Field Equilibrium Finite Elements for Structural Analysis

Many finite elements used in structural analysis possess deficiencies like shear locking, incompressibility locking, poor stress predictions within the element domain, violent stress oscillation, poor convergence etc. An approach that can probably overcome many of these problems would be to consider elements in which the assumed displacement functions satisfy the equations of stress field equilibrium. In this method, the finite element will not only have nodal equilibrium of forces, but also have inner stress field equilibrium. The displacement interpolation functions inside each individual element are truncated polynomial solutions of differential equations. Such elements are likely to give better solutions than the existing elements.In this thesis, a new family of finite elements in which the assumed displacement function satisfies the differential equations of stress field equilibrium is proposed. A general procedure for constructing the displacement functions and use of these functions in the generation of elemental stiffness matrices has been developed. The approach to develop field equilibrium elements is quite general and various elements to analyse different types of structures can be formulated from corresponding stress field equilibrium equations. Using this procedure, a nine node quadrilateral element SFCNQ for plane stress analysis, a sixteen node solid element SFCSS for three dimensional stress analysis and a four node quadrilateral element SFCFP for plate bending problems have been formulated.For implementing these elements, computer programs based on modular concepts have been developed. Numerical investigations on the performance of these elements have been carried out through standard test problems for validation purpose. Comparisons involving theoretical closed form solutions as well as results obtained with existing finite elements have also been made. It is found that the new elements perform well in all the situations considered. Solutions in all the cases converge correctly to the exact values. In many cases, convergence is faster when compared with other existing finite elements. The behaviour of field consistent elements would definitely generate a great deal of interest amongst the users of the finite elements.

Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.

Photothermal deflection studies on heat transport in intrinsic and extrinsic InP

Laser induced transverse photothermal deflection technique has been employed to determine the thermal parameters of InP doped with Sn, S and Fe as well as intrinsic InP. The thermal diffusivity values of these various samples are evaluated from the slope of the curve plotted between the phase of photothermal deflection signal and pump-probe offset. Analysis of the data shows that heat transport and hence the thermal diffusivity value, is greatly affected by the introduction of dopant. It is also seen that the direction of heat flow with respect to the plane of cleavage of semiconductor wafers influences the thermal diffusivity value. The results are explained in terms of dominating phonon assisted heat transfer mechanism in semiconductors.

Study of solvent effect in laser emission from Coumarin 540 dye solution

The results of a brief investigation of the amplified spontaneous emission and lasing characteristics of Coumarin 540 dye in as many as ten different solvents are reported. It has been found that C 540 dye solutions contained within a rectangular quartz cuvette give laser emission with well resolved equally spaced modes when pumped with a 476 nm beam. The modes were found to originate from the subcavities formed by the plane-parallel walls of the cuvette containing the high-gain medium. While the quantum yield remains a decisive factor, a clear correlation between the total width of the emission spectra and the refractive indices of the solvents of the respective samples has been demonstrated. The well-resolved mode structure exhibited by the emission spectra gives clear evidence of the lasing action taking place in the gain medium, and the number of modes enables us to compare the gain of the media in different samples. A detailed discussion of the solvent effect in the lasing characteristics of C540 in different solutions is given.

