Shortcomings of discontinuous-pressure finite element methods on a class of transient problems

Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield Solutions of comparable accuracy, and that the choice of interpolation is dictated by which of the two is more efficient. In this work, we show that using discontinuous-pressure interpolations can yield inaccurate solutions at large times on a class of transient problems, while the continuous-pressure formulation yields solutions that are in good agreement with the analytical Solution.

Computation of Thermal Stress Intensity Factors for Bimaterial Interface Cracks Using Domain Integral Method

The concept of domain integral used extensively for J integral has been applied in this work for the formulation of J(2) integral for linear elastic bimaterial body containing a crack at the interface and subjected to thermal loading. It is shown that, in the presence of thermal stresses, the J(k) domain integral over a closed path, which does not enclose singularities, is a function of temperature and body force. A method is proposed to compute the stress intensity factors for bimaterial interface crack subjected to thermal loading by combining this domain integral with the J(k) integral. The proposed method is validated by solving standard problems with known solutions.

Bond graph model of doubly fed three phase induction motor using the Axis Rotator element for frame transformation

Induction motor is a typical member of a multi-domain, non-linear, high order dynamic system. For speed control a three phase induction motor is modelled as a d–q model where linearity is assumed and non-idealities are ignored. Approximation of the physical characteristic gives a simulated behaviour away from the natural behaviour. This paper proposes a bond graph model of an induction motor that can incorporate the non-linearities and non-idealities thereby resembling the physical system more closely. The model is validated by applying the linearity and idealities constraints which shows that the conventional ‘abc’ model is a special case of the proposed generalised model.

Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.

A Legendre spectral element model for sloshing and acoustic analysis in nearly incompressible fluids

A new spectral finite element formulation is presented for modeling the sloshing and the acoustic waves in nearly incompressible fluids. The formulation makes use of the Legendre polynomials in deriving the finite element interpolation shape functions in the Lagrangian frame of reference. The formulated element uses Gauss-Lobatto-Legendre quadrature scheme for integrating the volumetric stiffness and the mass matrices while the conventional Gauss-Legendre quadrature scheme is used on the rotational stiffness matrix to completely eliminate the zero energy modes, which are normally associated with the Lagrangian FE formulation. The numerical performance of the spectral element formulated here is examined by doing the inf-sup test oil a standard rectangular rigid tank partially filled with liquid The eigenvalues obtained from the formulated spectral element are compared with the conventional equally spaced node locations of the h-type Lagrangian finite element and the predicted results show that these spectral elements are more accurate and give superior convergence The efficiency and robustness of the formulated elements are demonstrated by solving few standard problems involving free vibration and dynamic response analysis with undistorted and distorted spectral elements. and the obtained results are compared with available results in the published literature (C) 2009 Elsevier Inc All rights reserved

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

New rational interpolation functions for finite element analysis of rotating beams

A rotating beam finite element in which the interpolating shape functions are obtained by satisfying the governing static homogenous differential equation of Euler–Bernoulli rotating beams is developed in this work. The shape functions turn out to be rational functions which also depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. These rational functions yield the Hermite cubic when rotation speed becomes zero. The new element is applied for static and dynamic analysis of rotating beams. In the static case, a cantilever beam having a tip load is considered, with a radially varying axial force. It is found that this new element gives a very good approximation of the tip deflection to the analytical series solution value, as compared to the classical finite element given by the Hermite cubic shape functions. In the dynamic analysis, the new element is applied for uniform, and tapered rotating beams with cantilever and hinged boundary conditions to determine the natural frequencies, and the results compare very well with the published results given in the literature.

'Wet N2O oxidation' process and interface state density characterization of nanoscale nitrided SiO2 for flash memory application

In this paper we first present the 'wet N2O' furnace oxidation process to grow nitrided tunnel oxides in the thickness range 6 to 8 nm on silicon at a temperature of 800 degrees C. Electrical characteristics of MOS capacitors and MOSFETs fabricated using this oxide as gate oxide have been evaluated and the superior features of this oxide are ascertained The frequency response of the interface states, before and after subjecting the MOSFET gate oxide to constant current stress, is studied using a simple analytical model developed in this work.

Phase-Field Simulation of Fusion Interface Events during Solidification of Dissimilar Welds: Effect of Composition Inhomogeneity

We investigate the events near the fusion interfaces of dissimilar welds using a phase-field model developed for single-phase solidification of binary alloys. The parameters used here correspond to the dissimilar welding of a Ni/Cu couple. The events at the Ni and the Cu interface are very different, which illustrate the importance of the phase diagram through the slope of the liquidus curves. In the Ni side, where the liquidus temperature decreases with increasing alloying, solutal melting of the base metal takes place; the resolidification, with continuously increasing solid composition, is very sluggish until the interface encounters a homogeneous melt composition. The growth difficulty of the base metal increases with increasing initial melt composition, which is equivalent to a steeper slope of the liquidus curve. In the Cu side, the initial conditions result in a deeply undercooled melt and contributions from both constrained and unconstrained modes of growth are observed. The simulations bring out the possibility of nucleation of a concentrated solid phase from the melt, and a secondary melting of the substrate due to the associated recalescence event. The results for the Ni and Cu interfaces can be used to understand more complex dissimilar weld interfaces involving multiphase solidification.

