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 Title
 Hybrid stress analysis using digitized photoelastic data and numerical methods.
 Creator
 Mahfuz, Hassan, Florida Atlantic University, Case, Robert O., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

Equations of stressdifference elasticity, derived from the equations of equilibrium and compatibility for a twodimensional stress field, are solved for arbitrarily digitized, singly and multiply connected domains. Photoelastic data determined experimentally along the boundary provide the boundary values for the solution of the three elliptic partial differential equations by the finite difference method. A computerized method is developed to generate grid mesh, weighting functions and nodal...
Show moreEquations of stressdifference elasticity, derived from the equations of equilibrium and compatibility for a twodimensional stress field, are solved for arbitrarily digitized, singly and multiply connected domains. Photoelastic data determined experimentally along the boundary provide the boundary values for the solution of the three elliptic partial differential equations by the finite difference method. A computerized method is developed to generate grid mesh, weighting functions and nodal connectivity within the digitized boundary for the solution of these partial differential equations. A method is introduced to digitize the photoelastic fringes, namely isochromatics and isoclinics, and to estimate the values of sigma1  sigma2, sigma x  sigma y and tau xy at each nodal point by an interpolation technique. Interpolated values of the stress parameters are used to improve the initial estimate and hence the convergence of the iterative solution of the system of equations. Superfluous boundary conditions are added from the digitized photoelastic data for further speeding up the rate of convergence. The boundary of the domain and the photoelastic fringes are digitized by physically traversing the cursor along the boundary, and the digitized information is scanned horizontally and vertically to generate internal and boundary nodal points. A linear search determines the nodal connectivity and isolates the boundary points for the input of the boundary values. A similar scanning method estimates the photoelastic parameters at each nodal point and also finds the points closest to the tint of passage of each photoelastic fringe. Stress values at these close points are determined without interpolation and are subsequently used as superfluous boundary conditions in the iteration scheme. Successive overrelaxation is applied to the classical GaussSeidel method for final enhancement of the convergence of the iteration process. The iteration scheme starts with an accelerating factor other than unity and estimates the spectral radius of the iteration matrix from the two vector norms. This information is used to estimate a temporary value of the optimum relaxation parameter, omega[opt], which is used for a fixed number of iterations to approximate a better value of the accelerating factor. The process is continued until two successive estimates differ by a given tolerance or the stopping criteria are reached. Detailed techniques of developing the code for mesh generation, photoelastic data collection and boundary value interpolation to solve the elliptic boundary value problems are presented. Three separate examples with varying stress gradients and fringe patterns are presented to test the validity of the code and the overall method. Results are compared with the analytical and experimental solutions, and the significant improvement in the rate of convergence is demonstrated.
Show less  Date Issued
 1989
 PURL
 http://purl.flvc.org/fcla/dt/11934
 Subject Headings
 Strains and stresses, Photoelasticity, Numerical analysisData processing
 Format
 Document (PDF)
 Title
 Shamir's secret sharing scheme using floating point arithmetic.
 Creator
 Finamore, Timothy., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Implementing Shamir's secret sharing scheme using floating point arithmetic would provide a faster and more efficient secret sharing scheme due to the speed in which GPUs perform floating point arithmetic. However, with the loss of a finite field, properties of a perfect secret sharing scheme are not immediately attainable. The goal is to analyze the plausibility of Shamir's secret sharing scheme using floating point arithmetic achieving the properties of a perfect secret sharing scheme and...
Show moreImplementing Shamir's secret sharing scheme using floating point arithmetic would provide a faster and more efficient secret sharing scheme due to the speed in which GPUs perform floating point arithmetic. However, with the loss of a finite field, properties of a perfect secret sharing scheme are not immediately attainable. The goal is to analyze the plausibility of Shamir's secret sharing scheme using floating point arithmetic achieving the properties of a perfect secret sharing scheme and propose improvements to attain these properties. Experiments indicate that property 2 of a perfect secret sharing scheme, "Any k1 or fewer participants obtain no information regarding the shared secret", is compromised when Shamir's secret sharing scheme is implemented with floating point arithmetic. These experimental results also provide information regarding possible solutions and adjustments. One of which being, selecting randomly generated points from a smaller interval in one of the proposed schemes of this thesis. Further experimental results indicate improvement using the scheme outlined. Possible attacks are run to test the desirable properties of the different schemes and reinforce the improvements observed in prior experiments.
Show less  Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3342048
 Subject Headings
 Signal processing, Digital techniques, Mathematics, Data encryption (Computer science), Computer file sharing, Security measures, Computer algorithms, Numerical analysis, Data processing
 Format
 Document (PDF)
 Title
 Statistics preserving spatial interpolation methods for missing precipitation data.
 Creator
 El Sharif, Husayn., College of Engineering and Computer Science, Department of Civil, Environmental and Geomatics Engineering
 Abstract/Description

Deterministic and stochastic weighting methods are commonly used methods for estimating missing precipitation rain gauge data based on values recorded at neighboring gauges. However, these spatial interpolation methods seldom check for their ability to preserve site and regional statistics. Such statistics and primarily defined by spatial correlations and other sitetosite statistics in a region. Preservation of site and regional statistics represents a means of assessing the validity of...
Show moreDeterministic and stochastic weighting methods are commonly used methods for estimating missing precipitation rain gauge data based on values recorded at neighboring gauges. However, these spatial interpolation methods seldom check for their ability to preserve site and regional statistics. Such statistics and primarily defined by spatial correlations and other sitetosite statistics in a region. Preservation of site and regional statistics represents a means of assessing the validity of missing precipitation estimates at a site. This study evaluates the efficacy of traditional interpolation methods for estimation of missing data in preserving site and regional statistics. New optimal spatial interpolation methods intended to preserve these statistics are also proposed and evaluated in this study. Rain gauge sites in the state of Kentucky are used as a case study, and several error and performance measures are used to evaluate the tradeoffs in accuracy of estimation and preservation of site and regional statistics.
Show less  Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3355568
 Subject Headings
 Numerical analysis, Meteorology, Statistical methods, Spatial analysis (Statistics), Data processing, Atmospheric physics, Statistical methods, Geographic information systems, Mathematical models
 Format
 Document (PDF)