A numerical method for separation of stresses in photo-orthotropic elasticity

A numerical method is suggested for separation of stresses in photo-orthotropic elasticity using the numerical solution of compatibility equation for orthotropic case. The compatibility equation is written in terms of a stress parameter S analogous to the sum of principal stresses in two-dimensional isotropic case. The solution of this equation provides a relation between the normal stresses. The photoelastic data give the shear stress and another relation between the two normal stresses. The accuracy of the numerical method and its application to practical problems are illustrated with examples.

Extending lagrange interpolation to develop a 4-node quadrilateral element

Today finite element method is a well established tool in engineering analysis and design. Though there axe many two and three dimensional finite elements available, it is rare that a single element performs satisfactorily in majority of practical problems. The present work deals with the development of 4-node quadrilateral element using extended Lagrange interpolation functions. The classical univariate Lagrange interpolation is well developed for 1-D and is used for obtaining shape functions. We propose a new approach to extend the Lagrange interpolation to several variables. When variables axe more than one the method also gives the set of feasible bubble functions. We use the two to generate shape function for the 4-node arbitrary quadrilateral. It will require the incorporation of the condition of rigid body motion, constant strain and Navier equation by imposing necessary constraints. The procedure obviates the need for isoparametric transformation since interpolation functions are generated for arbitrary quadrilateral shapes. While generating the element stiffness matrix, integration can be carried out to the accuracy desired by dividing the quadrilateral into triangles. To validate the performance of the element which we call EXLQUAD4, we conduct several pathological tests available in the literature. EXLQUAD4 predicts both stresses and displacements accurately at every point in the element in all the constant stress fields. In tests involving higher order stress fields the element is assured to converge in the limit of discretisation. A method thus becomes available to generate shape functions directly for arbitrary quadrilateral. The method is applicable also for hexahedra. The approach should find use for development of finite elements for use with other field equations also.

Elastic analysis of pin joints

The advent of large and fast digital computers and development of numerical techniques suited to these have made it possible to review the analysis of important fundamental and practical problems and phenomena of engineering which have remained intractable for a long time. The understanding of the load transfer between pin and plate is one such. Inspite of continuous attack on these problems for over half a century, classical solutions have remained limited in their approach and value to the understanding of the phenomena and the generation of design data. On the other hand, the finite element methods that have grown simultaneously with the recent development of computers have been helpful in analysing specific problems and answering specific questions, but are yet to be harnessed to assist in obtaining with economy a clearer understanding of the phenomena of partial separation and contact, friction and slip, and fretting and fatigue in pin joints. Against this background, it is useful to explore the application of the classical simple differential equation methods with the aid of computer power to open up this very important area. In this paper we describe some of the recent and current work at the Indian Institute of Science in this last direction.

Computational algorithms inspired by biological processes and evolution

In recent times computational algorithms inspired by biological processes and evolution are gaining much popularity for solving science and engineering problems. These algorithms are broadly classified into evolutionary computation and swarm intelligence algorithms, which are derived based on the analogy of natural evolution and biological activities. These include genetic algorithms, genetic programming, differential evolution, particle swarm optimization, ant colony optimization, artificial neural networks, etc. The algorithms being random-search techniques, use some heuristics to guide the search towards optimal solution and speed-up the convergence to obtain the global optimal solutions. The bio-inspired methods have several attractive features and advantages compared to conventional optimization solvers. They also facilitate the advantage of simulation and optimization environment simultaneously to solve hard-to-define (in simple expressions), real-world problems. These biologically inspired methods have provided novel ways of problem-solving for practical problems in traffic routing, networking, games, industry, robotics, economics, mechanical, chemical, electrical, civil, water resources and others fields. This article discusses the key features and development of bio-inspired computational algorithms, and their scope for application in science and engineering fields.

Accurate performance analysis of single and opportunistic AF relay cooperation with imperfect cascaded channel estimates

Given the significant gains that relay-based cooperation promises, the practical problems of acquisition of channel state information (CSI) and the characterization and optimization of performance with imperfect CSI are receiving increasing attention. We develop novel and accurate expressions for the symbol error probability (SEP) for fixed-gain amplify-and-forward relaying when the destination acquires CSI using the time-efficient cascaded channel estimation (CCE) protocol. The CCE protocol saves time by making the destination directly estimate the product of the source-relay and relay-destination channel gains. For a single relay system, we first develop a novel SEP expression and a tight SEP upper bound. We then similarly analyze an opportunistic multi-relay system, in which both selection and coherent demodulation use imperfect estimates. A distinctive aspect of our approach is the use of as few simplifying approximations as possible, which results in new results that are accurate at signal-to-noise-ratios as low as 1 dB for single and multi-relay systems. Using insights gleaned from an asymptotic analysis, we also present a simple, closed-form, nearly-optimal solution for allocation of energy between pilot and data symbols at the source and relay(s).

ABOUT FORMS OF ELECTRONIC AND IONIC DEVICES WITH THERMIONIC CATHODES.

