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91.
In nonlinear elasticity the exact geometry of deformation is combined with general constitutive relations. This allows a very sophisticated interaction of deformations in different material directions. Based on the Cosserat theory for planar deformations of nonlinearly elastic rods we demonstrate some paradoxical bending effects caused by a nontrivial interaction of extension, flexure, and shear. The analytical results are illustrated by numerical examples. 相似文献
92.
93.
94.
We study four measures of problem instance behavior that might account for the observed differences in interior-point method
(IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry
measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-)
condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the
level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure
the sample correlation (CORR) between these measures and IPM iteration counts (solved using the software SDPT3) when these
measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with
IPM iterations (CORR = 0.901), and provides a very good explanation of IPM iterations, particularly for problem instances
with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence
of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal
solution is essentially uncorrelated with IPM iterations.
This research has been partially supported through the MIT-Singapore Alliance. 相似文献
95.
Recently, Freund and Nachtigal proposed the quasi-minimal residual algorithm (QMR) for solving general nonsingular non-Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix—vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose-free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving singular systems is explored. First, a convergence result for the general class of Krylov-subspace methods applied to singular systems is presented. Then, it is shown that QMR and TFQMR both converge for consistent singular linear systems with coefficient matrices of index 1. Singular systems of this type arise in Markov chain modeling. For this particular application, numerical experiments are reported. 相似文献
96.
L. B. Freund 《Journal of Elasticity》1972,2(4):341-349
Summary An expression for the energy flux into the tip of an extending crack in terms of the dynamic elastic field of the crack is derived on the basis of an overall energy rate balance. It is shown that the energy flux depends only on the near-tip elastic field. The expression is compared to other expressions for this dependence which have been proposed by Atkinson and Eshelby, by Achenbach and by Erdogan. The energy flux is calculated in terms of the stress intensity factor for a particular plane strain problem and an antiplane strain problem.
Supported by the United States Atomic Energy Commission through Contract AT (11-1)-3084 with Brown University. 相似文献
Résumé Sur la base d'un équilibre énergétique dynamique global, le flux d'énergie convergeant vers l'extrémité d'une tissure en propagation est exprimé en fonction du champ élastique dynamique de la fissure. II est démontré que ce flux d'énergie ne dépend que du champ élastique au voisinage immédiat de l'extremité de la fissure, L'expression obtenue est comparée aux expressions précédemment proposées par MM. Atkinson et Eshelby, Mr. Achenbach, et Mr. Erdogan. Le flux d'énergie est évalué en fonction du facteur d'intensité des contraintes dans les cas particuliers d'un problème de déformation plane et d'un problème dans lequel la direction du cisaillement est horizontale.
Supported by the United States Atomic Energy Commission through Contract AT (11-1)-3084 with Brown University. 相似文献
97.
The paper studies differential equations of the form u′(x) = f(x, u(x), λ(x)), u(x0) = u0, where the right‐hand side is merely measurable in x. In particular sufficient conditions for the continuous and the differentiable dependence of solution u on the data and on the parameter λ are stated. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
98.
Abstract To avoid glitches due to Bragg reflection we use boron carbide anvils for our high pressure EXAFS experiments. Since boron carbide precludes the ruby fluorescence pressure calibration we use the EXAFS of selected materials to measure the reduction with pressure of the nearest neighbor distance and infer the pressure from an isothermal equation of state. The requirements for a good pressure calibrant and the difficulties in EXAFS data analysis are discussed. Cu, NaBr and RbCl have successfully been tested as pressure calibrants. 相似文献
99.
100.
A. Freund 《Monatshefte für Chemie / Chemical Monthly》1882,3(1):798-798
Ohne Zusammenfassung 相似文献