Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates

This paper presents a unified exact analysis for the statics and dynamics of a class of thick laminates. A three-dimensional, linear, small deformation theory of elasticity solution is developed for the bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. All the nine elastic constants of orthotropy are taken into account. The solution is formally exact and leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems. For free vibration of plates, the present analysis yields a triply infinite spectrum of frequencies instead of only one doubly infinite spectrum by thin plate theory or three doubly infinite spectra by Reissner-Mindlin type analyses. Some numerical results are presented for plates and laminates. Comparison of results from thin plate, Reissner and Mindlin analyses with these yield some important conclusions regarding the validity and effects of the assumptions made in the approximate theories.

Vibration of rectangular orthotropic plates

An approximate analytical procedure has been given to solve the problem of a vibrating rectangular orthotropic plate, with various combinations of simply supported and clamped boundary conditions. Numerical results have been given for the case of a clamped square plate. Nomenclature 2a, 2b sides of the rectangular plate h plate thickness Eprime x , Eprime y , EPrime, G elastic constants of te orthotropic material D x Eprime x h 3/12 D y Eprime y h 3/12 H xy EPrimeh 3/12+Gh 3/6 D x , D y and H xy are rigidity constants of the orthotropic platergr mass of the plate per unit area ngr Poisson's ratio W deflection of the plate p circular frequency gamma b/a ratio X m , Y characteristic functions of the vibrating beam problem -lambda rgrp 2 a 2 b 2/H xy the frequency parameter.

TOTEM early measurements

The status of the TOTEM experiment is described as well as the prospects for the measurements in the early LHC runs. The primary goal of TOTEM is the measurement of the total p-p cross section, using a method independent of the luminosity. A final accuracy of 1% is ex- pected with dedicated β∗ = 1540 m runs, while at the beginning a 5% resolution is achievable with a β∗ = 90 m optics. Accordingly to the running scenarios TOTEM will be able to measure the elastic scattering in a wide range of t and to study the cross-sections and the topologies of diffractive events. In a later stage, physics studies will be extended to low-x and forward physics collaborating with CMS as a whole experimental apparatus.

Observation of Exclusive Charmonium Production and γγ→μ+μ- in pp̅ Collisions at √s=1.96 TeV

We have observed the reactions p+pbar --> p+X+pbar, with X being a centrally produced J/psi, psi(2S) or chi_c0, and gamma+gamma --> mu+mu-, in proton- antiproton collisions at sqrt{s} = 1.96 TeV using the Run II Collider Detector at Fermilab. The event signature requires two oppositely charged muons, each with pseudorapidity |eta| mu+mu-. Events with a J/psi and an associated photon candidate are consistent with exclusive chi_c0 production through double pomeron exchange. The exclusive vector meson production is as expected for elastic photo- production, gamma+p --> J/psi(psi(2S)) + p, which is observed here for the first time in hadron-hadron collisions. The cross sections ds/dy(y=0) for p + pbar --> p + X + pbar with X = J/psi, psi(2S) orchi_c0 are 3.92+/-0.62 nb, 0.53+/-0.14 nb, and 75+/-14 nb respectively. The cross section for the continuum, with |eta(mu+/-)|

Resistometric studies of solute-vacancy interactions and clustering kinetics in an FCC matrix [AlZn Alloy with Ag, Ce, Dy, Li, Nb, Pt, Sb, Y, or Yb]

Al-4.4 a/oZn and Al-4.4 a/oZn with Ag, Ce, Dy, Li, Nb, Pt, Y, or Yb, alloys have been investigated by resistometry with a view to study the solute-vacancy interactions and clustering kinetics in these alloys. Solute-vacancy binding energies have been evaluated for all these elements by making use of appropriate methods of evaluation. Ag and Dy additions yield some interesting results and these have been discussed in the thesis. Solute-vacancy binding energy values obtained here have been compared with other available values and discussed. A study of the type of interaction between vacancies and solute atoms indicates that the valency effect is more predominant than the elastic effect.

