首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 15 毫秒
1.
    
On employing isoparametric, piecewise linear shape functions over a flat triangular domain, exact expressions are derived for all surface potentials involved in the numerical solution of three‐dimensional singular and hyper‐singular boundary integral equations of potential theory. These formulae, which are valid for an arbitrary source point in space, are represented as analytic expressions over the edges of the integration triangle. They can be used to solve integral equations defined on polygonal boundaries via the collocation method or may be utilized as analytic expressions for the inner integrals in the Galerkin technique. In addition, the constant element approximation can be directly obtained with no extra effort. Sample problems solved by the collocation boundary element method for the Laplace equation are included to validate the proposed formulae. Published in 2008 by John Wiley & Sons, Ltd.  相似文献   

2.
    
An original approach to the solution of linear elastic domain decomposition problems by the symmetric Galerkin boundary element method is developed. The approach is based on searching for the saddle‐point of a new potential energy functional with Lagrange multipliers. The interfaces can be either straight or curved, open or closed. The two coupling conditions, equilibrium and compatibility, along an interface are fulfilled in a weak sense by means of Lagrange multipliers (interface displacements and tractions), which enables non‐matching meshes to be used at both sides of interfaces between subdomains. The accuracy and robustness of the method is tested by several numerical examples, where the numerical results are compared with the analytical solution of the solved problems, and the convergence rates of two error norms are evaluated for h‐refinements of matching and non‐matching boundary element meshes. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

3.
    
A new class of fitted operator finite difference methods are constructed via non‐standard finite difference methods ((NSFDM)s) for the numerical solution of singularly perturbed differential difference equations having both delay and advance arguments. The main idea behind the construction of our method(s) is to replace the denominator function of the classical second‐order derivative with a positive function derived systematically in such a way that it captures significant properties of the governing differential equation and thus provides the reliable numerical results. Unlike other FOFDMs constructed in standard ways, the methods that we present in this paper are fairly simple to construct (and thus enrich the class of fitted operator methods by adding these new methods). These methods are shown to be ε‐uniformly convergent with order two which is the highest possible order of convergence obtained via any fitted operator method for the problems under consideration. This paper further clarifies several doubts, e.g. why a particular scheme is not suitable for the whole range of values of the associated parameters and what could be the possible remedies. Finally, we provide some numerical examples which illustrate the theoretical findings. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

4.
    
This study documents the first attempt to extend the singular boundary method, a novel meshless boundary collocation method, for the solution of 3D elasticity problems. The singular boundary method involves a coupling between the regularized BEM and the method of fundamental solutions. The main idea here is to fully inherit the dimensionality and stability advantages of the former and the meshless and integration‐free attributes of the later. This makes it particularly attractive for problems in complex geometries and three dimensions. Four benchmark 3D problems in linear elasticity are well studied to demonstrate the feasibility and accuracy of the proposed method. The advantages, disadvantages, and potential applications of the proposed method, as compared with the FEM, BEM, and method of fundamental solutions, are also examined and discussed. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

5.
    
  相似文献   

6.
An indirect Boundary Element Method is employed for the static analysis of homogeneous isotropic and linear elastic Kirchhoff plates of an arbitrary geometry. The objectives of this paper consists of a construction and a study of the resulting boundary integral equations as well as a development of stable powerful algorithms for their numerical approximation. These equations involve integrals with high-order kernel singularities. The treatment of singular and hypersingular integrals and a construction of solutions in the neighborhood of the irregular points on the boundary are discussed. Numerical examples illustrate the procedure and demonstrate its advantages. © 1997 by John Wiley & Sons, Ltd.  相似文献   

7.
    
