sérgio Gustavo Ferreira Cordeiro, Edson Denner Leonel
Mechanical collapse in a wide range of materials occurs due to the growth of internal discontinuities. Such discontinuities, commonly denominated cracks, are explained consistently according to fracture mechanics theory. When the fracture process zone in front of the crack tip is sufficiently large, nonlinear mechanical effects appear and cannot be neglected. To allow a robust and general mechanical representation of such nonlinear phenomena, numerical techniques are required. In this context, this study presents an efficient nonlinear solution technique coupled to algebraic Boundary Element Method (BEM) equations to model the crack propagation process in anisotropic quasi-brittle bodies, using wood as a particular case. This nonlinear technique, called the Tangent Operator (TO), incorporates the derivative set of constitutive nonlinear laws into the algebraic BEM equations. The proposed nonlinear formulation was applied in mechanical analyses involving multi-crack growth and crack propagation in anisotropic media. The numerical results obtained by BEM/TO were compared with experimental and numerical responses available in the literature. In addition to the accuracy observed, the TO demonstrated faster convergence when compared with the classical approach.
PubDate: 2015-12-20T10:59:30Z
- Abstract: Publication date: March 2016
- Analytical transformation of volume integral for the time-stepping BEM
analysis of 2D transient heat conduction in anisotropic media- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Y.C. Shiah, Yu-Cheng Chaing, Toshiro Matsumoto
Despite the extensive study of the transient heat conduction analysis for isotropic media by the boundary element method (BEM), its relevant researches in transient heat conduction in anisotropic media still remain relatively scarce indeed. In the time-stepping BEM scheme for the transient heat conduction, the transient effect reveals itself as an additional volume integral that conventionally requires domain discretization for direct integration. However, such domain discretization will destroy the BEM׳s most distinctive nature that only the boundary needs to be discretized. In this paper, the domain integral is analytically transformed to the boundary so that the BEM׳s nature of boundary discretization is completely restored. Moreover, the domain mapping technique is combined with this transformed time-stepping scheme to treat the 2D transient heat conduction in anisotropic media. Without any internal treatments or special approximations like in other schemes, the transformed time-stepping scheme can be applied to effectively solve the problem of transient heat conduction in anisotropic media.
PubDate: 2015-12-20T10:59:30Z
- Abstract: Publication date: March 2016
- Mesh-free simulation of liquid sloshing subjected to harmonic excitations
- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Nan-Jing Wu, Shih-Chun Hsiao, Han-Lun Wu
In this study a mesh-free numerical model for simulating 3-D free-surface potential flows is established. A time-marching scheme in Lagrangian aspect is chosen for the specification of boundary conditions on the moving and deforming free surface while a local polynomial collocation method is applied for solving the Laplace equation at each time step. This collocation method is employed because the partial derivatives of the solution are calculated accurately. The trajectory of each free-surface node can thus be predicted precisely due to the accurate estimation of the partial derivatives of velocity potential, which represent components of the velocity vector at that specific node. The numerical model is applied to the simulation of free surface waves by the liquid sloshing in rectangular, square and cylindrical swaying tanks. Fairly good agreements are observed in the comparison of numerical results with experimental data. Because the partial derivatives of the velocity components are accurately calculated, the pressure distribution in the domain can also be acquired by solving the pressure Poisson equation separately.
PubDate: 2015-12-20T10:59:30Z
- Abstract: Publication date: March 2016
- Localized radial basis function scheme for multidimensional transient
generalized newtonian fluid dynamics and heat transfer- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): D.L. Young, S.P. Hu, C.S. Wu
The local radial basis function (RBF) scheme is developed to simulate 2D and 3D heat transfer and flow dynamics of generalized Newtonian fluids (GNF). The local RBF scheme is a meshless numerical method based on radial basis functions with localized technique. The procedure of localization reduces the computational cost more efficiently than the traditional global RBF method. This meshless method does not require mesh generation, numerical integration and only needs point collocation. Besides, it is very easy to interpolate physical values and its derivatives everywhere in the domain. We consider one isothermal and three non-isothermal multidimensional transient GNF fluid and heat problems in this paper. The dynamic viscosity of the GNF is specified as two different models: the power law model (temperature independent) or Cross model (temperature dependent). The viscous heating is also considered in this work. Numerical results show that the local RBF scheme is stable and accurate as far as the four tested cases are concerned.
