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.

Design of Cyclophanes: Synthesis and Study of Photophysical and Biomolecular Recognition Properties

Development of organic molecules that exhibit selective interactions with different biomolecules has immense significance in biochemical and medicinal applications. In this context, our main objective has been to design a few novel functionaIized molecules that can selectively bind and recognize nucleotides and DNA in the aqueous medium through non-covalent interactions. Our strategy was to design novel cycIophane receptor systems based on the anthracene chromophore linked through different bridging moieties and spacer groups. It was proposed that such systems would have a rigid structure with well defined cavity, wherein the aromatic chromophore can undergo pi-stacking interactions with the guest molecules. The viologen and imidazolium moieties have been chosen as bridging units, since such groups, can in principle, could enhance the solubility of these derivatives in the aqueous medium as well as stabilize the inclusion complexes through electrostatic interactions.We synthesized a series of water soluble novel functionalized cyclophanes and have investigated their interactions with nucleotides, DNA and oligonucIeotides through photophysical. chiroptical, electrochemical and NMR techniques. Results indicate that these systems have favorable photophysical properties and exhibit selective interactions with ATP, GTP and DNA involving electrostatic. hydrophobic and pi-stacking interactions inside the cavity and hence can have potential use as probes in biology.

Acoustic radiation and scattering from cylindrical bodies and analysis of transducer arrays

New mathematical methods to analytically investigate linear acoustic radiation and scattering from cylindrical bodies and transducer arrays are presented. Three problems of interest involving cylinders in an infinite fluid are studied. In all the three problems, the Helmholtz equation is used to model propagation through the fluid and the beam patterns of arrays of transducers are studied. In the first problem, a method is presented to determine the omni-directional and directional far-field pressures radiated by a cylindrical transducer array in an infinite rigid cylindrical baffle. The solution to the Helmholtz equation and the displacement continuity condition at the interface between the array and the surrounding water are used to determine the pressure. The displacement of the surface of each transducer is in the direction of the normal to the array and is assumed to be uniform. Expressions are derived for the pressure radiated by a sector of the array vibrating in-phase, the entire array vibrating in-phase, and a sector of the array phase-shaded to simulate radiation from a rectangular piston. It is shown that the uniform displacement required for generating a source level of 220 dB ref. μPa @ 1m that is omni directional in the azimuthal plane is in the order of 1 micron for typical arrays. Numerical results are presented to show that there is only a small difference between the on-axis pressures radiated by phased cylindrical arrays and planar arrays. The problem is of interest because cylindrical arrays of projectors are often used to search for underwater objects. In the second problem, the errors, when using data-independent, classical, energy and split beam correlation methods, in finding the direction of arrival (DOA) of a plane acoustic wave, caused by the presence of a solid circular elastic cylindrical stiffener near a linear array of hydrophones, are investigated. Scattering from the effectively infinite cylinder is modeled using the exact axisymmetric equations of motion and the total pressures at the hydrophone locations are computed. The effect of the radius of the cylinder, a, the distance between the cylinder and the array, b, the number of hydrophones in the array, 2H, and the angle of incidence of the wave, α, on the error in finding the DOA are illustrated using numerical results. For an array that is about 30 times the wavelength and for small angles of incidence (α<10), the error in finding the DOA using the energy method is less than that using the split beam correlation method with beam steered to α; and in some cases, the error increases when b increases; and the errors in finding the DOA using the energy method and the split beam correlation method with beam steered to α vary approximately as a7 / 4 . The problem is of interest because elastic stiffeners – in nearly acoustically transparent sonar domes that are used to protect arrays of transducers – scatter waves that are incident on it and cause an error in the estimated direction of arrival of the wave. In the third problem, a high-frequency ray-acoustics method is presented and used to determine the interior pressure field when a plane wave is normally incident on a fluid cylinder embedded in another infinite fluid. The pressure field is determined by using geometrical and physical acoustics. The interior pressure is expressed as the sum of the pressures due to all rays that pass through a point. Numerical results are presented for ka = 20 to 100 where k is the acoustic wavenumber of the exterior fluid and a is the radius of the cylinder. The results are in good agreement with those obtained using field theory. The directional responses, to the plane wave, of sectors of a circular array of uniformly distributed hydrophones in the embedded cylinder are then computed. The sectors are used to simulate linear arrays with uniformly distributed normals by using delays. The directional responses are compared with the output from an array in an infinite homogenous fluid. These outputs are of interest as they are used to determine the direction of arrival of the plane wave. Numerical results are presented for a circular array with 32 hydrophones and 12 hydrophones in each sector. The problem is of interest because arrays of hydrophones are housed inside sonar domes and acoustic plane waves from distant sources are scattered by the dome filled with fresh water and cause deterioration in the performance of the array.

Process Improvement of Coir Pith Degradation Involving White Rot Fungi By Substitution of Urea With Nitrogen Fixing Bacteria and Application of Biodegraded Coir Pith as Plant Growth Medium

In this study, a novel improved technology could be developed to convert the recalcitrant coir pith into environmental friendly organic manure. The standard method of composting involves the substitution of urea with nitrogen fixing bacteria viz. Azotobacter vinelandii and Azospirillum brasilense leading to the development of an improved method of coir pith. The combined action of the microorganisms could enhance the biodegradation of coir pith. In the present study, Pleurotus sajor caju, an edible mushroom which has the ability to degrade coir pith, and the addition of nitrogen fixing bacteria like Azotobacter vinelandii and Azospirillum brasilense could accelerate the action of the fungi on coir pith. The use of these microorganisms brings about definite changes in the NPK, Ammonia, Organic Carbon and Lignin contents in coir pith. This study will encourage the use of biodegraded coir pith as organic manure for agri/horti purpose to get better yields and can serve as a better technology to solve the problem of accumulated coir pith in coir based industries