共查询到20条相似文献,搜索用时 171 毫秒
1.
We present an effective cohesive discrete crack method in the context of the Reproducing Kernel Particle Method (RKPM) in order to study fracture of concrete structures. The discrete crack approach is based on the visibility method and a simple node splitting scheme. We also present an effective implementation of the visibility method and an iteration free algorithm by including the cohesive force term directly into the stiffness equations. The crack is represented by straight-line segments and the cohesive zone model is employed to model the post-localization behavior of concrete. The method is applied to several examples involving mode I and mixed-mode fracture. These results are compared to experimental data and show good agreement. 相似文献
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《Journal of Applied Mathematics and Mechanics》2003,67(1):99-110
Generally two-dimensional and three-dimensional formulations of the non-linear crack problem when the crack surfaces do not overlap for a non-uniform anisotropic linearly elastic body are considered. The first derivative of the potential energy function with respect to the perturbation parameter and its representation in the form of an invariant integral over an arbitrary closed contour are obtained for a general form of the differentiable perturbation of a region with a cut, using the method of material derivatives. The sufficient conditions for the existence of an invariant energy integral are derived in general form, and examples of invariant integrals are constructed for different types of perturbations and a different geometry of the cut. 相似文献
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利用最小化方法对含未知边界的不适定方程组进行正则化处理,然后依次迭代更新边界和相应的密度函数,最终得到反演的边界.给出一些数值例子以表明这种方法是有效的和可行的。 相似文献
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V. I. Fabrikant 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(1):121-135
A simple, yet effective solution is derived to the
problem of a penny-shaped crack, whose faces are bridged by
fibers, and subjected to normal loading. The mathematical
apparatus developed by the author earlier (Fabrikant, 1989,
1991) is used to reduce the governing integral equation to a
sequence of integrals of elementary functions, which can be easily
solved by the method of collocations. The case of uniform
loading is considered as an example. The accuracy of the
obtained solution is rigorously verified by different
criteria. 相似文献
5.
We consider the rectilinear propagation of a semi-infinite crack with constant velocity in a crystal structure. We obtain the solutions of homogeneous boundary-value problems for the corresponding difference-differential operators in spaces of one and two dimensions. We give a justification of the computational aspect of the problem. Bibliography: 8 titles.Translated fromProblemy Matematicheskogo Analiza, No. 12, 1992, pp. 127–153. 相似文献
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Stphane Andrieux Amel Ben Abda Mohamed Jaoua 《Mathematical Methods in the Applied Sciences》1998,21(10):895-906
This paper deals with the detection of emergent plane cracks, by using boundary measurements. An identifiability result (uniqueness of the solution) is first proved. Then, we look at the stability of this solution with respect to the measurement. A weak stability result is proved, as well as a Lipshitz stability result for straight cracks, by using domain-derivative techniques. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd. 相似文献
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《Journal of Computational and Applied Mathematics》2002,149(1):335-339
There are three famous criteria for the prediction on the direction of crack extension: maximum energy release rate criterion, local symmetric criterion and maximum stress criterion. It has already been proved that these criteria are different. In this paper, we show how to measure the difference between maximum energy release rate criterion and maximum stress criterion. The results in this paper and special solutions in Amestoy and Leblond (Internat. J. Solids Struct. 29 (1992) 465) indicate that it is enough to use the maximum stress criterion for the numerical prediction of crack path, if the stress intensity factor of the shearing mode is not too big. 相似文献
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《Journal of Applied Mathematics and Mechanics》1998,62(5):807-817
Results obtained in recent years in an attempt to construct a general (physically and geometrically) non-linear crack theory are described. 相似文献
10.
Ductile fracture is of high interest for industrial Manufacturing. Here we attempt to model this material degradation with a combined approach of non-local continuum damage mechanics and discrete fracture mechanics using the eXtended Finite Element Method. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
Gianni Dal Maso Gianluca Orlando Rodica Toader 《NoDEA : Nonlinear Differential Equations and Applications》2015,22(3):449-476
We consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain. 相似文献
12.
Crack initiation and stable crack growth under monotonic loading in steels has been studied using an elastic-plastic finite element analysis. The fracture criterion used for crack initiation and stable crack growth was the critical strain energy density. In addition the shift core method for the analysis of crack extension was used. In the shift core modelling method, crack advance is simulated by moving the coordinates of the core region which surrounds the crack tip, to obtain the stiffness reduction. Simultaneously the core itself geometrically undergoes a simple rigid-body motion or translation during the crack extension. The analytically calculated and experimentally measured load for crack initiation and the subsequent stable crack growth agreed well. 相似文献
13.
An exact solution to the problem of the distribution of stresses in a transversally isotropic elastic body with inner elliptic
crack is given. An assumption that the linearly varying pressure acts on the surface of the crack is made. The intensity coefficients
of stresses at the vertex of the crack are found. Bibliography: 5 titles.
Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 79, 1995, pp. 117–124. Original 相似文献
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N. P. Novikov 《Mechanics of Composite Materials》1968,4(4-6):585-586
The structure of the end regions of progressive cracks in polypropylene and polyethylene films with different supermolecular structures is examined. It is established that in the end region the opposite sides of the crack are connected by oriented polymer.Institute of Problems of Mechanics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 741–742, July–August, 1968. 相似文献
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Using the fundamental solution of interface crack and the method of finite-part integral, the problem of three-dimensional interface crack is reduced to solve a set of two-dimensional hypersingular integrodifferential equations with unknown displacement discontinuities of crack surface. Then a systematically theoretical analysis for solving these equations is presented. 相似文献
18.
《Applied Mathematical Modelling》1998,22(3):197-204
This paper presents a stochastic model of fatigue-induced crack propagation in metallic materials. The crack growth rate predicted by the model is guaranteed to be non-negative. The model structure is built upon the underlying principle of Karhunen–Loève expansion and does not require solutions of stochastic differential equations in either Wiener integral or Itô integral setting. As such this crack propagation model can be readily adapted to damage monitoring and remaining life prediction of stressed structures. The model results have been verified by comparison with experimental data of time-dependent fatigue crack statistics for 2024-T3 and 7075-T6 aluminum alloys. 相似文献
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It is important to investigate the effects of heat conduction of crack interior on thermoelastic fields of a cracked material. In this paper, an extended thermal-medium crack model is proposed to address the influences of the thermal conductivity inside an opening crack on the induced thermoelastic fields. Then the problem of a penny-shaped crack in a transversely isotropic material is investigated under applied mechanical and uniform heat flow loadings. Based on the Hankel transform technique, the governing partial differential equations are transformed to ordinary differential equations, then to a system of coupled dual integral equations. The thermoelastic fields around the penny-shaped crack are obtained explicitly by solving the derived dual integral equations. Numerical results are reported to show the influences of the thermal conductivity of crack interior on partial insulation coefficient, temperature change across crack and thermal stress intensity factor. As compared to the known thermal-medium crack model, the proposed one exhibits more applicability. 相似文献