Geometrically nonlinear composite shells with integrated piezoelectric layers

In order to show the significance of considering nonlinear deformations in piezoelectrical structures, a geometrical nonlinear shell element with integrated piezoelectric layers is introduced. The strain‐displacement relations are implemented using firstorder shear deformation theory with small strains but moderate rotations. The element has been tested on several benchmark problems and it can be concluded that the effect of geometrical nonlinearity is significant when the sensor properties of the piezoelectrical layers are predicted. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Environmental Stress Cracking of Polymers Monitored by Fatigue Crack Growth Experiments

This article describes fatigue crack growth experiments to investigate the degradation of the durability of polymers due to fluid environments. The degrading effect of media causing stress cracking can be observed on the fracture surfaces of tested samples by scanning electron microscopy. Strategies to improve environmental stress cracking like changes in molecular weight, orientation, toughening with rubber particles of different sizes are discussed. Fatigue crack growth experiments can be employed as a very fast and effective screening method.     

A numerical method for computing the response of composites with periodic microstructure

The stress‐strain response of a periodic structure due to an applied eigenstrain field is investigated. The periodic structure allows reduction of the problem to a representative volume element (RVE) problem. A review of Fourier series as a particular method of solving the set of differential equations is given, and an example problem is studied. Results of the latter method are compared to results obtained using discrete Fourier transforms in a different way.     

Facile conversion of ammonia to a nitride in a rhenium system that cleaves dinitrogen

Rhenium complexes with aliphatic PNP pincer ligands have been shown to be capable of reductive N₂ splitting to nitride complexes. However, the conversion of the resulting nitride to ammonia has not been observed. Here, the thermodynamics and mechanism of the hypothetical N–H bond forming steps are evaluated through the reverse reaction, conversion of ammonia to the nitride complex. Depending on the conditions, treatment of a rhenium(iii) precursor with ammonia gives either a bis(amine) complex [(PNP)Re(NH₂)₂Cl]⁺, or results in dehydrohalogenation to the rhenium(iii) amido complex, (PNP)Re(NH₂)Cl. The N–H hydrogen atoms in this amido complex can be abstracted by PCET reagents which implies that they are quite weak. Calorimetric measurements show that the average bond dissociation enthalpy of the two amido N–H bonds is 57 kcal mol⁻¹, while DFT computations indicate a substantially weaker N–H bond of the putative rhenium(iv)-imide intermediate (BDE = 38 kcal mol⁻¹). Our analysis demonstrates that addition of the first H atom to the nitride complex is a thermochemical bottleneck for NH₃ generation.

Rhenium–PNP complexes split N₂ to nitrides, but the nitrides do not give ammonia. Here, the thermodynamics of the hypothetical N–H bond forming steps are evaluated through the reverse reaction, showing that the first H addition is the bottleneck.     

Lifetime measurements of metastable states in CRYRING

Collinear ion beam laser spectroscopy has been utilized in the ion storage ring CRYRING in order to measure lifetimes of metastable states in singly charged ions. The laser light has been used for selective probing of the population decay of individual fine structure or hyperfine structure states. With the use of a mechanical shutter, time resolved studies could be performed with millisecond resolution. In another experiment, the cw laser light was used to optically pump stored ions from the ground state into a specific metastable state. With most of the stored ions in the metastable state, direct observation of the decay of the forbidden transition from the metastable state to the ground state could be observed passively. Measurements of metastable lifetimes in Ca⁺, Sr⁺, Xe⁺ and Eu⁺ will be discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

A Finite Element Formulation for the Nonlinear Analysis of Piezoelectric Three-Dimensional Beam Structures

A finite element formulation for a three-dimensional piezoelectric beam which includes geometrical and material nonlinearities is presented. To account for the piezoelectric effect, the coupling between the mechanical stress and the electrical displacement is considered. Based on the Timoshenko theory, an eccentric beam formulation is introduced which provides an efficient model to analyze piezoelectric structures. The geometrically nonlinear assumption allows the calculation of large deformations including buckling analysis. A quadratic approximation of the electric potential through the cross section of the beam ensures the fulfilment of the charge conservation law exactly. This assumption leads to a finite element formulation with six mechanical and five electrical degrees of freedom per node. To take into account the typical ferroelectric hysteresis phenomena, a nonlinear material model is essential. For this purpose, the phenomenological Preisach model is implemented into the beam formulation which provides an efficient determination of the remanent part of the polarization. The applicability of the introduced beam formulation is discussed with respect to available data from literature. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Mixed Finite Element Formulation for Piezoelectric Materials

A geometrically nonlinear finite element formulation to analyze multi-field problems as they arise e.g. in piezoelectric or magnetostrictive materials is presented. Here we focus on piezoelectric problems. The formulation is based on a Hu-Washizu functional considering six independent fields. These are displacements u , electric potential ϕ, strains E , stresses S , electric field , and the electric flux density . The finite element approximation leads to an 8-node hexahedral element with u and ϕ as nodal degrees of freedom. The fields E , S , , and are interpolated on element level by employing some internal degrees of freedom. These fields do not require continuity across the element boundaries, thus the internal degree of freedoms are eliminated on element level by a static condensation. The geometrically non-linear theory allows large deformations and accounts for stability problems. To fulfill the charge conservation law in bending dominated situations exactly a quadratic approximation of the electric potential is necessary. This leads in general to additional nodal degrees of freedom, which is circumvented by the presented formulation by employing appropriate interpolations of and . Numerical examples show that the locking effect which arise in low order elements are significantly reduced and that the element provides good accuracy with respect to experimental data. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Beamforming and Interference Cancellation for Capacity Gain in Mobile Networks

The growth of wireless communication continues. There is a demand for more user capacity from new subscribers and new services such as wireless internet. In order to meet these expectations new and improved technology must be developed. A way to increase the capacity of an existing mobile radio network is to exploit the spatial domain in an efficient way. An antenna array adds spatial domain selectivity in order to improve the Carrier-to-Interference ratio (C/I) as well as Signal-to-Noise Ratio (SNR). An adaptive antenna array can further improve the Carrier-to-Interference ratio (C/I) by suppressing interfering signals and steer a beam towards the user. The suggested scheme is a combination of a beamformer and an interference canceller.The proposed structure is a circular array consisting of K omni-directional elements and combines fixed beamforming with interference cancelling. The fixed beamformers use a weight matrix to form multiple beams. The interference cancelling stage suppresses undesired signals, leaking into the desired beam.The desired signal is filtered out by the fixed beamforming structure. Due to the side-lobes, interfering signals will also be present in this beam. Two alternative strategies were chosen to cancel these interferers; use the other beamformer outputs as inputs to an adaptive interference canceller; or regenerate the outputs from the other beamformer outputs and generate clean signals which are used as inputs to adaptive interference cancellers.Resulting beamformer patterns as well as interference cancellation simulation results are presented. Two different methods have been used to design the beamformer weights, Least Square (LS) and minimax optimisation. In the minimax optimisation a semi-infinite linear programming approach was used. Although the optimisation plays an essential role in the performance of the beamformer, this paper is focused on the application rather then the optimisation methods.