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.

Role of trace element of the growth and Physiology of selected microalgae

The main objective of the study is primarily to determine the magnitude of selected trace elements, the concentrations of which would possibly accelerate growth resulting in larger biomass and sustained period of exponential phase for economically viable harvest. The study on the effect of three trace elements namely Cu, Mn and Zn on two species of algae,ISOChrySiS galbana Parke and Synechocystib salina Wislouch under different conditions of salinity, PH and temperature involves several combinations for each metal, from which the relative set of conditions has been adduced. The scheme of the experiments was statistically designed for interpretation of data and factors were assessed and graded according to relative importance. The methodology adopted for data interpretation is analysis of variance by split-plot design method. The thesis has been divided into five chapters. The introductory chapter explains the relevance of the research work undertaken. Chapter 11 gives a review on the work pertaining to the above mentioned three trace elements in relation to nutrition as well as on the toxic aspects about which there is an abundance of literature. Chapter Ill presents a detailed description of the material and specialised methods followed for the study. The results and conclusions of the various experiments on effect of metals on growth and other physiological activities are discussed in Chapters IV and V.

Strength Predictions of Hat Stiffened Plate

Hat Stiffened Plates are used in composite ships and are gaining popularity in metallic ship construction due to its high strength-to-weight ratio. Light weight structures will result in greater payload, higher speeds, reduced fuel consumption and environmental emissions. Numerical Investigations have been carried out using the commercial Finite Element software ANSYS 12 to substantiate the high strength-to-weight ratio of Hat Stiffened Plates over other open section stiffeners which are commonly used in ship building. Analysis of stiffened plate has always been a matter of concern for the structural engineers since it has been rather difficult to quantify the actual load sharing between stiffeners and plating. Finite Element Method has been accepted as an efficient tool for the analysis of stiffened plated structure. Best results using the Finite Element Method for the analysis of thin plated structures are obtained when both the stiffeners and the plate are modeled using thin plate elements having six degrees of freedom per node. However, one serious problem encountered with this design and analysis process is that the generation of the finite element models for a complex configuration is time consuming and laborious. In order to overcome these difficulties two different methods viz., Orthotropic Plate Model and Superelement for Hat Stiffened Plate have been suggested in the present work. In the Orthotropic Plate Model geometric orthotropy is converted to material orthotropy i.e., the stiffeners are smeared and they vanish from the field of analysis and the structure can be analysed using any commercial Finite Element software which has orthotropic elements in its element library. The Orthotropic Plate Model developed has predicted deflection, stress and linear buckling load with sufficiently good accuracy in the case of all four edges simply supported boundary condition. Whereas, in the case of two edges fixed and other two edges simply supported boundary condition even though the stress has been predicted with good accuracy there has been large variation in the deflection predicted. This variation in the deflection predicted is because, for the Orthotropic Plate Model the rigidity is uniform throughout the plate whereas in the actual Hat Stiffened Plate the rigidity along the line of attachment of the stiffeners to the plate is large as compared to the unsupported portion of the plate. The Superelement technique is a method of treating a portion of the structure as if it were a single element even though it is made up of many individual elements. The Superelement has predicted the deflection and in-plane stress of Hat Stiffened Plate with sufficiently good accuracy for different boundary conditions. Formulation of Superelement for composite Hat Stiffened Plate has also been presented in the thesis. The capability of Orthotropic Plate Model and Superelement to handle typical boundary conditions and characteristic loads in a ship structure has been demonstrated through numerical investigations.