Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at     

Water wave radiation by a sphere submerged in water with an ice-cover

Using the multipoles method, we formulate the problems of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. In each case this leads to an infinite system of linear equations which are solved numerically by standard techniques. The added-mass and damping coefficients for a heaving and swaying sphere are obtained and depicted graphically against the wave number for various values of the radius of the submerged sphere and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the added-mass and damping coefficient for water with a free surface are recovered.     

Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

Moisture sorption, transport, and hydrolytic degradation in polylactide

Management of moisture penetration and hydrolytic degradation of polylactide (PLA) is extremely important during the manufacturing, shipping, storage, and end-use of PLA products. Moisture transport, crystallization, and degradation, in PLA have been measured through a variety of experimental techniques including size-exclusion chromatography, differential scanning calorimetry, and X-ray diffraction. Quartz crystal microbalance and dynamic vapor sorption experiments have also been used to measure moisture sorption isotherms in PLA films with varying crystallinity. A surprising result is that, within the accuracy of the experiments, crystalline and amorphous PLA films exhibit identical sorption isotherms.     

Chirospecific Syntheses of Conformationally Constrained 7-Azabicycloheptane Amino Acids by Transannular Alkylation

A new method is reported for the chirospecific preparation of optically pure 1-carboxy-7-azabicycloheptane amino acids for the generation of peptidomimetics as conformational probes. The method allows for the multigram preparation of these amino acid analogues through use of a thiolactam sulfide contraction and a transannular alkylation sequence as the key C-C bond-forming steps, starting from L-glutamic acid. The route provides access to two common intermediates, 7-(benzyloxycarbonyl)-1-carboxy-7-azabicyclo[2.2.1]-3-heptane and (1S,4R)-7-(benzyloxycarbonyl)-1-carboxy-7-azabicyclo[2.2.1]-3-heptanone tert-butyl ester, for elaboration to symmetrical and chiral amino acid homologues, respectively. Decarboxylation of the C-1 carboxy unit of the latter intermediate also demonstrated the applicability of the method for a short, chirospecific preparation of a (+)-epibatidine intermediate, (1S,4R)-7-(tert-butyloxycarbonyl)-1-carboxy-7-azabicyclo[2.2.1]-3-heptanone.     

Synthesis of spiro-fused (C5)-isoxazolino-(C4)-pyrazolones (1-oxa-2,7,8-triazaspiro[4,4]-2,8-dien-6-ones) via 1,3-dipolar cycloaddition and cycloelimination

An efficient and selective method for the synthesis of spiro-fused (C5)-isoxazolino-(C4)-pyrazolones (C) is reported. The process consists of utilizing the Baylis-Hillman reaction-or a quicker, stepwise MAC procedure-to give I followed by 1,3-dipolar cycloaddition and Swern oxidation to give beta-ketoesters H, which were condensed with hydrazine derivatives to provide hydrazones that underwent cycloelimination. These novel spiro-fused (C5)-isoxazolino-(C4)-pyrazolones were confirmed by spectroscopic analysis as well as single-crystal X-ray of 5. We also concluded that all condensations/cycloeliminations, except with hydrazine itself, were more effective with catalysts or higher reaction temperatures. For example, TiCl(4) was an efficient catalyst for hydrazone formation and cycloelimination with methylhydrazine, while phenyl-, benzyl-, and (4-methoxyphenyl)hydrazine reacted effectively without catalyst in refluxing xylene.