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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.
This work provides a preliminary contribution in the context of analytical integrations of strongly and hyper singular kernels
in boundary element methods (BEMs) in 3D. It concerns the integral of 1/r
3 over a triangle in R
3, that plays a fundamental role in BEMs in 3D, especially for the Galerkin implementation. Because the existence of the aforementioned
integral depends on the position of the source point, all significant instances of the position of the source point will be
considered and detailed. For its interest in the context of BEM, the integral is also considered in the more general sense
of finite part of Hadamard.
Received 6 August 2001 相似文献
3.
In this paper, an integral equation method to the inclusion-crack interaction problem in three-dimensional elastic medium
is presented. The method is implemented following the idea that displacement integral equation is used at the source points
situated in the inclusions, whereas stress integral equation is applied to source points along crack surfaces. The displacement
and stress integral equations only contain unknowns in displacement (in inclusions) and displacement discontinuity (along
cracks). The hypersingular integrals appearing in stress integral equation are analytically transferred to line integrals
(for plane cracks) which are at most weakly singular. Finite elements are adopted to discretize the inclusions into isoparametric
quadratic 10-node tetrahedral or 20-node hexahedral elements and the crack surfaces are decomposed into discontinuous quadratic
quadrilateral elements. Special crack tip elements are used to simulate the variation of displacements near the crack front. The stress intensity factors along the crack front are calculated. Numerical
results are compared with other available methods.
Received: 28 January 2002 / Accepted: 4 June 2002
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 7101/99 E). 相似文献
4.
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
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.
The application of the eXtended finite element method (X-FEM) to thermal problems with moving heat sources and phase boundaries
is presented. Of particular interest is the ability of the method to capture the highly localized, transient solution in the
vicinity of a heat source or material interface. This is effected through the use of a time-dependent basis formed from the
union of traditional shape functions with a set of evolving enrichment functions. The enrichment is constructed through the
partition of unity framework, so that the system of equations remains sparse and the resulting approximation is conforming.
In this manner, local solutions and arbitrary discontinuities that cannot be represented by the standard shape functions are
captured with the enrichment functions. A standard time-projection algorithm is employed to account for the time-dependence
of the enrichment, and an iterative strategy is adopted to satisfy local interface conditions. The separation of the approximation
into classical shape functions that remain fixed in time and the evolving enrichment leads to a very efficient solution strategy.
The robustness and utility of the method is demonstrated with several benchmark problems involving moving heat sources and
phase transformations.
Received 20 May 2001 / Accepted 19 December 2001 相似文献
7.
A study of turbulence/combustion interactions in a relatively large turbulent diffusion flame of an axisymmetric methane
jet into air is presented. A first order k–ɛ turbulence closure model is used along with two different models (equal scales and non-equal scales) for the submodel describing
the scalar dissipation rate. The flamelet concept is used to model the turbulent combustion along with a joint mixture fraction/strain
rate probability density function (PDF) for the prediction of the average parameters of the turbulent diffusion flame. The
numerical approach is that of Patankar and Spalding, while the flamelet simulations are obtained from the RUN-1DL code of
Rogg and co-workers based on a 17 species detailed reaction mechanism. The chosen configuration is that of the experimentally
studied turbulent diffusion flame of Streb [1]. A comparison between these experimental results and the obtained numerical
ones is thus presented. Relatively good agreements are obtained which show the usefulness of the two-scale model compared
to the classical one-scale model for predicting turbulent diffusion flames. Nonetheless some discrepancies are obtained in
the outer and downstream regions of the jet, especially in comparison with the experimental data. These are attributed to
short coming of the considered turbulence model and soot radiation which is not accounted for.
Received: 2 May 2002 / Accepted: 31 January 2003 相似文献
8.
The extended system is known as a reliable algorithm for the direct computation of instability points on the equilibrium
path of mechanical structures. This article describes the application of the extended system as critical point computation
method to mechanical contact problems. In this type of problems inequality constraints have to be considered. Moreover a prediction
method based on the extended system algorithm is presented which allows the detection of favorable starting values for a critical
point computation on the equilibrium path.
Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many
years. 相似文献
9.
This paper considers the wrinkling phenomenon of membranes for the special case of a linear relationship between membrane
forces and strains. Beginning from basic equations of regular wrinkling, the problem is treated analytically. An application
of the theory to simple examples will be given.
Received: 10 September 2002 / Accepted: 11 November 2002 相似文献
10.
A cell vertex finite volume method for the solution of steady compressible turbulent flow problems on unstructured hybrid
meshes of tetrahedra, prisms, pyramids and hexahedra is described. These hybrid meshes are constructed by firstly discretising
the computational domain using tetrahedral elements and then by merging certain tetrahedra. A one equation turbulence model
is employed and the solution of the steady flow equations is obtained by explicit relaxation. The solution process is accelerated
by the addition of a multigrid method, in which the coarse meshes are generated by agglomeration, and by parallelisation.
The approach is shown to be effective for the simulation of a number of 3D flows of current practical interest.
Sponsored by The Research Council of Norway, project number 125676/410
Dedicated to the memory of Prof. Mike Crisfield, a respected colleague 相似文献
11.
In this work we consider solutions for the Euler-Bernoulli and Timoshenko theories of beams in which material behavior may
be elastic or inelastic. The formulation relies on the integration of the local constitutive equation over the beam cross
section to develop the relations for beam resultants. For this case we include axial, bending and shear effects. This permits
consideration in a direct manner of elastic and inelastic behavior with or without shear deformation.
A finite element solution method is presented from a three-field variational form based on an extension of the Hu–Washizu
principle to permit inelastic material behavior. The approximation for beams uses equilibrium satisfying axial force and bending
moments in each element combined with discontinuous strain approximations. Shear forces are computed as derivative of bending
moment and, thus, also satisfy equilibrium. For quasi-static applications no interpolation is needed for the displacement
fields, these are merely expressed in terms of nodal values. The development results in a straight forward, variationally
consistent formulation which shares all the properties of so-called flexibility methods. Moreover, the approach leads to a
shear deformable formulation which is free of locking effects – identical to the behavior of flexibility based elements.
The advantages of the approach are illustrated with a few numerical examples.
Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many
years. 相似文献
12.
A recursive method based on the Kalman filtering is developed to solve inverse natural convection problems of estimating
the unsteady nonuniform wall heat flux from temperature measurements in the flow. By employing the Karhunen–Loève Galerkin
procedure that reduces the Boussinesq equation to a small set of ordinary differential equations, the computational difficulties
associated with the Kalman filtering for the partial differential equations are overcome. The present method is assessed through
several numerical experiments, and is found to yield satisfactory results.
Received 20 January 2001 / Accepted 31 May 2001 相似文献
13.
A general procedure to perform shape design sensitivity analysis for two-dimensional periodic thermal diffusion problems
is developed using boundary integral equation formulation. The material derivative concept to describe shape variation is
used. The temperature is decomposed into a steady state component and a perturbation component. The adjoint variable method
is used by utilizing integral identities for each component. The primal and adjoint systems are solved by boundary element
method. The sensitivity results compared with those by finite difference show good accuracy. The shape optimal design problem
of a plunger model for the panel of a television bulb, which operates periodically, is solved as an example. Different objectives
and amounts of heat flux allowed are studied. Corresponding optimum shapes of the cooling boundary of the plunger are obtained
and discussed.
Received 15 August 2001 / Accepted 28 February 2002 相似文献
14.
This paper presents a two-dimensional model for identification of the phase change front in a continuous casting process.
The transport phenomena encountered in the considered process are solved by Boundary Element Method (BEM). For the known set
of external boundary conditions, the whole problem is solved in two subdomains separated by a phase change front whose position
is updated during the iteration process. The solution scheme involves the application of a front tracking procedure based
on using sensitivity coefficients to find the correct position of the phase change front modelled by Bezier splines. The main
features of the developed algorithms were investigated by several numerical tests, the most important results of which are
presented in this article.
Received 6 November 2000 相似文献
15.
