Numerical solution of integro-differential and singular integral equations for plate bending problems

Two integral equation formulations for the determination of the vertical displacement and the bending moment around holes in an elastic plate are presented. Each formulation consists of two equations, the first one an integral equation and an integro-differential equation and the second one two singular integral equations. The equations are solved using B-splines as approximations to the unknowns and the method is applied to the case of one elliptic hole in a twisted plate.

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Zusammenfassung Zwei verschiedene Integralgleichungssysteme für die Bestimmung von die Durchbiegung und die Biegemoment in einer gelochten elastischen Platte werden entwickelt. Die eine Systeme besteht von einer Integralgleichung und einer Integro-Differentialgleichung und die andere von zwei singulären Integralgleichungen von Cauchy'schen Typus. Bei der Auflösung der Systeme werden die unbekannten mit Hilfe B-splines ausgedrückt. Beide Systeme werden benutzt in dem Fall von einer elliptischen Loch in einer uendlichen, tordierten Platte.

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An abbreviated version of this paper was included in a paper Integral equation solutions to mechanical problems. A review and an application to plate theory which will appear in the Proceedings from second national congress of theoretical and applied mechanics, Druzba, Bulgaria, 1973.     

Evolution of a fast flame behind an induction zone

It has been shown that pressure waves can have a large effect on the burning rate of flames. In this paper, the evolution of convection-driven fast flame, which is acoustically linked to a shock wave via an induction zone, is examined in detail. It is found that there is positive feedback mechanism and the asymptotic model breaks down as blow up occurs. Comparison is made between the case of a piston driving a shock wave into a combustible atmosphere with these studies of a shock wave passing through an existing premixed flame. Received 4 August 1995 / Accepted 20 March 1996     

The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field

Three-dimensional density information of a double free air jet was acquired using optical tomography. The projections of the density field were measured using the background oriented schlieren method (BOS). Preceding the free jet measurements, the sensitivity, accuracy and resolution of the BOS method were investigated. The sensitivity depends mostly on the focal length of the lens used, the relative position of the object between camera and background and the smallest detectable shift in the image plane. The accuracy was found to be sufficiently high to apply a tomographic reconstruction process. The resolution is determined by the transfer function of the BOS-method. It is not constant and depends on the size of the interrogation windows used for the cross-correlation-algorithm. The reconstruction of the free jet was computed, using filtered back projection. The reconstructed 3D density field shows with good resolution the typical diamond structure of the density distribution in under-expanded free jets.     

Stress and deformation analysis from reduced-scale plastic-model testing

The use of scale models, which are made from plastic material, for stress and deformation analysis of missile nose-cone structures is discussed. The special strain-gage application and testing techniques, which are required because of the use of plastic materials, are detailed.The utilization of relatively inexpensive simplified models for the investigation of two specific design conditions is cited. The first case is a stress and deformation study of a thin, constant-thickness, shallow spherical shell which is supported by a circumferential line reaction and subjected to uniform external pressure. Comparisons are made with a recently published theoretical analysis of the problem.The second case is a particular design problem which is concerned with the determination of the stress and deformation in a variable-thickness, shallow spherical shell with several various-size cutouts. The shell is loaded with a varying external-pressure load which is reacted by a circumferential line load at the periphery. Influence curves for both stress and deformation are given.Some limitations of plastic-model testing are reviewed, and guides to successful use of the method are given.Paper was presented at 1959 SESA Spring Meeting held in Washington, D. C. on May 20–22.     

Temperature development based on technological analysis: Fast rolling as an example

Summary The mean rise in temperature with plastic strain due to the work of plastic deformation, taking account of the temperature-dependence of yield stress, is investigated when conduction effects are neglected and results for one particular example are presented. An adaptation of the well-known Siebel-Karman analysis for sheet rolling is examined, and results for the particular case of rolling a medium carbon steel are given in detail. The temperature-dependent property of the yield stress in cold-rolling at moderate reductions is shown not to have a large effect on factors such as roll-torque, though the actual temperature increase generated is a significant one. Examples are given of how the temperature of the material increases in its passage through the roll gap.     

