Effect of boundary condition description on convergence of solution in a boundary-value problem

It is well known that the numerical accuracy of a series solution to a boundary-value problem by the direct method depends on the technique of approximate satisfaction of the boundary conditions and on the stage of truncation of the series. On the other hand, it does not appear to be generally recognized that, when the boundary conditions can be described in alternative equivalent forms, the convergence of the solution is significantly affected by the actual form in which they are stated. The importance of the last aspect is studied for three different techniques of computing the deflections of simply supported regular polygonal plates under uniform pressure. It is also shown that it is sometimes possible to modify the technique of analysis to make the accuracy independent of the description of the boundary conditions.

Thermal stresses in rectangular plates

A method of determining the thermal stresses in a flat rectangular isotropic plate of constant thickness with arbitrary temperature distribution in the plane of the plate and with no variation in temperature through the thickness is presented. The thermal stress have been obtained in terms of Fourier series and integrals that satisfy the differential equation and the boundary conditions. Several examples have been presented to show the application of the method.

Chain of excitation spot generation by aperture engineering

An optical technique is proposed for obtaining multiple excitation spots. Phase-matched counter propagating extended depth-of-focus fields were superimposed along the optical axis for generating multiple localized excitation spots. Moreover, the filtering effect due to the optical mask increases the lateral resolution. Proposed technique introduces the concept of simultaneous multiplane excitation and improves three-dimensional resolution. (C) 2010 American Institute of Physics.

Free convection heat transfer in vertical annuli

Free convection heat transfer in vertical concentric, cylindrical annuli is investigated analytically and experimentally. The approximate double boundary layer model used by Emery and Chu for the case of vertical parallel plates is extended to the present case in obtaining heat transfer correlations in laminar free convection. Different correlations for the inner cylinder depending on the radius to the length ratio of the inner cylinder and the Rayleigh number, were used in the derivation of correlations for the annuli. The results for the case of short cylinders inside tubes are in agreement (within about 10 per cent) with the existing correlations. For other cases, namely long cylinders in annuli and wires in annuli, experiments conducted show the agreement of the analysis with experiments.

Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation TW - T∞ = Nxn. The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.

Compliance of rough cylinders in compression

Compression of a rough turned cylinder between two hard, smooth, flat plates has been analysed with the aid of a mathematical model based on statistical analysis. It is assumed that the asperity peak heights follow Gaussian or normal and beta distribution functions and that the loaded asperities comply as though they are completely isolated from the neighbouring ones. Equations have been developed for the loadcompliance relation of the real surface using a simplified relation of the form W0 = K1δn for the load-compliance of a single asperity. Parameters K1 and n have considerable influence on the load-compliance curve and they depend on the material, tip angle of the asperity, standard deviation of the asperity peak height distribution and the density of the asperities.

Investigating novelty-outcome relationships in engineering design

Design creativity involves developing novel and useful solutions to design problems The research in this article is an attempt to understand how novelty of a design resulting from a design process is related to the kind of outcomes. described here as constructs, involved in the design process A model of causality, the SAPPhIRE model, is used as the basis of the analysis The analysis is based on previous research that shows that designing involves development and exploration of the seven basic constructs of the SAPPhIRE model that constitute the causal connection between the various levels of abstraction at which a design can be described The constructs am state change, action, parts. phenomenon. input. organs. and effect The following two questions are asked. Is there a relationship between novelty and the constructs? If them is a relationship, what is the degree of this relationship? A hypothesis is developed to answer the questions an increase in the number and variety of ideas explored while designing should enhance the variety of concept space. leading to an increase in the novelty of the concept space Eight existing observational studies of designing sessions are used to empirically validate the hypothesis Each designing session involves an individual designer. experienced or novice. solving a design problem by producing concepts and following a think-aloud protocol. The results indicate dependence of novelty of concept space on variety of concept space and dependence of variety of concept space on variety of idea space. thereby validating the hypothesis The Jesuits also reveal a strong correlation between novelty and the constructs, correlation value decreases as the abstraction level of the constructs reduces. signifying the importance of using constructs at higher abstraction levels for enhancing novelty

CFD tools in engineering design studies and medical sciences

In the recent time CFD tools have become increasingly useful in the engineering design studies especially in the area of aerospace vehicles. This is largely due to the advent of high speed computing platforms in addition to the development of new efficient algorithms. The algorithms based on kinetic schemes have been shown to be very robust and further meshless methods offer certain advantages over the other methods. Preliminary investigations of blood flow visualization through artery using CFD tool have shown encouraging results which further needs to be verified and validated.

