Numerical modelling of twin helical spring under tensile loading

This paper presents a 3D geometric modelling of a twin helical spring and its finite element analysis to study the spring mechanical behaviour under tensile axial loading. The spiralled shape graphic design is achieved through the use of Computer Aided Design (CAD) tools, of which a finite element model is generated. Thus, a 3D 18-dof pentaedric elements are employed to discretise the complex “wired-shape” of the spring, allowing the analysis of the mechanical response of the twin spiralled helical spring under an axial load. The study provides a clear match between the evolution of the theoretical and the numerical tensile and compression normal stresses, being of sinusoidal behaviour. The overall equivalent stress isovalues increases radially from 0° to 180°, being maximal on the internal radial zone at the section 180°. On the other hand, the minimum stress level is located in the centre of the filament cross section.     

Synthesis of substituted 1,4-diazepines and 1,5-benzodiazepines using an efficient heteropolyacid-catalyzed procedure

An efficient and improved procedure for the synthesis of 1,4-diazepine and 1,5-benzodiazepine derivatives via the reaction of ketimine intermediates with aldehydes in the presence of Keggin-type heteropolyacids (HPAs) was developed. High yields and short reaction times were obtained for both electron-releasing and electron-withdrawing substituted 1,4-diazepine and 1,5-benzodiazepines derivatives.     

Syntheses and crystal structures of new vanadium(IV) oxyphosphates M(VO)2(PO4)2 with M = Co,Ni

We have extended our research interest on titanium oxyphosphates (M^II(TiO)₂(PO₄)₂, with M^II = Mg, Fe, Co, Ni, Cu, Zn) to vanadium oxyphosphates M^II(V^IVO)₂(PO₄)₂ (M^II = Co, Ni). For each compound two phases, named α and β according to synthesis conditions, have been stabilized at room temperature, then characterized. The four crystal structures M(VO)₂(PO₄)₂ (α and β for M = Co, Ni) have been determined in monoclinic P2₁/c space group using X-ray single crystals diffraction data. Structure of the α phase is derived from the Li(TiO)(PO₄) (orthorhombic Pnma) and LiNi_0.50(TiO)₂(PO₄)₂ (monoclinic P2₁/c) types, with cell parameters: a = 6.310(1) Å, b = 7.273(1) Å, c = 7.432(1) Å, β = 90.43(1)° for M = Co, and a = 6.297(2) Å, b = 7.230(2) Å, c = 7.421(2) Å, β = 90.36(2)° for M = Ni. Structure of the β phase is derived from the Ni(TiO)₂(PO₄)₂-type (monoclinic P2₁/c) with cell parameters: a = 7.2742(2) Å, b = 7.2802(2) Å, c = 7.4550(2) Å, β = 120.171(2)° for M = Co, and a = 7.2691(2) Å, b = 7.2366(2) Å, c = 7.4453(2) Å, β = 120.231(2)° for M = Ni. All these structures consist of a three dimensional (3D) framework built up of infinite chains of tilted corner-sharing [VO₆] octahedra, cross-linked by corner-sharing [PO₄] tetrahedra. The M²⁺ ion (M = Co, Ni) is located in a triangular based antiprism which shares faces with two [VO₆] octahedra. Structural filiation is discussed based on a common structural unit, a sheet where divalent cations M²⁺ (M = Co, Ni) are inserted. A thermal study of the α ? β transition is also presented.     

How to drive imine–enamine tautomerism of pyronic derivatives of biological interest – A theoretical and experimental study of substituent and solvent effects

An investigation of the tautomerism of five series of aminated pyronic compounds of pharmacological interest was carried out using NMR experiments and standard quantum mechanical B3LYP/6-311+G** calculations. The obtained results indicate that among four possible tautomers, imine and enamine forms are the two predominating ones in the gas phase as well as in solution. Depending on the nature of the substituting group, the enamine or the imine form is the most stable tautomer, the calculations being in agreement with experiment. The calculated equilibrium constants in the gas phase and in solution show that the enamine form is stabilized by polar solvents, in all cases. NBO analysis explains well the predominance of a form over another one when changing a substituting group. We give indications on how to favour the imine form which is preferred for synthesis purposes.     

Modelisation of thermoelastic linear behaviour of tungsten filaments in simple and twin helical spring configurations

By trying to increase the luminosity or the life expectancy of an incandescent lamp, an idea consists of a series of successive rolling up of the tungsten filament. This gives geometrical configurations of filaments named simple, twin, or triple helical spring, etc… In this paper, we will limit only to the cases of the simple and twin helical spring filaments. Under the combined effects of the high temperature and the stresses induced by its own weight, the filament creeps by becoming plastically deformed in a permanent and a continuously manner, until the rupture. The theoretical study of the behaviour of these filaments needs the knowledge of internal efforts distribution, deformations modes, and their evolutions. The present work consists on an elastic structural analysis which must be the first step. Since the objective is also to study the influence of the filament self-weight solicitation, the orientation (or position) with respect to gravitational direction should be taken into account. Numerical results are obtained by finite element method. They showed a negligible influence of the solicitations due to the variation of the temperature with respect to those of the self-weight, and a relative sensitivity to the position changes for the twin helical spring filament. For this later, we have developed an analytical method which is only valid in the case of a vertical position. Because of some difficulties, the comparison between the numerical and analytical results could not be carried out directly. However, the analytical approach proved to be qualitatively useful for the analysis of numerical results.