Shear-induced aggregation and break up of fibril clusters close to the percolation concentration

To probe the behaviour of fibrillar assemblies of ovalbumin under oscillatory shear, close to the percolation concentration, c_p (7.5%), rheo-optical measurements and Fourier transform rheology were performed. Different results were found close to c_p (7.3%), compared to slightly further away from c_p (6.9 and 7.1%). For 6.9 and 7.1%, a decrease in complex viscosity, and a linear increase in birefringence, n, with increasing strain was observed, indicating deformation and orientation of the fibril clusters. For 7.3%, a decrease in complex viscosity was followed by an increase in complex viscosity with increasing strain, which coincided with a strong increase in n, dichroism, n, and the intensity of the normalized third harmonic (I₃/I₁). This regime was followed by a second decrease in complex viscosity, where n,n and I₃/I₁ decreased. In the first regime where the viscosity was decreasing with increasing strain, deformation and orientation of existing clusters takes place. At higher oscillatory shear, a larger deformation occurs and larger structures are formed, which is most likely aggregation of the clusters. Finally, at even higher strains, the clusters break up again. An increase in complex viscosity, n, n and I₃/I₁ was observed when a second strain sweep was performed 30 min after the first. This indicates that the shear-induced cluster formation and break up are not completely reversible, and the initial cluster size distribution is not recovered after cessation of flow.     

Towards Predicting Partitioning of Enzymes between Macromolecular Phases: Effects of Polydispersity on the Phase Behavior of Nonadditive Hard Spheres in Solution

The ability to separate enzymes, or cells or viruses, from a mixture is important and can be realized by the incorporation of the mixture into a macromolecular solution. This incorporation may lead to a spontaneous phase separation, with one phase containing the majority of one of the species of interest. Inspired by this phenomenon, we studied the theoretical phase behavior of a model system composed of an asymmetric binary mixture of hard spheres, of which the smaller component was monodisperse and the larger component was polydisperse. The interactions were modeled in terms of the second virial coefficient and could be additive hard sphere (HS) or nonadditive hard sphere (NAHS) interactions. The polydisperse component was subdivided into two subcomponents and had an average size ten or three times the size of the monodisperse component. We gave the set of equations that defined the phase diagram for mixtures with more than two components in a solvent. We calculated the theoretical liquid–liquid phase separation boundary for the two-phase separation (the binodal) and three-phase separation, the plait point, and the spinodal. We varied the distribution of the polydisperse component in skewness and polydispersity, and we varied the nonadditivity between the subcomponents as well as between the main components. We compared the phase behavior of the polydisperse mixtures with binary monodisperse mixtures for the same average size and binary monodisperse mixtures for the same effective interaction. We found that when the compatibility between the polydisperse subcomponents decreased, the three-phase separation became possible. The shape and position of the phase boundary was dependent on the nonadditivity between the subcomponents as well as their size distribution. We conclude that it is the phase enriched in the polydisperse component that demixes into an additional phase when the incompatibility between the subcomponents increases.     

The Mitochondrial Protein MitoNEET as a Probe for the Allostery of Glutamate Dehydrogenase

The proteins glutamate dehydrogenase (GDH) and mitoNEET are both targets of drug development efforts to treat metabolic disorders, cancer, and neurodegenerative diseases. However, these two proteins differ starkly in the current knowledge about ligand binding sites. MitoNEET is a [2Fe-2S]-containing protein with no obvious binding site for small ligands observed in its crystal structures. In contrast, GDH is known to have a variety of ligands at multiple allosteric sites thereby leading to complex regulation in activity. In fact, while GDH can utilize either NAD(H) or NADP(H) for catalysis at the active site, only NAD(H) binds at a regulatory site to inhibit GDH activity. Previously, we found that mitoNEET forms a covalent bond with GDH in vitro and increases the catalytic activity of the enzyme. In this study we evaluated the effects of mitoNEET binding on the allosteric control of GDH conferred by inhibitors. We examined all effectors using NAD or NADP as the coenzyme to determine allosteric linkage by the NAD-binding regulatory site. We found that GDH activity, in the presence of the inhibitory palmitoyl-CoA and EGCG, can be rescued by mitoNEET, regardless of the coenzyme used. This suggests that mitoNEET rescues GDH by stabilizing the open conformation.     

Heteroarylation of unactivated C–H bonds suitable for late-stage functionalization

The late-stage introduction of diverse heterocycles onto complex small molecules enables efficient access to new medicinally relevant compounds. An attractive approach to such a transformation would utilize the ubiquitous aliphatic C–H bonds of a complex substrate. Herein, we report a system that enables direct C–H heteroarylation using a stable, commercially available O-alkenylhydroxamate with heterocyclic sulfone partners. The C–H heteroarylation proceeds efficiently with a range of aliphatic substrates and common heterocycles, and is a rare example of heteroarylation of strong C–H bonds. Importantly, the present approach is amenable to late-stage functionalization as the substrate is the limiting reagent in all cases.

The late-stage introduction of diverse heterocycles onto complex small molecules enables efficient access to new medicinally relevant compounds.