The effects of stall surfaces and milk yield on the lying behavior of dairy cow

The importance of lying behavior to dairy cows and the feasible definition of lying has attracted many studies on the subject. Cattle show both behavioral and physiological stress responses when subjected to thwarting of their lying behavior. If cows are unable to lie down they later compensate for lost lying time when possible. Environmental factors such as housing and bedding systems have been noted to affect the time spent lying, but there is usually large variation in lying time between individuals. Internal factors such as the reproductive stage, age and health of cows affect their lying time and can cause variation. However, the effect of higher milk production on behavior has not previously been illuminated. The objective of this study was to provide data applicable for the improvement of resting conditions of cows. The preference of stall surface material, differences in normal behavior per unit time and various health measures were observed. The aim was to evaluate lying behavior and cow comfort on different stall bedding materials. In addition, the effect of milk yield on behavior was examined in a tie stall experiment. The preferences for surface materials were investigated in 5 experiments using 3 surface materials with bedding manipulations. According to the results, the cows preferred abundant straw bedding and soft rubber mats. However, they showed an aversion to sand bedding. Some individuals even refused to use stalls with sand when no organic bedding material was present. However, this study was unable to determine the reason for the avoidance, as neither the sand particle size nor thermal properties appeared critical. However, previous exposure to particular surface materials increased the preference for them. The amount of straw bedding was found to be an important factor affecting the preferences for stalls, and the lying time in stalls increased when the flooring softness was improved by applying straw or by installing elastic mats. Despite sand being the least preferred flooring material in preference tests, the health of legs improved during exposure to sand-floored stalls. Moreover cows using sand were cleaner than those that used straw stalls. Thus, sand bedding entailed some health benefits despite the contradictory results of preference tests, which more strongly reflected the perceptions of individual animals. Milk yield was observed to affect behavior by reducing the lying time, possibly due to factors other than longer duration of eating. High yielding cows seemed to intensify their lying bouts, as they were observed to lie with the neck muscles relaxed sooner after lying down than lower yielding cows. In conclusion, cows were found to prefer softer stall surface materials and organic bedding material. In addition, the lying time was reduced by a high milk yield, although the lying time seemed to be important for resting. Cows might differ in the needs for their lying environment. The management of dairy cows should eliminate any unnecessary prevention of lying, as even in tie-stalls high yielding cows seem to be affected by time constraints. Adding fresh bedding material to stalls increases the comfort of any stall flooring material.

Lattice vibrations and specific heat of zinc blende

The dispersion relations, frequency distribution function and specific heat of zinc blende have been calculated using Houston's method on (1) A short range force (S. R.) model of the type employed in diamond by Smith and (2) A long range model assuming an effective charge Ze on the ions. Since the elastic constant data on ZnS are not in agreement with one another the following values were used in these calculations: {Mathematical expression}. As compared to the results on the S. R. model, the Coulomb force causes 1. A splitting of the optical branches at (000) and a larger dispersion of these branches; 2. A rise in the acoustic frequency branches the effect being predominant in a transverse acoustic branch along [110]; 3. A bridging of the gap of forbidden frequencies in the S. R. model; 4. A reduction of the moments of the frequency distribution function and 5. A flattening of the Θ- T curve. By plotting (Θ/Θ0) vs. T., the experimental data of Martin and Clusius and Harteck are found to be in perfect coincidence with the curve for the short range model. The values of the elastic constants deduced from the ratio Θ0 (Theor)/Θ0 (Expt) agree with those of Prince and Wooster. This is surprising as several lines of evidence indicate that the bond in zinc blende is partly covalent and partly ionic. The conclusion is inescapable that the effective charge in ZnS is a function of the wave vector {Mathematical expression}.

Adhesively-bonded Patch Repair with Composites

Adhesively-bonded composite patch repairs over cracked or corrosion-damaged metallic aircraft structures have shown great promise for extending life of ageing structures. This study presents the numerical investigation into the interface behaviour of adhesively-bonded cracked aluminum alloy substrate patched with fibre-reinforced composite material. The adhesive is modelled as an elasto-plastic bilinear material to characterise the debond behaviour, while the defective substrate is regarded as linear elastic continuum. Two typical patch shapes were selected based on information available in the literature. Geometric and material nonlinear analyses for square and octagonal patches were performed to capture peel and shear stresses developed between the substrate and the patch to examine the possibility of interface delamination/debonding. Parametric studies on adhesive thickness and patch thickness were carried out to predict their infuence on damage tolerance of repaired structures.

Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems

We investigate the scalar K pi form factor at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using at input the values of the form factor at t = 0 and the Callan-Treiman point, we obtain stringent constraints on the slope and curvature parameters of the Taylor expansion at the origin. Also, we predict a quite narrow range for the higher-order ChPT corrections at the second Callan-Treiman point.

The fracture toughness of bulk metallic glasses

Stiffness, strength, and toughness are the three primary attributes of a material, in terms of its mechanical properties. Bulk metallic glasses (BMGs) are known to exhibit elastic moduli at a fraction lower than crystalline alloys and have extraordinary strength. However, the reported values of fracture toughness of BMGs are highly variable; some BMGs such as the Zr-based ones have toughness values that are comparable to some high strength steels and titanium alloys, whereas there are also BMGs that are almost as brittle as silicate glasses. Invariably, monolithic BMGs exhibit no or low crack growth resistance and tend to become brittle upon structural relaxation. Despite its critical importance for the use of BMGs as structural materials, the fracture toughness of BMGs is relatively poorly understood. In this paper, we review the available literature to summarize the current understanding of the mechanics and micromechanisms of BMG toughness and highlight the needs for future research in this important area.

Anomalous behavior of hydrodynamic modes in the two dimensional shear flow of a granular material

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell Boltzmann distribution and a Hermite polynomial expansion in the velocity components; this form is inserted into them Boltzmann equation and solved to obtain the coeificients of the terms in the expansion. The solution is obtained using an expansion in the parameter epsilon =(1 - e)(1/2), and terms correct to epsilon(4) are retained to obtain an approximate solution; the error due to the neglect of higher terms is estimated at about 5% for e = 0.7. A small perturbation is placed on the distribution function in the form of a Hermite polynomial expansion for the velocity variations and a Fourier expansion in the spatial coordinates: this is inserted into the Boltzmann equation and the growth rate of the Fourier modes is determined. It is found that in the hydrodynamic limit, the growth rates of the hydrodynamic modes in the flow direction have unusual characteristics. The growth rate of the momentum diffusion mode is positive, indicating that density variations are unstable in the limit k--> 0, and the growth rate increases proportional to kslash} k kslash}(2/3) in the limit k --> 0 (in contrast to the k(2) increase in elastic systems), where k is the wave vector in the flow direction. The real and imaginary parts of the growth rate corresponding to the propagating also increase proportional to kslash k kslash(2/3) (in contrast to the k(2) and k increase in elastic systems). The energy mode is damped due to inelastic collisions between particles. The scaling of the growth rates of the hydrodynamic modes with the wave vector I in the gradient direction is similar to that in elastic systems. (C) 2000 Elsevier Science B.V. All rights reserved.

Behaviour of Bi-adhesive Joints

The use of relatively low modulus adhesive at the ends of overlap in a bi-adhesive bondline of a bonded joint can reduce the stress concentration significantly and, therefore, potentially lead to higher strength of the joint. This study presents the two-dimensional and three-dimensional nonlinear (geometric and material) finite element analyses of adhesively bonded single lap joints having modulus-graded bondline under monotonic loading conditions. The adhesives were modelled as an elasto-plastic multi-linear material, while the substrates were regarded as both linear elastic and bi-linear elasto-plastic material. The computational simulations have been performed to investigate the bondline behaviour by studying the stress and strain distributions both at the mid-plane as well as at the interface of the bondline. It has been observed that the static strength is higher for joints with bi-adhesive bondlines compared to those with single adhesives in bondline. Higher joint strength has also been observed for optimum bi-adhesive bondline ratio through parametric studies. Effects of load level, and bondline thickness on stress distribution in the bi-adhesive bondline have also been studied. 3D analysis results reveal the existence of complex multi-axial stress/strain state at the ends of the overlap in the bondline which cannot be observed in 2D plane strain analysis. About 1/3rd of the width of the joint from the free edge in the width direction has 3D stress state, especially in the compliant adhesive of the bondline. Magnitudes of longitudinal and lateral stress/strain components are comparable to peel stress/strain components. It has also been analytically shown that the in-plane global stiffness of the joint remains unaffected by modulus gradation of the bondline adhesive. (C) Koninklijke Brill NV, Leiden, 2010.

