A new parallel overlapped domain decomposition method for nonlinear dynamic finite element analysis

In this paper a new parallel algorithm for nonlinear transient dynamic analysis of large structures has been presented. An unconditionally stable Newmark-beta method (constant average acceleration technique) has been employed for time integration. The proposed parallel algorithm has been devised within the broad framework of domain decomposition techniques. However, unlike most of the existing parallel algorithms (devised for structural dynamic applications) which are basically derived using nonoverlapped domains, the proposed algorithm uses overlapped domains. The parallel overlapped domain decomposition algorithm proposed in this paper has been formulated by splitting the mass, damping and stiffness matrices arises out of finite element discretisation of a given structure. A predictor-corrector scheme has been formulated for iteratively improving the solution in each step. A computer program based on the proposed algorithm has been developed and implemented with message passing interface as software development environment. PARAM-10000 MIMD parallel computer has been used to evaluate the performances. Numerical experiments have been conducted to validate as well as to evaluate the performance of the proposed parallel algorithm. Comparisons have been made with the conventional nonoverlapped domain decomposition algorithms. Numerical studies indicate that the proposed algorithm is superior in performance to the conventional domain decomposition algorithms. (C) 2003 Elsevier Ltd. All rights reserved.

Steady compressible flow of cohesionless granular materials through a wedge-shaped bunker

A continuum model based on the critical-state theory of soil mechanics is used to generate stress, density, and velocity profiles, and to compute discharge rates for the flow of granular material in a mass flow bunker. The bin–hopper transition region is idealized as a shock across which all the variables change discontinuously. Comparison with the work of Michalowski (1987) shows that his experimentally determined rupture layer lies between his prediction and that of the present theory. However, it resembles the former more closely. The conventional condition involving a traction-free surface at the hopper exit is abandoned in favour of an exit shock below which the material falls vertically with zero frictional stress. The basic equations, which are not classifiable under any of the standard types, require excessive computational time. This problem is alleviated by the introduction of the Mohr–Coulomb approximation (MCA). The stress, density, and velocity profiles obtained by integration of the MCA converge to asymptotic fields on moving down the hopper. Expressions for these fields are derived by a perturbation method. Computational difficulties are encountered for bunkers with wall angles θw [gt-or-equal, slanted] 15° these are overcome by altering the initial conditions. Predicted discharge rates lie significantly below the measured values of Nguyen et al. (1980), ranging from 38% at θw = 15° to 59% at θw = 32°. The poor prediction appears to be largely due to the exit condition used here. Paradoxically, incompressible discharge rates lie closer to the measured values. An approximate semi-analytical expression for the discharge rate is obtained, which predicts values within 9% of the exact (numerical) ones in the compressible case, and 11% in the incompressible case. The approximate analysis also suggests that inclusion of density variation decreases the discharge rate. This is borne out by the exact (numerical) results – for the parameter values investigated, the compressible discharge rate is about 10% lower than the incompressible value. A preliminary comparison of the predicted density profiles with the measurements of Fickie et al. (1989) shows that the material within the hopper dilates more strongly than predicted. Surprisingly, just below the exit slot, there is good agreement between theory and experiment.

Numerical Modelling of the Observed Diurnal Cycle of Indian Monsoon Rainfall

We have analysed the diurnal cycle of rainfall over the Indian region (10S-35N, 60E-100E) using both satellite and in-situ data, and found many interesting features associated with this fundamental, yet under-explored, mode of variability. Since there is a distinct and strong diurnal mode of variability associated with the Indian summer monsoon rainfall, we evaluate the ability of the Weather Research and Forecasting Model (WRF) to simulate the observed diurnal rainfall characteristics. The model (at 54km grid-spacing) is integrated for the month of July, 2006, since this period was particularly favourable for the study of diurnal cycle. We first evaluate the sensitivity of the model to the prescribed sea surface temperature (SST), by using two different SST datasets, namely, Final Analyses (FNL) and Real-time Global (RTG). It was found that with RTG SST the rainfall simulation over central India (CI) was significantly better than that with FNL. On the other hand, over the Bay of Bengal (BoB), rainfall simulated with FNL was marginally better than with RTG. However, the overall performance of RTG SST was found to be better than FNL, and hence it was used for further model simulations. Next, we investigated the role of the convective parameterization scheme on the simulation of diurnal cycle of rainfall. We found that the Kain-Fritsch (KF) scheme performs significantly better than Betts-Miller-Janjić (BMJ) and Grell-Devenyi schemes. We also studied the impact of other physical parameterizations, namely, microphysics, boundary layer, land surface, and the radiation parameterization, on the simulation of diurnal cycle of rainfall, and identified the “best” model configuration. We used this configuration of the “best” model to perform a sensitivity study on the role of various convective components used in the KF scheme. In particular, we studied the role of convective downdrafts, convective timescale, and feedback fraction, on the simulated diurnal cycle of rainfall. The “best” model simulations, in general, show a good agreement with observations. Specifically, (i) Over CI, the simulated diurnal rainfall peak is at 1430 IST, in comparison to the observed 1430-1730 IST peak; (ii) Over Western Ghats and Burmese mountains, the model simulates a diurnal rainfall peak at 1430 IST, as opposed to the observed peak of 1430-1730 IST; (iii) Over Sumatra, both model and observations show a diurnal peak at 1730 IST; (iv) The observed southward propagating diurnal rainfall bands over BoB are weakly simulated by WRF. Besides the diurnal cycle of rainfall, the mean spatial pattern of total rainfall and its partitioning between the convective and stratiform components, are also well simulated. The “best” model configuration was used to conduct two nested simulations with one-way, three-level nesting (54-18-6km) over CI and BoB. While, the 54km and 18km simulations were conducted for the whole of July, 2006, the 6km simulation was carried out for the period 18 - 24 July, 2006. The results of our coarse- and fine-scale numerical simulations of the diurnal cycle of monsoon rainfall will be discussed.

