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71.
各向异性两相材料尖劈奇性场的非协调元分析 总被引:2,自引:1,他引:2
提出了一个基于位移的、分析柱状各向异性两相材料尖劈端部邻域的奇性位移场和应力场问题的非协调元特征分析法. 该方法从柱状扇区的散度定理出发,将柱状扇区控制方程的弱式化为一个与虚功原理相同形式的方程,采用一种新的非协调元技术把所导出的``虚功原理'转化为标准一阶特征方程的求解问题. 非协调元法中,尖劈端部邻域的位移场假定没有采用奇异变换技术,有限元的单元形式是一维的. 将柱状各向异性两相材料尖劈视为``广义平面应变'问题,位移场与坐标z无关,只关注界面端的幂奇异性而不考虑对数奇异性. 运用该方法给出了柱状各向异性两相材料尖劈端部奇性应力指数、奇性位移角分布和应力角分布的算例. 所有的计算结果表明,该方法使用的单元少而且精度较高. 相似文献
72.
Luc Hillairet 《Journal of Functional Analysis》2005,226(1):48-89
On an euclidean surface with conical singularities, the wave-trace is expected to be singular at L where L is the length of some diffractive periodic geodesic. In this paper, we compute the leading term of the singularity brought to the trace by a regular, isolated diffractive geodesic and by a regular family of periodic non-diffractive geodesic. These results can be applied to polygons. 相似文献
73.
Trond Stlen Gustavsen 《Mathematische Nachrichten》2006,279(11):1185-1194
We prove dimension formulas for the cotangent spaces T 1 and T 2 for a class of rational surface singularities by calculating a correction term in the general dimension formulas. We get that it is zero if the dual graph of the rational surface singularity X does not contain a particular type of configurations, and this generalizes a result of Theo de Jong stating that the correction term c (X ) is zero for rational determinantal surface singularities. In particular our result implies that c (X ) is zero for Riemenschneiders quasi‐determinantal rational surface singularities, and this also generalizes results for quotient singularities. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
74.
Anastasios Mallios 《International Journal of Theoretical Physics》2006,45(8):1552-1588
“Geometry,” in the sense of the classical differential geometry of smooth manifolds (CDG), is put under scrutiny from the point of view of Abstract Differential Geometry (ADG). We explore potential physical implications of viewing things under the light of ADG, especially matters concerning the “gauge theories” of modern physics, when the latter are viewed (as they are actually regarded currently) as “physical theories of a geometrical character.” Thence, “physical geometry,” in connection with physical laws and the associated with them, within the background spacetime manifoldless context of ADG, “differential” equations, are also being discussed. 相似文献
75.
G. S. Whiston 《Nonlinear dynamics》1991,2(5):335-351
Elementary applications of singularity theory to dynamical systems are outlined. The main idea is to consider the geometry of the wrinkled surface generated by the time development of a one variable solution as a function of initial conditions or system parameters. Applications of singularity theory to vibro-impacting systems are discussed in some detail and further applications to dynamics are briefly reviewed. 相似文献
76.
Hongya Gao 《Journal of Mathematical Analysis and Applications》2003,281(1):253-263
We first prove a local weighted integral inequality for conjugate A-harmonic tensors. Then, as an application of our local result, we prove a global weighted integral inequality for conjugate A-harmonic tensors in Ls(μ)-averaging domains, which can be considered as a generalization of the classical result. Finally, we give applications of the above results to quasiregular mappings. 相似文献
77.
We establish the best possible condition for point singularities to be removable for nonlinear elliptic equations in divergent
form with lower order terms from the non-linear Kato classes.
相似文献
78.
Alexei Bespalov 《Numerical Methods for Partial Differential Equations》2008,24(4):1159-1180
The article considers a three‐dimensional crack problem in linear elasticity with Dirichlet boundary conditions. The crack in this model problem is assumed to be a smooth open surface with smooth boundary curve. The hp‐version of the boundary element method with weakly singular operator is applied to approximate the unknown jump of the traction which is not L2‐regular due to strong edge singularities. Assuming quasi‐uniform meshes and uniform distributions of polynomial degrees, we prove an a priori error estimate in the energy norm. The estimate gives an upper bound for the error in terms of the mesh size h and the polynomial degree p. It is optimal in h for any given data and quasi‐optimal in p for sufficiently smooth data. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
79.
Katica Hedrih 《Nonlinear Analysis: Hybrid Systems》2008,2(2):310-334
A survey in the form of a review of the author’s research results in the area of dynamics of coupled rotations and coupled systems is presented. The theorem on the existence of a trigger of the coupled singularities and the separatrix in the form of the number eight is presented with a few examples of coupled rotations of the simple systems with debalances. Also, a survey of models and dynamics of coupled systems composed of a number of deformable bodies (plates, beams or belts) with different properties of materials and discrete layer properties is presented and mathematically described. The constitutive stress–strain relations for materials of the coupled sandwich structure elements are presented for different properties: elastic, viscoelastic and creeping. The characteristic modes of the coupled system vibrations are obtained and analyzed for different kinds of materials and structure composition. The visualization of the characteristic numbers and modes and eigenamplitude forms are presented. Structural analysis of sandwich structure vibrations is done. 相似文献
80.
We show how some differential geometric ideas help to resolve some singularities of ordinary differential systems. Hence a
singular problem is replaced by a regular one, which facilitates further analysis of the system. The methods employed are
constructive and the regularized systems can also be used for numerical computations.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献