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The objective of this research is to assess the performance of interface elements in the finite element method. Interface elements are implemented in the finite element codes such as MSC.NASTRAN, which is used in this study. Interface elements in MSC.NASTRAN provide a tool to transition between a shell-meshed region to another shell-meshed region as well as from a shell-meshed region to a solid-meshed region. Often, in practice shell elements are layered on shell elements or on solid elements without the use of interface elements. This is potentially inaccurate arising in mismatched degrees of freedom. In the case of a shell-to-shell interface, we consider the case in which the two regions have mismatched nodes along the boundary. Interface elements are used to connect these mismatched nodes. The interface elements are especially useful in global/local analysis, where a region with a dense mesh interfaces to a region with a less dense mesh. Interface elements are used to help avoid using special transition elements between two meshed regions. This is desirable since the transition elements can be severely distorted and cause poor results. Accurate results are obtained in shell-shell and shell-solid combinations. The most interesting result is that not using interface elements can lead to severe inaccuracies. This difficulty is illustrated by computing the stress concentration of a sharp elliptical hole.

This dissertation describes enhancements made to the finite element program, SAGE, and research on the performance of deep excavations. SAGE was developed at Virginia Tech for analysis of soil-structure interaction problems (Morrison, 1995). The purpose of the work described in this text with SAGE was to increase the capabilities of the program for soil-structure analysis. The purpose of the research on deep excavations was to develop a deeper understanding of the behavior of excavation support systems. The significant changes made to SAGE during this study include implementation of Biot Consolidation, implementation of axisymmetric analysis, and creation of a steady state seepage module. These changes as well as several others are described. A new manual for the program is also included. A review of published studies of deep excavation performance and recent case histories is presented. Factors affecting the performance of excavation support systems are examined, and performance data from recent published case histories is compared to data from Goldberg et al.'s 1976 report to the Federal Highway Administration. The design, construction, and performance of the deep excavation for the Dam Number 2 Hydroelectric Project is described. Finite element analyses of the excavation that were performed with SAGE are presented and discussed. / Ph. D.

No / The torsional response of rotor systems comprising bearings, inertia discs, and relatively long, slim shafts is considered. Lumped, finite element and hybrid, distributed-lumped parameter procedures are employed to represent the rotor systems of concern in efforts aimed at increasing accuracy, integrity, and computational efficiency. Rotor, shaft, and bearing elements of arbitrary dimensions, constructed from materials with differing mechanical properties, can be accommodated within the system models formulated. General results for multiple rotor assemblies are derived. Simple computational techniques are employed to obtain the frequency response and time domain characteristics for the models proposed. Analytical validation of the resonance conditions identified is provided. Application studies are presented for purposes of comparison.

Using a finite element method, we numerically solve the time-dependent Ginzburg-Landau equations of superconductivity to explore vortex nucleation in type II superconductors. We consider a cylindrical geometry and simulate the transition from a superconducting state to a mixed state. Using saddle-node bifurcation theory we evaluate the superheating field for a cylinder. We explore how surface roughness and thermal fluctuations influence vortex nucleation. This allows us to simulate material inhomogeneities that may lead to instabilities in superconducting resonant frequency cavities used in particle accelerators.

Using a finite element method, we numerically solve the time-dependent Ginzburg-Landau equations of superconductivity to explore vortex nucleation in type II superconductors. We consider a cylindrical geometry and simulate the transition from a superconducting state to a mixed state. Using saddle-node bifurcation theory we evaluate the superheating field for a cylinder. We explore how surface roughness and thermal fluctuations influence vortex nucleation. This allows us to simulate material inhomogeneities that may lead to instabilities in superconducting resonant frequency cavities used in particle accelerators.

<p> A computer program is written to calculate the deflections and stresses in a shell of general nature.</p> <p> An oblique. truncated pyramid, built of aluminium plates is used for illustration and experimental analysis. </p> <p> Theoretical values of deflections and stresses are compared with the experimental results. </p> / Thesis / Master of Engineering (MEngr)

An algorithm is presented for the solution of mechanical contact problems using the displacement based Finite Element Method. The corrections are applied as forces at the global level, together with any corrections for other nonlinearities, without having to nominate either body as target or contactor. The technique requires statically reducing the global stiffness matrices to each degree of freedom involved in contact. Nodal concentrated force are redistributed as continuous tractions. These tractions are re-integrated over the element domains of the opposing body. This creates a set of virtual elements which are assembled to provide a convenient mesh of the properties of the opposing body no matter what its actual discretizaton into elements. Virtual nodal quantities are used to calculate corrective forces that are optimal to first order. The work also presents a derivation of refereritial strain tensors. This sheds new light on the updated Lagrangian formulation, gives a complete and correct incremental form for the Lagrangian strain tensor and illustrates the role of the reference configuration and what occurs when it is changed. / Thesis / Doctor of Philosophy (PhD)