Robust prediction of residual velocities and ballistic limits of projectiles for impact on thin aluminium plates

This paper deals with the simulation-driven study of the impact of hardened steel projectiles on thin aluminium target plates using explicit finite element analysis as implemented in LS-DYNA. The evaluation of finite element modelling includes a comprehensive mesh convergence study using shell elements for representing target plates and the solid element-based representation of ogivalnosed projectiles. A user-friendly automatic contact detection algorithm is used for capturing interaction between the projectile and the target plate. It is shown that the proper choice of mesh density and strain rate-dependent material properties is crucial as these parameters significantly affect the computed residual velocity. The efficacy of correlation with experimental data is adjudged in terms of a 'correlation index' defined in the present study for which values close to unity are desirable.By simulating laboratory impact tests on thin aluminium plates carried out by earlier investigators, extremely good prediction of experimental ballistic limits has been observed with correlation indices approaching unity. Additional simulation-based parametric studies have been carried out and results consistent with test data have been obtained. The simulation procedures followed in the present study can be applied with confidence in designing thin aluminium armour plates for protection against low calibre projectiles.

A survey of wind engineering studies in India

In this paper, the work that has been done in several laboratories and academic institutions in India in the area of wind engineering in the past 20–30 years has been reviewed. Studies on extreme and mean hourly winds, philosophies adopted in model studies in wind tunnels and some of the important results that have been obtained are described. Suggestions for future studies are indicated.

Using Water as a Design Element in Crystal Engineering. Host-Guest Compounds of Hydrated 3,5-Dihydroxybenzoic Acid

Thirteen host guest compounds of 3,5-dihydroxybenzoic acid (DHBA) have been structurally characterized. Water molecules occupy the peripheries of a hexagonal void, created with DHBA molecules, and act as ``hooks'' to connect the guest molecules with the host-framework via hydrogen bonding. The ``water hook'' is an OH group acting as a donor. Consequently, the guest molecules were chosen so that they contain good hydrogen bond acceptor functionalities. A number of multicomponent hydrates were isolated with stoichiometries (DHBA)(x)(H2O). (guest),. Of these, compounds with the following as guests were obtained as crystals that were good enough for single crystal work: ethyl acetate (EtOAc), diethyl oxalate, dimethyl oxalate, di(n-propyl) oxalate, diethyl malonate, diethyl succinate, chloroacetonitrile, N,N-dimethyl formamide (DMF), acetone, dimethyl sulfoxide (DMSO), 1-propanol, and 2-butanol. From 2-butanol, a hemihydrate, (DHBA)(2)(H2O), was also obtained concomitantly. Further to guest stabilization, water acts as a good mediator of effective crystal packing and also determines the topology of the host framework. En the present series of compounds, the role of water is wide ranging, and it is not easy to classify it specifically as a host or as a guest.

Non-darcy double-diffusive mixed convection from heated vertical and horizontal plates in saturated porous media

The non-darcy mixed convection flows from heated vertical and horizontal plates in saturated porous media have been considered using boundary layer approximations. The flows are considered to be driven by multiple buoyancy forces. The similarity solutions for both vertical and horizontal plates have been obtained. The governing equations have been solved numerically using a shooting method. The heat transfer, mass transfer and skin friction are reduced due to inertial forces. Also, they increase with the buoyancy parameter for aiding flow and decrease for the opposing flow. For aiding flow, the heat and mass transfer coefficients are found to approach asymptotically the forced or free convection values as the buoyancy parameter approaches zero or infinity.

On higher order shear deformation theory of laminated composite panels

In this paper we examine the suitability of higher order shear deformation theory based on cubic inplane displacements and parabolic normal displacements, for stress analysis of laminated composite plates including the interlaminar stresses. An exact solution of a symmetrical four layered infinite strip under static loading has been worked out and the results obtained by the present theory are compared with the exact solution. The present theory provides very good estimates of the deflections, and the inplane stresses and strains. Nevertheless, direct estimates of strains and stresses do not display the required interlaminar stress continuity and strain discontinuity across the interlaminar surface. On the other hand, ‘statically equivalent stresses and strains’ do display the required interlaminar stress continuity and strain discontinuity and agree very closely with the exact solution.

Crystal engineering: A brief overview

Crystal structures of organic and metal-organic compounds have been determined in enormous numbers over the past century, and at the time of writing this review, the Cambridge Structural Database has just crossed the half million mark. The possibility of designing a particular crystal packing is, however, of more recent origin and the subject of crystal engineering has addressed this possibility, more or less systematically, during the past 30 years. Crystal engineering demands a detailed and thorough knowledge of intermolecular interactions, which act as the supramolecular glue that binds molecules into crystals. It also requires systematic strategies for the design of a crystal, the architectural blueprint as it were. Finally, this enterprise needs to be geared towards a useful property in that the crystal that is being designed is a functional one. All these features of the subject are directly or indirectly connected with the fact that there is a very large database of known crystal structures that is available to the crystal engineer. This review attempts to briefly survey the current scenario in this expanding subject.