Modelling matrix damage and fibre–matrix interfacial decohesion in composite laminates via a multi-fibre multi-layer representative volume element (MRVE)

A three-dimensional multi-fibre multi-layer micromechanical finite element model was developed for the prediction of mechanical behaviour and damage response of composite laminates. Material response and micro-scale damage mechanism of cross-ply, [0/90]_ns, and angle-ply, [±45]_ns, glass-fibre/epoxy laminates were captured using multi-scale modelling via computational micromechanics. The framework of the homogenization theory for periodic media was used for the analysis of the proposed ‘multi-fibre multi-layer representative volume element’ (M²RVE). Each layer in M²RVE was represented by a unit cube with multiple randomly distributed, but longitudinally aligned, fibres of equal diameter and with a volume fraction corresponding to that of each lamina (equal in the present case). Periodic boundary conditions were applied to all the faces of the M²RVE. The non-homogeneous stress–strain fields within the M²RVE were related to the average stresses and strains by using Gauss’ theorem in conjunction with the Hill–Mandal strain energy equivalence principle. The global material response predicted by the M²RVE was found to be in good agreement with experimental results for both laminates. The model was used to study effect of matrix friction angle and cohesive strength of the fibre–matrix interface on the global material response. In addition, the M²RVE was also used to predict initiation and propagation of fibre–matrix interfacial decohesion and propagation at every point in the laminae.     

The geometric Neumann problem for the Liouville equation

Let Ω denote the upper half-plane ${\mathbb{R}_+^2}$ or the upper half-disk ${D_{\varepsilon}^+\subset \mathbb{R}_+^2}$ of center 0 and radius ${\varepsilon}$ . In this paper we classify the solutions ${v\in\;C^2(\overline{\Omega}\setminus\{0\})}$ to the Neumann problem $$\left\{\begin{array}{lll}{\Delta v+2 Ke^v=0\quad {\rm in}\,\Omega\subseteq \mathbb{R}^2_+=\{(s, t)\in \mathbb{R}^2: t >0 \},}\\ {\frac{\partial v}{\partial t}=c_1e^{v/2}\quad\quad\quad{\rm on}\,\partial\Omega\cap\{s >0 \},}\\ {\frac{\partial v}{\partial t}=c_2e^{v/2}\quad\quad\quad{\rm on}\,\partial\Omega\cap\{s <0 \},}\end{array}\right.$$ where ${K, c_1, c_2 \in \mathbb{R}}$ , with the finite energy condition ${\int_{\Omega} e^v < \infty}$ As a result, we classify the conformal Riemannian metrics of constant curvature and finite area on a half-plane that have a finite number of boundary singularities, not assumed a priori to be conical, and constant geodesic curvature along each boundary arc.     

An efficient one pot synthesis of 3‐(2‐oxo‐2H‐chromen‐3‐yl)‐6H,8H‐pyrimido[4,5‐c]pyridazine‐5,7‐dionesl

An easy, simple and versatile one step synthesis of 3‐(2‐oxo‐2H‐chromen‐3‐yl)‐6H,8H‐pyrimido[4,5‐c]‐pyridazine‐5,7‐diones is reported by reaction of 3‐acetylcoumarins ( 1 ) with alloxan monohydrate ( 2 ) in acetic acid followed by hydrazine hydrate.     

A Facile One Pot Synthesis of 2-Aryl-4-[2H-2-oxo-[1]benzopyran-3-yl] 2,3-dihydro and 2,5-Dihydro-1,5-benzothiazepines

3-acetyl coumarins on condensation with various aromatic aldehydes in the presence of piperidine gave corresponding chalcones in a solid state under solvent free conditions. These chalcones are isolated and characterized. The in-situ-formed chalcones (1) are also converted into corresponding 2-aryl-4-[2H-2-oxo[1]benzopyran-3-yl]-2,3-dihydro (3) and 2,5-dihydro-1,5-benzothiazepines (4) in one step by interacting with orthoamino thiophenol. Both the 2,3-dihydro (3) and 2,5-dihydrobenzothiazepines (4) have been converted into same tetrahydrobenzothiazepine (5). Finally, the tetrahydrobenzo thiazepine (5) is converted into its acetyl derivative (11). The structures of the title compounds have been confirmed on the basis of their microanalytical, IR, ¹ H NMR, and mass spectral data.     

