Fourier Transform in Bounded Domains

The functional analysis, the concept of distributionsu in the sense of Schwartz [7] andtheir extension given by Gelfand and Shilov [5]to ultradistributions u ,enables us to find by the means of the Fourier transform a secondlanguage to characterize physical behaviour. Almost any expressionwith physical meaning can be transformed, even if it isformulated in domains with complicated boundaries and evenif it is not integrable.Numerical procedures in the transformed space can bedeveloped in analogy to those well known in engineeringmechanics like the methods of Finite or BoundaryElements (FEM or BEM). Basis of the approaches presentedhere is the analytical representation of characteristicdistribution of a domain and the theorem of Parseval whichstates the invariance of energy in respect to thetransformation. In addition, the concept of thecharacteristic distribution leads to a very simplederivation of the Green-Gauss formulas fundamental for theBoundary or Finite Elements (e.g. [6]).     

ON A GENERALIZATION OF BERTRAND’S THEOREM

Bertrand’s theorem for the determination of the applied forces to a holonomicsystem from one of its first integrals,is extended to nonholonomic systems.Someinteresting applications of this new result are also given.     

Mechanical model of lung parenchyma as a two-phase porous medium

The anatomy and geometry of the lung at the micro- and macroscopic level have been described briefly. A notion of lung parenchyma — a macroscopically continuous medium whose mechanical properties result from those of microstructural components — has been adapted. Simplifying assumptions propounded in the constitutive model have been discussed. Two phases have been distinguished in the medium: the solid phase — a highly deformable, nonlinearly elastic skeleton in the form of a thin-walled tissue structure on the micro-scale — and the fluid phase — perfect gas (air) filterating through the structure. General constitutive relations for both phases and their mechanical interactions have ben formulated. Further, the fundamental set of differential equations of the quasi-static coupled problem has been developed. Large deformations, material nonlinearities, and dependence of permeability on skeleton deformation have been included. Matrix formulation of the problem has been presented from the point of view of the finite element method. An implicit iterative time integration scheme has been proposed. The algorithm has been illustrated with results of simple numerical tests.     

力学系统的扩散运动及量子化

研究位形由扩散过程定义的力学系统．利用变分的路径计算给出系统广义坐标表示的动力学方程，该方程连同连续方程描述系统量子波动随时间演化的概率进程．文末的表示定理指出，在满足适当正规条件的扩散过程和Ｓｃｈｒｄｉｎｇｅｒ方程的解（波函数）之间存在一一对应关系     

DRIVING FORCE AND DEFORMATION ANALYSIS FOR DYNAMIC CRACK PROPAGATION IN GAS PIPELINES UNDER DIFFERENT BOUNDARY CONDITIONS

In the light of a growing need for fracture control of rapid crack propagation(RCP)ingas pipelines,a program PFRAC(Pipeline FRacture Analysis Code)has been developed to analysethc various events.In this paper,by using PFRAC for the simulation of axial crack propagation in gaspipelines,a number of dynamic analysis issues rclating to boundary effects for uncracked and crackedpipes are investigated.This indicates that the boundary conditions along the length of the pipe play animportant role for fracture analysis in the pipe.In contrast.the boundary condutions at thc ends of along pipeline have little effect on the dynamic fracture events.     

Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow

In a previous article the authors introduced a Lagrange multiplier based fictitious domain method. Their goal in the present article is to apply a generalization of the above method to: (i) the numerical simulation of the motion of neutrally buoyant particles in a three-dimensional Poiseuille flow; (ii) study – via direct numerical simulations – the migration of neutrally buoyant balls in the tube Poiseuille flow of an incompressible Newtonian viscous fluid. Simulations made with one and several particles show that, as expected, the Segré–Silberberg effect takes place. To cite this article: T.-W. Pan, R. Glowinski, C. R. Mecanique 333 (2005).     

Finite element approximation of field dislocation mechanics

A tool for studying links between continuum plasticity and dislocation theory within a field framework is presented. A finite element implementation of the geometrically linear version of a recently proposed theory of field dislocation mechanics (J. Mech. Phys. Solids 49 (2001) 761; Proc. Roy. Soc. 459 (2003) 1343; J. Mech. Phys. Solids 52 (2004) 301) represents the main idea behind the tool. The constitutive ingredients of the theory under consideration are simply elasticity and a specification of dislocation velocity and nucleation. The set of equations to be approximated are non-standard in the context of solid mechanics applications. It comprises the standard second-order equilibrium equations, a first-order div-curl system for the elastic incompatibility, and a first-order, wave-propagative system for the evolution of dislocation density. The latter two sets of equations require special treatment as the standard Galerkin method is not adequate, and are solved utilizing a least-squares finite element strategy. The implementation is validated against analytical results of the classical elastic theory of dislocations and analytical results of the theory itself. Elastic stress fields of dislocation distributions in generally anisotropic media of finite extent, deviation from elastic response, yield-drop, and back-stress are shown to be natural consequences of the model. The development of inhomogeneity, from homogeneous initial conditions and boundary conditions corresponding to homogeneous deformation in conventional plasticity, is also demonstrated. To our knowledge, this work represents the first computational implementation of a theory of dislocation mechanics where no analytical results, singular solutions in particular, are required to formulate the implementation. In particular, a part of the work is the first finite element implementation of Kröner's linear elastic theory of continuously distributed dislocations in its full generality.     

Contrôle par rotation ou par aspiration de l'écoulement autour d'un cylindre calculé par Simulation des Grandes Échelles

Control of the flow around a circular cylinder is studied using Large Eddy Simulation. The influence of control by rotation and suction on the flow characteristics is considered for several Reynolds numbers. Comparisons with experiments were conducted at $\mathit{Re}={10}^5$ for the flow with and without control. A drag reduction up to 30% is obtained for an usual suction intensity. To cite this article: G. Fournier et al., C. R. Mecanique 333 (2005).     

Microstructures réalisant toute compressibilité ou conductivité encadrée par les bornes de Hashin et Shtrikman

The conductivity or bulk modulus of an isotropic composite consisting of two well-ordered isotropic phases is situated between the lower and upper bounds of Hashin and Shtrikman. This work is concerned with the construction of two new microstructures capable of realizing every conductivity or bulk modulus comprised between these bounds. The two microstructures obtained, appearing to be simpler than those presented in the literature to achieve the same purpose, have the property that the variation of the corresponding conductivity or bulk modulus is strictly monotone with respect to the geometric parameter characterizing them. To cite this article: Q.-C. He, H.L. Quang, C. R. Mecanique 333 (2005).     

An optimal control approach to the analysis of inelastic structures under cyclic loading

Optimal control theory is used to study the asymptotic behaviour of elasto-viscoplastic structures under cyclic loading. With this approach, the asymptotic state is found as the solution of a minimization problem. General properties of this method are established. A simple thermomechanical problem is studied to illustrate and validate this approach. An interest of the proposed method lies in its capacity to handle other nonlinearities than plasticity. To illustrate this point, the approach is extended to the coupled viscoplasticity/frictionless contact problem. Some numerical results are given for an elasto-viscoplastic half-plane under cyclic frictionless indentation.