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.

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.

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.