Stress induced phase transition in monomolecular perfluroalkylsilane film self assembled on aluminium surface

We control the stiffnesses of two dual double cantelevers placed in series to control penetration into a perflurooctyltrichlorosilane monolayer self assembled on aluminium and silicon substrates. The top cantilever which carries the probe is displaced with respect to the bottom cantilever which carries the substrate, the difference in displacement recorded using capacitors gives penetration. We further modulate the input displacement sinusoidally to deconvolute the viscoelastic properties of the monolayer. When the intervention is limited to the terminal end of the molecule there is a strong viscous response in consonance with the ability of the molecule to dissipate energy by the generation of gauche defects freely. When the intervention reaches the backbone, at a contact mean pressure of 0.2GPa the damping disappears abruptly and the molecule registers a steep rise in elastic modulus and relaxation time constant, with increasing contact pressure. We offer a physical explanation of the process and describe this change as due to a phase transition from a liquid like to a solid like state.

Protein sequence design on the basis of topology optimization techniques -Using continuous modeling of discrete amino acid types

The notion of optimization is inherent in protein design. A long linear chain of twenty types of amino acid residues are known to fold to a 3-D conformation that minimizes the combined inter-residue energy interactions. There are two distinct protein design problems, viz. predicting the folded structure from a given sequence of amino acid monomers (folding problem) and determining a sequence for a given folded structure (inverse folding problem). These two problems have much similarity to engineering structural analysis and structural optimization problems respectively. In the folding problem, a protein chain with a given sequence folds to a conformation, called a native state, which has a unique global minimum energy value when compared to all other unfolded conformations. This involves a search in the conformation space. This is somewhat akin to the principle of minimum potential energy that determines the deformed static equilibrium configuration of an elastic structure of given topology, shape, and size that is subjected to certain boundary conditions. In the inverse-folding problem, one has to design a sequence with some objectives (having a specific feature of the folded structure, docking with another protein, etc.) and constraints (sequence being fixed in some portion, a particular composition of amino acid types, etc.) while obtaining a sequence that would fold to the desired conformation satisfying the criteria of folding. This requires a search in the sequence space. This is similar to structural optimization in the design-variable space wherein a certain feature of structural response is optimized subject to some constraints while satisfying the governing static or dynamic equilibrium equations. Based on this similarity, in this work we apply the topology optimization methods to protein design, discuss modeling issues and present some initial results.

High temperature mechanical properties of thermal barrier coated superalloy applied to combustor liner of aero engines

High temperature load controlled fatigue, hot tensile and accelerated creep properties of thermal barrier coated (TBC) Superni C263 alloy used as a candidate material in combustor liner of aero engines are highlighted in this paper. Acoustic emission technique has been utilised to characterise the ductile-brittle transition teperature the bond coat. Results revealed that the DBTT (ductile to brittle transition temperature) of this bond coat is around 923 K, which is in close proximity to the value reported for CoCrAlY type of bond coat. Finite element technique, used for analysing the equivalent stresses in the bond coat well within the elastic limit, revealed the highest order of equivalent stress at 1073 K as the bond coat is ductile above 923 K. The endurance limit in fatigue and the life of TBC coated composite under accelerated creep conditions are substantially higher than those of the substrate material. Fractographic features at high stresses under fatigue showed intergranular cleavage whereas those at low stresses were transgranular and ductile in nature. Delamination of the bond coat and spallation of the TBC at high stresses during fatigue was evident. Unlike in the case of fatigue, the mode of fracture in the substrate at very high stresses was transgranular whereas that at low stresses was intergranular in creep.