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.     

Naproxen derivatives: Synthesis,reactions, and biological applications

This review describes the synthesis and reactions of naproxen derivatives and highlights the effects of compounds containing the naproxen moiety in important biological applications.     

Solvatochromic responses and pH effects on the electronic spectra of some azo derivatives of 1-amino-2-hydroxy-4-naphthalenesulfonic acid

Synthesis and characterization of five arylazo derivatives of 1-amino-2-hydroxy-4-naphthalenesulfonic acid (H₂L¹) are reported. The UV/Vis absorption spectra of the parent compound (H₂L¹) and its arylazo derivatives (H₂L²–H₄L⁶) have been measured at room temperature in seven solvents of different polarities and with variable parameters. The electronic transitions were analyzed using SPSS program, linear regression technique and Kamlet–Taft’s equation to permit a good understanding of solvent-induced spectral shifts. The electronic absorption spectra of the prepared compounds containing different substituents were studied in aqueous solutions at different pH values. The pK values of the investigated compounds were evaluated spectrophotometrically. The prevailing acid species present at any pH range are judged from the constructed distribution diagrams.     

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.     

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.     

Parameter estimation for a two-parameter bathtub-shaped lifetime distribution

A two-parameter distribution was revisited by Chen (2000) [7]. This distribution can have a bathtub-shaped or increasing failure rate function which enables it to fit real lifetime data sets. Maximum likelihood and Bayes estimates of the two unknown parameters are discussed in this paper. It is assumed in the Bayes case that the unknown parameters have gamma priors. Explicit forms of Bayes estimators cannot be obtained. Different approximations are used to establish point estimates and two sided Bayesian probability intervals for the parameters. Monte Carlo simulations are applied to the comparison between the maximum likelihood estimates and the approximate Bayes estimates obtained under non-informative prior assumptions. Analysis of a real data set is also been presented for illustrative purposes.     

On optimality and duality theorems of nonlinear disjunctive fractional minmax programs

This paper is concerned with the study of optimality conditions for disjunctive fractional minmax programming problems in which the decision set can be considered as a union of a family of convex sets. Dinkelbach’s global optimization approach for finding the global maximum of the fractional programming problem is discussed. Using the Lagrangian function definition for this type of problem, the Kuhn–Tucker saddle point and stationary-point problems are established. In addition, via the concepts of Mond–Weir type duality and Schaible type duality, a general dual problem is formulated and some weak, strong and converse duality theorems are proven.     

First principle study of a bimolecular thin film on Ag(1 1 1) surface

The formation of melamine–PTCDI bimolecular networks deposited on Ag(1 1 1) is studied by means of first principle calculations. Emphasis is placed on the interplay of the inter-molecular hydrogen bonds and the molecule–substrate contacts. Our simulations show rather strong distortions of the adsorbed molecules near the contact points due to the influence the hydrogen bonds. Despite this, the charge transfer from the substrate to a PTCDI molecule remains almost the same (0.9 e⁻) as obtained for an isolated PTCDI molecule. A detailed analysis of the topological features of the electronic density reveals that the charge transfer modifies the two types of hydrogen bonds in opposite ways, weakening the central bond and strengthening the two lateral ones, while roughly keeping a constant binding energy. Altogether, the influence of the substrate on the molecular network is proved to be weak.