The theory of boundary eigensolutions for boundary value problems is applied to the development of computational mechanics formulations. The boundary element and finite element methods that result are consistent with the mathematical theory of boundary value problems. Although the approach is quite general, this paper focuses on potential problems. For these problems, both methods employ potential and boundary flux as primary variables. Convergence characteristics of the new flux‐oriented finite element method are also developed. By utilizing suitable boundary weight functions, the formulations are written exclusively in terms of bounded quantities, even for non‐smooth problems involving notches, cracks and mixed boundary conditions. The results of numerical experiments indicate that the algorithms perform in concert with the underlying theory and thus provide an attractive alternative to existing approaches. Beyond this, the approach developed here provides a new perspective from which to view computational mechanics, and can be used to obtain a better understanding of boundary element and finite element methods. Comparisons with closed‐form boundary eigensolutions are also presented in order to provide a means for assessing the numerical methods. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

8.
    
This paper investigates the evaluation of the sensitivity, with respect to tangential perturbations of the singular point, of boundary integrals having either weak or strong singularity. Both scalar potential and elastic problems are considered. A proper definition of the derivative of a strongly singular integral with respect to singular point perturbations should accommodate the concomitant perturbation of the vanishing exclusion neighbourhood involved in the limiting process used in the definition of the integral itself. This is done here by esorting to a shape sensitivity approach, considering a particular class of infinitesimal domain perturbations that ‘move’ individual points, and especially the singular point, but leave the initial domain globally unchanged. This somewhat indirect strategy provides a proper mathematical setting for the analysis. Moreover, the resulting sensitivity expressions apply to arbitrary potential-type integrals with densities only subjected to some regularity requirements at the singular point, and thus are applicable to approximate as well as exact BEM solutions. Quite remarkable is the fact that the analysis is applicable when the singular point is located on an edge and simply continuous elements are used. The hypersingular BIE residual function is found to be equal to the derivative of the strongly singular BIE residual when the same values of the boundary variables are substituted in both SBIE and HBIE formulations, with interesting consequences for some error indicator computation strategies. © 1998 John Wiley & Sons, Ltd.  相似文献   

9.
A simple demonstration of the existence of the Cauchy principal value (CPV) of the strongly singular surface integral in the Somigliana Identity at a non-smooth boundary point is presented. First a regularization of the strongly singular integral by analytical integration of the singular term in the radial direction in pre-image planes of smooth surface patches is carried out. Then it is shown that the sum of the angular integrals of the characteristic of the tractions of the Kelvin fundamental solution is zero, a formula for the transformation of angles between the tangent plane of a suface patch and the pre-image plane at smooth mapping of the surface patch being derived for this purpose.  相似文献   

10.
    
This paper is concerned with an effective numerical implementation of the Trefftz boundary element method, for the analysis of two‐dimensional potential problems, defined in arbitrarily shaped domains. The domain is first discretized into multiple subdomains or regions. Each region is treated as a single domain, either finite or infinite, for which a complete set of solutions of the problem is known in the form of an expansion with unknown coefficients. Through the use of weighted residuals, this solution expansion is then forced to satisfy the boundary conditions of the actual domain of the problem, leading thus to a system of equations, from which the unknowns can be readily determined. When this basic procedure is adopted, in the analysis of multiple‐region problems, proper boundary integral equations must be used, along common region interfaces, in order to couple to each other the unknowns of the solution expansions relative to the neighbouring regions. These boundary integrals are obtained from weighted residuals of the coupling conditions which allow the implementation of any order of continuity of the potential field, across the interface boundary, between neighbouring regions. The technique used in the formulation of the region‐coupling conditions drives the performance of the Trefftz boundary element method. While both of the collocation and Galerkin techniques do not generate new unknowns in the problem, the technique of Galerkin presents an additional and unique feature: the size of the matrix of the final algebraic system of equations which is always square and symmetric, does not depend on the number of boundary elements used in the discretization of both the actual and region‐interface boundaries. This feature which is not shared by other numerical methods, allows the Galerkin technique of the Trefftz boundary element method to be effectively applied to problems with multiple regions, as a simple, economic and accurate solution technique. A very difficult example is analysed with this procedure. The accuracy and efficiency of the implementations described herein make the Trefftz boundary element method ideal for the study of potential problems in general arbitrarily‐shaped two‐dimensional domains. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