Numerical Investigations on Soil Structure Interaction of Multistorey Frames

Frames are the most widely used structural system for multistorey buildings. A building frame is a three dimensional discrete structure consisting of a number of high rise bays in two directions at right angles to each other in the vertical plane. Multistorey frames are a three dimensional lattice structure which are statically indeterminate. Frames sustain gravity loads and resist lateral forces acting on it. India lies at the north westem end of the Indo-Australian tectonic plate and is identified as an active tectonic area. Under horizontal shaking of the ground, horizontal inertial forces are generated at the floor levels of a multistorey frame. These lateral inertia forces are transferred by the floor slab to the beams, subsequently to the columns and finally to the soil through the foundation system. There are many parameters that affect the response of a structure to ground excitations such as, shape, size and geometry of the structure, type of foundation, soil characteristics etc. The Soil Structure Interaction (SS1) effects refer to the influence of the supporting soil medium on the behavior of the structure when it is subjected to different types of loads. Interaction between the structure and its supporting foundation and soil, which is a complete system, has been modeled with finite elements. Numerical investigations have been carried out on a four bay, twelve storeyed regular multistorey frame considering depth of fixity at ground level, at characteristic depth of pile and at full depth. Soil structure interaction effects have been studied by considering two models for soil viz., discrete and continuum. Linear static analysis has been conducted to study the interaction effects under static load. Free vibration analysis and further shock spectrum analysis has been conducted to study the interaction effects under time dependent loads. The study has been extended to four types of soil viz., laterite, sand, alluvium and layered.The structural responses evaluated in the finite element analysis are bending moment, shear force and axial force for columns, and bending moment and shear force for beams. These responses increase with increase in the founding depth; however these responses show minimal increase beyond the characteristic length of pile. When the soil structure interaction effects are incorporated in the analysis, the aforesaid responses of the frame increases upto the characteristic depth and decreases when the frame has been analysed for the full depth. It has been observed that shock spectrum analysis gives wide variation of responses in the frame compared to linear elastic analysis. Both increase and decrease in responses have been observed in the interior storeys. The good congruence shown by the two finite element models viz., discrete and continuum in linear static analysis has been absent in shock spectrum analysis.

Investigations on Broadband Plannar Monoplole Antennas with Truncated Ground Plane

The space constraints on wireless gadgets is a challenge to antenna designers as the ground plane dimensions of the printed monopole significantly affect s the antenna characteristics.Investigations on ground plane truncations have led to the development of an extremely broad band printed monopole antenna.Omnidirectional radiation characteristics with moderate gain makes this antenna highly suitable for mobile/wireless applications .This thesis also highlights the development of UWB printed antenna along with design equations .Optimum ground plane dimensions for compact antenna applications,folding technique for miniaturization and double folding for dual band application are the other highlights of this thesis.

Strip-loaded hollow dielectric H-plane sectoral horn antennas for square radiation pattern

The radiation characteristics of a new type of hollow dielectric H-plane sectoral horn antenna are presented. Metallic strips of optimum length are loaded on the H-walls of the sectoral horns. The effects of strip loading for producing square patterns in the H plane are discussed.

Wave-vector dependence of spin and density multipole excitations in quantum dots

We have employed time-dependent local-spin density-functional theory to analyze the multipole spin and charge density excitations in GaAs-AlxGa1-xAs quantum dots. The on-plane transferred momentum degree of freedom has been taken into account, and the wave-vector dependence of the excitations is discussed. In agreement with previous experiments, we have found that the energies of these modes do not depend on the transferred wave vector, although their intensities do. Comparison with a recent resonant Raman scattering experiment [C. Schüller et al., Phys. Rev. Lett. 80, 2673 (1998)] is made. This allows us to identify the angular momentum of several of the observed modes as well as to reproduce their energies

Multiple edges of a quantum Hall system in a strong electric

In this paper we show that if the electrons in a quantum Hall sample are subjected to a constant electric field in the plane of the material, comparable in magnitude to the background magnetic field on the system of electrons, a multiplicity of edge states localized at different regions of space is produced in the sample. The actions governing the dynamics of these edge states are obtained starting from the well-known Schrödinger field theory for a system of nonrelativistic electrons, where on top of the constant background electric and magnetic fields, the electrons are further subject to slowly varying weak electromagnetic fields. In the regions between the edges, dubbed as the "bulk," the fermions can be integrated out entirely and the dynamics expressed in terms of a local effective action involving the slowly varying electromagnetic potentials. It is further shown how the bulk action is gauge noninvariant in a particular way, and how the edge states conspire to restore the U(1) electromagnetic gauge invariance of the system. In the edge action we obtain a heretofore unnoticed gauge-invariant term that depends on the particular edge. We argue that this term may be detected experimentally as different edges respond differently to a monochromatic probe due to this term

Nucleation in supersaturated solutions 3He in 4He at negative pressure.

Depending on the 3He concentration, thermal nucleation in 3-4He supersaturated liquid mixtures at negative pressures may be originated either by bubble or by 3rich drop formation. We have investigated this phenomenon within a density-functional approach, determining the regions in the pressure¿3He-concentration plane where bubbles or drops likely drive the nucleation process. As an illustrative example, we also give the homogeneous nucleation pressure corresponding to 50 and 100 mK temperature.

