Simulations numériques de différentes méthodes d'éléments finis pour les problèmes de contact avec frottementNumerical implementation of different finite element methods for contact problems with friction

In this Note, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers. Several numerical studies corresponding to this choice are achieved in the PLAST2 code. To cite this article: L. Baillet, T. Sassi, C. R. Mecanique 331 (2003).     

Effects of initial geometric imperfections on dynamic behavior of rectangular plates

The present work deals with the influence of initial geometric imperfections on the dynamic behavior of simply supported rectangular plates subjected to the action of periodic in-plane forces. The nonlinear large-deflection plate theory used in this analysis corresponds to the dynamic analog of von Karman's theory. The temporal response is analyzed by the first-order generalized asymptotic method. The solution for the temporal equations of motion takes into account the possibility of existence of simultaneous forced and parametric vibrations. The results indicate that the presence of initial imperfections may significantly raise the resonance frequencies, cause the plate to exhibit a soft spring behavior and improve slightly the stability of the plate by reducing the area of its instability zones. Furthermore, the presence of initial imperfections induces forced vibrations which interact with parametric vibrations in order to generate a competitive hesitation phenomenon in the transition zone.     

About the Cohomology of the Lie Superalgebra of Vector Fields on ℝ n|n

In this article, we compute the first space of cohomology of Vect (? ^n|n ), the Lie superalgebra of vector fields on the supermanifold ? ^n|n with coefficients in 𝒻 (? ^n|n ), the space of smooth functions on ? ^n|n . We give a super analog of the cohomologies of vector fields that where studied for instance by Fuchs [2 Fuchs , D. B. ( 1986 ). Cohomology of Infinite Dimensional Lie Algebras . New York : Consultants Bureau . [Google Scholar]]. This work allows us to classify the deformations of the action of Vect(? ^n|n ) on 𝒻 (? ^n|n ).     

CFD modeling of convection heat transfer using 1.7 MHz and 24 kHz ultrasonic waves: a comparative study

The effects of 24 kHz and 1.7 MHz ultrasonic waves on heat transfer from a thin platinum wire are investigated. The results revealed that the 1.7 MHz ultrasound waves could increase the heat transfer rate more efficiently than the lower frequency one. The CFD modeling of ultrasonication was performed to compare heat transfer, predict fluid flow patterns. The CFD results were validated by the experimental results with an excellent agreement.     

In-phantom neutron dose distribution for bladder cancer cases treated with high-energy photons

This work presents an estimation of the neutron dose distribution for common bladder cancer cases treated with high-energy photons of 15 MV therapy accelerators. Neutron doses were measured in an Alderson phantom, using TLD 700 and 600 thermoluminescence dosimeters, resembling bladder cancer cases treated with high-energy photons from 15 MV LINAC and having a treatment plan using the four-field pelvic box technique. Thermal neutron dose distribution in the target area and the surrounding tissue was estimated. The sensitivity of all detectors for both gamma and neutrons was estimated and used for correction of the TL reading. TLD detectors were irradiated with a Co⁶⁰ gamma standard source and thermal neutrons at the irradiation facility of the National Institute for Standards (NIS). The TL to dose conversion factor was estimated in terms of both Co⁶⁰ neutron equivalent dose and thermal neutron dose. The dose distribution of photo-neutrons throughout each target was estimated and presented in three-dimensional charts and isodose curves. The distribution was found to be non-isotropic through the target. It varied from a minimum of 0.23 mSv/h to a maximum of 2.07 mSv/h at 6 cm off-axis. The mean neutron dose equivalent was found to be 0.63 mSv/h, which agrees with other published literature. The estimated average neutron equivalent to the bladder per administered therapeutic dose was found to be 0.39 mSv Gy^?1, which is also in good agreement with published literature. As a consequence of a complete therapeutic treatment of 50 Gy high-energy photons at 15 MV, the total thermal neutron equivalent dose to the abdomen was found to be about 0.012 Sv.     

Study on structural, thermal, sintering and conductivity of Cu-Co doubly substituted Bi4V2O11

Doubly substitution of vanadium by Cu and Co in the limit of 10% in Bi₄V₂O₁₁, has led to the formation of the Bi₄V_1.8Cu_0.2−xCo_xO_10.7 solid solution. X-ray diffraction shows that all the compositions present a tetragonal symmetry. The thermal analysis has revealed that the polymorph γ' phase, which is formed by a partial ordering of oxygen ions in the γ high temperature form, is stabilized at room temperature. The influence of sintering temperature on the microstructure of the samples was investigated by the scanning electron microscopy (SEM). The ceramics sintered at 820 °C for more than 3 hours present micro-craks. The evolution of the electrical conductivity with temperature and the degree of substitution has been investigated by impedance spectroscopy. The sample with x=0.1 presents the highest value of the conductivity ≈4.6×10⁻² S·cm⁻¹ at 600 °C.     

Null-controllability of some reaction–diffusion systems with one control force

This work is concerned with the null-controllability of semilinear parabolic systems by a single control force acting on a subdomain.     

Boundary stabilization of a Bresse‐type system

In this paper, we are concerned with asymptotic stability of a class of Bresse‐type system with three boundary dissipations. The beam has a rigid body attached to its free end. We show that exponential stabilization can be achieved by applying force and moment feedback boundary controls on the shear, longitudinal, and transverse displacement velocities at the point of contact between the mass and the beam. Our method is based on the operator semigroup technique, the multiplier technique, and the contradiction argument of the frequency domain method. Copyright © 2015 John Wiley & Sons, Ltd.     

The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory

We study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory, and the friction is modeled with Tresca’s law and the foundation is assumed to be electrically conductive. First we derive the classical variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field with a time-dependent variational equation for the potential field. Then we prove the existence of a unique weak solution to the model. Moreover, the proof is based on arguments of evolution equations and on the Banach fixedpoint theorem.