11.
A coupled model resulting from the boundary element method and eigen‐analysis is proposed in this paper to analyse the stress field at crack tip. This new combine method can yield several terms of the non‐singular stress in the Williams asymptotic expansion. Then the maximum circumferential stress (MCS) criterion taken the non‐singular stress into account is introduced to predict the brittle fracture of cracked structures. Two earlier experiments are re‐examined by the present numerical method and the role of the non‐singular stress in the brittle fracture is investigated. Results show that if more terms of non‐singular stress are taken into account, the predicted crack propagation direction and the critical loading by MCS criterion are much closer to the existing experimental results, especially for dominating mode II loading conditions. Moreover, numerical results manifest that Williams series expansion can describe the stress field further from the crack tip if more non‐singular stress terms are adopted.  相似文献   

12.
    
This paper presents a study of the performance of the non‐linear co‐ordinate transformations in the numerical integration of weakly singular boundary integrals. A comparison of the smoothing property, numerical convergence and accuracy of the available non‐linear polynomial transformations is presented for two‐dimensional problems. Effectiveness of generalized transformations valid for any type and location of singularity has been investigated. It is found that weakly singular integrals are more efficiently handled with transformations valid for end‐point singularities by partitioning the element at the singular point. Further, transformations which are excellent for CPV integrals are not as accurate for weakly singular integrals. Connection between the maximum permissible order of polynomial transformations and precision of computations has also been investigated; cubic transformation is seen to be the optimum choice for single precision, and quartic or quintic one, for double precision computations. A new approach which combines the method of singularity subtraction with non‐linear transformation has been proposed. This composite approach is found to be more accurate, efficient and robust than the singularity subtraction method and the non‐linear transformation methods. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

13.
    
The boundary spectral method for solving three-dimensional non-lifting potential problems is developed. This method combines spectral approximations and the direct numerical integration such as Gaussian quadrature or trapezoidal rules successfully. The singularities of the integral equation are completely removed by subtracting known solutions from the Laplace equation. After discretization, every element of the resultant matrix only contains integrals with non-singular kernels. Therefore, all the integrals can be implemented easily and efficiently. By spectral approximations, the unknown variable is expressed as a truncated series of basis functions, which are orthogonal usually. Instead of solving the variables at collocation points in the conventional methods, the coefficients of basis functions are determined in the spectral approach. It is shown that the new method reduces a lot of number of unknowns, storage of matrix elements, and computer time for solving the algebraic equations. © 1998 John Wiley & Sons, Ltd.  相似文献   

14.
    
Boundary integral equations with extremely singular (i.e., more than hypersingular) kernels would be useful in several fields of applied mechanics, particularly when second‐ and third‐order derivatives of the primary variable are required. However, their definition and numerical treatment pose several problems. In this paper, it is shown how to obtain these boundary integral equations with still unnamed singularities and, moreover, how to efficiently and reliably compute all the singular integrals. This is done by extending in full generality the so‐called direct approach. Only for definiteness, the method is presented for the analysis of the deflection of thin elastic plates. Numerical results concerning integrals with singularities up to order r−4 are presented to validate the proposed algorithm. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

15.
    
A sinh transformation has recently been proposed to improve the numerical accuracy of evaluating nearly singular integrals using Gauss–Legendre quadrature. It was shown that the transformation could improve the accuracy of evaluating such integrals, which arise in the boundary element method, by several orders of magnitude. Here, this transformation is extended in an iterative fashion to allow the accurate evaluation of similar types of integrals that have more spiked integrands. Results show that one iteration of this sinh transformation is preferred for nearly weakly singular integrals, whereas two iterations lead to several orders of magnitude improvement in the evaluation of nearly strongly singular integrals. The same observation applies when considering integrals of derivatives of the two‐dimensional boundary element kernel. However, for these integrals, more iterations are required as the distance from the source point to the boundary element decreases. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

16.
    
