UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.
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Item ANALYSIS OF STEADY-STATE AND DYNAMICAL RADIALLY-SYMMETRIC PROBLEMS OF NONLINEAR VISCOELASTICITY(2015) Stepanov, Alexey; Antman, Stuart S.; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis treats radially symmetric steady states and radially symmetric motions of nonlinearly elastic and viscoelastic plates and shells subject to dead-load and hydrostatic pressures on their boundaries and with the plate subject to centrifugal force. The plates and shells are described by specializations of the exact (nonlinear) equations of three-dimensional continuum mechanics. The treatment in every case is very general and encompasses large classes of constitutive functions (characterizing the material response). We first treat the radially symmetric steady states of plates and shells and the radially symmetric steady rotations of plates. We show that the existence, multiplicity, and qualitative behavior of solutions for problems accounting for the live loads due to hydrostatic pressure and centrifugal force depend critically on the material properties of the bodies, physically reasonable refined descriptions of which are given and examined here with great care, and on the nature of boundary conditions.The treatment here, giving new and sharp results, employs several different mathematical tools, ranging from phase-plane analysis to the mathematically more sophisticated direct methods of the Calculus of Variations, fixed-point theorems, and global continuation methods, each of which has different strengths and weaknesses for handling intrinsic difficulties in the mechanics. We then treat the initial-boundary-value problems for the radially symmetric motions of annular plates and spherical shells that consist of a nonlinearly viscoelastic material of strain-rate type. We discuss a range of physically natural constitutive equations. We first show that when the material is strong in a suitable sense relative to externally applied loads, solutions exist for all time, depend continuously on the data, and consequently are unique. We study the role of the constitutive restrictions and that of the regularity of the data in ensuring the preclusion of a total compression and of an infinite extension for finite time. We then show that when the material is not sufficiently strong then under certain conditions on the (hydrostatic) pressure terms there are globally defined unbounded solutions and there are solutions that blow up in finite time. The practical importance of these results is that for each problem involving live loads they furnish thresholds in material response delimiting materials for which solutions are ill behaved. A mathematical or numerical study limited to a particular class of materials may dangerously indicate well-behaved solutions when there are other realistic materials for which solutions are ill behaved. Moreover this work furnishes so-called trivial solutions for the subsequent study (not given here) of bifurcation of stable equilibrium configurations from these trivial solutions.Item An Analysis of Vehicle Fires and Potential Methods to Reduce Their Severity Through More Stringent Material Standards(2008-06-17) Patronik, Evan; Mowrer, Frederick; Fire Protection Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In the United States, more than 1 in every 12 fire fatalities occurs in a passenger road vehicle; vehicle fires claim roughly 1200 injuries, $1.3 billion in property loss, and 490 lives annually. Very little progress has been made over the last several decades to confront the hazards of vehicle fires, but recently researchers and standards organizations have begun addressing these challenges. A literature review of the progress made and methods of reducing fire severity through technologies and standards was conducted. NFPA 556 is one proposed standard aimed at mitigating the hazards to occupants of vehicle fires; it was used to analyze the fire retardancy of a new, fire-resistant acoustic insulation material through small, bench, and large-scale testing. The feasibility of the use of this material in new vehicles for the reduction of losses was assessed through a cost-benefit analysis. Upon review of the results, it was determined that the new insulation did not pass all the requirements of NFPA 556. However, the standard does include stringent requirements, so the improved performance of the material should not be underappreciated. Based on the literature search and experiments, this standard, in combination with other fire protection technologies, provides a basis for improved vehicle fire safety.