Application of ‘Operational Quadrature Methods’ in Time Domain Boundary Element Methods

The usual time domain Boundary Element Method (BEM) contains fundamentalsolutions which are convoluted with time-dependent boundary data andintegrated over the boundary surface. Here, a new approach for theevaluation of the convolution integrals, the so-called OperationalQuadrature Methods developed by Lubich, is presented. In thisformulation, the convolution integral is numerically approximated by aquadrature formula whose weights are determined using the Laplacetransform of the fundamental solution and a linear multisep method. Tostudy the behaviour of the method, the numerical convolution of afundamental solution with a unit step function is compared with theanalytical result. Then, a time domain Boundary Element formulationapplying the Operational Quadrature Methods is derived. For thisformulation only the fundamental solutions in Laplace domain arenecessary. The properties of the new formulation are studied with anumerical example.     

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]).     

热压电变分原理

热释电介的许多传感器及机敏结构或中的关键材料，本文系统地讨论了在基础理论和数值计算中极具重要地位的各类变分原理，包括准静态变分原理、动态变分原理和关于固有频率的变分原理。最后建立了关于静态压电要板的变分原理，并由此导出了各向异性压电板的控制方程及边界条件。     

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.     

Turbulent boundary layer manipulation by outer-layer devices

A turbulent boundary layer manipulated by outer-layer devices has been studied. Experiments have been conducted in the 0.70 by 0.50 m² low speed wind tunnel of the Modesto Panetti Aeronautical Laboratory of the Politecnico di Torino. Mean values and turbulent quantities measured in the natural and manipulated boundary layers are shown for comparison. The mechanisms to explain the observed skin friction and turbulence reduction are discussed. The manipulator wake effect, consisting in decoupling the wall-region from the boundary layer outer-region, is stressed in the present results.

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Sommario Viene studiato uno strato limite turbolento manipolato, utilizzando la tecnica degli outer-layer devices. Gli esperimenti sono stati condotti nella galleria del vento 0.70×0.50 m² del Laboratorio di Aeronautica Modesto Panetti del Politecnico di Torino. Sono confrontati risultati relativi ai casi di flusso non manipolato e manipolato. Vengono discussi i meccanismi che conducono alla riduzione dello sforzo di attrito a parete e delle quantità turbolente; in particolare si punta l'attenzione sull'effetto decorrelante della scia del manipolatore.

     

Computational and experimental studies of convective fluid motion and heat transfer in inclined non-rectangular enclosures

Computational and experimental studies of the fluid motion and heat transfer characteristics of an incompressible fluid contained in a non-rectangular inclined enclosure are described in this paper. The enclosure has two 45° inclined side walls one of which was heated and the other cooled. The remaining two sides of the enclosure are parallel and insulated. The enclosure was rotated about the long axis in steps of 30° through 360°. Experiments were performed to study the effects of Rayleigh number, aspect ratios and orientation of the enclosure. The computational method uses a mesh transformation technique coupled with the introduction of ‘false transient’ parameters for the steady state solution of the problem. The experimental method uses smoke for flow visualization studies. With aspect ratios of 3 and 6, the results indicate that the heat transfer and fluid motion within the enclosure is a strong function of both the Rayleigh number and the cavity orientation angle. A minimum and a maximum mean Nusselt number occurred as the angle of inclination was increased from 0 to 360°. A transition in the mode of circulation occurred at the angle corresponding to the minimum or maximum rate of heat transfer. Stream lines and isotherms are presented for the most representative cases     

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).