A new transformation technique is introduced for evaluating the two‐dimensional nearly singular integrals, which arise in the solution of Laplace's equation in three dimensions, using the boundary element method, when the source point is very close to the element of integration. The integrals are evaluated using (in a product fashion) a transformation which has recently been used to evaluate one‐dimensional near singular integrals. This sinh transformation method automatically takes into account the position of the projection of the source point onto the element and also the distance b between the source point and the element. The method is straightforward to implement and, when it is compared with a number of existing techniques for evaluating two‐dimensional near singular integrals, it is found that the sinh method is superior to the existing methods considered, both for potential integrals across the full range of b values considered (0<b?10), and for flux integrals where b>0.01. For smaller values of b, the use of the Lmethod is recommended for flux integrals. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

17.
    
The boundary knot method (BKM) of very recent origin is an inherently meshless, integration‐free, boundary‐type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non‐singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection–diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

18.
    
An implementation of the boundary element method requires the accurate evaluation of many integrals. When the source point is far from the boundary element under consideration, a straightforward application of Gaussian quadrature suffices to evaluate such integrals. When the source point is on the element, the integrand becomes singular and accurate evaluation can be obtained using the same Gaussian points transformed under a polynomial transformation which has zero Jacobian at the singular point. A class of integrals which lies between these two extremes is that of ‘nearly singular’ integrals. Here, the source point is close to, but not on, the element and the integrand remains finite at all points. However, instead of remaining flat, the integrand develops a sharp peak as the source point moves closer to the element, thus rendering accurate evaluation of the integral difficult. This paper presents a transformation, based on the sinh function, which automatically takes into account the position of the projection of the source point onto the element, which we call the ‘nearly singular point’, and the distance from the source point to the element. The transformation again clusters the points towards the nearly singular point, but does not have a zero Jacobian. Implementation of the transformation is straightforward and could easily be included in existing boundary element method software. It is shown that, for the two‐dimensional boundary element method, several orders of magnitude improvement in relative error can be obtained using this transformation compared to a conventional implementation of Gaussian quadrature. Asymptotic estimates for the truncation errors are also quoted. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

19.
Helmholtz声学边界积分方程中奇异积分的计算   总被引：5，自引：0，他引：5  
提出了一种非等参单元的四边形坐标变换,它将积分的曲面单元映射为另一四边形单元,通过两次坐标变换引入的雅可比行列式可以消除Helmholtz声学边界积分方程中的弱奇异型O(1／r))积分．而且利用δr／δn以及坐标变换可以同时消除坐标变换无法消除的Cauchy型(O(1／r^2))奇异积分,并给出了消除奇异性的详细证明．该方法给Helmholtz声学边界积分方程中的弱奇异积分与Cauchy奇异积分的计算以及编程提供了极大便利。  相似文献   

20.
    
We present a new solution to accelerate the boundary integral equation method (BIEM). The calculation time of the BIEM is dominated by the evaluation of the layer potential in the boundary integral equation. We performed this task using MDGRAPE‐2, a special‐purpose computer designed for molecular dynamics simulations. MDGRAPE‐2 calculates pairwise interactions among particles (e.g. atoms and ions) using hardwired‐pipeline processors. We combined this hardware with an iterative solver. During the iteration process, MDGRAPE‐2 evaluates the layer potential. The rest of the calculation is performed on a conventional PC connected to MDGRAPE‐2. We applied this solution to the Laplace and Helmholtz equations in three dimensions. Numerical tests showed that BIEM is accelerated by a factor of 10–100. Our rather naive solution has a calculation cost of O(N2 × Niter), where N is the number of unknowns and Niter is the number of iterations. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号