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1.
A general-purpose integral formulation is proposed for the analysis of the interaction between inclusions and cracks embedded
in an elastic isotropic homogeneous infinite medium subjected to a remote loading. This formulation is tailored for the inclusions
of arbitrary shapes with the presence of cracks. The discretization is limited to the inclusions (with continuous quadratic
triangular and quadrilateral elements) and the cracks (using discontinuous quadratic elements). For the calculation of the
stress intensity factors at the crack tips, special crack tip elements are used to model the variation of the displacements near the crack tips. Maximum circumferential stress criterion is adopted to determine the
crack propagating direction. Numerical results of benchmark examples are compared with other available methods.
Received: 8 January 2002 / Accepted: 24 September 2002 相似文献
2.
C.Y. Dong 《Engineering Fracture Mechanics》2008,75(13):3952-3965
The integral equation formulations of an infinite homogeneous isotropic medium containing various inclusions, cracks and rigid lines are presented. The present integral equation formulations contain the displacements (no tractions) over the inclusion-matrix interfaces, the discontinuous displacements over crack surfaces and the axial and the shear forces along rigid-line inclusions. Besides, the sub-domain boundary element method is also used in the present research. Numerical results from the present method and the sub-domain boundary element method are compared and discussed. 相似文献
3.
An integral equation approach is presented to investigate the interaction between cracks and rigid-line inclusions embedded
in an infinite isotropic elastic matrix subject to remote loading. The relevant fundamental solutions in the integral formulation
are presented. Special tip elements are used to simulate the variation of the discontinuous displacements over the crack surfaces, and the axial and shear forces along the rigid-line
inclusions. The stress intensity factors at the crack tips and at the ends of the rigid-line inclusions are computed and compared
with available solutions.
Received: 6 August 2002 / Accepted: 3 February 2003
The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special
Administration Region, China (Project No.: HKU 7011/01E). The authors would like to thank two reviewers for their constructive
comments and suggestions to the paper. The comments of Professor H.P. Hong at the Department of Civil and Environmental Engineering
of the University of Western Ontario of Canada are also appreciated. 相似文献
4.
D. G. Pavlou 《Computational Mechanics》2002,29(3):254-264
Green's function is obtained for the infinite bimaterial elastic solid, containing an internal circular interface crack,
loaded by a unit tangential co-axial circular source. An axisymmetric direct boundary integral equation (BIE) is used for
the analysis of a finite bimaterial axisymmetric body containing an internal circular interface crack and a finite homogeneous
cracked cylinder, both under torsional loading. Using the proposed technique, no discretization of the crack surface is necessary.
Numerical results for both examples as obtained by the proposed method are presented and discussed.
Received: 29 October 2001 / Accepted: 29 May 2002 相似文献
5.
An integral method is investigated and developed in the current work. The effects of the parameters of inlet distortions
on the trend of downstream flow feature in compressor are simulated. Other than the drag-to-lift ratio of the blade and the
inlet incidence angle, it is found that the distorted inlet velocity is another essential parameter to control the distortion
in propagation. Based on this study, a novel critical distortion line and corresponding critical distortion factor are proposed
to express the effect of the two essential inlet parameters on the propagation of distortion, namely, the inlet incidence
angle and the distorted inlet velocity. From the viewpoint of compressor efficiency, the propagation of inlet flow distortion
is further described by a compressor critical performance and its critical characteristic. The results present a useful physical
insight to an axial flow compressor behavior and asymptotic behavior of the propagation of inlet distortion, and confirm the
active role of compressor in determining the velocity distribution when compressor responds to an inlet flow distortion.
Received: 20 December 2001 / Accepted: 21 August 2002
The authors would like to thank HQ RSAF for permission to publish this work, their financial support and encouragement. The
first author wants to acknowledge Prof. Frank Marble of California Institute of Technology, for bringing the problem to the
author's attention and for his helpful discussion. 相似文献
6.
