Curved composite beams—optimum lay-up for buckling by ranking

Instability of laminated curved composite beams made of repeated sublaminate construction is studied using finite element method. In repeated sublaminate construction, a full laminate is obtained by repeating a basic sublaminate which has a smaller number of plies. This paper deals with the determination of optimum lay-up for buckling by ranking of such composite curved beams (which may be solid or sandwich). For this purpose, use is made of a two-noded, 16 degress of freedom curved composite beam finite element. The displacements u, v, w of the element reference axis are expressed in terms of one-dimensional first-order Hermite interpolation polynomials, and line member assumptions are invoked in formulation of the elastic stiffness matrix and geometric stiffness matrix. The nonlinear expressions for the strains, occurring in beams subjected to axial, flexural and torsional loads, are incorporated in a general instability analysis. The computer program developed has been used, after extensive checking for correctness, to obtain optimum orientation scheme of the plies in the sublaminate so as to achieve maximum buckling load for typical curved solid/sandwich composite beams.

Synthesis of Cost-Optimal Shell-and-Tube Heat Exchangers

Synthesis of cost-optimal shell-and-tube heat exchangers is a difficult task since it involves a large number of parameters. An attempt is made in this article to simplify the process of choosing the parameter values that will minimize the cost of any heat exchanger satisfying a given heat duty and a particular set of constraints. The simplification is based on decoupling of the geometric and the thermal aspects of the problem. The concept of curves for cost-optimal design is introduced and is shown to simplify the synthesis process for shell-and-tube heat exchangers.

In-Network Computation in Random Wireless Networks: A PAC Approach to Constant Refresh Rates with Lower Energy Costs

We propose a method to compute a probably approximately correct (PAC) normalized histogram of observations with a refresh rate of Theta(1) time units per histogram sample on a random geometric graph with noise-free links. The delay in computation is Theta(root n) time units. We further extend our approach to a network with noisy links. While the refresh rate remains Theta(1) time units per sample, the delay increases to Theta(root n log n). The number of transmissions in both cases is Theta(n) per histogram sample. The achieved Theta(1) refresh rate for PAC histogram computation is a significant improvement over the refresh rate of Theta(1/log n) for histogram computation in noiseless networks. We achieve this by operating in the supercritical thermodynamic regime where large pathways for communication build up, but the network may have more than one component. The largest component however will have an arbitrarily large fraction of nodes in order to enable approximate computation of the histogram to the desired level of accuracy. Operation in the supercritical thermodynamic regime also reduces energy consumption. A key step in the proof of our achievability result is the construction of a connected component having bounded degree and any desired fraction of nodes. This construction may also prove useful in other communication settings on the random geometric graph.

A heuristic clustering algorithm using union of overlapping pattern-cells

Relative geometric arrangements of the sample points, with reference to the structure of the imbedding space, produce clusters. Hence, if each sample point is imagined to acquire a volume of a small M-cube (called pattern-cell), depending on the ranges of its (M) features and number (N) of samples; then overlapping pattern-cells would indicate naturally closer sample-points. A chain or blob of such overlapping cells would mean a cluster and separate clusters would not share a common pattern-cell between them. The conditions and an analytic method to find such an overlap are developed. A simple, intuitive, nonparametric clustering procedure, based on such overlapping pattern-cells is presented. It may be classified as an agglomerative, hierarchical, linkage-type clustering procedure. The algorithm is fast, requires low storage and can identify irregular clusters. Two extensions of the algorithm, to separate overlapping clusters and to estimate the nature of pattern distributions in the sample space, are also indicated.

Segmenting point-sampled surfaces

Extracting features from point-based representations of geometric surface models is becoming increasingly important for purposes such as model classification, matching, and exploration. In an earlier paper, we proposed a multiphase segmentation process to identify elongated features in point-sampled surface models without the explicit construction of a mesh or other surface representation. The preliminary results demonstrated the strength and potential of the segmentation process, but the resulting segmentations were still of low quality, and the segmentation process could be slow. In this paper, we describe several algorithmic improvements to overcome the shortcomings of the segmentation process. To demonstrate the improved quality of the segmentation and the superior time efficiency of the new segmentation process, we present segmentation results obtained for various point-sampled surface models. We also discuss an application of our segmentation process to extract ridge-separated features in point-sampled surfaces of CAD models.

A Smooth Finite Element Method Based on Reproducing Kernel DMS-Splines

The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials There is thus a case for combining these advantages in a so-called hybrid scheme or a `smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C-p (p >= 1) continuity One such recent attempt, a NURBS based parametric bridging method (Shaw et al 2008b), uses polynomial reproducing, tensor-product non-uniform rational B-splines (NURBS) over a typical FE mesh and relies upon a (possibly piecewise) bijective geometric map between the physical domain and a rectangular (cuboidal) parametric domain The present work aims at a significant extension and improvement of this concept by replacing NURBS with DMS-splines (say, of degree n > 0) that are defined over triangles and provide Cn-1 continuity across the triangle edges This relieves the need for a geometric map that could precipitate ill-conditioning of the discretized equations Delaunay triangulation is used to discretize the physical domain and shape functions are constructed via the polynomial reproduction condition, which quite remarkably relieves the solution of its sensitive dependence on the selected knotsets Derivatives of shape functions are also constructed based on the principle of reproduction of derivatives of polynomials (Shaw and Roy 2008a) Within the present scheme, the triangles also serve as background integration cells in weak formulations thereby overcoming non-conformability issues Numerical examples involving the evaluation of derivatives of targeted functions up to the fourth order and applications of the method to a few boundary value problems of general interest in solid mechanics over (non-simply connected) bounded domains in 2D are presented towards the end of the paper