An efficient methodology is presented to solve inverse solidification problems. In the procedure, the latent heat effects
are implemented by introducing pseudo heat sources near the moving interface. The material properties can be temperature dependent.
To account for the nonlinear part of the governing differential equations, a finite-boundary element formulation is employed.
To reduce the oscillations in the solution, a sequential regularization scheme is used. A procedure for proper selection of
regularization parameters is presented. To smooth the solutions further, a secondary regularization scheme is introduced and
employed. Two complete examples are presented to demonstrate the applicability and the accuracy of the methods.
Received: 1 March 2002 / Accepted: 10 February 2003 相似文献
16.
The propagation of strong distortion at inlet of an axial compressor is investigated by applying the critical distortion
line and the integral method. The practical applications, such as the inlet conditions of flaming of leakage fuel during mid-air
refueling process, are implemented to show the details of the numerical methodology used in analysis of the axial flow compressor
behavior and the propagation of inlet distortion. 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 simulated results
present a useful physical insight to the significant effects of inlet parameters on the distortion extension, velocity, and
compressor characteristics. The distortion level, incidence angle and the size of distortion area at compressor inlet, and
the rotor blade speed are found being the major parameters affecting the mass flow rate of engine.
Received: 20 October 2002 / Accepted: 28 January 2003
The authors would like to thank HQ RSAF of Air Logistic Department, Singapore for permission to publish this work, their
financial support and encouragement. 相似文献
17.
Considering the combined effect of boundary approximation and numerical integration, error estimates for the isoparametric
mixed finite element solution of fourth order elliptic problems with variable coefficients in convex domains, which, in the
particular case of aniso-/ortho-/ isotropic plate bending problems, gives a direct and simultaneous approximation to bending
moment tensor field Ψ=(ψ
ij
)
1≤i,j≤2
and displacement field `u', have been developed. Results of numerical experiments justify the theoretical results.
Received 20 July 2001 / Accepted 28 November 2001 相似文献
18.
A. S. Goltsev 《Computational Mechanics》2002,28(3-4):325-330
The force problem of fracture mechanics for orthotropic body is solved by boundary element method. The equations of plane
strain state are used. The key point of this paper is obtaining the influence functions for finite segment with constant displacement
discontinuities in the main axes of orthotropy. They have been deduced by means of two-dimensional Fourier transform and theory
of generalized functions. The straight crack under the action of uniform tension in the infinity is considered by using obtained
influence functions. The calculations were carried out for isotropic and two orthotropic materials.
Received 6 November 2000 相似文献
19.
A general algorithm of the distance transformation type is presented in this paper for the accurate numerical evaluation
of nearly singular boundary integrals encountered in elasticity, which, next to the singular ones, has long been an issue
of major concern in computational mechanics with boundary element methods. The distance transformation is realized by making
use of the distance functions, defined in the local intrinsic coordinate systems, which plays the role of damping-out the
near singularity of integrands resulting from the very small distance between the source and the integration points. By taking
advantage of the divergence-free property of the integrals with the nearly hypersingular kernels in the 3D case, a technique
of geometric conversion over the auxiliary cone surfaces of the boundary element is designed, which is suitable also for the
numerical evaluation of the hypersingular boundary integrals. The effects of the distance transformations are studied and
compared numerically for different orders in the 2D case and in the different local systems in the 3D case using quadratic
boundary elements. It is shown that the proposed algorithm works very well, by using standard Gaussian quadrature formulae,
for both the 2D and 3D elastic problems.
Received: 20 November 2001 / Accepted: 4 June 2002
The work was supported by the Science Foundation of Shanghai Municipal Commission of Education. 相似文献
20.
Fractional differential equations of degree 1<α<2 are considered in this paper. A summary of numerical schemes for the time-domain
solution of such problems is given. While all these methods require evaluation of the history of the state variables, an alternative
concept recently published by Yuan and Agrawal (2002), which is computationally more efficient, is further developed. This
scheme is based on a transformation of the original integro-differential problem into a system of linear differential equations.
Here, parallels to the theory of internal variables are drawn.
Received: 18 June 2002 / Accepted: 12 July 2002 相似文献