We present a semi-analytical approach for three-dimensional elastostatic normal contact problems with friction. The numerical
approach to iteration on contact area and stick zone size is supported by an underlying analytical solution relating normal
and tangential surface tractions to surface displacements in three coordinate directions. The governing equations are fully
coupled. The analytical surface displacement solutions for a basic loading element have been derived elsewhere (Li and Berger
2001), and the total surface displacements are constructed as a superposition of deflections due to overlapping pyramid load
segments. This approach requires no interpolation scheme for the field variables, which distinguishes it from other numerical
techniques such as the FEM, BEM, and meshless methods. A background grid is defined only on the contact surfaces, and iteration
approaches are used to determine a convergent configuration for contact domain and stick zone size. The approach is exercised
on several normal contact problems, with and without friction, and the results compare favorably to existing analytical and
numerical solutions.
Received: 10 July 2002 / Accepted: 3 December 2002
The authors appreciate the support of the UC Department of Mechanical Engineering and the UC Office of the Vice President
for Research, who jointly provided funds for this work. 相似文献
7.
In the present paper the Trefftz function as a test function is used to derive the local boundary integral equations (LBIE)
for linear elasticity. Since Trefftz functions are regular, much less requirements are put on numerical integration than in
the conventional boundary integral method. The moving least square (MLS) approximation is applied to the displacement field.
Then, the traction vectors on the local boundaries are obtained from the gradients of the approximated displacements by using
Hooke's law. Nodal points are randomly spread on the domain of the analysed body. The present method is a truly meshless method,
as it does not need a finite element mesh, either for purposes of interpolation of the solution variables, or for the integration
of the energy. Two ways are presented to formulate the solution of boundary value problems. In the first one the local boundary
integral equations are written in all nodes (interior and boundary nodes). In the second way the LBIE are written only at
the interior nodes and at the nodes on the global boundary the prescribed values of displacements and/or tractions are identified
with their MLS approximations. Numerical examples for a square patch test and a cantilever beam are presented to illustrate
the implementation and performance of the present method.
Received 6 November 2000 相似文献
8.
9.
In this paper, the nonlinear response of elastic membranes with arbitrary shape under partial and full ponding loads has
been analyzed. Large deflections are considered, which result from nonlinear kinematic relations. The problem is formulated
in terms of the displacements components and the three coupled nonlinear governing equations are solved using the analog equation
method (AEM). The membrane may be prestressed either by prescribed boundary displacements or tractions. Using the concept
of the analog equation the three coupled nonlinear equations are replaced by three uncoupled Poisson's equations with fictitious
sources under the same boundary conditions. Subsequently, the fictitious sources are established using a procedure based on
the BEM and the displacement components as well as the stress resultants at any point of the membrane are evaluated from their
integral representations. In addition to the geometrical nonlinearity, the ponding problem is itself nonlinear, because the
ponding load depends on the deflection surface that it produces. Iterative schemes are developed which converge to the equilibrium
state of the membrane under the ponding loads. Several membranes are analyzed which illustrate the method and demonstrate
its efficiency and accuracy. The method has all the advantages of the pure BEM, since the discretization and integration is
limited only to the boundary.
Received 28 July 2001 相似文献
10.
A localized differential quadrature (LDQ) method and its application to the 2D wave equation 总被引:1,自引:0,他引:1
Differential Quadrature (DQ) is a numerical technique of high accuracy, but it is sensitive to grid distribution and requires
that the number of grid points cannot be too large. These two requirements greatly restrict wider applications of DQ method.
Through a simplified stability analysis in this paper, it is concluded that these two limitations are due to stability requirements.
This analysis leads us to propose to localize differential quadrature to a small neighbourhood so as to keep the balance of
accuracy and stability. The derivatives at a grid point are approximated by a weighted sum of the points in its neighbourhood
rather than of all grid points. The method is applied to the one- and two-dimensional wave equations. Numerical examples show
the present method produces very accurate results while maintaining good stability. The proposed method enables us to solve
more complicated problems and enhance DQ's flexibility significantly.
