Influence of various types of load-dependent supports on the stability of a compressible column model

Summary The nonlinear behaviour and static stability of a compressible elastic column whose flexural resistance changes as it is loaded is studied. A two-degree-of-freedom, compressible rod model of the column is analysed. Various types of load-stiffness relationships are considered. Post-buckling behaviour under static unidirectional loads is investigated. Singularities of the equilibrium paths of the column are classified according to the slenderness ratio of the column and the load-stiffness relationship of its support.On leave from Department of Mechanical Engineering, University of Toronto, 5 King's College Road Toronto, Ontario, Canada, M5S 1A4     

Computation of nonlinear functionals in particle methods

We consider the numerical computation of nonlinear functionals of distribution functions approximated by point measures. Two methods are described and estimates for the speed of convergence as the number of points tends to infinity are given. Moreover, numerical results for the entropy functional are presented.     

Analysis of ink flow in a mimeograph printer based on the mechanics of fluid-filled poroelastic solids

Summary To understand some main ink flow mechanisms in a mimeograph printer, the continuum mechanics theory of fluid-saturated porous solids is applied to analyze the ink flow through screens and a printing master, which are modeled by a fluid-filled poroelastic single layer. The layer is assumed to be pressed by a press roller from below and to be subjected from above to the hydrodynamic lubrication pressure induced between a printing drum and an ink roller. Nonlinear elasticity of the layer and dependence of the permeability on its deformation are taken into account. The numerical results show some important results: e.g., squeezing-out of the ink from the layer by the layer compaction by the press roller plays an important role, especially for the case where the compression duration is small in comparison with the characteristic time of the ink-filled poroelastic layer.     

A route to chaos in a nonlinear oscillator with delay

Summary The paper presents an analysis of the transition from regular to chaotic motion in a Van der Pol-Duffing's oscillator with delay after a Hopf bifurcation. The conditions for the occurrence of the Hopf bifurcation have been determined by means of the approximate method. For the parameters near the bifurcation point a computer simulation of the vibrating system had been performed and the evolution of the system from regular motion to chaos has been analysed at the decrease of the value of the dimensionless damping coefficient.With 2 Figures     

The incorporation of yield surface distortion into a unified constitutive model,part 2: Predictive capabilities

Summary The MATMOD-4V-DISTORTION model has been derived [1] with the intent of improving the MATMOD-4V model by adding the capability to predict distortions of small strain offset yield surfaces. This model is compared against a variety of experimental data to verify its behavior. Model simulations are compared with experimental data for proportional and nonproportional prestress histories and the effect of yield definition is also investigated. Finally, the same model which predicts a flattening of the yield surface in space is used to predict a rotation of the yield surface in ₁-₂ coordinates.With 9 Figures     

Stromdichte- und Magnetfeldverteilung bei einer Anordnung aus Platten und vielen parallelen Stromleitern

Übersicht Die vorliegende Arbeit befaßt sich mit der gesamten Stromdichte- und Magnetfeldverteilung in vielen flachen leitenden Platten konstanter Permeabilität, die bei einer Anordnung aus diesen Platten und vielen parallelen stromführenden Leitern angeordnet in mehreren Lagen entsteht. Unter Anwendung der Maxwellschen Differentialgleichungen und durch Einführung des Vektorpotentials werden allgemeine Gleichungen für die Komponenten der magnetischen Induktion im zweidimensionalen Feldraum aufgestellt. Die Stromdichteverteilung in den leitenden Platten, in denen Wirbelströme entstehen, wird aus dem Vektorpotential hergeleitet. Zunächst werden die Platten unendlich lang angenommen und die entsprechenden Gleichungen in Integralform aufgestellt, für deren Lösung die Gauss-Laguerresche Methode angewandt wird. Dann werden die Platten beiderseits durch Eisenwände begrenzt, womit die Gleichungen unter Berücksichtigung der Randbedingungen in Summenform ausgedrückt werden.

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Distribution of current and magnetic field density in flat conductive plates in an array composed from plates and many parallel conductors

Contents In the present research work the overall distribution of current and magnetic field density in many flat plates of constant magnetic permeability has been investigated, which applies to an array composed from the flat plates and many parallel conductors installed in many layers. Use of Maxwell's differential equations and vector potential results in general equations for the components of magnetic density in two dimensional field space. The distribution of current density in the conductive plates, where eddy currents are taken into account, is obtained from the vector potential. Initially the flat plates are considered being of infinite length, and with appropriate arrangement of the boundary conditions, the model applies to flat plates limited to both sides by iron partitions. Examples are given for both cases, where for the plates of infinite length the Gauss-Laguerre method is applied.

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Liste der Symbole A Vektorpotential - B Magnetische Induktion - I ₁ Stromstärke eines Leiters - N ₁ Anzahl der parallelen Leiter - N ₂ Anzahl der parallelen Platten - Permeabilität des Plattenmaterials - _r Relative Permeabilitätskonstante des Plattenmaterials - Leitfähigkeit - b Breite des Hauptstreukanals - i Stromdichte der Platten samt Wirbelströme - h ₁ Höhe der Leiter - a ₁ Breite der Leiterlagen - a Plattendicke - s Breite des Nebenstreukanals - c Abstand der letzten Platte von der Eisenwand - g Plattenhöhe - x, z, , Dimensionen - Q, K Integrationskonstanten - k ganze Zahl     

A combinatorial study of the rigidity of planar structures

Summary A combinatorial method is presented for examining the rigidity of planar structures. In this approach, an expansion process is used for the formation of a statically determinate substructure, known as a -tree of a structure. The algorithm of Lováz and Yemini, and the method of Sugihara are employed for the recognition of the elementary subgraphs, during this process.With 4 Figures     

Acoustic waves in solids with random cavities,II: Energy density considerations

Summary The propagation of acoustic plane and line-polarized waves in an isotropic solid containing random cavities is studied theoretically and experimentally. The effect of the cavities on the energy density and macroscopic propagation parameters of the acoustic waves is considered and the relationships between the cavities volume concentration, their average dynamic shape factor and the dynamic overall stiffness moduli of the solid are derived in the long wave approximation.     

From Natural Methylation to Versatile Alkylations Using Halide Methyltransferases

Halide methyltransferases (HMTs) enable the enzymatic synthesis of S-adenosyl-l -methionine (SAM) from S-adenosyl-l -homocysteine (SAH) and methyl iodide. Characterisation of a range of naturally occurring HMTs and subsequent protein engineering led to HMT variants capable of synthesising ethyl, propyl, and allyl analogues of SAM. Notably, HMTs do not depend on chemical synthesis of methionine analogues, as required by methionine adenosyltransferases (MATs). However, at the moment MATs have a much broader substrate scope than the HMTs. Herein we provide an overview of the discovery and engineering of promiscuous HMTs and how these strategies will pave the way towards a toolbox of HMT variants for versatile chemo- and regioselective biocatalytic alkylations.