PubDate: 2015-12-20T10:59:30Z
- Abstract: Publication date: March 2016
- Numerical analysis of SH wave field calculations for various types of a
multilayered anisotropic inclusion- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Jungki Lee, Hyechang Lee, Hogwan Jeong
The Parallel Volume Integral Equation Method (PVIEM) is applied for the analysis of elastic wave scattering problems in an unbounded isotropic solid containing various types of a multilayered anisotropic inclusion. It should be noted that this numerical method does not require the use of the Green׳s function for the multilayered anisotropic inclusion-only the Green׳s function for the unbounded isotropic matrix is needed. This method can also be applied to solve general elastodynamic problems involving arbitrary shape and number of inhomogeneous and/or multilayered anisotropic inclusions. A detailed analysis of the SH wave scattering is presented for various types of a multilayered orthotropic inclusion. Numerical results are presented for the displacement and stress fields at the interfaces of the multilayered inclusion in a broad frequency range. Parallel volume integral equation method as a pioneer of numerical analysis enables us to investigate the effects of single/multiple layer(s), multilayer׳s shape and geometry, isotropy/anisotropy, and softness/hardness of the multilayered anisotropic inclusion on displacements and stresses at the interfaces of the inclusion.
PubDate: 2015-12-20T10:59:30Z
- Abstract: Publication date: March 2016
- A novel numerical manifold method with derivative degrees of freedom and
without linear dependence- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Huo Fan, Hong Zheng, Siming He, Zhongming Jiang
A new high-order NMM is described in detail. The derivative degrees of freedom with physical meaning, which have been used in discontinuous deformation analysis (DDA), continue to be employed in the NMM. A new local displacement approximation, whose order is promoted, is suggested for the NMM. The local approximation makes the NMM get rid of the issue of the linear dependence (LD) and makes the NMM possess the substantive characteristic of a continuous stress field at the “star points”. An existing stress post-processing technology, which does not lead to a forfeit of the abovementioned essential characteristic, is reinvented to improve the stress accuracy of the displacement-based method. The recurrence formula of the initial stress matrix is also generalized and revised to adapt to the proposed NMM. Moreover, a simplified inhibition approach is presented to deal with the free expansion (FE) problem of manifold element. Several typical examples are given to demonstrate the effectiveness of the proposed NMM.
PubDate: 2015-12-16T10:36:45Z
- Abstract: Publication date: March 2016
- The scalability of the matrices in direct Trefftz method in 2D Laplace
problem- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): M. Borkowski
This paper presents an interesting property of the matrices that may be obtained with the use of direct Trefftz method. It is proved analytically for 2D Laplace problem that values of the elements of matrices describing the capacitance of two scaled domains are inversely proportional to the scalability factor. As an example of the application the capacitance extraction problem is chosen. Concise description of the algorithm in which the scalability property can be utilized is given. Furthermore some numerical results of the algorithm are presented.