Received: 23 October 2001 / Accepted: 3 July 2002 相似文献
11.
Y.Z. Chen 《Engineering Analysis with Boundary Elements》2012,36(2):137-146
This paper provides a numerical solution for an infinite plate containing two dissimilar elastic inclusions, which is based on complex variable boundary integral equation (CVBIE). The original problem is decomposed into two problems. One is an interior boundary value problem (BVP) for two elastic inclusions, while other is an exterior BVP for the matrix with notches. After performing discretization for the coupled boundary integral equations (BIEs), a system of algebraic equations is formulated. The inverse matrix technique is suggested to solve the relevant algebraic equations, which can avoid using the assembling of some matrices. Several numerical examples are carried out to prove the efficiency of suggested method and the hoop stress along the interface boundary is evaluated. 相似文献
12.
A parallel implementation for the finite volume method (FVM) for three-dimensional (3D) viscoelastic flows is developed on
a distributed computing environment through Parallel Virtual Machine (PVM). The numerical procedure is based on the SIMPLEST
algorithm using a staggered FVM discretization in Cartesian coordinates. The final discretized algebraic equations are solved
with the TDMA method. The parallelisation of the program is implemented by a domain decomposition strategy, with a master/slave
style programming paradigm, and a message passing through PVM. A load balancing strategy is proposed to reduce the communications
between processors. The three-dimensional viscoelastic flow in a rectangular duct is computed with this program. The modified
Phan-Thien–Tanner (MPTT) constitutive model is employed for the equation system closure. Computing results are validated on
the secondary flow problem due to non-zero second normal stress difference N
2. Three sets of meshes are used, and the effect of domain decomposition strategies on the performance is discussed. It is
found that parallel efficiency is strongly dependent on the grid size and the number of processors for a given block number.
The convergence rate as well as the total efficiency of domain decomposition depends upon the flow problem and the boundary
conditions. The parallel efficiency increases with increasing problem size for given block number. Comparing to two-dimensional
flow problems, 3D parallelized algorithm has a lower efficiency owing to largely overlapped block interfaces, but the parallel
algorithm is indeed a powerful means for large scale flow simulations.
Received: 2 July 2002 / Accepted: 15 November 2002
This research is supported by an A⋆STAR Grant EMT/00/011. 相似文献
13.
An efficient numerical method is proposed for 2-d potential problems in anisotropic media with continuously variable material
coefficients. The method is based on the local integral relationships (integral form of balance equation and/or integral equations
utilizing fundamental solutions) and consistent approximation of field variable using standard domain-type elements. The accuracy
and convergence of the proposed method is tested by several examples and compared with benchmark analytical solutions. 相似文献
14.
This paper presents a numerical model for three-dimensional transversely isotropic bimaterials based on the boundary element
formulation. The point force solutions expressed in a united-form for distinct eigenvalues are studied for transversely isotropic
piezoelectricity and pure elasticity. A boundary integral formulation is implemented for the modeling of two-phase materials.
In this study, the stress distributions are computed for a near interface flaw. The influences of the shape and location of
the flaw on the the stress concentration are examined. The accuracy of the numerical procedures is validated through selected
example problems and comparison studies.
Received 3 October 2001 / Accepted 9 April 2002 相似文献
15.
Lighthill的声类比(acoustic analogy)是目前气动声定量预测中应用最为广泛的一种方法。使用非齐次波动方程的Kirchhoff积分公式对Ligthhill方程进行求解。Kirchhoff公式中的延迟时间表示不同位置点声源对场点声压叠加时的相位作用,推导时强调延迟时间函数的导数运算。基于Kirchhoff积分公式对于有物体存在于流场中的情况,详细推导了Curle解,并对Curle公式中的各声源项进行了分析。文章有助于气动声学初学者正确地认识声类比理论,加深对Curle公式的理解。 相似文献
16.
