Optimization of support positions to maximize the fundamental frequency of structures

In this paper, the position optimization of simple supports is implemented to maximize the fundamental frequency of a beam or plate structure. Both elastic and rigid supports are taken into account. First, the frequency sensitivity with respect to the movement of a simple support is derived using the discrete method. By means of the shape functions of the finite element method, closed‐form sensitivity formulations are developed straightforwardly. Then, a heuristic approach, called evolutionary shift method, is presented for optimizing support positions with a fixed grid mesh scheme. Based on the design sensitivity analysis, the support with the highest efficiency is shifted in priority along the elementary edges with the interval (step) of the elementary size. To facilitate the convergence of the process, the interpolation technique is employed to evaluate the solution more accurately. Finally, three numerical examples are presented to demonstrate the validity of the sensitivity analysis and the effectiveness of the optimization method. Copyright © 2004 John Wiley & Sons, Ltd.     

Thomas Fincke und die <Emphasis Type="Italic">Geometria rotundi</Emphasis>

Thomas Fincke (January 6^th, 1561–April 24^th, 1656), born in Flensburg (Germany), was one of the very most important and significant scientists in Denmark during the seventeenth century, a mathematician and astrologer and physician in the beginning of modern science, a representative of humanism and an influentual academic organizer. He studied in Strasbourg (since 1577) and Padua (since 1583) and received his M.D. in Basel (1587), he practised as a physician throughout his life (since 1587 or 1590) and became a professor at Copenhagen (1591). But he was best known because of his Geometriae rotundi libri XIIII (1583), a famous book on plane and spherical trigonometry, based not on Euclid but on Petrus Ramus. In this influentual work, in which Fincke introduced the terms tangent and secant and probable first noticed the Law of Tangents and the so-called Newton-Oppel-Mauduit-Simpson-Mollweide-Gauss-formula, he showed himself to be „abreast of the mathematics of his time“.      

Bemerkungen zu “Himmelsbeobachtungen in karolingischer Zeit

Additional remarks are given for the data of auroras during the earlier centuries.     

Local Strain Measurement within Tendon

Abstract:  Tendon is a dense connective tissue, responsible for transmitting the forces generated by muscles to the skeleton. It is composed of a hierarchical arrangement of crimped collagen fibres, interspersed with proteoglycan matrix and cells, known as tenocytes. During physiological loading, tendons are subjected to strains in the region of 5–6%, which result in the straightening and realignment of the collagen fibres, generating variable local strain fields within the tendon. This study demonstrates a technique for analysing local strains within viable tendon explants, during both loading and unloading of the tissue. Samples were strained in a custom-designed rig, allowing real-time visualisation of cell nuclei, used as local discrete markers, on a confocal microscope. Results indicated that local strains within the fascicle are smaller than the applied strains, never exceeding 1.2%, even at 8% gross applied strain. By contrast, the sliding of adjacent collagen units was recorded at each strain increment in this study, reaching a mean maximum of 3.9% of the applied displacement. Loading–unloading studies indicated that sliding behaviour is reversible up to strains of 5%, and provides the major extension mechanism within the rat-tail tendon. This technique can be extended to further analyse shearing behaviour within the matrix.     

Auto-correlation function analysis of phase formation in iron ion-implanted amorphous silicon layers

High-resolution transmission electron microscopy (HRTEM) in conjunction with autocorrelation function (ACF) analysis have been applied to investigate the evolution of structural order in iron ion-implanted amorphous silicon layers. β-FeSi₂ nanocrystallites as small as 5 nm in size were detected in 600 °C annealed for 60 min a-Si layers. The embedded nanocrystalline β-FeSi₂ was found to grow in the interlayer with annealing temperature.     

Electrosprayed and selenized Cu/In metal particle films

Nano-particulate copper and indium metal layers of 1-2 μm have been deposited by non-vacuum techniques such as doctor blade, screen printing and electrospray using alcoholic suspension pastes. Electrospray showed a high efficiency of material usage and yielded the most uniform morphology. The metal precursor layers were subjected to a thermal treatment (500-600 °C) in selenium vapor to convert the porous metal layers into CuInSe₂ compound layers. The chemical conversion, investigated by X-ray diffraction, showed the presence of the In₂O₃ impurity phase in the precursor as well as in the selenized layers.     

Influence of ion bombardment on the properties and microstructure of unbalanced magnetron deposited niobium coatings

The effect of the ion bombardment to unbalanced magnetron deposited, approximately 1.5 and 4.5 μm thick, Nb coatings have been investigated as the bias voltage was varied from U_B=−75 to −150 V. Increasing bias voltage increased the hardness of the coating from 4.5 to 8.0 GPa. This was associated with residual stress and Ar incorporation into the Nb lattice. Strong {110} texture developed in the samples deposited at low bias voltages, while beyond U_B=−100 V a {111} texture became dominant. However, strong {111} texture was observed only with the thicker 3Nb coatings. Secondary electron microscopy investigation of the coating topography showed fewer defects in the thicker coatings. All coatings exhibited good corrosion resistance, with the thicker coatings clearly outperforming the thinner ones. Excessive bias voltages (U_B=−150 V) was found to lead to poor adhesion and loss of corrosion resistance.     

Accuracy Investigations of Boundary Element Methods for the Solution of Laplace Equations

Boundary element methods (BEMs) are approved methods for an efficient numerical solution of problems, which are based on a Laplace equation. Here, the solution of electrostatic field problems, steady current flow field problems, and magnetostatic field problems is considered. Focus of this paper is on investigations of accuracy of direct formulations, which are based on Green's theorem. Different types of coupling of computational domains are examined with respect to accuracy and convergence behavior of iterative solvers of the linear system of equations. Furthermore, the influence of singular and nearly singular integrals and the influence of matrix compression techniques to the accuracy of the solution are observed     

Thermal Stressed State of a Hollow Metallic Cylinder under the Action of Electromagnetic Fields in the Mode of Damped Sinusoid

We determine the temperature fields and stresses formed in a long hollow conducting cylinder under the action of pulsed electromagnetic fields specified by the values of the axial component of the vector of intensity of a uniform magnetic field on the inner and outer surfaces. We consider the case where the electromagnetic action obeys the law of damped sinusoid on the inner and outer surfaces of the cylinder.