Semiclassical theory of shot noise in ballistic n+in+ semiconductor structures: relevance of Pauli and long range Coulomb interactions

We work out a semiclassical theory of shot noise in ballistic n+-i-n+ semiconductor structures aiming at studying two fundamental physical correlations coming from Pauli exclusion principle and long-range Coulomb interaction. The theory provides a unifying scheme which, in addition to the current-voltage characteristics, describes the suppression of shot noise due to Pauli and Coulomb correlations in the whole range of system parameters and applied bias. The whole scenario is summarized by a phase diagram in the plane of two dimensionless variables related to the sample length and contact chemical potential. Here different regions of physical interest can be identified where only Coulomb or only Pauli correlations are active, or where both are present with different relevance. The predictions of the theory are proven to be fully corroborated by Monte Carlo simulations.

Formation of elliptically polarized beam from h-plane sectoral horns using corrugated flanges

The flange technique, suggested by Reynolds72 is simple technique to improve antenna characteristics. Using flange technique we can trim the antenna characteristic by suitably adjusting the flange parameters75. Later corrugated flanges87 are used for beam shaping. The important parameters of the corrugated flanges are (a) flange angle, (b) flange width, (c) flange position, (d) conductivity of the flange, (e) amplitude excitation of the flange elements, (f) period of corrugation etc. Compared to a compound horn the flange technique offers great convenience in trimming antenna characteristics. Horns are commonly used as a feed in radar and satellite communications. A large number of work had been done to improve the characteristics of horn antennas. It is an established fact that grooved walls on the inner surface of a horn can improve the antenna characteristics44. Corrugated comb surface can be used for the circular polarization98, tilt of polarization99 etc. This suggests the possibility to combine these two phenomena and to obtain a resultant beam. This thesis presents the result of an investigation to study the possibility of controlling different antenna characteristics like polarization, beam shaping, matching etc, using corrugated flange techniques.

Chaotic dynamics of electric-field domains in periodically driven superlattices

Self-sustained time-dependent current oscillations under dc voltage bias have been observed in recent experiments on n-doped semiconductor superlattices with sequential resonant tunneling. The current oscillations are caused by the motion and recycling of the domain wall separating low- and high-electric-field regions of the superlattice, as the analysis of a discrete drift model shows and experimental evidence supports. Numerical simulation shows that different nonlinear dynamical regimes of the domain wall appear when an external microwave signal is superimposed on the dc bias and its driving frequency and driving amplitude vary. On the frequency-amplitude parameter plane, there are regions of entrainment and quasiperiodicity forming Arnold tongues. Chaos is demonstrated to appear at the boundaries of the tongues and in the regions where they overlap. Coexistence of up to four electric-field domains randomly nucleated in space is detected under ac+dc driving.

Photometric and fundamental plane studies of galaxies

Determining the morphological parameters that describe galaxies has always been a challenging task. The studies on the correlations between different photometric as well as spectroscopic parameters of the galaxies help in understanding their structure, properties of the stars and gas which constitute the galaxy, the various physical and chemical processes which determine the properties, and galaxy formation and evolution. In the last few decades, the advent of Charge Coupled Devices (CCDs) and near infrared arrays ha\·e provided quick and reliable digitized data acquisition, in the optical and near infrared bands. This has provided an avalanche of data, which can be processed using sophisticated image analysis techniques to obtain information about the morphology of galaxies. The photometric analysis performed in this thesis involve the extraction of structural parameters of early type gala.xies imaged in the near infrared K (2.2ttm) band, obtaining correlations between these, parameters and using them to constrain the large scale properties of galaxi,~s.

Recording multiple holographic gratings in silver-doped photopolymer using peristrophic multiplexing

Plane-wave transmission gratings were stored in the same location of silver- doped photopolymer ¯lm using peristrophic multiplexing techniques. Constant and vari- able exposure scheduling methods were adopted for storing gratings in the ¯lm using He{Ne laser (632.8 nm). The role of recording geometry on the dynamic range of the ma- terial was studied by comparing the results obtained from both techniques. Peristrophic multiplexing with rotation of the ¯lm in a plane normal to the bisector of the incident beams resulted in better homogenization of di®raction e±ciencies and larger M/# value.