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1.
In the framework of linear elasticity, singularities occur in domains with non-smooth boundaries. Particularly in Fracture Mechanics, the local stress field near stress concentrations is of interest. In this work, singularities at re-entrant corners or sharp notches in Reissner-Mindlin plates are studied. Therefore, an asymptotic solution of the governing system of partial differential equations is obtained by using a complex potential approach which allows for an efficient calculation of the singularity exponent λ. The effect of the notch opening angle and the boundary conditions on the singularity exponent is discussed. The results show, that it can be distinguished between singularities for symmetric and antisymmetric loading and between singularities of the bending moments and the transverse shear forces. Also, stronger singularities than the classical crack tip singularity with free crack faces are observed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
The plane problem of a bi- or trimaterial-junction, consisting of dissimilar, homogeneous, isotropic and linear elastic sectors is considered. The asymptotic behaviour of the stresses of this composite situation is analyzed by the complex variable method, based on an appropriate choice of the Kolosov-potentials which are applicable in the vicinity of the vertex. In the analyses, the identification of the singularity exponent is emphasized. With the help of a novel approach it is demonstrated how to derive some solutions for the orders of the stress singularities at bi- and trimaterial combinations in a closed-form analytical manner. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
We investigate asymptotic properties of solutions to mixed boundary value problems of thermopiezoelectricity (thermoelectroelasticity)
for homogeneous anisotropic solids with interior cracks. Using the potential methods and theory of pseudodifferential equations
on manifolds with boundary we prove the existence and uniqueness of solutions. The singularities and asymptotic behaviour
of the mechanical, thermal and electric fields are analysed near the crack edges and near the curves, where the types of boundary
conditions change. In particular, for some important classes of anisotropic media we derive explicit expressions for the corresponding
stress singularity exponents and demonstrate their dependence on the material parameters. The questions related to the so
called oscillating singularities are treated in detail as well.
This research was supported by the Georgian National Science Foundation grant GNSF/ST07/3-170 and by the German Research Foundation
grant DFG 436 GEO113/8/0-1. 相似文献
4.
In this paper,new Levin methods are presented for calculating oscillatory integrals with algebraic and/or logarithmic singularities.To avoid singularities,the technique of singularity separation is applied and then the singular ODE occurring in classic Levin methods is converted into two kinds of non-singular ODEs.The solutions of one can be obtained explicitly,while the other kind of ODEs can be solved efficiently by collocation methods.The proposed methods can attain arbitrarily high asymptotic orders and also enjoy superalgebraic convergence with respect to the number of collocation points.Several numerical experiments are presented to validate the efficiency of the proposed methods. 相似文献
5.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(3):269-274
In the framework of thin linear elastic plates it is known that the solutions of both the three-dimensional problem and the Reissner-Mindlin plate model can be developed into asymptotic expansions. By comparing the particular asymptotic expansions with respect to the half-thickness ɛ of the plate in the case of periodic boundary conditions on the lateral side, the shear correction factor in the Reissner-Mindlin plate model can be determined in such a way that this model approximates the three-dimensional solution with one order of the plate thickness better than the classical Kirchhoff model. This fails for hard clamped lateral boundary conditions so that the Reissner-Mindlin model is in this case asymptotically as good as the Kirchhoff model. 相似文献
6.
In this paper, we study the asymptotic behavior of critical points of a Gross-Pitaevskii energy, which is proposed as a model for rotationally forced Bose-Einstein condensate. We prove that the limiting singularity set is one-dimensional rectifiable. We also establish the convergence result for critical points away from limiting singularities. 相似文献
7.
Susan Szczepanski 《Inventiones Mathematicae》1989,96(1):185-204
Summary The isolated singularities of complex hypersurfaces are studied by considering the topology of the highly connected submanifolds of spheres determined by the singularity. By introducing the notion of the link of a perturbation of the singularity and using techniques of surgery theory, we are able to describe which invariants associated to a singularity can be used to determine the cobordism type of the singularity.It is shown that the cobordism type is determined by the set of weakly distinguished bases. This result is used to draw a distinction between the classical case of two variables and the higher dimensional problem. That is, we show that the result of Le which states that the cobordism and topological classifications of singularities coincide in the classical dimension does not hold for singularities of functions of more than three variables. Examples of topologically distinct but cobordant singularities are obtained using results of Ebeling. 相似文献
8.
