No description available.

The objective of this study is to develop and implement practical and accurate methods for prediction of the workpiece dynamics during a complete machining cycle of the workpiece, so that FRFs of the workpiece can be used in chatter stability analysis. For this purpose, a structural modification method is used since it is an efficient tool for updating FRFs due to structural modifications. The removed mass is considered as a structural modification to the finished workpiece in order to determine the FRFs at different stages of the process. The method is implemented in a computer code and demonstrated on representative parts such as turbine blades. The predictions are compared and verified with the data obtained using FEA. The FRFs are used in chatter stability analyses, and the effect of part dynamics on stability is studied.

A stiffened DKT shell element is formulated for the linear static analysis of stiffened plates and shells. Three-noded triangular shell elements and two-noded beam elements with 18 and 12 degrees of freedom are used respectively in the formulation. The stiffeners follow the nodal lines of the shell element. Eccentricity of the stiffener is taken into account. The dynamic and stability characteristic of the element is also investigated. With the developed computer program, the results obtained by the proposed element agrees fairly well with the existing literature.

A theoretical study is conducted for the lateral torsional buckling of wooden beam-deck assemblies consisting of twin beams braced by tongue-and-groove decking at the top. Two models are developed, each with a series of analytical and numerical solutions formulated. The first model targets twin-beam-deck assemblies where deck boards and other components are detailed to provide full continuous lateral restraint while the second model is built for situations where the beams are allowed to sway laterally and the relative lateral movement between the beams is partially restrained by the deck boards. In the first model, focus is on wind uplift while in the second model, both gravity and uplift loading scenarios are investigated. In the first model, an energy method is adopted and the principle of stationary potential energy is evoked to formulate closed-form solutions, energy-based solutions and a finite element solution. The validity of the present solutions is verified against a finite element based ABAQUS model. Similarly, a family of solutions is developed under the sway model and verified against the ABAQUS. Parametric studies are conducted for both models to examine the effects of various variables on the buckling capacity. A comparative investigation on the behavioral difference between the two models under ABAQUS is also presented. Overall, the restraining effects of deck boards bracing either on the beam compression or tension side is observed to have a significant influence on the lateral torsional buckling capacity of the twin-beam-deck assemblies.

No description available.

Modeling at the structural scale most often requires the use of beam and shell elements. This simplification reduces modeling complexity and computation requirements but sacrifices the accuracy of through-the-thickness information. Several studies have reported various design approaches for analyzing functionally graded material structures. One of these studies proposed a two-node beam element for functionally graded materials (FGMs) based on first order shear deformable (FOSD) theory. The derivation of governing equations included spatial temperature variation. However, only the constant temperature case was carried through in the element formulation. This investigation explore the effects of spatial temperature variation in the axial and through-the-thickness direction of this proposed element and present a new standard three-node beam finite element modified for structure constructed of FGMs. Also, the influence of the temperature dependency of the thermo-elastic material properties on the thermal stresses distribution was studied. In addition, variations in the layer thicknesses within multilayer beam models were studied to determine the effect on stresses and factor of safety. Finally, based on the specific factor of safety, which combines together the strength and mass of the beam, the best layer thicknesses for the beam models were established. The key contributions expected from this research are: 1. development and implementation of a three-node beam element as a finite element code into the commercial computational tool MATLAB® to analyze thermo-mechanical stresses in structures constructed of functionally graded materials; 2. a strategy to simulate different load cases in structures constructed of functionally graded materials; 3. an analysis of the influence of the FGM interlayer thickness on the factor of safety/specific gravity ratio in structures constructed of functionally graded materials under thermo-mechanical loads; 4. and an analysis/comparison of the advantages/benefits of using structures constructed of functionally graded materials with respect to those constructed with homogenous materials.

