Lower Bound Axisymmetric Limit Analysis Using Drucker-Prager Yield Cone and Simulation with Mohr-Coulomb Pyramid

This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker-Prager (D-P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D-P yield cone with the Mohr-Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors N-c, N-q and N-gamma have been computed, as a function of phi, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.

Experimental Studies on Drop Formation at the Tip of Melting Rods

Drop formation at the conical tips of melting rods has been experimentally studied using the transparent wax-alcohol/acetonitrile system. The effects of cone angle, rod diameter, immersion depth, and bath temperature on the detached drop mass have been studied over a wide range, besides recording useful qualitative information based on visual observation. The experimental results suggest that the phenomenon of drop formation at the tip of melting rods has a close parallel with the drop formation at conical tips, at least on a qualitative basis. However, the results could not be quantified owing to difficulties in characterizing the physical properties of the system, despite efforts to minimize them.

An absolute method for the determination of surface tension of liquids using pendent drop profiles

Drop formation at conical tips which is of relevance to metallurgists is investigated based on the principle of minimization of free energy using the variational approach. The dimensionless governing equations for drop profiles are computer solved using the fourth order Runge-Kutta method. For different cone angles, the theoretical plots of XT and ZT vs their ratio, are statistically analyzed, where XT and ZT are the dimensionless x and z coordinates of the drop profile at a plane at the conical tip, perpendicular to the axis of symmetry. Based on the mathematical description of these curves, an absolute method has been proposed for the determination of surface tension of liquids, which is shown to be preferable in comparison with the earlier pendent-drop profile methods.

Analysis of an internally mountable accelerometer balance system for use with non-isotropic models in shock tunnels

Knowledge of drag force is an important design parameter in aerodynamics. Measurement of aerodynamic forces at hypersonic speed is a challenge and usually ground test facilities like shock tunnels are used to carry out such tests. Accelerometer based force balances are commonly employed for measuring aerodynamic drag around bodies in hypersonic shock tunnels. In this study, we present an analysis of the effect of model material on the performance of an accelerometer balance used for measurement of drag in impulse facilities. From the experimental studies performed on models constructed out of Bakelite HYLEM and Aluminum, it is clear that the rigid body assumption does not hold good during the short testing duration available in shock tunnels. This is notwithstanding the fact that the rubber bush used for supporting the model allows unconstrained motion of the model during the short testing time available in the shock tunnel. The vibrations induced in the model on impact loading in the shock tunnel are damped out in metallic model, resulting in a smooth acceleration signal, while the signal become noisy and non-linear when we use non-isotropic materials like Bakelite HYLEM. This also implies that careful analysis and proper data reduction methodologies are necessary for measuring aerodynamic drag for non-metallic models in shock tunnels. The results from the drag measurements carried out using a 60 degrees half angle blunt cone is given in the present analysis.

Investigation of Missile-Shaped Body with Forward-Facing Cavity at Mach 8

A blunt-nosed hypersonic missile mounted with a forward-facing cavity is a good alternative to reduce the stagnation heating rates. The effects of a forward-racing cavity on heat transfer and aerodynamic coefficients are addressed in this paper. Tests were carried out in hypersonic shock tunnel HST2, at a hypersonic Mach number of 8 using a 41 deg apex-angle blunt cone. The aerodynamic forces on the test model with and without a forward-facing cavity at various angles of attack are measured by using an internally mountable accelerometer force balance system. Heat flux measurements have been carried out on the test model with and without a forward-facing cavity of the entire surface at zero degree angle of attack with platinum sensors. A numerical simulation was also carried out using the computational fluid dynamics code (CFX-Ansys 5.7). An important result of this study is that the smaller cavity diameter has the highest lift-to-drag ratio, whereas the medium cavity has the highest heat flux reduction. Theshock structure around the test model has also been visualized using the Schlieren flow visualization technique. The visualized shock structure and the measured aerodynamic forces on the missile-shaped body with cavity configurations agree well with the axisymmetric numerical simulations.

Analysis of drop formation at conical tips : 1. Theory

The phenomenon of drop formation at conical tips under near zero flow conditions has been investigated using a theoretical approach. The analysis permits the prediction of drop profile and drop volume, until the onset of instability. A semiempirical approach based on the similarity of drop shapes has been adopted to predict the detaching drop volumes at conical tips. The effects of base diameter of the cone, cone angle, interfacial tension, and the densities of the drop and the surrounding fluid on the maximum and detached drop volumes are predicted.