Determination of molybdenum by extraction of its thiocyanate into ethyl methyl ketone

A simple, sensitive and selective spectrophotometric method for determination of molybdenum is described. A solution containing 100 mug of Mo in 2.5M hydrochloric acid is treated with ascorbic acid and ammonium thiocyanate and after standing for 8 min is shaken with an equal volume of ethyl methyl ketone for 30 sec. The absorbance of the complex is measured at 465 nm against a reagent blank. The complex is stable for 1 hour. There is no interference from Re(VII), SO(2-)(4), Cl(-), CH(3)COO(-), PO(3-)(4), NO(-)(3), C(2)O(2-)(4), citrate or tartrate, and at least 5 mg of U(VI), 10 mg of Cr(III, VI), Th, or Ni, and 20 mg of W(VI) Can be tolerated. Vanadium(V) interferes at the 500 mug level, and fluoride slightly decreases the absorbance.     

Strong Law of Large Numbers for Banach Space Valued Fuzzy Random Variables

In this paper we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of Banach space valued fuzzy random variables.     

Solving the capacitated lot-sizing problem with backorder consideration

In this research, we formulate and solve a type of the capacitated lot-sizing problem. We present a general model for the lot-sizing problem with backorder options, that can take into consideration various types of production capacities such as regular time, overtime and subcontracting. The objective is to determine lot sizes that will minimize the sum of setup costs, holding cost, backorder cost, regular time production costs, and overtime production costs, subject to resource constraints. Most existing formulations for the problem consider the special case of the problem where a single source of production capacity is considered. However, allowing for the use of alternate capacities such as overtime is quite common in many manufacturing settings. Hence, we provide a formulation that includes consideration of multiple sources of production capacity. We develop a heuristic based on the special structure of fixed charge transportation problem. The performance of our algorithm is evaluated by comparing the heuristic solution value to lower bound value. Extensive computational results are presented.     

Adsorption of51Cr(VI) on manganese dioxide from aqueous solution

Sorption of⁵¹Cr(VI) by MnO₂ has been studied as a function of pH and ionic concentration in the presence of certain added cations and anions. The findings are explained in the light of deprotonation/hydroxyl ion association reaction on oxide surface and its subsequent interaction with the tracer. Infrared spectroscopy has shown the chemical interaction of Cr(VI) on the surface of MnO₂. The influence of certain interfering ions has been shown on the sorption of⁵¹Cr(VI) on MnO₂ surface. An attempt has been made to concentrate traces of⁵¹Cr under optimum experimental conditions. The experimental observation shows that the activity sorbed under specified conditions can be recovered appreciably by leaching the pre-adsorbed carrier.     

Dependence of nanocrystalline SnO2 particle size on synthesis route

Very fine SnO₂ powders were produced by (a) slow and (b) forced hydrolysis of aqueous SnCl₄ solutions and (c) hydrolysis of tin(IV)-isopropoxide dissolved in isopropanol (sol-gel route) and then characterized by X-ray powder diffraction, Fourier transform infrared and laser Raman spectroscopies, TEM and BET. The XRD patterns showed the presence of the cassiterite structure. As found from XRD line broadening the crystallite sizes of all powders were in the nanometric range. TEM results also showed that the sizes of SnO₂ particles in all powders are in nanometric range. Very fine SnO₂ powders showed different features in the FT-IR spectra, depending on the route of their synthesis. The reference Raman spectrum of SnO₂ showed four bands at 773, 630, 472 and 86 (shoulder) cm⁻¹, as predicted by group theory. Very fine SnO₂ powders showed additional Raman bands, in dependence on their synthesis. The broad Raman band at 571 cm⁻¹ was ascribed to amorphous tin(IV)-hydrous oxide. The additional Raman bands at 500, 435 and 327 cm⁻¹ were recorded for nanosized SnO₂ particles produced by forced hydrolysis of SnCl₄ solutions. However, these additional Raman bands were not observed for nanosized SnO₂ particles produced by slow hydrolysis of SnCl₄ solution or the sol-gel route. The aggregation effects of nanosized particles were considered in the interpretation of the Raman band at 327 cm⁻¹. The method of low frequency Raman scattering was applied for SnO₂ particle size determination. On the basis of these measurements it was concluded that the size of SnO₂ particles was also in the nanometric range and that, the sol-gel particles heated to 400 °C consisted of several SnO₂ crystallites.     

Comparison of HPTLC and HPLC for Determination of Econazole Nitrate in Topical Dosage Forms

JPC – Journal of Planar Chromatography – Modern TLC - HPTLC and HPLC methods have been established for separation and quantitative determination of econazole nitrate. HPTLC was...