Surfaces are rough, unless special care is taken to make them atomically smooth. Roughness exists at all scales, and any surface-producing operation affects the roughness in certain degrees, specific to the production process. When two surfaces are brought close to each other, contact is established at many isolated locations. The number and size of these contact islands depend on the applied load, material properties of the surfaces and the nature of roughness. These contact islands affect the tribological properties of the contacting surfaces. The real contact area, which is the sum total of the area of contacting islands, is much smaller than the apparent contact area dictated by the macroscopic geometry of the contacting surfaces. Since the total load is supported by these contact islands, the local contact pressure will be very high, and dependent on the local microscopic geometry of the roughness. Thus understanding the deformation behaviour of the rough surfaces will lead to better understanding of friction and wear properties of the surfaces. In this work, the interaction of these contact islands with each other is studied when two surfaces are in contact and sliding past each other. Asperities can be thought of as basic units of roughness. The geometry and the distribution of heights of asperities can be used to define the roughness. For example, one of the earliest models of roughness is that of hemispherical asperities carrying smaller hemispherical asperities on their back, which in turn carry smaller asperities, and soon. In the present study the asperities are assumed to be of uniform size, shape and distribution. Normal and tangential loading response of these asperities with a rigid indenter is studied through elastic-plastic plane strain finite element studies. As a rigid indenter is loaded onto a surface with a regular array of identical asperities, initial contact is established at a single asperity. The plastic zone is initially confined within the asperity. When the load is increased ,the elastic-plastic boundary moves towards the free surface of the asperity, and the contact pressure decreases. The geometry and spacing are determined when the neighbouring asperities come into contact. The plastic zone in these asperities is constrained, and hence contact pressure sustained by these asperities is larger. As the indentation progresses, more asperities come into contact in a similar way. If a tangential displacement is now applied to the indenter, the von Mises stress contours shift in the direction of indenter displacement. As the tangential displacement increases, the number of asperities in contact with the indenter decreases gradually before reaching a steady sliding state. The tangential sliding force experienced by the indenter arises from two components. One is the frictional resistance between the contacting surfaces and the other is due to the plastic deformation of the substrate. If the surface is completely elastic, it has been seen that the sliding force is purely due to the specified friction coefficient. For the smooth surface, as the subsurface makes the transition from purely elastic to confined plastic zone, plasticity breaks out on the free surface, hence the sliding force increases. For surfaces with asperities, even at very small load, the asperities deform plastically and hence the sliding force is considerably higher. The frictional force is experimentally measured by sliding a spherical indenter on smooth and rough surfaces. These experimental results are qualitatively compared with two dimensional finite element results. It has been observed that for rough surface, sliding force is considerablyhigherthanthesmoothsurface,asisobservedinsimu-lations at lower loads. In contrast to the simulations, the sliding force decreases at higher loads for both the smooth and rough surfaces.