Stabilizing a pulsed field emission from an array of carbon nanotubes

In this paper, we propose a new design configuration for a carbon nanotube (CNT) array based pulsed field emission device to stabilize the field emission current. In the new design, we consider a pointed height distribution of the carbon nanotube array under a diode configuration with two side gates maintained at a negative potential to obtain a highly intense beam of electrons localized at the center of the array. The randomly oriented CNTs are assumed to be grown on a metallic substrate in the form of a thin film. A model of field emission from an array of CNTs under diode configuration was proposed and validated by experiments. Despite high output, the current in such a thin film device often decays drastically. The present paper is focused on understanding this problem. The random orientation of the CNTs and the electromechanical interaction are modeled to explain the self-assembly. The degraded state of the CNTs and the electromechanical force are employed to update the orientation of the CNTs. Pulsed field emission current at the device scale is finally obtained by using the Fowler-Nordheim equation by considering a dynamic electric field across the cathode and the anode and integration of current densities over the computational cell surfaces on the anode side. Furthermore we compare the subsequent performance of the pointed array with the conventionally used random and uniform arrays and show that the proposed design outperforms the conventional designs by several orders of magnitude. Based on the developed model, numerical simulations aimed at understanding the effects of various geometric parameters and their statistical features on the device current history are reported.

Numerical modeling of the contaminant Transport through stratified soil

The transport processes of the dissolved chemicals in stratified or layered soils have been studied for several decades. In case of the solute transport through stratified layers, interface condition plays an important role in determining appropriate transport parameters. First‐ type and third‐ type interface conditions are generally used in the literature. A first‐type interface condition will result in a continuous concentration profile across the interface at the expense of solute mass balance. On the other hand, a discontinuity in concentration develops when a third‐ type interface condition is used. To overcome this problem, a combined first‐ and third‐ type condition at the interface has been widely employed which yields second‐ type condition. This results in a similar break‐through curve irrespective of the layering order, which is non‐physical. In this work, an interface condition is proposed which satisfies the mass balance implicitly and brings the distinction between the breakthrough curves for different layering sequence corroborating with the experimental observations. This is in disagreement with the earlier work by H. M. Selim and co‐workers but, well agreement with the hypothetical result by Bosma and van der Zee; and Van der Zee.

Fully Comprehensive Geometrically Non-Linear Dynamic Analysis of Multi-Body Beam Systems with Elastic Couplings

This paper is concerned with the dynamic analysis of flexible,non-linear multi-body beam systems. The focus is on problems where the strains within each elastic body (beam) remain small. Based on geometrically non-linear elasticity theory, the non-linear 3-D beam problem splits into either a linear or non-linear 2-D analysis of the beam cross-section and a non-linear 1-D analysis along the beam reference line. The splitting of the three-dimensional beam problem into two- and one-dimensional parts, called dimensional reduction,results in a tremendous savings of computational effort relative to the cost of three-dimensional finite element analysis,the only alternative for realistic beams. The analysis of beam-like structures made of laminated composite materials requires a much more complicated methodology. Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here.The analysis methodology can be viewed as a 3-step procedure. First, the sectional properties of beams made of composite materials are determined either based on an asymptotic procedure that involves a 2-D finite element nonlinear analysis of the beam cross-section to capture trapeze effect or using strip-like beam analysis, starting from Classical Laminated Shell Theory (CLST). Second, the dynamic response of non-linear, flexible multi-body beam systems is simulated within the framework of energy-preserving and energy-decaying time integration schemes that provide unconditional stability for non-linear beam systems. Finally,local 3-D responses in the beams are recovered, based on the 1-D responses predicted in the second step. Numerical examples are presented and results from this analysis are compared with those available in the literature.