《Journal of Computational and Applied Mathematics》2005,174(2):271-313
We present a toolbox for extracting asymptotic information on the coefficients of combinatorial generating functions. This toolbox notably includes a treatment of the effect of Hadamard products on singularities in the context of the complex Tauberian technique known as singularity analysis. As a consequence, it becomes possible to unify the analysis of a number of divide-and-conquer algorithms, or equivalently random tree models, including several classical methods for sorting, searching, and dynamically managing equivalence relations. 相似文献
9.
In this work we present a singular function boundary integral method for elliptic problems with boundary singularities. In this method, the approximation is constructed from the truncated asymptotic expansion for the solution near the singular point and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multiplier functions. The resulting discrete problem is posed and solved on the boundary of the domain, away from the point of singularity. We are able to show that the method approximates the generalized stress intensity factors, i.e. the coe cients in the asymptotic expansion, at an exponential rate. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
P. Karamian‐Surville J. Sanchez‐Hubert E. Sanchez Palencia 《Mathematical Methods in the Applied Sciences》2003,26(17):1451-1485
We consider problems of statics of thin elastic shells with hyperbolic middle surface subjected to boundary conditions ensuring the geometric rigidity of the surface. The asymptotic behaviour of the solutions when the relative thickness tends to zero is then given by the membrane approximation. It is a hyperbolic problem propagating singularities along the characteristics. We address here the reflection phenomena when the propagated singularities arrive to a boundary. As the boundary conditions are not the classical ones for a hyperbolic system, there are various cases of reflection. Roughly speaking, singularities provoked elsewhere are not reflected at all at a free boundary, whereas at a fixed (or clamped) boundary the reflected singularity is less singular than the incident one. Reflection of singularities provoked along a non‐characteristic curve C are also considered. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
11.
Richard Montgomery Vidya Swaminathan Mikhail Zhitomirskii 《Journal of Fixed Point Theory and Applications》2008,3(2):353-378
A standard method for resolving a plane curve singularity is the method of blow-up. We describe a less-known alternative method
which we call prolongation, in honor of Cartan’s work in this direction. This method is known to algebraic geometers as Nash
blow-up. With each application of prolongation the dimension of the ambient space containing the new “prolonged” singularity
increases by one. The new singularity is tangent to a canonical plane field on the ambient space. Our main result asserts
that the two methods, blow-up and prolongation, yield the same resolution for unibranched singularities. The primary difficulties
encountered are around understanding the prolongation analogues of the exceptional divisors from blow-up. These analogues
are called critical curves. Most of the critical curves are abnormal extremals in the sense of optimal control theory as it
applies to rank 2 distributions (2 controls).
Dedicated to V. I. Arnol’d and his creative force 相似文献
12.
I. G. Shcherbak 《Journal of Mathematical Sciences》1992,60(5):1681-1693
We define the decomposition of a boundary singularity as a pair (a singularity in the ambient space together with a singularity of the restriction to the boundary). We prove that the Lagrange transform is an involution on the set of boundary singularities that interchanges the singularities that occur in the decomposition of a boundary singularity. We classify the boundary singularities for which both of these singularities are simple. Bibliography: 8 titles.Translated fromTrudy Seminara imeni I. G. Petrovskogo, No. 15, pp. 55–69, 1991. 相似文献
13.
《Applied and Computational Harmonic Analysis》2020,48(3):993-1029
Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth functions. With an implicit representation of image singularities sets, the proposed model inflicts different strength of regularization on smooth and singular image regions and edges. The proposed edge driven model is robust to both image approximation and singularity estimation. The implicit formulation also enables an asymptotic analysis of the proposed models and a rigorous connection between the discrete model and a general continuous variational model. Finally, numerical results on image inpainting and deblurring show that the proposed model is compared favorably against several popular image restoration models. 相似文献
14.