The finite element method (FEM) is a widely-used numerical tool in the fields of structural dynamics, acoustics and electromagnetics. In this work, our goal is to develop robust FEM strategies for solving problems in the areas of acoustics, structures and electromagnetics, and then extend these strategies to solve multi-physics problems such as magnetohydrodynamics and structural acoustics. We now briefly describe the finite element strategies developed in each of the above domains. In the structural domain, we show that the trapezoidal rule, which is a special case of the Newmark family of algorithms, conserves linear and angular momenta and energy in the case of undamped linear elastodynamics problems, and an ‘energy-like measure’ in the case of undamped acoustic problems. These conservation properties, thus, provide a rational basis for using this algorithm. In linear elastodynamics variants of the trapezoidal rule that incorporate ‘high-frequency’ dissipation are often used, since the higher frequencies, which are not approximated properly by the standard displacement-based approach, often result in unphysical behavior. Instead of modifying the trapezoidal algorithm, we propose using a hybrid FEM framework for constructing the stiffness matrix. Hybrid finite elements, which are based on a two-field variational formulation involving displacement and stresses, are known to approximate the eigenvalues much more accurately than the standard displacement-based approach, thereby either bypassing or reducing the need for high-frequency dissipation. We show this by means of several examples, where we compare the numerical solutions obtained using the displacementbased and hybrid approaches against analytical solutions. We also present a monolithic formulation for the solution of structural acoustic problems based on the hybrid finite element approach. In the area of electromagnetics, since our goal is to ultimately couple the electromagnetic analysis with structural or fluid variables in a ‘monolithic’ framework, we focus on developing nodal finite elements rather than using ‘edge elements’. It is well-known that conventional nodal finite elements can give rise to spurious solutions, and that they cannot capture singularities when the domains are nonconvex and have sharp corners. The commonly used remedies of either adding a penalty term or using a potential formulation are unable to address these problems satisfactorily. In order to overcome this problem, we first develop several mixed finite elements in two and three dimensions which predict the eigenfrequencies (including their multiplicities) accurately, even for non-convex domains. In this proposed formulation, no ad-hoc terms are added as in the penalty formulation, and the improvement is achieved purely by an appropriate choice of the finite element spaces for the different variables. For inhomogeneous domains, ‘double noding’ is used to enforce the appropriate continuity conditions at an interface. Although the developed mixed FEM works very accurately for all 2D geometries and regular Cartesian 3D geometries, it has so far not yielded success for curved 3D geometries. Therefore, for 3D harmonic and transient analysis problems, we propose and use a modified form of the potential formulation that overcomes the disadvantages of the standard potential method, especially on non-convex domains. Electromagnetic radiation and scattering in an exterior domain traditionally involved imposing a suitable absorbing boundary condition (ABC) on the truncation boundary of the numerical domain to inhibit reflection from it. In this work, based on the Wilcox asymptotic expansion of the electric far-field, we propose an amplitude formulation within the framework of the nodal FEM, whereby the highly oscillatory radial part of the field is separated out a-priori so that the standard Lagrange interpolation functions have to capture a relatively gently varying function. Since these elements can be used in the immediate vicinity of the radiator or scatterer (with few exceptions which we enumerate), it is more effective compared to methods of imposing ABCs, especially for high-frequency problems. We show the effectiveness of the proposed formulation on a wide variety of radiation and scattering problems involving both conducting and dielectric bodies, and involving both convex and non-convex domains with sharp corners. The Time Domain Finite Element Method (TDFEM) has been used extensively to solve transient electromagnetic radiation and scattering problems. Although conservation of energy in electromagnetics is well-known, we show in this work that there are additional quantities that are also conserved in the absence of loading. We then show that the developed time-stepping strategy (which is closely related to the trapezoidal rule) mimics these continuum conservation properties either exactly or to a very good approximation. Thus, the developed numerical strategy can be said to be ‘unconditionally stable’ (from an energy perspective) allowing the use of arbitrarily large time-steps. We demonstrate the high accuracy and robustness of the developed method for solving both interior and exterior domain radiation problems, and for finding the scattered field from conducting and dielectric bodies. In the field of magneto-hydrodynamics, we develop a monolithic strategy based on a continuous velocity-pressure formulation that is known to satisfy the Babuska-Brezzi (BB) conditions. The magnetic field is interpolated in the same way as the velocity field, and the entire formulation is within a nodal finite element framework. Both transient and steady-state formulations are developed for two- and three-dimensional geometries. An exact linearization of the monolithic strategy ensures that rapid (quadratic) convergence is achieved within each time (or load) step, while the stable nature of the interpolations used ensure that no instabilities arise in the solution. Good agreement with analytical solutions, even with the use of very coarse meshes, shows the efficacy of the developed formulation.

