A family of lower- and higher-order transversal linearization techniques in non-linear stochastic engineering dynamics

Sample pathwise numerical integration of noise-driven engineering dynamical systems cannot generally be performed beyond a limited level of accuracy, especially when the noise processes are modelled using (filtered) white noises. Recently, a locally transversal linearization (LTL) strategy has been proposed by the author (Proc Roy Soc London A 2001; 457 :539–566) for direct integration of deterministic and stochastic non-linear dynamical systems. The present effort is focussed on a host of extensions along with detailed theoretical error analyses of the linearization approach, especially as applied to problems in non-linear stochastic engineering dynamics. Thus, to begin with, estimates of local and global error orders in the basic LTL scheme are obtained separately for the displacement and velocity vectors when the system is driven either by a set of additive noises or by an arbitrary combination of (independently evolving) additive and multiplicative noises. Following this, a new family of higher-order LTL schemes is proposed in order to improve upon the basic LTL method and the associated error orders are established. A stepwise implementation of the lower- and higher-order versions of the LTL method, along with certain computational aspects, is also outlined. The proposed schemes are numerically illustrated, to a limited extent, for a single degree-of-freedom (SDOF) and a two degree-of-freedom (TDOF) non-linear engineering systems under additive and/or multiplicative white noise excitations. Copyright © 2004 John Wiley & Sons, Ltd.     

A direct stiffness analysis of a composite beam with partial interaction

The use of the conventional semi-analytical stiffness method in finite element analysis, in which interpolation polynomials are used to develop the stiffness relationships, leads to problems of curvature locking when beam-type elements are developed for composite members with partial interaction between the materials of which it is comprised. The curvature locking phenomenon that occurs for composite steel–concrete members is quite well reported, and the general approach to minimizing the undesirable ramifications of curvature locking has been to use higher-order polynomials with increasing numbers of internal nodes. This paper presents an alternate formulation based on a direct stiffness approach rather than starting from pre-defined interpolation polynomials, and which does not possess the undesirable locking characteristics. The formulation is based on a more general approach for a bi-material composite flexural member, whose constituent materials are joined by elastic shear connection so as to provide partial interaction. The stiffness relationships are derived, and these are applied to a simply supported and a continuous steel–concrete composite beam to demonstrate the efficacy of the method, and in particular its ability to model accurately both very flexible and very stiff shear connection that causes difficulties when implemented in competitive semi-analytical algorithms. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Stability of Circular Cylindrical Shells with a Single Local Dent

The theoretical-and-experimental investigation has been performed on the stability of smooth cylindrical shells of steel with a single local dent. All the shells manufactured using the same process were tested with the fulfillment of identical conditions for observations and measurements. Theoretical calculations were carried out by the mesh method with the use of the nonlinear theory of shells. A comparison of the experimental and theoretical values of the critical loads has been made. The theoretical-and-experimental approach proposed enables one to evaluate the quality of shells by studying local dents and other specific imperfections.     

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     

Preparation and properties of heavy-metal halide glasses

We have studied the effect of In³⁺, Pb²⁺, Gd³⁺, and Cl (heavier ions) substitutions for Al³⁺, Ba²⁺, La³⁺, and F^? on the crystallization stability and UV/IR optical properties of HBLAN fluorohafnatc glasses (HfF₄-BaF₂-LaF₃-AlF₃-NaF system). We obtained stable glasses containing InF₃ and BaCl₂ instead of AlF₃ and BaF₂, respectively, and offering increased IR transmission. The presence of CCl₄ in the process atmosphere and the removal of oxygen-containing impurities via directional solidification are shown to have an advantageous effect on the optical quality of the glasses. The fluoride-chloride glasses are capable of accommodating about 1.5 times higher levels of rare-earth activators in comparison with their fluoride analogs.     

Analysis of operating conditions of ground-fault protection schemes for generator stator winding

This paper presents results of simulation studies of the influence of methods of grounding the stator winding of the unit-connected generator neutral on the operating conditions of a 100-percent ground-fault protection excited by the third-harmonic voltage ratio in the generator neutral and at its terminals. The analysis was performed for a generator with the neutral grounded through a ground-fault neutralizer, a third-harmonic stop filter, a resistor, and a capacitive voltage divider. The influence of the parameters of the particular elements of the grounding circuits on the voltage-feeding measuring element of the protection was determined. The capacitance to ground of the generator breakers was taken into account. The simulations were run for 1110-MVA unit-connected generator at ground faults along the whole length of the generator stator winding. It has been found that the method of grounding the generator neutral and the parameter of the grounding elements significantly influences the operating conditions of this protection. It is shown that through the proper selection of these parameters, the ground-fault protection of whole stator winding, counting from the generator neutral to the terminals is ensured.