Application of Maclaurin Series in Structural Analysis

In the simple theory of flexure of beams, the slope, bending moment, shearing force, load and other quantities are functions of a derivative of y with respect to x. It is shown that the elastic curve of a transversely loaded beam can be represented by the Maclaurin series. Substitution of the values of the derivatives gives a direct solution of beam problems. In this paper the method is applied to derive the Theorem or three moments and slope deflection equations. The method is extended to the solution of a rigid portal frame. Finally the method is applied to deduce results on which the moment distribution method of analyzing rigid frames is based.

Indentation strength of a piezoelectric ceramic: Experiments and simulations

The spherical indentation strength of a lead zirconate titanate (PZT) piezoelectric ceramic was investigated under poled and unpoled conditions and with different electrical boundary conditions (arising through the use of insulating or conducting indenters). Experimental results show that the indentation strength of the poled PZT is higher than that of the unpoled PZT. The strength of a poled PZT under a conducting indenter is higher than that under an insulating indenter. Poling direction (with respect to the direction of indentation loading) did not significantly affect the strength of material. Complementary finite element analysis (FEA) of spherical indentation of an elastic, linearly coupled piezoelectric half-space is conducted for rationalizing the experimental observations. Simulations show marked dependency of the contact stress on the boundary conditions. In particular, contact stress redistribution in the Coupled problem leads to a change in the fracture initiation, from Hertzian cracking in the unpoled material to Subsurface damage initiation in poled PZT. These observations help explain the experimental ranking of strength the PZT in different material conditions or under different boundary conditions.

Structure and dynamics of two-dimensional sheared granular flows

The structure and dynamics of the two-dimensional linear shear flow of inelastic disks at high area fractions are analyzed. The event-driven simulation technique is used in the hard-particle limit, where the particles interact through instantaneous collisions. The structure (relative arrangement of particles) is analyzed using the bond-orientational order parameter. It is found that the shear flow reduces the order in the system, and the order parameter in a shear flow is lower than that in a collection of elastic hard disks at equilibrium. The distribution of relative velocities between colliding particles is analyzed. The relative velocity distribution undergoes a transition from a Gaussian distribution for nearly elastic particles, to an exponential distribution at low coefficients of restitution. However, the single-particle distribution function is close to a Gaussian in the dense limit, indicating that correlations between colliding particles have a strong influence on the relative velocity distribution. This results in a much lower dissipation rate than that predicted using the molecular chaos assumption, where the velocities of colliding particles are considered to be uncorrelated.

Modeling dynamic demand response using Monte Carlo simulation and interval mathematics for boundary estimation

With the rapid development of various technologies and applications in smart grid implementation, demand response has attracted growing research interests because of its potentials in enhancing power grid reliability with reduced system operation costs. This paper presents a new demand response model with elastic economic dispatch in a locational marginal pricing market. It models system economic dispatch as a feedback control process, and introduces a flexible and adjustable load cost as a controlled signal to adjust demand response. Compared with the conventional “one time use” static load dispatch model, this dynamic feedback demand response model may adjust the load to a desired level in a finite number of time steps and a proof of convergence is provided. In addition, Monte Carlo simulation and boundary calculation using interval mathematics are applied for describing uncertainty of end-user's response to an independent system operator's expected dispatch. A numerical analysis based on the modified Pennsylvania-Jersey-Maryland power pool five-bus system is introduced for simulation and the results verify the effectiveness of the proposed model. System operators may use the proposed model to obtain insights in demand response processes for their decision-making regarding system load levels and operation conditions.

Breakage of viscoelastic drops in turbulent stirred dispersions

The existing models of drop breakage in stirred turbulent dispersions are applicable only to purely viscous dispersed phases. In their present form, they are found to underpredict the diameters of the largest stable drops formed when a viscoelastic fluid is dispersed into a Newtonian liquid. In purely viscous fluids, the turbulent stresses are opposed both by the stresses due to interfacial tension and the viscous stresses generated as the drop deforms. In viscoelastic fluids, drop deformation produces additional retractive elastic stresses which also oppose turbulent stresses. As the deformation rates are large, the retractive stresses can be large in magnitude. Assuming that these additional stresses decay with time, a model of viscoelastic drop breakage in turbulent stirred dispersions has been developed. The new model quantitatively predicts the dmax of viscoelastic fluids. The model, however, does not predict the observation that when the time constant of the fluid becomes large (λ > 0.5 s), the fluid can not be dispersed into droplets up to agitator speeds of about 10 rps in our equipment.

Tree growth relationships and silvicultural tools to assist stand management in private native spotted gum dominant forests in Queensland and northern New South Wales.