Effect of wall thickness on the end corrections of the extended inlet and outlet of a double-tuned expansion chamber

Simple expansion chambers, the simplest of the muffler configurations, have very limited practical application due to the presence of periodic troughs in the transmission loss spectrum which drastically lower the overall transmission loss of the muffler. Tuned extended inlet and outlet can be designed to nullify three-fourths of these troughs, making use of the plane wave theory. These cancellations would not occur unless one altered the geometric lengths for the extended tube in order to incorporate the effect of evanescent higher-order modes (multidimensional effect) through end corrections or lumped inertance approximation at the area discontinuities or junctions. End corrections of the extended inlet and outlet have been studied by several researchers. However the effect of wall thickness of the inlet/outlet duct on end correction has not been studied explicitly. This has significant effect on the tuning of an extended inlet/outlet expansion chamber. It is investigated here experimentally as well as numerically (through use of 3-D FEM software) for stationary medium. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.

A geodesic constant method for computing high-frequency mutual coupling between antennas on general quadric cylinders

A Geodesic Constant Method (GCM) is outlined which provides a common approach to ray tracing on quadric cylinders in general, and yields all the surface ray-geometric parameters required in the UTD mutual coupling analysis of conformal antenna arrays in the closed form. The approach permits the incorporation of a shaping parameter which permits the modeling of quadric cylindrical surfaces of desired sharpness/flatness with a common set of equations. The mutual admittance between the slots on a general parabolic cylinder is obtained as an illustration of the applicability of the GCM.

Phenyl-Ring-Bearing Cationic Surfactants: Effect of Ring Location on the Micellar Structure

A series of isomeric cationic surfactants (S1-S5) bearing a long alkyl chain that carries a 1,4-phenylene unit and a trimethyl ammonium headgroup was synthesized; the location of the phenyl ring within the alkyl tail was varied in an effort to understand its influence on the amphiphilic properties of the surfactants. The cmc's of the surfactants were estimated using ionic conductivity measurements and isothermal calorimetric titrations (ITC); the values obtained by the two methods were found to be in excellent agreement. The ITC measurements provided additional insight into the various thermodynamic parameters associated with the micellization process. Although all five surfactants have exactly the same molecular formula, their micellar properties were seen to vary dramatically depending on the location of the phenyl ring; the cmc was seen to decrease by almost an order of magnitude when the phenyl ring was moved from the tail end (cmc of S1 is 23 mM) to the headgroup region (cmc of S5 is 3 mM). In all cases, the enthalpy of micellization was negative but the entropy of micellization was positive, suggesting that in all of these systems the formation of micelles is both enthalpically and entropically favored. As expected, the decrease in cmc values upon moving the phenyl ring from the tail end to he headgroup region is accompanied by an increase in the thermodynamic driving force (Delta G) for micellization. To understand further the differences in the micellar structure of these surfactants, small-angle neutron scattering (SANS) measurements were carried out; these measurements reveal that the aggregation number of the micelles increases as the cmc decreases. This increase in the aggregation number is also accompanied by an increase in the asphericity of the micellar aggregate and a decrease in the fractional charge. Geometric packing arguments are presented to account for these changes in aggregation behavior as a function of phenyl ring location.

Local variability and base sequence effects in DNA crystal structures.

The importance and usefulness of local doublet parameters in understanding sequence dependent effects has been described for A- and B-DNA oligonucleotide crystal structures. Each of the two sets of local parameters described by us in the NUPARM algorithm, namely the local doublet parameters, calculated with reference to the mean z-axis, and the local helical parameters, calculated with reference to the local helix axis, is sufficient to describe the oligonucleotide structures, with the local helical parameters giving a slightly magnified picture of the variations in the structures. The values of local doublet parameters calculated by NUPARM algorithm are similar to those calculated by NEWHELIX90 program, only if the oligonucleotide fragment is not too distorted. The mean values obtained using all the available data for B-DNA crystals are not significantly different from those obtained when a limited data set is used, consisting only of structures with a data resolution of better than 2.4 A and without any bound drug molecule. Thus the variation observed in the oligonucleotide crystals appears to be independent of the quality of their crystallinity. No strong correlation is seen between any pair of local doublet parameters but the local helical parameters are interrelated by geometric relationships. An interesting feature that emerges from this analysis is that the local rise along the z-axis is highly correlated with the difference in the buckle values of the two basepairs in the doublet, as suggested earlier for the dodecamer structures (Bansal and Bhattacharyya, in Structure & Methods: DNA & RNA, Vol. 3 (Eds., R.H. Sarma and M.H. Sarma), pp. 139-153 (1990)). In fact the local rise values become almost constant for both A- and B-forms, if a correction is applied for the buckling of the basepairs. In B-DNA the AA, AT, TA and GA basepair sequences generally have a smaller local rise (3.25 A) compared to the other sequences (3.4 A) and this seems to be an intrinsic feature of basepair stacking interaction and not related to any other local doublet parameter. The roll angles in B-DNA oligonucleotides have small values (less than +/- 8 degrees), while mean local twist varies from 24 degrees to 45 degrees. The CA/TG doublet sequences show two types of preferred geometries, one with positive roll, small positive slide and reduced twist and another with negative roll, large positive slide and increased twist.(ABSTRACT TRUNCATED AT 400 WORDS)