PubDate: 2015-12-12T10:33:37Z
- Abstract: Publication date: March 2016
- Vibration of FG-CNT reinforced composite thick quadrilateral plates
resting on Pasternak foundations- Abstract: Publication date: March 2016
Source:Engineering Analysis with Boundary Elements, Volume 64
Author(s): Z.X. Lei, L.W. Zhang, K.M. Liew
This paper considers the free vibration behaviors of functionally graded carbon nanotube (FG-CNT) reinforced composite thick straight-sided quadrilateral plates resting on Pasternak foundations. The IMLS-Ritz method is used in this study. The FG-CNT reinforced composite plates considered are having the CNT reinforced uniaxially aligned in the axial direction with its material properties graded in the thickness direction. The first-order shear deformation theory (FSDT) is employed for formulation of the energy functional to incorporate the effects of transverse shear deformation and rotary inertia. Several example problems are considered with different boundary conditions. Convergence studies for the example problems are performed to demonstrate the numerical stability of the improved moving least-squares Ritz (IMLS-Ritz) method. Besides, the accuracy of the IMLS-Ritz results is examined by comparing with the published values. Close agreement is found from the comparison study. Parametric studies are conducted for various types of CNTs distributions, CNT ratios, aspect ratios, plate geometries and thickness-to-height ratios under different boundary conditions.
PubDate: 2015-12-12T10:33:37Z
- Abstract: Publication date: March 2016
- Boundary methods for mixed boundary problems of Laplace׳s equation
in elliptic domains with elliptic holes- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Li-Ping Zhang, Zi-Cai Li, Ming-Gong Lee
The particular solutions (PS) and fundamental solutions (FS) in polar coordinates can be found in many textbooks, but with much less coverage in elliptic coordinates (Chen et al., 2010 [5], Chen et al., 2012 [6], Morse and Feshbach, 1953 [20], Li et al., 2015 [18]). Since the elliptic domains with elliptic holes may be found in some engineering problems, the PS and the FS expansions in elliptic coordinates are essential for numerical computations. For Dirichlet problems of Laplace׳s equation in elliptic domains, the null field method (NFM), the interior field method (IFM) and the collocation Trefftz method (CTM) are reported in [18]. There seems to exist few reports for mixed problems, where the Dirichlet and Neumann conditions are assigned on the exterior and the interior boundaries, simultaneously. This paper is devoted to such mixed problems by the NFM and the IFM, and the explicit algebraic equations are derived for elliptic domains. Besides, other effective particular solutions (PS) are sought, and the collocation Trefftz method (CTM) [16] is employed. The CTM may be used for Robin problems in elliptic domains. The effective algorithms for the mixed problems of Laplace׳s equation on elliptic domains are the main goal of this paper. The techniques of the mixed techniques in this paper can be applied to Dirichlet problems, the dual techniques are called in Chen and Hong (1999 [4]), Hong and Chen (1988 [8]), and Portela et al. (1992 [21]). A preliminary study for the dual techniques is one goal of this paper.
PubDate: 2015-12-03T05:36:34Z
- Abstract: Publication date: February 2016
- Crane hook stress analysis upon boundary interpolated reproducing kernel
particle method- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Y.X. Qin, W.T. Xie, H.P. Ren, X. Li
The mechanical property of a crane hook is analyzed by using the boundary interpolated reproducing kernel particle method (BIRKPM). It is deduced by combining the interpolated reproducing kernel particle (IRKP) method with the boundary integral equation (BIE) method which aims to solve elastic mechanics plane stress. In the BIRKPM, the shape function constructed by the IRKP method possesses interpolation character at any scatter node. Because of this property, the boundary conditions can be applied directly for the BIRKPM and the new method has high precision and less computing time. When using this method to analyze a laminated crane hook, the results could agree well with the results concluded from the finite element method, and this could prove the validity of the new method.