The precise integration and differential quadrature methods are two new unconditionally stable numerical schemes to approximate
time derivative with more than the second order accuracy. Recent studies showed that compared with the Houbolt and Newmark
methods, they produced more accurate solutions with large time step for the problems where response is primarily dominated
by low and intermediate frequency modes. This paper aims to investigate these time schemes in the context of the dual reciprocity
BEM (DRBEM) formulation of various shock-excited scalar elastic wave problems, where high modes have important affect on traction
response. The Houbolt method was widely recommended in many literatures for such DRBEM dynamic formulations. However, this
study found that the damped Newmark algorithm was the most efficient and accurate for impact traction analysis in conjunction
with the DRBEM. The precise integration and differential quadrature methods are shown inapplicable for such shock-excited
problems due to the absence of numerical damping. On the other hand, we also found that to achieve the same order of accuracy,
the differential quadrature method required much less computing effort than the precise integration method due to the use
of the Bartels–Stewart algorithm solving the resulting Lyapunov matrix analogization equation.
Received 6 November 2000 相似文献
17.
Marcus Hausdorf Werner M. Seiler 《Applicable Algebra in Engineering, Communication and Computing》2002,13(3):163-207
We describe an adaption of a differential algebraic completion algorithm for linear systems of partial differential equations
that allows us to deduce intrinsic differential geometric information like the number of prolongations and projections needed
for the completion. This new hybrid algorithm represents a much more efficient realisation of the classical Cartan–Kuranishi
completion than previous purely geometric ones.
A classical problem in geometric completion theory is the existence of δ-singular coordinate systems in which the algorithms
do not terminate. We develop a new and a very simple criterion for δ-singularity based on a comparison of the Janet and the
Pommaret division. This criterion can also be used for the direct construction of δ-regular coordinates.
Received: July 28, 2000; revised version: October 16, 2001 相似文献
18.
A variant of the boundary element method, called the boundary contour method (BCM), offers a further reduction in dimensionality.
Consequently, boundary contour analysis of two-dimensional (2-D) problems does not require any numerical integration at all.
While the method has enjoyed many successful applications in linear elasticity, the above advantage has not been exploited
for Stokes flow problems and incompressible media. In order to extend the BCM to these materials, this paper presents a development
of the method based on the equations of Stokes flow and its 2-D kernel tensors. Potential functions are derived for quadratic
boundary elements. Numerical solutions for some well-known examples are compared with the analytical ones to validate the
development.
Received 28 August 2001 / Accepted 15 January 2002 相似文献
19.
A meshfree method based on the first-order least-squares formulation for linear elasticity is presented. In the authors'
previous work, the least-squares meshfree method has been shown to be highly robust to integration errors with the numerical
examples of Poisson equation. In the present work, conventional formulation and compatibility-imposed formulation for linear
elastic problems are studied on the convergence behavior of the solution and the robustness to the inaccurate integration
using simply constructed background cells. In the least-squares formulation, both primal and dual variables can be approximated
by the same function space. This can lead to higher rate of convergence for dual variables than Galerkin formulation. In general,
the incompressible locking can be alleviated using mixed formulations. However, in meshfree framework these approaches involve
an additional use of background grids to implement lower approximation space for dual variables. This difficulty is avoided
in the present method and numerical examples show the uniform convergence performance in the incompressible limit. Therefore
the present method has little burden of the requirement of background cells for the purposes of integration and alleviating
the incompressible locking.
Received: 16 December 2001 / Accepted: 4 November 2002 相似文献
20.
J. T. Katsikadelis 《Computational Mechanics》2002,29(2):170-177
A boundary-only solution is presented for dynamic analysis of elastic membranes under large deflections. The solution procedure
is based on the analog equation method (AEM). According to this method, the three coupled nonlinear second order hyperbolic
partial differential equations in terms of displacements, which govern the response of the membrane, are replaced with three
Poisson's quasi-static equations under fictitious time dependent sources. The fictitious sources are established using a BEM-based
procedure and the displacements as well as the stress resultants at any point are evaluated from their integrals representations.
Numerical examples are presented which illustrate the method.
Received 16 December 2000 / Accepted 25 April 2002 相似文献