Electromagnetic flow meters are simple, rugged, non-invasive flow measuring instruments, which are extensively employed in many applications. In particular, they are ideally suited for the flow rate measurement of liquid metals, which serve as coolants in fast breeder reactors. In such applications, theoretical evaluation of the sensitivity turns out to be the best possible choice. Invariably, an evaluation of the associated electromagnetic fields forms the first step. However, due to the complexity of the problem, only numerical field computational approach would be feasible. In the pertinent literature, couple of e orts could be found which employ the well-known Galerkin Finite Element Method (GFEM) for the required task. However, GFEM is known to suffer from the numerical stability problem even at moderate flow rates. This problem is quite common in fluid dynamics area and several stabilization schemes have been suggested as a remedial measure. Among such schemes, the Streamline Upwinding Petrov Galerkin (SU/PG) method is a simple and widely employed approach. The same has been adopted in some of the moving conductor literatures for obtaining a stable solution. Nevertheless, in fluid dynamics literature, it has been shown that the SU/PG solution can suffer from distortion/peaking at the boundary. The remedial measures proposed are nonlinear in nature and hence are computationally demanding. Also, even the SU/PG scheme by itself requires significant additional computation for quadratic and higher order elements. Further, the value of stabilization parameter is not accurately known for 2D and 3D problems. The present work is basically an attempt to address the above problem for flow meter and other rectilinearly moving conductor problems. More specifically, but for the requirement of (graded) structured mesh along the flow direction, it basically aims to address a more general class of problems not just limited to the flow meter. Following the classical approach employed in fluid dynamics literature, first the problem is studied in its 1D form. It was observed that a relatively better performance of GFEM over FDM scheme is basically due to the difference in their Right Hand Side (RHS) terms, which represents the applied magnetic field. Taking clue from this, it was envisaged that a better insight to the numerical problem can be obtained by using the control system theory's transfer function approach. An application of FDM or GFEM to the 1D form of the governing equation, leads to flalge-braic equations with space variable in discrete form. Hence, a Z-transform based approach is employed to relate the applied magnetic field to the vector potential of the resulting reaction magnetic field. It is then shown that the presence of a pole at Z = -1 is basically responsible for the oscillations in the numerical solution. It is then proposed that by using the control systems pole-zero cancellation principle, stability can be brought into the numerical solution. This requires suitable modification of RHS terms in the discretised equations and accordingly, two novel schemes have been proposed which works within the framework of GFEM. In author's considered opinion, the use of Z-transform for analysing the stability of the numerical schemes and the idea of employing pole-zero cancellation to bring in stability, are first of its kind. In the first of the proposed schemes, the pole-zero cancellation is achieved by simply restating the input magnetic field in terms its vector potential. Solving the difference equations given by the application of FDM or GFEM to 1D version of the governing equation, it is analytically shown that the proposed scheme is absolutely stable at high flow rates. However, at midrange of flow rates there is a small error, which is analytically quantified. Then the scheme is applied to the original flow meter problem which has only axially varying applied field and the stability is demonstrated for an extensive range of flow rates. Note that the discretisation along the flow direction was restricted in the above exercise to graded regular mesh, which can readily be realised for problems involving rectilinearly moving conductors. In order to cater for more general cases in which the applied field varies in both axial and transverse directions, a second scheme is developed. Here the RHS term representing the input magnetic field is considered in a generic weighted average form. The required weights are evaluated by imposing apart from the need for an essential zero yielding term, the flux preservation and other symmetry conditions. The stability of this scheme is proven analytically for both 1D and 2D version of the problem using respectively, the 1D and 2D Z-transform based approaches. The analytical inferences are adequately validated with numerical exercises. Also, the small error present for the midrange of flow rates is analytically quantified. Then the second scheme is applied to the actual flow meter with a general magnetic field pro le. The proposed scheme is shown to be very stable and accurate even at very high flow rates. As before, the discretisation was restricted to graded regular mesh along the flow direction. By solving for the standard TEAM No. 9 benchmark problem, applicability of the second scheme for other rectilinearly moving conductor problem has been adequately demonstrated. Even though the problems considered in this work readily permits the use of a graded regular mesh along the flow direction, for the sake of completeness, discretisation with arbitrary quadrilateral and triangular mesh is also considered. The performance of the proposed schemes for such cases even though found to deteriorate, is still shown to be considerably better than the GFEM. In summary, this work has successfully proposed two novel, computationally effcient and stable GFEM schemes for the simulation of electromagnetic flow meters and other rectilin early moving conductor problems.

The goal of this thesis is to develop a hybrid _nite element formulation to carry out stress analysis of arteries. To the best of our knowledge, a hybrid _nite element impel mentation of the Holzapfel-Ogden artery model has not been carried out before. Since arteries are thin `shell-type' structures, they are subjected to membrane, shear and volumetric locking in case when standard _nite elements are used. Since hybrid _nite elements are known to overcome these problems, we develop hybrid hexahedral element formulations (both lower and higher-order) for artery analysis. We demonstrate The better coarse mesh accuracy of hybrid elements, which are based on a two-_eld variational formulation, over conventional displacement based elements. Typically, wend that three or four extra levels of renement are required with conventional elements to achieve the ame accuracy as hybrid elements. The recently proposed Holzapfel-Ogden constitutive model for the artery and its implementation both within the conventional and hybrid _nite element frameworks is discussed. The numerical implementation is particularly challenging due to the presence of _bers which can only take tensile loads. The mathematically exact tangent stiness matrix that we have derived in this work is crucial in ensuring convergence of the numerical strategy.