Investigations on Structural response of Water Backed Perforated plates

The study envisaged herein contains the numerical investigations on Perforated Plate (PP) as well as numerical and experimental investigations on Perforated Plate with Lining (PPL) which has a variety of applications in underwater engineering especially related to defence applications. Finite element method has been adopted as the tool for analysis of PP and PPL. The commercial software ANSYS has been used for static and free vibration response evaluation, whereas ANSYS LS-DYNA has been used for shock analysis. SHELL63, SHELL93, SOLID45, SOLSH190, BEAM188 and FLUID30 finite elements available in the ANSYS library as well as SHELL193 and SOLID194 available in the ANSYS LS-DYNA library have been made use of. Unit cell of the PP and PPL which is a miniature of the original plate with 16 perforations have been used. Based upon the convergence characteristics, the utility of SHELL63 element for the analysis of PP and PPL, and the required mesh density are brought out. The effect of perforation, geometry and orientation of perforation, boundary conditions and lining plate are investigated for various configurations. Stress concentration and deflection factor are also studied. Based on these investigations, stadium geometry perforation with horizontal orientation is recommended for further analysis.Linear and nonlinear static analysis of PP and PPL subjected to unit normal pressure has been carried out besides the free vibration analysis. Shock analysis has also been carried out on these structural components. The analytical model measures 0.9m x 0.9m with stiffener of 0.3m interval. The influence of finite element, boundary conditions, and lining plate on linear static response has been estimated and presented. Comparison of behavior of PP and PPL in the nonlinear strain regime has been made using geometric nonlinear analysis. Free vibration analysis of the PP and PPL has been carried out ‘in vacuum’ condition and in water backed condition, and the influence of water backed condition and effect of perforation on natural frequency have been investigated.Based upon the studies on the vibration characteristics of NPP, PP and PPL in water backed condition and ‘in vacuum’ condition, the reduction in the natural frequency of the plate in immersed condition has been rightly brought out. The necessity to introduce the effect of water medium in the analysis of water backed underwater structure has been highlighted.Shock analysis of PP and PPL for three explosives viz., PEK, TNT and C4 has been carried out and deflection and stresses on plate as well as free field pressure have been estimated using ANSYS LS-DYNA. The effect of perforations and the effect of lining plate have been predicted. Experimental investigations of the measurement of free field pressure using PPL have been conducted in a shock tank. Free field pressure has been measured and has been validated with finite element analysis results. Besides, an experiment has been carried out on PPL, for the comparison of the static deflection predicted by finite element analysis.The distribution of the free field pressure and the estimation of differential pressure from experimentation and the provision for treating the differential pressure as the resistance, as a part of the design load for PPL, has been brought out.

Finite Element Analysis of Warship Structures

Warships are generally sleek, slender with V shaped sections and block coefficient below 0.5, compared to fuller forms and higher values for commercial ships. They normally operate in the higher Froude number regime, and the hydrodynamic design is primarily aimed at achieving higher speeds with the minimum power. Therefore the structural design and analysis methods are different from those for commercial ships. Certain design guidelines have been given in documents like Naval Engineering Standards and one of the new developments in this regard is the introduction of classification society rules for the design of warships.The marine environment imposes subjective and objective uncertainties on ship structure. The uncertainties in loads, material properties etc.,. make reliable predictions of ship structural response a difficult task. Strength, stiffness and durability criteria for warship structures can be established by investigations on elastic analysis, ultimate strength analysis and reliability analysis. For analysis of complicated warship structures, special means and valid approximations are required.Preliminary structural design of a frigate size ship has been carried out . A finite element model of the hold model, representative of the complexities in the geometric configuration has been created using the finite element software NISA. Two other models representing the geometry to a limited extent also have been created —- one with two transverse frames and the attached plating alongwith the longitudinal members and the other representing the plating and longitudinal stiffeners between two transverse frames. Linear static analysis of the three models have been carried out and each one with three different boundary conditions. The structural responses have been checked for deflections and stresses against the permissible values. The structure has been found adequate in all the cases. The stresses and deflections predicted by the frame model are comparable with those of the hold model. But no such comparison has been realized for the interstiffener plating model with the other two models.Progressive collapse analyses of the models have been conducted for the three boundary conditions, considering geometric nonlinearity and then combined geometric and material nonlinearity for the hold and the frame models. von Mises — lllyushin yield criteria with elastic-perfectly plastic stress-strain curve has been chosen. ln each case, P-Delta curves have been generated and the ultimate load causing failure (ultimate load factor) has been identified as a multiple of the design load specified by NES.Reliability analysis of the hull module under combined geometric and material nonlinearities have been conducted. The Young's Modulus and the shell thickness have been chosen as the variables. Randomly generated values have been used in the analysis. First Order Second Moment has been used to predict the reliability index and thereafter, the probability of failure. The values have been compared against standard values published in literature.

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

Studies in quantum field theory at finite temperature

The thesis deals with certain quantum field systems exhibiting spontaneous symmetry breaking and their response to temperature. These models find application in diverse branches such as particle physics, solid state physics and non~linear optics. The nature of phase transition that these systems may undergo is also investigated. The thesis contains seven chapters. The first chapter is introductory and gives a brief account of the various phenomena associated with spontaneous symmetry breaking. The chapter closes with anote on the effect of temperature on quantum field systems. In chapter 2, the spontaneous symmetry breaking phenomena are reviewed in more detail. Chapter 3, deals with the formulation of ordinary and generalised sine-Gordon field theories on a lattice and the study of the nature of phase transition occurring in these systems. In chapter 4, the effect of temperature on these models is studied, using the effective potential method. Chapter 5 is a continuation of this study for another model, viz, the m6 model. The nature of phase transition is also studied. Chapters 5 and 6 constitute a report of the investigations on the behaviour of coupling constants under thermal excitation D1 $4 theory, scalar electrodynamics, abelian and non-abelian gauge theories