Non-linear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects

This paper presents an analytical approach to investigate the non-linear axisymmetric response of functionally graded shallow spherical shells subjected to uniform external pressure incorporating the effects of temperature. Material properties are assumed to be temperature-independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for shallow spherical shells are derived by using the classical shell theory and specialized for axisymmetric deformation with both geometrical non-linearity and initial geometrical imperfection are taken into consideration. One-term deflection mode is assumed and explicit expressions of buckling loads and load-deflection curves are determined due to Galerkin method. Stability analysis for a clamped spherical shell shows the effects of material and geometric parameters, edge restraint and temperature conditions, and imperfection on the behavior of the shells.     

Size-dependent heterogeneity benefits the mechanical performance of bone

Heterogeneity of biological materials, such as bone, tooth, and mollusc shells, plays a key role in determining their mechanical performance (e.g. the strength, damage tolerance, etc.). Here, we quantify heterogeneities in elasticity and inelasticity of bovine cortical bone between 100 nm and a few microns and identify a characteristic length scale (λ_c) of approximately 200 nm. Below λ_c the mechanical heterogeneity of bone is pronounced and exhibits a strong nonlinear size-dependence, while above λ_c the heterogeneity is much less. Such size-dependent heterogeneity benefits the mechanical performance of bone since it not only promotes the energy dissipation at nanoscale, but also suppresses heterogeneity-induced stress concentration and strain localization at larger length scales. This is one of the possible mechanisms functioning at multiple length scales that make bone a well-designed tough natural material. Utilizing experimentally measured data, systematic computational simulations were carried out, showing that the heterogeneity in inelasticity, rather than elasticity, plays a dominant role in promoting energy dissipation during deformation. Possible parameters that determine the inelasticity heterogeneity (e.g. mean value and standard deviation of heterogeneous yield stress) and therefore affect energy dissipation are investigated under typical deformation modes of bone. The analysis presented suggests that there exists an optimum ratio of macroscopic strength to elastic modulus for improving energy dissipation under tension. All these findings are of great value to the design and synthesis of improved bio-inspired composites.     

A Construction of Multiresolution Analysis on Interval

We present a concrete method of constructing multiresolution analysis on interval. The method generalizes the corresponding results of Cohen, Daubechies and Vial [Appl. Comput. Harmonic Anal., 1（1993）, 54-81]. By the use of the subdivision operator, the expressions of the constructed functions are more compact. Furthermore, the method reveals more clearly some properties of multiresolution analysis with certain approximation order.     

Simple Preparation of the Photocatalyst of Sn^2＋ -doped Titania

TiO2 is widely used as photocatalyst because of its optical and electronic properties, low cost, chemical stability, non-toxicity and applicability to the treatment of a large variety of pollutants1. The activities of photocatalyst were influenced by the …     

Reactions of [60]Fullerene with Di(azidomethyl) benzenes

Alargenumberofadditionsto[6O]fullerenehavebeeninvestigated.However,mostoftheworkhaveconcentratedontheformationofthemono-additionproductS0f[60]fullerene'-Thedevelopment0fselechveroutestomultipleadductShascurrentlybecomethefrontierinthechendstryof[60]fuIlerene'~'.FollowingtheaPplicahonoftether-directedremotefunctionalizati0ntotheregi0specificformati0nofthedi-andtriadductSof[60]fullerene,F.Diederichetal6alsodescribed'awayforthedirectdifunctionalizationof[60]fullerenebasedonacyclizationreachono…     

Study of neutral-charged particle correlations in high energy collisions

Recent experiments at Serpukhov, NAL, and CERN indicate a strong correlation between neutral and charged pions produced in high energy collisions, in contrast to the trend shown by data at lower energies. This study of the energy and charge dependence of these correlations indicates that they do not depend upon the initial state particles and that they are in reasonable agreement with the critical fluid gas model. These high energy correlation data are also studied in terms of a semi-inclusive Koba-Nielsen-Olesen scaling relation.     

High asymmetric induction in diels-alder additions of cyclopentadiene to acrylates derived from isoborneol

Starting from (R)-(+)- and from (S)-(?)-camphor the chiral alcohols $\text{1}$, $\text{2}$ and $\text{3}$ have been prepared; their acrylates II underwent TiCl₂(OR)₂-promoted Diels-Alder additions to cyclopentadiene giving efficiently in a predictable manner either the (2R)- or the (2S)-adducts III with up to virtually quantitative asymmetric induction.     

Diffusion of HDO in pure and acid-doped ice films

In these experiments, a few bilayers of D(2)O were vapor-deposited on a pure crystalline H(2)O ice film or an ice film doped with a small amount of HCl. Upon deposition, H/D isotopic exchange quickly converted the D(2)O layer into an HDO-rich mixture layer. Infrared absorption spectroscopy followed the changes of the HDO from the initial HDO mixture layer to HDO isolated in the H(2)O ice film. This was possible because isolated HDO in H(2)O ice has a unique, sharp peak in the O-D stretch region that can be distinguished from the broad peak due to the initial HDO mixture layer. The absorbance of isolated HDO displayed first-order kinetics and was attributed to diffusion of HDO from the HDO-rich mixture layer into the underlying H(2)O ice film. While negligible diffusion was observed for pure ice films and for ice films with HCl concentrations up to 1 x 10(-4) mole fraction, diffusion of HDO occurred for higher concentrations of (2-20) x 10(-4) mole fraction HCl with a concentration-independent rate constant. The diffusion under these conditions followed Arrhenius behavior for T = 135-145 K yielding E(a) = 25 +/- 5 kJ/mol. The mechanism for the HDO diffusion involves either (i) molecular self-diffusion or (ii) long-range H/D diffusion by a series of multiple proton hop and orientational turn steps. While these spectroscopic results compare favorably with recent studies of molecular self-diffusion in low-temperature ice films, the diffusion results from all the ice film studies at low temperatures (ca. T < 170 K) differ from earlier bulk ice studies at higher temperatures (ca. T > 220 K). A comparison and discussion of the various diffusion studies are included in this report.