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61.
In this Note we present a justification of the kinematic assumptions for thin-walled rods with shallow profile. These assumptions are fundamental to writing the one-dimensional equilibrium equations for such structures. The obtained kinematics are different from the Vlassov case, which is only valid for strongly curved profiles. They are also different from the that classically used in shell theory. The justification given in this Note is based on an asymptotic approach. To cite this article: L. Grillet et al., C. R. Mecanique 333 (2005). 相似文献
62.
Anish Roy 《Journal of the mechanics and physics of solids》2006,54(8):1711-1743
In Part I of this set of two papers, a model of mesoscopic plasticity is developed for studying initial-boundary value problems of small scale plasticity. Here we make qualitative, finite element method-based computational predictions of the theory. We demonstrate size effects and the development of strong inhomogeneity in simple shearing of plastically constrained grains. Non-locality in elastic straining leading to a strong Bauschinger effect is analyzed. Low shear strain boundary layers in constrained simple shearing of infinite layers of polycrystalline materials are not predicted by the model, and we justify the result based on an examination of the no-dislocation-flow boundary condition. The time-dependent, spatially homogeneous, simple shearing solution of PMFDM is studied numerically. The computational results and an analysis of continuous dependence with respect to initial data of solutions for a model linear problem point to the need for a nonlinear study of a stability transition of the homogeneous solution with decreasing grain size and increasing applied deformation. The continuous-dependence analysis also points to a possible mechanism for the development of spatial inhomogeneity in the initial stages of deformation in lower-order gradient plasticity theory. Results from thermal cycling of small scale beams/films with different degrees of constraint to plastic flow are presented showing size effects and reciprocal-film-thickness scaling of dislocation density boundary layer width. Qualitative similarities with results from discrete dislocation analyses are noted where possible.We discuss the convergence of approximate solutions with mesh refinement and its implications for the prediction of dislocation microstructure development, motivated by the notion of measure-valued solutions to conservation laws. 相似文献
63.
64.
We demonstrate the ability to determine stress intensity factors in orthotropic materials directly from measured temperatures
away from the crack and using far-field expressions for the stresses. This is advantageous, recognizing that recorded thermoelastic
data can be very unreliable near the tip of a crack. In addition to singular terms that govern in the immediate vicinity of
the crack tip, the present series expressions for the stresses contain higher-order finite terms. Little measured input information
is needed and data acquisition positions can be selected largely at the user's discretion. 相似文献
65.
Claude Valle Jean-Marie Souriau Gry de Saxc Danielle Fortun 《Comptes Rendus Mecanique》2004,332(12):1013-1018
We show that the affine structure of the 3-dimensional space is deeply enmeshed with the static laws expression. The relevance of tensorial rules for calculus in mechanics is thus enhanced. The virtual work principle is stated precisely but a little twist is given to the usual statements: the tensorial nature of the so-called virtual displacement vector is asserted to be covariant. To cite this article: C. Vallée et al., C. R. Mecanique 332 (2004).
Résumé
Nous montrons que la structure affine de l'espace tridimensionnel est fortement imbriquée avec l'expression des lois de la statique. La pertinence de l'application des règles du calcul tensoriel à la mécanique est ainsi renforcée. Le principe des travaux virtuels est établi précisément avec une seule entorse aux exposés classiques : la nature tensorielle de l'habituel vecteur déplacement virtuel est affirmée covariante. Pour citer cet article : C. Vallée et al., C. R. Mecanique 332 (2004). 相似文献66.
The first part of this paper gives a theoretical study of the mechanics of contact of an AFM tip on viscous materials. Analytical expressions are derived showing the non-linear behaviors specifically related to the use of dynamic operation modes of AFM on viscous materials. A detailed analysis of the dissipated energy as a function of the tip indentation is presented. The second part is dedicated to a theoretical analysis investigating the domain of stability of the oscillator and the influence of the machine. The theoretical approach includes the electronic feedback loop used with the frequency modulation mode. Because the interaction between the tip and the sample produces a dynamical non-linear behavior, an unstable branch occurs that can change the stability of the oscillator. In particular, a sudden jump of the oscillating tip can be produced. In spite of the complexity of the problem, the analytical approach ends with two simple equations. The two equations provide an unambiguous way of discriminating between the contributions from the machine and the tip sample interaction. 相似文献
67.
A particle method has been used to simulate the vorticity transport in a two-dimensional flow of an incompressible inviscid fluid. In this method, not only the location and the circulation of the particle are used but also the moments of the internal vorticity. The transport equation for these moments has been derived from the vorticity transport equation. The method has been compared to the usual particle method as well as to Teng's elliptic vortex model. The test case is that of the evolution of two circular patches of vorticity already used by Teng. To cite this article: A. Beaudoin et al., C. R. Mecanique 330 (2002) 51–56 相似文献
68.
In this paper, the concept of covering domain is introduced to develop a general expression for the Fredholm Integral Equations
Method, by which elasticity problems of arbitrarily shaped bodies loaded by external forces can be solved. Some special expressions
are given for a body with non-zero remote stresses, or subjected to some concentrated forces on its boundary. The relationship
between the loading forces and solutions are also discussed. Some analytical solutions can be obtained for simple cases. When
numerical computations are needed for the solution, the method proves to have high precision and fast convergency. 相似文献
69.
A numerical study on the dynamic response of a mechanical system composed of two coaxial cylinders in relative rotation and unilateral contact with Coulomb friction is presented. This discussion complements the semi-analytical results on stick–slip waves given in Moirot, Nguyen, C. R. Acad. Sci. Paris Sér. IIb 328 (2000) 663–669, by some numerical simulations on the dynamic transition of the system from a given initial state to a surface wave. The case of stick–slip–separation waves is considered. To cite this article: A. Oueslati et al., C. R. Mecanique 331 (2003). 相似文献
70.
V. N. Chekhov 《International Applied Mechanics》2007,43(12):1359-1371
The paper addresses the important issue of allowing for the inelastic properties of rock in stability problems for a stratified
rock mass. A three-dimensional nonlinear problem statement is used. An exact method to study the surface instability of a
regularly layered semi-infinite medium is developed. New numerical results are obtained
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 68–81, December 2007. 相似文献