Film cooling at hypersonic Mach numbers using forward facing array of micro-jets

Experimental investigations are carried out in the IISc hypersonic shock tunnel on film cooling effectiveness of a single jet (diameter 2 mm and 0.9 mm), and an array forward facing of micro-jets (diameter 300 mu m each) of same effective area (corresponding to the respective single jet). The single jet and the corresponding micro-jets are injected from the stagnation zone of a blunt cone model (58, apex angle and nose radius of 35 mm). Nitrogen and Helium are injected as coolant gases. Experiments are performed at freestream Mach number 5.9, at 0 degrees angle of attack, with a stagnation enthalpy of 1.84 MJ/kg, with and without injections. The ratios of the jet stagnation pressure to the freestream pitot pressure used in the present study are 1.2 and 1.45. Up to 50% reduction in surface heat transfer rate was observed with the array of micro-jets, compared to that of the respective single jet with nitrogen as the coolant, while the corresponding eduction was up to 37% for helium injection, with the schlieren flow visualizations showing no major change in the shock standoff distance, and thus no major changes in other aerodynamic aspects such as drag.

Interval Data Classification under Partial Information: A Chance-Constraint Approach

This paper presents a Chance-constraint Programming approach for constructing maximum-margin classifiers which are robust to interval-valued uncertainty in training examples. The methodology ensures that uncertain examples are classified correctly with high probability by employing chance-constraints. The main contribution of the paper is to pose the resultant optimization problem as a Second Order Cone Program by using large deviation inequalities, due to Bernstein. Apart from support and mean of the uncertain examples these Bernstein based relaxations make no further assumptions on the underlying uncertainty. Classifiers built using the proposed approach are less conservative, yield higher margins and hence are expected to generalize better than existing methods. Experimental results on synthetic and real-world datasets show that the proposed classifiers are better equipped to handle interval-valued uncertainty than state-of-the-art.

Re-examination of one-point methods of liquid limit determination

This Paper deals with the analysis of liquid limit of soils, an inferential parameter of universal acceptance. It has been undertaken primarily to re-examine one-point methods of determination of liquid limit water contents. It has been shown by basic characteristics of soils and associated physico-chemical factors that critical shear strengths at liquid limit water contents arise out of force field equilibrium and are independent of soil type. This leads to the formation of a scientific base for liquid limit determination by one-point methods, which hitherto was formulated purely on statistical analysis of data. Available methods (Norman, 1959; Karlsson, 1961; Clayton & Jukes, 1978) of one-point liquid limit determination have been critically re-examined. A simple one-point cone penetrometer method of computing liquid limit has been suggested and compared with other methods. Experimental data of Sherwood & Ryley (1970) have been employed for comparison of different cone penetration methods. Results indicate that, apart from mere statistical considerations, one-point methods have a strong scientific base on the uniqueness of modified flow line irrespective of soil type. Normalized flow line is obtained by normalization of water contents by liquid limit values thereby nullifying the effects of surface areas and associated physico-chemical factors that are otherwise reflected in different responses at macrolevel.Cet article traite de l'analyse de la limite de liquidité des sols, paramètre déductif universellement accepté. Cette analyse a été entreprise en premier lieu pour ré-examiner les méthodes à un point destinées à la détermination de la teneur en eau à la limite de liquidité. Il a été démontré par les caractéristiques fondamentales de sols et par des facteurs physico-chimiques associés que les résistances critiques à la rupture au cisaillement pour des teneurs en eau à la limite de liquidité résultent de l'équilibre des champs de forces et sont indépendantes du type de sol concerné. On peut donc constituer une base scientifique pour la détermination de la limite de liquidité par des méthodes à un point lesquelles, jusqu'alors, n'avaient été formulées que sur la base d'une analyse statistique des données. Les méthodes dont on dispose (Norman, 1959; Karlsson, 1961; Clayton & Jukes, 1978) pour la détermination de la limite de liquidité à un point font l'objet d'un ré-examen critique. Une simple méthode d'analyse à un point à l'aide d'un pénétromètre à cône pour le calcul de la limite de liquidité a été suggérée et comparée à d'autres méthodes. Les données expérimentales de Sherwood & Ryley (1970) ont été utilisées en vue de comparer différentes méthodes de pénétration par cône. En plus de considérations d'ordre purement statistque, les résultats montrent que les méthodes de détermination à un point constituent une base scientifique solide en raison du caractère unique de la ligne de courant modifiée, quel que soit le type de sol La ligne de courant normalisée est obtenue par la normalisation de la teneur en eau en faisant appel à des valeurs de limite de liquidité pour, de cette manière, annuler les effets des surfaces et des facteurs physico-chimiques associés qui sans cela se manifesteraient dans les différentes réponses au niveau macro.

Effect of electric arc discharge on hypersonic blunt body drag

Experimental results on the effect of energy deposition using an electric arc discharge, upstream of a 60° half angle blunt cone configuration in a hypersonic flow is reported.Investigations involving drag measurements and high speed schlieren flow visualization have been carried out in hypersonic shock tunnel using air and argon as the test gases; and an unsteady drag reduction of about 50% (maximum reduction) has been observed in the energy deposition experiments done in argon environment. These studies also show that the effect of discharge on the flow field is more pronounced in argon environment as compared to air, which confirms that thermal effects are mainly responsible for flow alteration in presence of the discharge.