Spotted gum dominant forests occur from Cooktown in northern Queensland (Qld) to Orbost in Victoria (Boland et al. 2006) and these forests are commercially very important with spotted gum the most commonly harvested hardwood timber in Qld and one of the most important in New South Wales (NSW). Spotted gum has a wide range of end uses from solid wood products through to power transmission poles and generally has excellent sawing and timber qualities (Hopewell 2004). The private native forest resource in southern Qld and northern NSW is a critical component of the hardwood timber industry (Anon 2005, Timber Qld 2006) and currently half or more of the native forest timber resource harvested in northern NSW and Qld is sourced from private land. However, in many cases productivity on private lands is well below what could be achieved with appropriate silvicultural management. This project provides silvicultural management tools to assist extension staff, land owners and managers in the south east Qld and north eastern NSW regions. The intent was that this would lead to improvement of the productivity of the private estate through implementation of appropriate management. The other intention of this project was to implement a number of silvicultural experiments and demonstration sites to provide data on growth rates of managed and unmanaged forests so that landholders can make informed decisions on the future management of their forests. To assist forest managers and improve the ability to predict forest productivity in the private resource, the project has developed: • A set of spotted gum specific silvicultural guidelines for timber production on private land that cover both silvicultural treatment and harvesting. The guidelines were developed for extension officers and property owners. • A simple decision support tool, referred to as the spotted gum productivity assessment tool (SPAT), that allows an estimation of: 1. Tree growth productivity on specific sites. Estimation is based on the analysis of site and growth data collected from a large number of yield and experimental plots on Crown land across a wide range of spotted gum forest types. Growth algorithms were developed using tree growth and site data and the algorithms were used to formulate basic economic predictors. 2. Pasture development under a range of tree stockings and the expected livestock carrying capacity at nominated tree stockings for a particular area. 3. Above-ground tree biomass and carbon stored in trees. •A series of experiments in spotted gum forests on private lands across the study area to quantify growth and to provide measures of the effect of silvicultural thinning and different agro-forestry regimes. The adoption and use of these tools by farm forestry extension officers and private land holders in both field operations and in training exercises will, over time, improve the commercial management of spotted gum forests for both timber and grazing. Future measurement of the experimental sites at ages five, 10 and 15 years will provide longer term data on the effects of various stocking rates and thinning regimes and facilitate modification and improvement of these silvicultural prescriptions.

Magnetic resonance microimaging of cancer cell spheroid constructs

BACKGROUND Hydrogel-based cell cultures are excellent tools for studying physiological events occurring in the growth and proliferation of cells, including cancer cells. Diffusion magnetic resonance is a physical technique that has been widely used for the characterisation of biological systems as well as hydrogels. In this work, we applied diffusion magnetic resonance imaging (MRI) to hydrogel-based cultures of human ovarian cancer cells. METHODS Diffusion-weighted spin-echo MRI measurements were used to obtain spatially-resolved maps of apparent diffusivities for hydrogel samples with different compositions, cell loads and drug (Taxol) treatment regimes. The samples were then characterised using their diffusivity histograms, mean diffusivities and the respective standard deviations, and pairwise Mann-Whitney tests. The elastic moduli of the samples were determined using mechanical compression testing. RESULTS The mean apparent diffusivity of the hydrogels was sensitive to the polymer content, cell load and Taxol treatment. For a given sample composition, the mean apparent diffusivity and the elastic modulus of the hydrogels exhibited a negative correlation. CONCLUSIONS Diffusivity of hydrogel-based cancer cell culture constructs is sensitive to both cell proliferation and Taxol treatment. This suggests that diffusion-weighted imaging is a promising technique for non-invasive monitoring of cancer cell proliferation in hydrogel-based, cellularly-sparse 3D cell cultures. The negative correlation between mean apparent diffusivity and elastic modulus suggests that the diffusion coefficient is indicative of the average density of the physical microenvironment within the hydrogel construct.

Outdoor group portrait of Marga Abel, Franzche Wolf, Miss Mahler, Margot Frank and Else Hirschfeld; Bad Kissingen Portraits Groups Women

Handwritten caption: Wir tragen nur Bemberg-Seidenstruempfe! (We wear only Bemberg silk stockings!)

Effects of Isothermal and Adiabatic Thermal Loadings on Size and Strain Rate Dependence of Copper Nanowire