The miniaturization of electronic and ionic devices with thermionic cathodes and thc improvement of their vacuum properties are questions of very great interest to the electronic engineer. However there have bcen no proposals so far to analyse the problem of miniaturization of such devices In a fundamental way. The present work suggests a choice of the geometrical shape of the cathode, the anode and the envelope of the device, that may help towards such a fundamcnlal approach.It is shown that a design, in which the cathode and the envelope of the tube are made of thm prismatic shape and the anode coincides with the cnvclope, offers a slriknrg advantage over the conventional cylindrical design, in respect of over-all size. The use of the prismatic shape will lead to considerable economy in msterials and may facilitate simpler prodoct~ont echn~ques. I n respect of the miin criteria of vacuum, namely the grade of vacuum, the internal volume occupied by residual gases, the evolution of gases in the internal space and the diffusion of gases from outside into the devicc, it is shown that the prismatic form is at least as good as, if not somewhat superior lo, the cylindrical form.In the actual construction of thin prismatic tubes, manv practical problems will arise, the most important being the mechanical strength and stablity of the structure. But the changeover from the conventional cylindrical to the new prirmaiic form, with its basic advantages, is a development that merits close attention.

Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems

An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algorithms based on the quadrature points and the nodal points, respectively, are presented. Both the quadrature and the nodal point based operator-splitting algorithms are validated using a three-dimensional (3D) test problem. The numerical results obtained with the full 3D computations and the operator-split 2D + 1D computations are found to be in a good agreement with the analytical solution. Further, the optimal order of convergence is obtained in both variants of the operator-splitting algorithms. (C) 2012 Elsevier Inc. All rights reserved.

Wave propagation in elastic solids undergoing damage and growth process

Modeling and analysis of wave propagation in elastic solids undergoing damage and growth process are reported in this paper. Two types of diagnostic problems, (1) the propagation of waves in the presence of a slow growth process and (2) the propagation of waves in the presence of a fast growth process, are considered. The proposed model employs a slow and a fast time scale and a homogenization technique in the wavelength scale. A detailed analysis of wave dispersion is carried out. A spectral analysis reveals certain low-frequency bands, where the interaction between the wave and the growth process produces acoustic metamaterial-like behavior. Various practical issues in designing an efficient method of acousto-ultrasonic wave based diagnostics of the growth process are discussed. Diagnostics of isotropic damage in a ductile or quasi-brittle solid by using a micro-second pulsating signal is considered for computer simulations, which is to illustrate the practical application of the proposed modeling and analysis. The simulated results explain how an estimate of signal spreading can be effectively employed to detect the presence of a steady-state damage or the saturation of a process.

The effect of surface tension in porous wave maker problems

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Problems with geoengineering schemes to combat climate change

The accelerated rate of increase in atmospheric CO2 concentration in recent years has revived the idea of stabilizing the global climate through geoengineering schemes. Majority of the proposed geoengineering schemes will attempt to reduce the amount of solar radiation absorbed by our planet. Climate modelling studies of these so called 'sunshade geoengineering schemes' show that global warming from increasing concentrations of CO2 can be mitigated by intentionally manipulating the amount of sunlight absorbed by the climate system. These studies also suggest that the residual changes could be large on regional scales, so that climate change may not be mitigated on a local basis. More recent modelling studies have shown that these schemes could lead to a slow-down in the global hydrological cycle. Other problems such as changes in the terrestrial carbon cycle and ocean acidification remain unsolved by sunshade geoengineering schemes. In this article, I review the proposed geoengineering schemes, results from climate models and discuss why geoengineering is not the best option to deal with climate change.

Structural characteristics of a giant tropical liana and its mode of canopy spread in an alien environment

To circumvent the practical difficulties in research on tropical rainforest lianas in their natural habitat due to prevailing weather conditions, dense camouflaging vegetation and problems in transporting equipment for experimental investigations, Entada pursaetha DC (syn. Entada scandens Benth., Leguminosae) was grown inside a research campus in a dry subtropical environment. A solitary genet has attained a gigantic size in 17 years, infesting crowns of semi-evergreen trees growing in an area roughly equivalent to 1.6 ha. It has used aerially formed, cable-like stolons for navigating and spreading its canopy across tree gaps. Some of its parts which had remained unseen in its natural habitat due to dense vegetation are described. The attained size of this liana in a climatically different environment raises the question as to why it is restricted to evergreen rainforests. Some research problems for which this liana will be useful are pointed out.

Estimation of mineral-adhered biomass of Thiobacillusferrooxidans by protein assay-some problems and remedies

Enumeration of adhered cells of Thiobacillus ferrooxidans on sulphide minerals through protein assay poses problems due to interference from dissolved mineral constituents. The manner in which sulphide minerals such as pyrite, chalcopyrite, sphalerite, arsenopyrite and pyrrhotite interfere with bacterial protein estimation is demonstrated. Such interferences can be minimised either through dilution or addition of H2O2 to the filtrate after hot alkaline digestion of the biotreated mineral samples.

Maximal regularity for second order non-autonomous Cauchy problems

We consider some non-autonomous second order Cauchy problems of the form u + B(t)(u) over dot + A(t)u = f (t is an element of [0, T]), u(0) = (u) over dot(0) = 0. We assume that the first order problem (u) over dot + B(t)u = f (t is an element of [0, T]), u(0) = 0, has L-p-maximal regularity. Then we establish L-p-maximal regularity of the second order problem in situations when the domains of B(t(1)) and A(t(2)) always coincide, or when A(t) = kappa B(t).

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

Influence of Elastic-Constants on Mode-I Stress-Intensity Factors in 3-Dimensional Crack Problems

Plates with V-through edge notches subjected to pure bending and specimens with rectangular edge-through-notches subjected to combined bending and axial pull were investigated (under live-load and stress-frozen conditions) in a completely nondestructive manner using scattered-light photoelasticity. Stress-intensity factors (SIFs) were evaluated by analysing the singular stress distributions near crack-tips. Improved methods are suggested for the evaluation of SIFs. The thickness-wise variation of SIFs is also obtained in the investigation. The results obtained are compared with the available theoretical solutions.