The new binary pulsar and the observation of gravitational spin precession

The possibility of observing gravitational spin precession due to spin-orbit coupling in a binary pulsar system is considered. An analysis is presented which can aid in delineating the relevant physical effects from pulse-structure data. In this analysis, it is assumed that the pulsar radiation emanates from a cone whose axis is tilted with respect to the axis of rotation. It is found that the time-averaged pulse width and polarization sweep vary periodically with time and that this variation has a periodicity of the order of the spin-precession frequency averaged over a complete revolution. It is concluded that for an orbital period of about 180 years, it suffices to measure polarization data with an accuracy of a few parts in 100 over a period of six months to a year in order to uncover the effects of spin precession. The consistency of the analysis is checked, and the calculations are applied to a recently discovered binary pulsar.

Production of cast aluminium-graphite particle composites using a pellet method

Copper- and nickel-coated graphite particles can be successfully introduced into aluminium-base alloy melts as pellets to produce cast aluminium-graphite particle composites. The pellets were made by pressing mixtures of nickel- or copper-coated graphite particles and aluminium powders together at pressures varying between 2 and 20 kg mm–2. These pellets were dispersed in aluminium alloy melts by plunging and holding them in the melts using a refractory coated mild steel cone, until the pellets disintegrated and the powders were dispersed. The optimum pressure for the preparation of pellets was 2 to 5 kg mm–2 and the optimum size and percentage of aluminium powder were 400 to 1000mgrm and 35 wt% respectively. Under optimum conditions the recovery of the graphite particles in the castings was as high as 96%, these particles being pushed into the last freezing interdendritic regions. The tensile strength and the hardness of the graphite aluminium alloys made using the pellet method are comparable to those of similar composites made using gas injection or the vortex method. The pellet method however has the advantage of greater reproducibility and flexibility. Dispersion of graphite particles in the matrix of cast aluminium alloys using the pellet method increases their resistance to wear.

Microstructure and mechanical properties of unidirectionally solidified Al-Si-Ni ternary eutectic

Al-10.98 pct Si-4.9 pct Ni ternary eutectic alloy was unidirectionally solidified at growth rates from 1.39μm/sec to 6.95μm/sec. Binary Al-Ni and Al-Si eutectics prepared from the same purity metals were also solidified under similar conditions to characterize the growth conditions under the conditions of present study. NiAl3 phase appeared as fibers in the binary Al-Ni eutectic and silicon appeared as irregular plates in the binary Al-Si eutectic. However, in the ternary Al-Si-Ni eutectic alloy both NiAl3 and silicon phases appeared as irregular plates dispersed in α-Al phase, without any regular repctitive arrangement. The size and spacing of NiAl3 and Si platelets in cone shaped colonies decreased with an increase in the growth rate of the ternary eutectic. Examination of specimen quenched during unidirectional solidification indicated that the ternary eutectic grows with a non-planar interface with both Si and NiAl3 phases protruding into the liquid. It is concluded that it will be difficult to grow regular ternary eutectic structures even if only one phase has a high entropy of melting. The tensile strength and modulus of unidirectionally solidified Al-Si-Ni eutectic was lower than the chill cast alloys of the same composition, and decreased with a decrease in growth rate. Tensile modulus and strength of ternary Al-Si-Ni eutectic alloys was greater than binary Al-Si eutectic alloy under similar growth conditions, both in the chill cast and in unidirectionally solidified conditions.

Effect of soil variability on the bearing capacity of clay and in slope stability problems

Site-specific geotechnical data are always random and variable in space. In the present study, a procedure for quantifying the variability in geotechnical characterization and design parameters is discussed using the site-specific cone tip resistance data (qc) obtained from static cone penetration test (SCPT). The parameters for the spatial variability modeling of geotechnical parameters i.e. (i) existing trend function in the in situ qc data; (ii) second moment statistics i.e. analysis of mean, variance, and auto-correlation structure of the soil strength and stiffness parameters; and (iii) inputs from the spatial correlation analysis, are utilized in the numerical modeling procedures using the finite difference numerical code FLAC 5.0. The influence of consideration of spatially variable soil parameters on the reliability-based geotechnical deign is studied for the two cases i.e. (a) bearing capacity analysis of a shallow foundation resting on a clayey soil, and (b) analysis of stability and deformation pattern of a cohesive-frictional soil slope. The study highlights the procedure for conducting a site-specific study using field test data such as SCPT in geotechnical analysis and demonstrates that a few additional computations involving soil variability provide a better insight into the role of variability in designs.

A complete characterization of pre-Mueller and Mueller matrices in polarization optics

The Mueller-Stokes formalism that governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could require of a 4 x 4 real matrix M in order that it qualify to be the Mueller matrix of some physical system would be that M map Omega((pol)), the positive solid light cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is a need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability brings in additional constraints that a pre-Mueller matrix M mapping Omega((pol)) into itself needs to meet in order to be an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized. (C) 2010 Optical Society of America