Parametric finite element analyses of geocellsupported embankments

This paper presents the results from parametric finite element analyses of geocell-supported embankments constructed on weak foundation soils. A composite model is used to numerically simulate the improvement in the strength and stiffness of the soil as a result of geocell confinement. The shear strength of the geocell-encased soil is obtained as a function of the additional confining pressure due to the geocell encasement considering it as a thin cylinder subjected to internal pressure. The stiffness of the geocell-encased soil is obtained from the stiffness of the unreinforced soil and the tensile modulus of the geocell material using an empirical equation. The validity of the model is verified by simulating the laboratory experiments on model geocell-supported embankments. Parametric finite element analyses of the geocell-supported embankments are carried out by varying the dimensions of the geocell layer, the tensile strength of the material used for fabricating the geocell layer, the properties of the infill soil, and the depth of the foundation layer. Some important guidelines for selecting the geocell reinforcement to support embankments on weak foundation soils are established through these numerical studies.

The partition of unity finite element method for elastic wave propagation in Reissner-Mindlin plates

This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four-noded element for the Reissner-indlin plate is derived in this paper, which is free of shear locking. Such a locking-free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency-dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright (C)006 John Wiley & Sons, Ltd.

The Use of Liquid-Liquid Interface (Biphasic) for the Preparation of Benzenetricarboxylate Complexes of Cobalt and Nickel

New metal-organic frameworks (MOFs) [Ni(C12N2H10)(H2O)][C6H3(COO)2(COOH)] (I), [Co2(H2O)6][C6H3(COO)3]2·(C4N2H12)(H2O)2 (II), [Ni2(H2O)6][C6H3(COO)3]2·(C4N2H12)(H2O)2 (III), [Ni(C13N2H14)(H2O)][C6H3(COO)2(COOH)] (IV), [Ni3(H2O)8][C6H3(COO)3] (V) and [Co(C4N2H4)(H2O)][C6H3(COO)3] (VI) {C6H3(COOH)3 = trimesic acid, C12N2H10 = 1,10-phenanthroline, C4N2H12 = piperazine dication, C13N2H14 = 1,3-bis(4-pyridyl)propane and C4N2H4 = pyrazine} have been synthesized by using an interface between two immiscible solvents, water and cyclohexanol. The compounds are constructed from the connectivity between the octahedral M2+ (M = Ni, Co) ions coordinated by oxygen atoms of carboxylate groups and water molecules and/or by nitrogen atoms of the ligand amines and the carboxylate units to form a variety of structures of different dimensionality. Strong hydrogen bonds of the type O-H···O are present in all the compounds, which give rise to supramolecularly organized higher-dimensional structures. In some cases ··· interactions are also observed. Magnetic studies indicate weak ferromagnetic interactions in I, IV and V and weak antiferromagnetic interactions in the other compounds (II, III and VI). All the compounds have been characterized by a variety of techniques.

Small-angle x-ray scattering study of the aggregation of gold nanoparticles during formation at the toluene-water interface

We report the results of an in situ small-angle x-ray scattering (SAXS) study of the aggregation of gold nanoparticles formed by an interfacial reaction at the toluene-water interface. The SAXS data provide a direct evidence for aggregate formation of nanoparticles having 1.3 nm gold core and an organic shell that gives a core-core separation of about 2.5 nm. Furthermore, the nanoparticles do not occupy all the cites of 13-member cluster. This occupancy decreases with reaction time and indicate reorganization of the clusters that generates planner disklike structures. A gradual increase in fractal dimension from 1.82 to 2.05 also indicate compactification of cluster aggregation with reaction time, the final exponent being close to 2 expected for disklike aggregates.

Covalent tethering of the dimer interface annuls aggregation in thymidylate synthase

Thymidylate synthase (TS), a dimeric enzyme, forms large soluble aggregates at concentrations of urea (3.3-5 M), well below that required for complete denaturation, as established by fluorescence and size-exclusion chromatography. In contrast to the wild-type enzyme, an engineered mutant of TS (T155C/E188C/C244T), TSMox, in which two subunits are crosslinked by disulfide bridges between residues 155-188' and 188-155', does not show this behavior. Aggregation behavior is restored upon disulfide bond reduction in the mutant protein, indicating the involvement of interface segments in forming soluble associated species. Intermolecular disulfide crosslinking has been used as a probe to investigate the formation of larger non-native aggregates. The studies argue for the formation of large multimeric species via a sticky patch of polypeptide from the dimer interface region that becomes exposed on partial unfolding. Covalent reinforcement of relatively fragile protein-protein interfaces may be a useful strategy in minimizing aggregation of non-native structures in multimeric proteins.