Is tetramethyleneethane a ground state triplet?

We have examined a number of possible ways by which tetramethyleneethane (TME) can be a ground state triplet, as claimed by experimental studies, in violation of Ovchinnikov’s theorem for alternant hydrocarbons of equal bond lengths. Model exact π calculations of the low-lying states of TME, 3,4-dimethylenefuran and 3,4-dimethylenepyrrole were carried out using a diagrammatic valence bond approach. The calculations failed to yield a triplet ground state even after (a) tuning of electron correlation, (b) breaking alternancy symmetry, and (c) allowing for geometric distortions. In contrast to earlier studies of fine structure constants in other conjugated systems, the computedD andE values of all the low-lying triplet states of TME for various geometries are at least an order of magnitude different from the experimentally reported values. Incorporation of σ-π mixing by means of UHF MNDO calculations is found to favour a singlet ground state even further. A reinterpretation of the experimental results of TME is therefore suggested to resolve the conflict.

Squeezed states, photon-number distributions, and U(l) invariance

We study the photon-number distribution in squeezed states of a single-mode radiation field. A U(l)-invariant squeezing criterion is compared and contrasted with a more restrictive criterion, with the help of suggestive geometric representations. The U(l) invariance of the photon-number distribution in a squeezed coherent state, with arbitrary complex squeeze and displacement parameters, is explicitly demonstrated. The behavior of the photon-number distribution for a representative value of the displacement and various values of the squeeze parameter is numerically investigated. A new kind of giant oscillation riding as an envelope over more rapid oscillations in this distribution is demonstrated.

Studies on a stove for powdery biomass

The sawdust stove, classically known for several decades, is considered here in a scientific study. The poor ignition characteristics and smoky start up are related to improper geometric dimensions. Based on a parametric study, the startup procedure and the dimensions of the stove were modified to achieve a smooth start up. Also, the range of acceptable fuels was enlarged to include tiny unprocessed dry twigs, weeds and wood sticks o the extent of about 50%, with the rest being sawdust-like material. The efficiency of the stove was measured to be 30–40%, depending on the relative size and shape of the vessel and the power level of the stove. A simple procedure for designing this class of stove for various power levels, as well as burning times, is presented. A new concept of multiport design is also discussed.

The scratch hardness and friction of a soft rigid-plastic solid

The paper describes an experimental and analytical study of the normal and scratch hardnesses of a model soft rigid-plastic solid. The material known as ‘Plasticine’, a mixture of dry particles and a mineral oil, has been deformed with a range of rigid conical indentors with included angles of between 30° and 170°. The sliding velocity dependence of the computed scratch hardness and friction has been examined in the velocity range 0.19 mm/s to 7.3 m/s. Data are also described for the time dependence of the normal hardness and also the estimated rate dependence of the intrinsic flow stress. The latter values were estimated from data obtained during the upsetting of right cylinders. Three major conclusions are drawn from these data and the associated analysis. (1) A first-order account of the scratching force may be provided by adopting a model which sums the computed plastic deformation and interfacial sliding contributions to the total sliding work. This is tantamount to the adoption of the two-term non-interacting model of friction. (2) For this system during sliding, at high sliding velocities at least, the interface shear stress which defines the boundary condition is not directly related to the bulk shear stress. The interface rheological characteristics indicate an appreciable dependence on the imposed strain or strain rate. In particular, the relative contributions of the slip and stick boundary conditions appear to be a function of the imposed sliding velocity. (3) The computed normal and scratch hardness values are not simply interrelated primarily because of the evolving boundary conditions which appear to exist in the scratching experiments.

AB-initio study of alpha-silyl and beta-silyl substituent effects on vinyl radicals

The geometries of alpha- and beta-silyl substituted vinyl radicals and of alpha,beta-disilylvinyl radical have been optimised with the STO-3G and the STO-3G* basis sets. The relative stabilities of various conformers have been determined at the UMP2/6-31G* level. The stabilisation of vinyl radicals through alpha-silyl substitution is larger than that due to corresponding alkyl groups. The presence of an alpha-silyl group also leads to a tendency towards linearisation of the vinyl radical centre and a corresponding reduction in the inversion barrier. In marked contrast, the beta-silyl effect is negligible. The geometric, conformational and energetic consequences are insignificant. Overall, the silyl substituent effect at vinyl radicals is very different from that computed earlier for the vinyl cations, but qualitatively similar to that found in carbanions.