Adrian Langer 《Mathematische Zeitschrift》2000,235(3):591-614
We define Chern classes of reflexive sheaves using Wahl's relative local Chern classes of vector bundles. The main result
of the paper bounds contributions of singularities of a sheaf to the Riemann–Roch formula. Using it we are able to prove inequality
in Wahl's conjecture on relative asymptotic RR formula for rank 2 vector bundles. Moreover, we prove that if Wahl's conjecture
is true for a singularity then it is true for any its quotient. This implies Wahl's conjecture for quotient singularities
and for quotients of cones over elliptic curves.
Received March 2, 1998; in final form March 24, 1999 / Published online September 14, 2000 相似文献
15.
The present study is concerned with stress singularities in the core and face sheet interface of structural sandwich panels caused by an incompatibility in the modes of deformation associated with the homogeneous face sheets and the cellular core. The singularities are studied in a closed form asymptotic analysis and in a pure numerical approach based on the finite element method. It is shown that the singularity is of the pure, non oscillatory power law type with variable order depending on the cell wall angle and the cell wall material. 相似文献
16.
Summary The formal asymptotic analysis of Latifi et al. [4] suggests that the Mixmaster Universe model possesses movable transcendental
singularities and thus is nonintegrable in the sense that it does not satisfy the Painlevé property (i.e., singularities with
nonalgebraic branching). In this paper, we present numerical evidence of the nonintegrability of the Mixmaster model by studying
the singularity patterns in the complext-plane, wheret is the “physical” time, as well as in the complex τ-plane, where τ is the associated “logarithmic” time. More specifically,
we show that in the τ-plane there appears to exist a “natural boundary” of remarkably intricate structure. This boundary lies
at the ends of a sequence of smaller and smaller “chimneys” and consists of the type of singularities studied in [4], on which
pole-like singularities accumulate densely. We also show numerically that in the complext-plane there appear to exist complicated, dense singularity patterns and infinitely-sheeted solutions with sensitive dependence
on initial conditions. 相似文献
17.
Werner Simon 《PAMM》2005,5(1):317-318
Phase transformation plays an important role in thermodynamics and materials science. Based on the theory of singularities, a new method to construct phase diagrams is presented. Analysing singularities on base of root sequences, see Tamaschke [16], will help to develop singularity graphs, where workings by H. Whitney, R. Thom, and V. I. Arnold provide fundamentals. The generated singularity graphs build the starting point for singularity phase diagrams. A powerful characteristic of such singularity graphs is that higher-dimensional surfaces can be transformed to a two-dimensional diagram. The attained singularity diagram can be used in materials science for analytical models of temperature-concentrated diagrams. As tools from algebra and analysis build a sound basis for singularity diagrams, it is possible to evolve computer software generating these phase diagrams. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
Javier Fernández de Bobadilla 《Topology》2004,43(4):925-982
In this paper we develop a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known morsification results for non-isolated singularities and generalise them to a much wider context. We also show that deforming functions of finite codimension with respect to an ideal within the same ideal respects the Milnor fibration. Furthermore we present some applications of the theory: we introduce new numerical invariants for non-isolated singularities, which explain various aspects of the deformation of functions within an ideal; we define generalisations of the bifurcation variety in the versal unfolding of isolated singularities; applications of the theory to the topological study of the Milnor fibration of non-isolated singularities are presented. Using intersection theory in a generalised jet-space we show how to interpret the newly defined invariants as certain intersection multiplicities; finally, we characterise which invariants can be interpreted as intersection multiplicities in the above mentioned generalised jet space. 相似文献
19.
L. A. Kalyakin 《Theoretical and Mathematical Physics》1999,118(3):307-313
We construct an asymptotic (with respect to a small parameter) solution of the Cauchy problem for the perturbed Liouville
equation in the case where the unperturbed solution has singularities on timelike lines. We propose a modification of the
Krylov-Bogoliubov method that, in particular, allows us to find the asymptotic corrections to the singularity lines.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 3, pp. 390–397, March, 1999. 相似文献
20.
Using the theory of the mixed Hodge structure one can define a notion of exponents of a singularity.In 2000,Hertling proposed a conjecture about the variance of the exponents of a singularity.Here,we prove that the Hertling conjecture is true for isolated surface singularities with modality ≤ 2. 相似文献