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101.
本文根据各向异性材料的特征值与特征函数理论,用极其简单的矩阵形式,建立了复合楔形和裂纹止于两材料界面等情况下确定应力奇异阶次的特征方程,讨论了应力奇异性的一些特性,计算了各种情况下的应力奇异阶次。 相似文献
102.
G. C. Sih 《International Applied Mechanics》2006,42(1):1-18
Offered in this work is the development of a macro/meso/micro model that covers the lineal scale of 10−11 to 100 by application of the volume energy density function. Boundary constraints and defect geometries are shown to play a role
at the smaller scale in the same way as those at the macroscopic scale. Different orders of stress (or energy density) singularities
are used to describe the defect geometry and prevailing constraint via the boundary conditions in a way similar to singularity
adopted in classical fracture mechanics. Two classes of singularities have been identified in addition to classical one without
violating the finiteness conditions of the local displacement and energy density. Still the connection of results from the
different scales is no small task and is made possible by application of a scale multiplier. It is determined by considering
the interactive effects of the parameters at the different scales from the atomic to the macroscopic. Unlike the classical
boundary value problem approach, application of the scale multiplier has led to closed-form asymptotic multiscale solutions
that otherwise would not have been made possible. The procedure is demonstrated for the anti-plane shear of a macro-micro-atomic
model that accounts for imperfection at the different scales
Published in Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 3–22, January 2006. 相似文献
103.
A crack terminating at an interface of two dissimilar elastic materials is investigated. It is found that the asymptotic stress
field near the crack tip is in general composed of two parts with each part being characterized by one singularity. The detailed
relation of the two singularities with the bimaterial properties is given for some special cases of the crack. 相似文献
104.
T.-H. Chen C.-H. Chue H.-T. Lee 《Archive of Applied Mechanics (Ingenieur Archiv)》2004,74(3-4):248-261
Summary In this paper, the stress singularities for a cylindrically polarized piezoelectric wedge are investigated. The characteristic
equations are derived analytically by using the extended Lekhnitskii formulation. The piezoelectric material (PZT-4) is polarized
in the radial, circular or axial direction, respectively. Similar to the rectilinearly polarized piezoelectric problem, the
inplane and antiplane stress fields are uncoupled. The results show the variations of the singularity orders with the changes
of the wedge angle, material constants, polarized direction, and the boundary conditions. 相似文献
105.
106.
Tomohiro Okuma 《Mathematische Nachrichten》2015,288(2-3):343-352
From a resolution graph with certain conditions, Neumann and Wahl constructed an equisingular family of surface singularities called splice quotients. For this class some fundamental analytic invariants have been computed from their resolution graph. In this paper we give a method to compute the multiplicity of an abelian covering of a splice quotient from its resolution graph and the Galois group. 相似文献
107.
108.
Symplectic approach has emerged a popular tool in dealing with elasticity problems especially for those with stress singularities. However, anisotropic material problem under polar coordinate system is still a bottleneck. This paper presents a subfield method coupled with the symplectic approach to study the anisotropic material under antiplane shear deformation. Anisotropic material around wedge tip is considered to be consisted of many subfields with constant material properties which can be handled by the symplectic approach individually. In this way, approximate solutions of the stress and displacement can be obtained. Numerical examples show that the present method is very accurate and efficient for such wedge problems. Besides, this paper has extended the application of the symplectic approach and provides a new idea for wedge problems of anisotropic material. 相似文献
109.
In this paper, we study the convergence of Calabi–Yau manifolds under Kähler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of Calabi–Yau manifolds. 相似文献
110.
本文证明了任意环的整体Ding投射维数和整体Ding内射维数一致,研究了奇点范畴和相对于Ding模的稳定范畴间的关系,并刻画了Gorenstein (正则)环以及环的整体维数的有限性. 相似文献