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81.
幂硬化介质中平面应力动态裂纹的尖端弹塑性场 总被引:1,自引:0,他引:1
本文采用塑性动力学方程,对幂硬化介质中平面应力动态裂纹尖端场进行了渐近分析,其结果表明:在裂纹尖端附近,应力具有的奇异性,应变具有的奇异性,其中A是一个与塑性区尺寸有关的常数因子,r是离开裂纹尖端的距离,n为硬化指数,文中给出了尖端场的控制参量D,它依赖于马赫数;并且给出了各物理量的角函数。 相似文献
82.
Jiann-Quo Tarn 《Journal of Elasticity》2002,69(1-3):1-13
The issue of stress singularity in an elastic cylinder of cylindrically anisotropic materials is examined in the context of
generalized plane strain and generalized torsion. With a viewpoint that the singularity may be attributed to a conflicting
definition of anisotropy at r=0, we study the problem through a compound cylinder in which the outer cylinder is cylindrically anisotropic and the core
is transversely isotropic. By letting the radius of the core go to zero, the cylinder becomes one with the central axis showing
no conflict in the radial and tangential directions. Closed-form solutions are derived for the cylinder under pressure, extension,
torsion, rotation and a uniform temperature change. It is found that the stress is bounded everywhere, and singularity does
not occur if the anisotropy at r=0 is defined appropriately.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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86.
Pavol Brunovský Alexander Erdélyi Hans-Otto Walther 《Journal of Dynamics and Differential Equations》2004,16(2):393-432
A delay differential equation is presented which models how the behavior of traders influences the short time price movements of an asset. Sensitivity to price changes is measured by a parameter a. There is a single equilibrium solution, which is non-hyperbolic for all a>0. We prove that for a< 1 the equilibrium is asymptotically stable, and that for a>1 a 2-dimensional global center-unstable manifold connects the equilibrium to a periodic orbit. Its birth at a=1 is not of Hopf type and seems part of a Takens–Bogdanov scenario. 相似文献
87.
基于界面端奇异性理论的单纤维拔出试验的试件设计 总被引:1,自引:0,他引:1
在单纤维拔出试验中,由于试件的界面端存在应力奇异性,这使试验所得到的界面剪切强度数据失去合理性[1]。但从文献[1]关于微珠脱粘试验研究的结论中可以发现当基体的楔形角小于某临界角度后,微珠试件界面端应力奇异性几乎消失。由此启发我们设计出一种楔形角小于该纤维/基体系统临界角的锥面的拔出试件,这样即可以防止出现传统拔出试件在界面端的强应力奇异性,又可以避免微珠脱粘试验自身的缺陷。界面端具有任意楔形角的轴对称模型被用于分析和确定纤维/基体系统的临界角,对方程进行渐近展开和分离变量处理,根据边界条件可以得到关于特征值λ的特征方程,针对确定的纤维/基体系统可以得到特征值和楔形角的关系曲线,我们把应力奇异性指数等于-0.005时所对应的楔形角定义为临界角,以及根据临界角设计锥面拔出试件的方法。 相似文献
88.
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
89.
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
90.
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