PubDate: 2015-12-03T05:36:34Z
- Abstract: Publication date: February 2016
- Simulation of two-dimensional sloshing phenomenon by generalized finite
difference method- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Ting Zhang, Yu-Fei Ren, Chia-Ming Fan, Po-Wei Li
In this paper, a meshless numerical scheme, based on the generalized finite difference method (GFDM), is proposed to efficiently and accurately simulate the sloshing phenomenon in a two-dimensional numerical wave tank. When a numerical wave tank is excited horizontally or vertically, the disturbance on the free surface and the flow field in the tank is called sloshing. Based on the theorem of ideal fluid, the mathematical description of the sloshing problem is a time-dependent boundary value problem, governed by a second-order partial differential equation and two non-linear free-surface boundary conditions. In this paper, the GFDM and the explicit Euler method are adopted, respectively, for spatial and temporal discretizations of this moving-boundary problem. After the discretization by the explicit Euler method, the elevation of free surface is updated and a boundary value problem is yielded at every time step. Since the GFDM, a newly-developed domain-type meshless method, can truly get rid of time-consuming meshing generation and numerical quadrature, we adopted the GFDM to efficiently analyze this boundary value problem at every time step. To use the moving-least squares method of the GFDM can express the derivatives as linear combinations of nearby function values, such that the numerical procedures of the GFDM are very simple and efficient. We provided four numerical examples to verify the simplicity and the accuracy of the proposed meshless scheme. In addition, some factors of the proposed numerical scheme are systematically investigated via a series of numerical experiments.
PubDate: 2015-12-03T05:36:34Z
- Abstract: Publication date: February 2016
- Shape design optimization of road acoustic barriers featuring top-edge
devices by using genetic algorithms and boundary elements- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): R. Toledo, J.J. Aznárez, D. Greiner, O. Maeso
This paper presents a Boundary Elements (BE) approach for the efficiency improvement of road acoustic barriers, more specifically, for the shape design optimization of top-edge devices in the search for the best designs in terms of screening performance, usually represented by the insertion loss (IL). With this aim, a procedure coupling BE with Evolutionary Algorithm is proposed in pursuing barrier configurations with ever higher IL. The complexity normally associated with such designs raises the need to consider some geometric simplifications in order to ease the shape optimization processes. In this way, the overall barrier configuration is modeled as both thickness and null-thickness bodies (the boundary thickness is neglected), as representatives of very thin elements. Such an idealization requires a Dual Boundary Element formulation that allows the problem to be solved. The procedure is applied to 2D problems and numerical results are presented on the basis of simulations on noise barriers with three different top designs. It is a quite simple process that makes use of well-known both formulations and procedures. The improvements observed in the designs obtained invite to further studies in the same line on devices with similar applications.
PubDate: 2015-11-25T04:27:32Z
- Abstract: Publication date: February 2016
- Boundary face method for 3D contact problems with non-conforming contact
discretization- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Xingshuai Zheng, Jianming Zhang, Kai Xiong, Xiaomin Shu, Lei Han
Three-dimensional contact problems without friction have been studied using the boundary face method (BFM). In this paper, a non-conforming contact discretization approach is used to enforce the contact conditions between the two contact surfaces. This method is based on node-to-surface (NTS), and there is no need that the identical discretization is performed along the contact surfaces of both bodies. The contact equations are written explicitly with both tractions and displacements which are retained as unknowns in boundary integral equation (BIE). An iterative procedure is presented to determine the correct contact zone by obtaining a solution compatible with the contact conditions (no interpenetrations between the domains and no tensile on the final contact zone). Several numerical examples have been presented to illustrate the applicability of the method.
PubDate: 2015-11-25T04:27:32Z
- Abstract: Publication date: February 2016
- The electromagnetic-thermal dosimetry for the homogeneous human brain
model- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Mario Cvetković, Dragan Poljak, Akimasa Hirata
The electromagnetic-thermal dosimetry model of the human brain exposed to electromagnetic (EM) radiation is developed. The EM model based on the surface integral equation (SIE) formulation is derived using the equivalence theorem for the case of a lossy homogeneous dielectric body. The thermal dosimetry model of the brain is based on the form of Pennes׳ equation for heat transfer in biological tissue. The numerical solution of the EM model is carried out using the Method of Moments (MoM) while the bioheat equation is solved using the finite element method (FEM). Developed EM-thermal model has been applied for the internal dosimetry of the human brain to assess the absorbed EM energy and the consequent temperature rise due to the exposure of 900MHz plane wave. Due to the variability of various parameters, the sensitivity of the maximum, minimum and the average steady-state temperature, on the various thermal parameters have been examined, as well as the influence of the parameters variation on the temperature distribution in case of EM exposure. The proposed model may be found useful in the rapid assessment of the temperature distribution in the human brain, prior to having to deal with a tedious development of a more complex models.
