Growth and shape control of disks by bending and extension

Differential growth of thin elastic bodies furnishes a surprisingly simple explanation of the complex and intriguing shapes of many biological systems, such as plant leaves and organs. Similarly, inelastic strains induced by thermal effects or active materials in layered plates are extensively used to control the curvature of thin engineering structures. Such behaviour inspires us to distinguish and to compare two possible modes of differential growth not normally compared to each other, in order to reveal the full range of out-of-plane shapes of an initially flat disk. The first growth mode, frequently employed by engineers, is characterised by direct bending strains through the thickness, and the second mode, mainly apparent in biological systems, is driven by extensional strains of the middle surface. When each mode is considered separately, it is shown that buckling is common to both modes, leading to bistable shapes: growth from bending strains results in a double-curvature limit at buckling, followed by almost developable deformation in which the Gaussian curvature at buckling is conserved; during extensional growth, out-of-plane distortions occur only when the buckling condition is reached, and the Gaussian curvature continues to increase. When both growth modes are present, it is shown that, generally, larger displacements are obtained under in-plane growth when the disk is relatively thick and growth strains are small, and vice versa. It is also shown that shapes can be mono-, bi-, tri- or neutrally stable, depending on the growth strain levels and the material properties: furthermore, it is shown that certain combinations of growth modes result in a free, or natural, response in which the doubly curved shape of disk exactly matches the imposed strains. Such diverse behaviour, in general, may help to realise more effective actuation schemes for engineering structures. © 2012 Elsevier Ltd. All rights reserved.

Investigation of the dilution process for measurement of particulate matter from spark-ignition engines

Measurements of particulate matter (PM) from spark ignition (SI) engine exhaust using dilution tunnels will become more prevalent as emission standards are tightened. Hence, a study of the dilution process was undertaken in order to understand how various dilution related parameters affect the accuracy with which PM sizes and concentrations can be determined. A SI and a compression ignition (CI) engine were separately used to examine parameters of the dilution process; the present work discusses the results in the context of SI exhaust dilution. A Scanning Mobility Particle Sizer (SMPS) was used to measure the size distribution, number density, and volume fraction of PM. Temperature measurements in the exhaust pipe and dilution tunnel reveal the degree of mixing between exhaust and dilution air, the effect of flowrate on heat transfer from undiluted and diluted exhaust to the environment, and the minimum permissible dilution ratio for a maximum sample temperature of 52°C. Measurements of PM concentrations as a function of dilution ratio show the competing effects of temperature and particle/vapor concentrations on particle growth dynamics, which result in a range of dilution ratios-from 13 to 18-where the effect of dilution ratio, independent of flowrate, is kept to a minimum. This range of dilution ratios is therefore optimal in order to achieve repeatable PM concentration measurements. Particle dynamics during transit through the tunnel operating at the optimal dilution ratio was found statistically insignificant compared to data scatter. Such small differences in number concentration may be qualitatively representative of particle losses for SI exhaust, but small increases in PM volume fraction during transit through the tunnel may significantly underestimate accretion of mass due to unburned hydrocarbons (HCs) emitted by SI engines. The fraction of SI-derived PM mass due to adsorbed/absorbed vapor, estimated from these data, is consistent with previous chemical analyses of PM. © 1998 Society of Automotive Engineers, Inc.