Arc-Length Method for Frictional Contact Problems Using Mathematical Programming with Complementarity Constraints

A new formulation as well as a new solution technique is proposed for an equilibrium path-following method in two-dimensional quasistatic frictional contact problems. We consider the Coulomb friction law as well as a geometrical nonlinearity explicitly. Based on a criterion of maximum dissipation of energy, we propose a formulation as a mathematical program with complementarity constraints (MPEC) in order to avoid unloading solutions in which most contact candidate nodes become stuck. A regularization scheme for the MPEC is proposed, which can be solved by using a conventional nonlinear programming approach. The equilibrium paths of various structures are computed in cases such that there exist some limit points and/or infinite number of successive bifurcation points.     

On the (in)stability of quasi‐static paths of smooth systems: definitions and sufficient conditions

A concept of stability of quasi‐static paths is discussed in this paper that takes into account the existence of fast (dynamic) and slow (quasi‐static) time scales in the evolution of many mechanical systems. The proposed concept is essentially a continuity property with respect to the smallness of the initial perturbations (as in Lyapunov stability) and the smallness of the quasi‐static loading rate (that plays the role of the small parameter in singular perturbation problems). A related concept of attractiveness is also proposed. Several examples illustrate the relevance of the definitions. Sufficient conditions for attractiveness or for instability of quasi‐static paths of smooth systems are proved. Copyright © 2005 John Wiley & Sons, Ltd.     

A note on a modified version of the Poincaré-Birkhoff theorem

We show, by constructing a suitable area preserving homeomorphism without fixed points, that the twist condition considered at zero and at infinity in a recent modified version of the Poincaré-Birkhoff fixed point theorem cannot be interchanged.     

The sequestral capture of fluoride,nitrate and phosphate by metal-doped and surfactant-modified hybrid clay materials

Toxic anions removal for increased access to potable water remains a problem that has not been adequately addressed. This study, reports the successful preparation and modification of kaolinite-papaya seed based adsorbents under vacuum (VHYCA) for the removal of Nitrate (NO₃ ^?), Fluoride (F^?) and Phosphate (PO₄ ^3?). Modified adsorbents via metal-doping using Zinc were more efficient in removing these anions from aqueous solution compared with surfactant-modified adsorbents. However, both type of adsorbents showed a higher preference for NO₃ ^? removal with Zn-VHYCA and Fe-VHYCA adsorbents having 98 and 85% removal of the anion from aqueous solution, respectively. The removal of F^? and PO₄ ^3? was best achieved by Ortho-phenylenediamine (OP) and N,N,N′,N′-Tetramethyl-1,4-phenyldiaminedihydrochloride (TPD) modified VHYCA, respectively. However, Zn-VHYCA adsorbent showed comparable results with TPD-VHYCA in the removal of PO₄ ^3? from aqueous solution. Overall, the metal-doped hybrid clay adsorbents showed better efficiency for the removal of anions than the surfactant-modified hybrid clay adsorbents.     

Solution conformations for the flexible 1-chloro-1,1-difluoro-2-pentanol unveiled using multinuclear magnetic resonance

The preferred conformations of a small polyfunctional molecule containing fluorine, chlorine and hydroxyl groups, the 1-chloro-1,1-difluoro-2-pentanol (CDP), were completely elucidated using ¹H, ¹³C and ¹⁹F NMR in three different solvents. While the Cl-C-C-O dihedral angle was asserted using coupling constant data for the diastereotopic fluorines, the Et-C-C-O torsional angle was analyzed by means of ¹H NMR spectra with selective irradiation of the diastereotopic hydrogens and fluorines. In addition, unusual couplings of the hydroxyl hydrogen with a diastereotopic hydrogen and fluorines provided information on the O-H orientation. The behavior of ¹J_C,F when the solvents varied agrees with a weak F???HO intramolecular hydrogen bond. These findings were corroborated, and the governing interactions rationalized with the aid of high level CCSD(T) theoretical calculations. Noteworthy, hyperconjugation involving the electron-acceptor σ*_C-Cl orbital drives the conformational equilibrium rather than the fluorine gauche effect.