Geometrically Nonlinear Dynamics of Composite Four-Bar Mechanisms

This work intends to demonstrate the importance of geometrically nonlinear crosssectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the four beam reference curves. For thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses, more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the nonlinear, flexible fourbar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we shall attempt to identify and investigate a few problems where the cross-sectional nonlinearities are significant. This will be carried out by varying stacking sequences and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form nonlinear beam stiffness matrix. Numerical examples will be presented and results from this analysis will be compared with those available in the literature, for linear cross-sectional analysis and isotropic materials as special cases.

Numerical Study Of Heat Transfer From Pin Fin Heat Sink Using Steady And Pulsated Impinging Jets

The work reported in this thesis is an attempt to enhance heat transfer in electronic devices with the use of impinging air jets on pin-finned heat sinks. The cooling per-formance of electronic devices has attracted increased attention owing to the demand of compact size, higher power densities and demands on system performance and re-liability. Although the technology of cooling has greatly advanced, the main cause of malfunction of the electronic devices remains overheating. The problem arises due to restriction of space and also due to high heat dissipation rates, which have increased from a fraction of a W/cm2to 100s of W /cm2. Although several researchers have at-tempted to address this at the design stage, unfortunately the speed of invention of cooling mechanism has not kept pace with the ever-increasing requirement of heat re- moval from electronic chips. As a result, efficient cooling of electronic chip remains a challenge in thermal engineering. Heat transfer can be enhanced by several ways like air cooling, liquid cooling, phase change cooling etc. However, in certain applications due to limitations on cost and weight, eg. air borne application, air cooling is imperative. The heat transfer can be increased by two ways. First, increasing the heat transfer coefficient (forced convec- tion), and second, increasing the surface area of heat transfer (finned heat sinks). From previous literature it was established that for a given volumetric air flow rate, jet im-pingement is the best option for enhancing heat transfer coefficient and for a given volume of heat sink material pin-finned heat sinks are the best option because of their high surface area to volume ratio. There are certain applications where very high jet velocities cannot be used because of limitations of noise and presence of delicate components. This process can further be improved by pulsating the jet. A steady jet often stabilizes the boundary layer on the surface to be cooled. Enhancement in the convective heat transfer can be achieved if the boundary layer is broken. Disruptions in the boundary layer can be caused by pulsating the impinging jet, i.e., making the jet unsteady. Besides, the pulsations lead to chaotic mixing, i.e., the fluid particles no more follow well defined streamlines but move unpredictably through the stagnation region. Thus the flow mimics turbulence at low Reynolds number. The pulsation should be done in such a way that the boundary layer can be disturbed periodically and yet adequate coolant is made available. So, that there is not much variation in temperature during one pulse cycle. From previous literature it was found that square waveform is most effective in enhancing heat transfer. In the present study the combined effect of pin-finned heat sink and impinging slot jet, both steady and unsteady, has been investigated for both laminar and turbulent flows. The effect of fin height and height of impingement has been studied. The jets have been pulsated in square waveform to study the effect of frequency and duty cycle. This thesis attempts to increase our understanding of the slot jet impingement on pin-finned heat sinks through numerical investigations. A systematic study is carried out using the finite-volume code FLUENT (Version 6.2) to solve the thermal and flow fields. The standard k-ε model for turbulence equations and two layer zonal model in wall function are used in the problem Pressure-velocity coupling is handled using the SIMPLE algorithm with a staggered grid. The parameters that affect the heat transfer coefficient are: height of the fins, total height of impingement, jet exit Reynolds number, frequency of the jet and duty cycle (percentage time the jet is flowing during one complete cycle of the pulse). From the studies carried out it was found that: a) beyond a certain height of the fin the rate of enhancement of heat transfer becomes very low with further increase in height, b) the heat transfer enhancement is much more sensitive to any changes at low Reynolds number than compared to high Reynolds number, c) for a given total height of impingement the use of fins and pulsated jet, increases the effective heat transfer coefficient by almost 200% for the same average Reynolds number, d) for all the cases it was observed that the optimum frequency of impingement is around 50 − 100 Hz and optimum duty cycle around 25-33.33%, e) in the case of turbulent jets the enhancement in heat transfer due to pulsations is very less compared to the enhancement in case of laminar jets.