In the present paper, the size and strain rate effects on ultra-thin < 100 >/{100} Cu nanowires at an initial temperature of 10 K have been discussed. Extensive molecular dynamics (MD) simulations have been performed using Embedded atom method (EAM) to investigate the structural behaviours and properties under high strain rate. Velocity-Verlet algorithm has been used to solve the equation of motions. Two different thermal loading cases have been considered: (i) Isothermal loading, in which Nose-Hoover thermostat is used to maintain the constant system temperature, and (ii) Adiabatic loading, i.e., without any thermostat. Five different wire cross-sections were considered ranging from 0.723 x 0.723 nm(2) to 2.169 x 2.169 nm(2) The strain rates used in the present study were 1 x 10(9) s(-1), 1 x 10(8) s(-1), and 1 x 10(7) s(-1). The effect of strain rate on the mechanical properties of copper nanowires was analysed, which shows that elastic properties are independent of thermal loading for a given strain rate and cross-sectional dimension of nanowire. It showed a decreasing yield stress and yield strain with decreasing strain rate for a given cross- section. Also, a decreasing yield stress and increasing yield strain were observed for a given strain rate with increasing cross-sectional area. Elastic modulus was found to be similar to 100 GPa, which was independent of processing temperature, strain rate, and size for a given initial temperature. Reorientation of < 100 >/{100} square cross-sectional copper nanowire into a series of stable ultra-thin Pentagon copper nanobridge structures with dia of similar to 1 nm at 10 K was observed under high strain rate tensile loading. The effect of isothermal and adiabatic loading on the formation of such pentagonal nanobridge structure has been discussed.

Nanotribological and nanomechanical properties of plasma-polymerized polyterpenol thin films

Organic plasma polymers are currently attracting significant interest for their potential in the areas of flexible optoelectronics and biotechnology. Thin films of plasma-polymerized polyterpenol fabricated under varied deposition conditions were studied using nanoindentation and nanoscratch analyses. Coatings fabricated at higher deposition power were characterized by improved hardness, from 0.33 GPa for 10 W to 0.51 GPa for 100 W at 500-μN load, and enhanced wear resistance. The elastic recovery was estimated to be between 0.1 and 0.14. Coatings deposited at higher RF powers also showed less mechanical deformation and improved quality of adhesion. The average (R a) and root mean square (R q) surface roughness parameters decreased, from 0.44 nm and 0.56 nm for 10 W to 0.33 nm and 0.42 nm for 100 W, respectively.

Rotary veneering of plantation-grown spotted gum (Corymbia citriodora subsp. variegata) and Dunn's white gum (Eucalyptus dunnii)

This report evaluates the wood and veneer properties of plantation-grown spotted gum (Corymbia citriodora subsp. variegata, or CCV) and Dunn's white gum (Eucalyptus dunnii), grown at different stockings, in thinning trials near Ellangowan in north-east New South Wales (mean annual rainfall 1050 mm) and Kingaroy in south-east Queensland (mean annual rainfall 873 mm). Thinning trials were established at age seven years. Both species showed a significant increase in stem diameter growth of the dominant trees in response to thinning. At age 10 years, trees from the unthinned (950–1270 stems ha-1) and 300 stems ha-1 treatments were selected for veneering. Five dominant trees were felled from each combination of species x sites x thinning treatment. Diameter at breast height over bark of the selected trees ranged from 20 cm to 27 cm at Ellangowan, and 19 cm to 26 cm at Kingaroy. From each tree, 1.5 m long billets were removed at two positions: a butt billet from 0.3–1.8 m above ground and a top billet from approximately 5.5–7.0 m. Log end splitting was assessed 24 hours after harvesting and again after steaming, approximately four days after harvesting. Disks from just above both billets were collected for assessment of wood properties. Billets were peeled on a spindleless veneer lathe to produce a full veneer ribbon with a target green thickness of 2.8 to 3.0 mm. The 1.55 m wide (tangential dimension) veneer sheets were dried and graded according to AS/NZ Standard 2269:2008, which describes four veneer grades. Veneer samples taken along the length of the veneer ribbon, at regular intervals of 1.55 m, were tested for stiffness, shrinkage and density. Veneer length measurements were used to calculate the radial distance of each sample from the central axis of the billet. Overall veneer gross recoveries ranged from 50% to 70%. They were significantly lower at the Kingaroy site, for both species. The veneer recoveries achieved were 2–3 times higher than typical green off saw recoveries from small plantation hardwood logs of similar diameter. Most of the veneer recovered was classified as D-grade. CCV trees from the Ellangowan site yielded up to 38% of the better C-grade and higher grade veneers. The main limiting factors that prevented veneer from meeting higher grades were the presence of kino defects and encased knots. Splits in E. dunnii veneer also contributed to reduced grade quality. Log end splits were higher for E. dunnii than for CCV, and logs from Ellangowan exhibited more severe splitting. Split index was generally higher for top than for butt billets. Split index was strongly correlated with the average veneer grade from corresponding billets. The Ellangowan site, where rainfall was higher and trees grew faster, yielded significantly denser and stiffer veneers than did the drier sites near Kingaroy, where tree growth was slower. The difference was more pronounced for E. dunnii than for CCV. Differences in measured wood properties between thinned and unthinned treatments were generally small and not significant. On average, 10% of billet volume was lost during the peeling rounding-up process. Much of the wood laid down following thinning was removed during rounding-up, meaning the effect of thinning on veneer properties could not be effectively assessed. CCV was confirmed as having high veneer density and very good veneer stiffness, exceeding 15 GPa, making it very suitable for structural products. E. dunnii also demonstrated good potential as a useful structural plywood resource, achieving stiffness above 10 GPa. Veneer stiffness and density in CCV increased from pith to bark at both sites, while for E. dunnii there was a radial increase in these properties at the Ellangowan site only. At the drier Kingaroy site, veneer stiffness and density declined from mid-radius to the log periphery. This may be associated with prolonged drought from 2005 to 2009, corresponding to the later years of tree growth at the Kingaroy site. CCV appeared to be less sensitive to drought conditions. Standing tree acoustic velocity, determined by the Fakopp time-of-flight method, provided a reliable prediction of average veneer stiffness for both species (R2=0.78 for CCV and R2=0.90 for E. dunnii) suggesting that the Fakopp method may be a useful indicator of tree and stand quality, in terms of veneer stiffness in standing trees.