PubDate: 2015-11-25T04:27:32Z
- Abstract: Publication date: February 2016
- A new semi-analytic algorithm of nearly singular integrals on higher order
element in 3D potential BEM- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Zongjun Hu, Zhongrong Niu, Changzheng Cheng
By analyzing the geometric characteristics of 8-noded quadrilateral surface elements in three dimensional boundary element method (3D BEM), the relative distance from a source point to the integral element is defined. For the nearly singular integrals on higher order elements in 3D potential BEM, the equivalent integral kernels are constructed by the geometric analysis between the source point and the element in ρ θ system. Subtracting the equivalent kernels from and adding them back to the nearly singular kernels, the nearly singular surface integrals are transformed into the sum of both the non-singular integrals and the singular integrals. So the leading singular parts are separated. The former are computed efficiently by the Gaussian quadrature and the latter are performed with respect to the integral variables ρ and θ , respectively, in which the integrations with respect to ρ are expressed by analytical formulations. Consequently, a new semi-analytic algorithm is established to calculate the nearly strongly singular and hyper-singular surface integrals on higher order element in 3D BEM. Several examples about 3D heat conduction are given to demonstrate the efficiency and accuracy of the present semi-analytic algorithm in BE analysis. Moreover, the present algorithm is used to analyze very thin structures in 3D BEM.
PubDate: 2015-11-25T04:27:32Z
- Abstract: Publication date: February 2016
- A three-dimensional vortex method for the hydrodynamic solution of planing
cambered dihedral surfaces- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Stefano Brizzolara, Giuliano Vernengo
A new numerical approach based on the Vortex Lattice Method (VLM) for the solution of the hydrodynamic performances of cambered hulls in steady planing is formulated and validated. Due to its fully 3D formulation, the method can be applied to both cambered and un-cambered dihedral planing surfaces of any shape without any further approximation. The exact three-dimensional wetted surface of the hull is where the body boundary condition is fulfilled. The sprays region detaching both in front of the stagnation root line and from the wet portion of the chine are modeled in the numerical scheme by means of additional vortex lattice regions. The dynamic boundary condition at the stern of the hull is non-linear with respect to the perturbation potential. Results show the dynamic pressure consistently accounts for the 3D features of the flow especially in the case of cambered planing surfaces. The numerical method is verified by a systematic analysis against semi-empirical methods and it is finally validated with experimental results on prismatic as well as cambered dihedral planing surfaces. Excellent correlations are found for both types of planing surfaces that range in the same confidence interval of higher fidelity numerical models, such as RANSE solvers.
PubDate: 2015-11-21T04:07:37Z
- Abstract: Publication date: February 2016
- A BEM formulation in conjunction with parametric equation approach for
three-dimensional Cauchy problems of steady heat conduction- Abstract: Publication date: February 2016
Source:Engineering Analysis with Boundary Elements, Volume 63
Author(s): Fajie Wang, Wen Chen, Wenzhen Qu, Yan Gu
This study documents the first attempt to apply a nonsingular indirect boundary element method (BEM) for the solution of three-dimensional (3D) inverse heat conduction problems. The present BEM formulation avoids the calculation of hyper-singular integrals. Furthermore, the exact geometrical representation of computational domain is adopted by parametric equations to eliminate the errors in traditional approaches of polynomial shape functions. Due to its boundary-only discretizations and semi-analytical nature, the proposed method can be viewed as a competitive candidate for the solution of inverse problems. Four benchmark numerical examples indicate that the proposed method, in conjunction with proper regularization techniques, is accurate, computationally efficient and numerically stable for the solution of 3D inverse problems subjected to various levels of noise in input data.
PubDate: 2015-11-21T04:07:37Z
- Abstract: Publication date: February 2016