Tensionless contact of a finite circular plate

A general formulation is developed for the contact behavior of a finite circular plate with a tensionless elastic foundation. The gap distance between the plate and elastic foundation is incorporated as an important parameter. Unlike the previous models with zero gap distance and large/infinite plate radius, which assumes the lift-off/separation of a flexural plate from its supporting elastic foundation, this study shows that lift-off may not occur. The results show how the contact area varies with the plate radius, boundary conditions and gap distance. When the plate radius becomes large enough and the gap distance is reduced to zero, the converged contact radius close to the previous ones is obtained.     

Generalisations of the strain-energy function of linear elasticity to model biological soft tissue

Strain measures consistent with the linear, infinitesimal form of the strain-energy function are obtained within the context of isotropic, homogeneous, compressible, and non-linear elasticity. It will be shown that there are two distinct families of such measures. One family has already been much studied in the literature, the most important member being the strains whose principal values are a function only of the corresponding principal stretches. The second family of strains appears new. The motivation for studying such strains is the intuitive expectation that, for at least moderate deformations, a good fit with experimental data from material characterisation tests will be obtained with the corresponding strain-energy functions. In particular, there is the expectation that such models could prove useful for the modelling of biological soft tissue, whose physiological response is characterised by moderate strains. It will be shown that this is indeed the case for simple tension tests on porcine brain tissue.     

The impact of environmental constraints on short term harvesting: Use of planning tools and mathematical models

Both in New Zealand and Chile there exist important forest industries based mostly on pine plantations. The management of harvesting requires a series of activities such as building access roads, harvesting with skidders on flat terrain and cable logging for steep terrain, transportation from forest origins to destinations, such as a port, pulp plant and sawmills.These harvesting activities imply some potentially harmful environmental impacts such as water sedimentation, erosion and loss of scenic beauty. This has led to the proposal of several mitigating actions, such as creating riparian strips along rivers, avoiding the use of heavy machinery on fragile soils and minimizing road building.The degree of implementation of these mitigating actions differs in Chile and New Zealand. In New Zealand, the 1991 Resource Management Act regulated the implementation of environmental protection measures. In Chile a series of such measures have been implemented, but a set of definite regulations has not been defined yet and there is a need to develop an economic evaluation of the implementation of environmental measures in terms of reduced timber production and high harvesting costs, together with the benefits to the environment. To support decisions at tactical and operational levels, mathematical models have been developed both in Chile and New Zealand and are being used successfully by the timber industries. These models can be modified to consider diverse environmental protection measures. We analyze the implementation of these modifications and how the new models can help evaluate the economic impact of the protection measures. We show some preliminary results.     

Shaped Corrugated Horns for Cosmic Microwave Background Anisotropy Measurements

Novel corrugated horn have been modelled, manufactured and measured which give low-sidelobe patterns required by CMB Anisotropy experiments. These horns have a Back-to-Back structure with mode filtering at their centres. They are corrugated to give axial symmetric low-sidelobe patterns, profiled to reduce their length, and have a Gaussian flare at their entrance apertures to further suppress sidelobes to -40dB. Modelling and experimental results show excellent agreement to well below 50 dB.     

Redetermination of fac‐tris­(benzo­hydrox­am­ato)­iron(III) tri­hydrate

Due to its importance as a model for naturally occurring iron(III) siderophores such as desferriox­amine B, the crystal structure of the title compound, [Fe(C₇H₆NO₂)₃]·3H₂O, which was reported previously (R = 0.12, one of water mol­ecules disordered), has been redetermined (R = 0.041 without disorder). The complex has pseudo‐octahedral geometry around the Fe^III atom, with Fe—O bond lengths ranging from 1.9689 (18) to 2.0585 (17) Å and O—Fe—O bond angles in the chelate rings of 78.01 (7), 78.83 (7) and 78.95 (7)°. There is extensive hydrogen bonding involving the water mol­ecules and the hydro­xamate ligands.     

Transport Coefficients of Hydrogen and Argon–Hydrogen Plasmas

Calculated values of the viscosity, thermal conductivity, and electrical conductivity of hydrogen and mixtures of argon and hydrogen at high temperatures are presented. Combined ordinary, pressure, temperature, and electric field diffusion coefficients are also given for the mixtures. The calculations, which assume local thermodynamic equilibrium, are performed for atmospheric pressure plasmas in the temperature range from 300 to 30,000 K. The results are compared with those of previously published studies. Generally, the agreement is reasonable; those discrepancies that exist are attributed to the improved values of some of the collision integrals used here in calculating the transport coefficients.     

Synthesis of Oligonucleotides Carrying Anchoring Groups and Their Use in the Preparation of Oligonucleotide–Gold Conjugates

Oligodeoxynucleotide conjugates 1 – 15 carrying anchoring groups such as amino, thiol, pyrrole, and carboxy groups were prepared. A post‐synthetic modification protocol was developed. In this method 2′‐deoxy‐O⁴‐(p‐nitrophenyl)uridine‐3‐phosphoramidite was prepared and incorporated in oligonucleotides. After assembly, the modified nucleoside was made to react with different amines carrying the anchoring groups. At the same time, protecting groups were removed to yield the desired oligonucleotide conjugates. In a second approach, amino, thiol, and carboxylic groups were introduced into the 3′‐end of the oligonucleotides by preparing solid supports loaded with the appropriate amino acids. Oligonucleotide gold conjugates were prepared and their binding properties were examined.     

Simple Shearing of Incompressible and Slightly Compressible Isotropic Nonlinearly Elastic Materials

The classical problem of simple shear in nonlinear elasticity has played an important role as a basic pilot problem involving a homogeneous deformation that is rich enough to illustrate several key features of the nonlinear theory, most notably the presence of normal stress effects. Here our focus is on certain ambiguities in the formulation of simple shear arising from the determination of the arbitrary hydrostatic pressure term in the normal stresses for the case of an incompressible isotropic hyperelastic material. A new formulation in terms of the principal stretches is given. An alternative approach to the determination of the hydrostatic pressure is proposed here: it will be required that the stress distribution for a perfectly incompressible material be the same as that for a slightly compressible counterpart. The form of slight compressibility adopted here is that usually assumed in the finite element simulation of rubbers. For the particular case of a neo-Hookean material, the different stress distributions are compared and contrasted.     

Impact dynamics of MEMS switches

During operation, a MEMS switch is activated by an applied voltage. This causes the switch, often a doped silicon microbeam, to be attracted toward (pulled-into) a substrate. The component–substrate contact completes a circuit and permits the flow of current. Calculations for the minimum voltage required to achieve quasi-static pull-in are well documented. But for these quasi-static pull-in voltages to be meaningful, the voltage would have to be increased gradually until the critical value V_pull-inV_{\mathrm{pull\mbox{-}in}} is reached and the switch closes. Of course, practical considerations might require the switch to cycle on and off quickly, i.e., dynamically. This is particularly true in the case of radio frequency (RF) MEMS switches. In this paper, a model is developed and used to consider the dynamic pull-in characteristics of a clamped-clamped microbeam. This model includes inertial effects, structural and air damping (squeeze-film damping), as well as the impact behavior of the microbeam with the substrate. Parameter combinations leading to various types of behavior (no pull-in, air-bounce, wall bounce, etc.) are clearly identified. In an attempt to ensure fast switch closure and limit bouncing, two new applied voltage profiles are considered.