Computational analysis of multi-stepped beams and beams with linearly-varying heights implementing closed-form finite element formulation for multi-cracked beam elements

The model where the cracks are represented by means of internal hinges endowed with rotational springs has been shown to enable simple and effective representation of transversely-cracked slender Euler–Bernoulli beams subjected to small deflections. It, namely, provides reliable results when compared to detailed 2D and 3D models even if the basic linear moment–rotation constitutive law is adopted.This paper extends the utilisation of this model as it presents the derivation of a closed-form stiffness matrix and a load vector for slender multi-stepped beams and beams with linearly-varying heights. The principle of virtual work allows for the simple inclusion of an arbitrary number of transverse cracks. The derived at matrix and vector define an ‘exact’ finite element for the utilised simplified computational model. The presented element can be implemented for analysing multi-cracked beams by using just one finite element per structural beam member. The presented expressions for a stepped-beam are not exclusively limited to this kind of height variation, as by proper discretisation an arbitrary variation of a cross-section’s height can be adequately modelled.The accurate displacement functions presented for both types of considered beams complete the derivations. All the presented expressions can be easily utilised for achieving computationally-efficient and truthful analyses.     

Elimination of spiral waves in excitable media by magnetic induction

Nonlinear Dynamics - The formation of spiral waves in excitable media is a fascinating example of the beauty of nonlinear dynamics in spatiotemporal systems. Apart from the beauty of the patterns,...     

Analysis of nonconforming work as a tool for status analysis and continuous improvement

Absract  The methodology for statistical processing of reports on nonconforming work and unexpected situations which occur in the laboratory of Gamma-Ray Spectrometry Group at the Jožef Stefan Institute is presented. The results of statistical analyses are discussed. Pareto analysis has shown that the majority of cases of nonconforming work originates in errors made by personnel. The sociological and psychological aspects of strategies aimed at preventing careless work are discussed. It is proposed that motivation should be used as a tool against habits that lessen awareness during routine operations. Specific recommendations regarding communication with personnel are given. Received: 20 July 2001 Accepted: 24 October 2001     

Liquid-crystal-droplet optical microcavities

ABSTRACT

The use of liquid-crystal droplets as optical microcavities and lasers is reviewed and possible applications are discussed. Liquid-crystal droplets are prepared by simple methods that enable scalable production since their internal structure is formed by self-assembly. Light is trapped in droplets due to total internal reflection on the surface due to refractive index mismatch or because of a photonic bandgap structure in cholesteric liquid crystals (CLCs). Light confinement gives rise to a variety of optical modes and by employing a fluorescent dye end external optical pumping, lasing can be achieved. Liquid-crystal-droplet cavities are largely tunable by applying an electric field or a temperature change. Such cavities can be used as temperature and chemical sensors, and tunable light sources and filters in future integrated soft photonic circuits.     

Non-commutative extensions of the MacMahon Master Theorem

We present several non-commutative extensions of the MacMahon Master Theorem, further extending the results of Cartier-Foata and Garoufalidis-Lê-Zeilberger. The proofs are combinatorial and new even in the classical cases. We also give applications to the β-extension and Krattenthaler-Schlosser's q-analogue.     

Ab initio calculation of magnetic shielding and susceptibility. Finite perturbation calculation of susceptibility with GIAO's

The magnetic susceptibility of hydrogen fluoride is calculated with four different basis sets of gauge invariant atomic orbitals (GIAO's). The Roothaan equations are solved for various values of the magnetic field strength and the susceptibility is deduced by a numerical differentiation of the energy.