Coupled amplitude theory of nonlinear surface acoustic waves

The nonlinear propagation characteristics of surface acoustic waves on an isotropic elastic solid have been studied in this paper. The solution of the harmonic boundary value problem for Rayleigh waves is obtained as a generalized Fourier series whose coefficients are proportional to the slowly varying amplitudes of the various harmonics. The infinite set of coupled equations for the amplitudes when solved exhibit an oscillatory slow variation signifying a continuous transfer of energy back and forth among the various harmonics. A conservation relation is derived among all the harmonic amplitudes.

Biaxial-load effects on isopachics for a crack at the interface of dissimilar media

The plane problem of two dissimilar materials, bonded together and containing a crack along their common interface, which were subjected to a biaxial load at infinity, is examined by giving a closed-form expression for the first stress invariant of the normal stresses, which is equally valid everywhere, near to, and far from, the crack-tip region. This exact expression for the first-stress invariant is compared by constructing the respective isopachic-fringe patterns, to the approximate expression with non-singular terms, due to the biaxiality factor, for the same quantity. Significant differences between respective isopachic-patterns were found and their dependence on the elastic properties of both materials and the applied loads was demonstrated. The relative errors between the computedK I - andK II -components by using the approximate expression for the first stress-invariant and the accurate one, derived from closed-form solution along either isopachic-fringes or along circles and radii from the crack-tip have been given, indicating in some cases large discrepancies between exact and approximate solutions.

On the Transform Method of Solution of an External Crack Problem

The breakdown of the usual method of Fourier transforms in the problem of an external line crack in a thin infinite elastic plate is discovered and the correct solution of this problem is derived using the concept of a generalised Fourier transform of a type discussed first by Golecki [1] in connection with Flamant's problem.

Dynamics of dense sheared granular flows. Part 1. Structure and diffusion

Shear flows of inelastic spheres in three dimensions in the Volume fraction range 0.4-0.64 are analysed using event-driven simulations.Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to the line Joining the centres). Here, we have considered both e(t) = +1 and e(t) = e(n) (rough particles) and e(t) =-1 (smooth particles), and the normal coefficient of restitution e(n) was varied in the range 0.6-0.98. Care was taken to avoid inelastic collapse and ensure there are no particle overlaps during the simulation. First, we studied the ordering in the system by examining the icosahedral order parameter Q(6) in three dimensions and the planar order parameter q(6) in the plane perpendicular to the gradient direction. It was found that for shear flows of sufficiently large size, the system Continues to be in the random state, with Q(6) and q(6) close to 0, even for volume fractions between phi = 0.5 and phi = 0.6; in contrast, for a system of elastic particles in the absence of shear, the system orders (crystallizes) at phi = 0.49. This indicates that the shear flow prevents ordering in a system of sufficiently large size. In a shear flow of inelastic particles, the strain rate and the temperature are related through the energy balance equation, and all time scales can be non-dimensionalized by the inverse of the strain rate. Therefore, the dynamics of the system are determined only by the volume fraction and the coefficients of restitution. The variation of the collision frequency with volume fraction and coefficient of estitution was examined. It was found, by plotting the inverse of the collision frequency as a function of volume fraction, that the collision frequency at constant strain rate diverges at a volume fraction phi(ad) (volume fraction for arrested dynamics) which is lower than the random close-packing Volume fraction 0.64 in the absence of shear. The volume fraction phi(ad) decreases as the coefficient of restitution is decreased from e(n) = 1; phi(ad) has a minimum of about 0.585 for coefficient of restitution e(n) in the range 0.6-0.8 for rough particles and is slightly larger for smooth particles. It is found that the dissipation rate and all components of the stress diverge proportional to the collision frequency in the close-packing limit. The qualitative behaviour of the increase in the stress and dissipation rate are well Captured by results derived from kinetic theory, but the quantitative agreement is lacking even if the collision frequency obtained from simulations is used to calculate the pair correlation function used In the theory.