Numerical Analysis and Computation Commons^™

Correlation Of Finite Element Prediction And Experimental Measurements Of Aircraft Panel Structural Vibration, Olaf L. Storaasli

Mechanical & Aerospace Engineering Theses & Dissertations

With the rapid development of computational capabilities and the implementation of complex tools for commercial finite element programs, predicting structural dynamics and related acoustics of complex structures is presently achievable. Structural finite element modeling is a design tool widely utilized for analysis of problems of all kinds. However, high frequency vibration of complex structures, such as the reinforced aircraft panel used for this study, currently does not correlate well with experimental measurements using conventional modeling methods. An investigation into the commonly used modeling techniques as well as the new tools of commercial finite element analysis packages for the prediction of …

Ergodic Control Of Reflected Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

No abstract provided.

A Study Of The Numerical Implementation Of Multidisciplinary Design Optimization Strategies, Rodney A. Taylor

Mechanical & Aerospace Engineering Theses & Dissertations

Design optimization provides an organized, systematic, and efficient method for obtaining design improvements based upon a specified measure of design performance. In the multidisciplinary design optimization (MDO) environment efficient optimization techniques allow complex designs to be improved by managing conflicting disciplinary design goals so as to improve the global design. This thesis studies the implementation issues surrounding MDO techniques and strategies. To facilitate this investigation two testbed problems have been selected for study. These problems consider two approaches to the conceptual design of an aeroelastic wing. The first approach is based on an idealized, two-dimensional representation of an airfoil under …

Characteristic Spatial Quadratures For Discrete Ordinates Neutral Particle Transport On Arbitrary Tetrahedral Meshes, Charles R. Brennan

Theses and Dissertations

Characteristic spatial quadratures for discrete ordinates calculations on meshes of arbitrary tetrahedra are derived and tested, including the step (SC), linear (LC), and exponential (EC) characteristic quadratures and variants that assume constant distributions on cell faces. Tetrahedral meshes accurately model curved surfaces with few cells. A split cell approach subdivides tetrahedra along the streaming direction, reducing the transport to one dimension. Assumed forms of the cell source and entering flux distributions have sufficient parameters to match the zeroth and first spatial moments. These parameters are determined by analytically inverting a linear system (LC), or by numerical inversion using Newton's method …

Droplet Evaporation And Deformations In An Amplitude Modulated Ultrasonic Field, Nihad E. Daidzic, Rene Stadler, Adrian Melling

Aviation Department Publications

The aim of the report presented is the measurements of droplet oscillations.

Effective Behavior Of Clusters Of Microscopic Cracks Inside A Homogeneous Conductor, Kurt M. Bryan, Michael Vogelius

Mathematical Sciences Technical Reports (MSTR)

We study the effective behaviour of a periodic array of microscopic cracks inside a homoge­neous conductor. Special emphasis is placed on a rigorous study of the case in which the corresponding effective conductivity becomes nearly singular, due to the fact that adjacent cracks nearly touch. It is heuristically shown how thin clusters of such extremely close cracks may macroscopically appear as a single crack. The results have implications for our earlier work on impedance imaging.

On An Investment-Consumption Model With Transaction Costs, Marianne Akian, José Luis Menaldi, Agnès Sulem

Mathematics Faculty Research Publications

This paper considers the optimal consumption and investment policy for an investor who has available one bank account paying a fixed interest rate and n risky assets whose prices are log-normal diffusions. We suppose that transactions between the assets incur a cost proportional to the size of the transaction. The problem is to maximize the total utility of consumption. Dynamic programming leads to a variational inequality for the value function. Existence and uniqueness of a viscosity solution are proved. The variational inequality is solved by using a numerical algorithm based on policies, iterations, and multigrid methods. Numerical results are displayed …

Optimal Starting-Stopping Problems For Markov-Feller Processes, Jose-Luis Menaldi, Maurice Robin, Min Sun

Mathematics Faculty Research Publications

By means of nested inequalities in semigroup form we give a characterization of the value functions of the starting-stopping problem for general Markov-Feller processes. Next, we consider two versions of constrained problems on the nal state or on the final time. The plan is as follows:

1. Introduction
2. Nested variational inequalities
3. Solution of optimal starting-stopping problem
4. Problems with constraints

References.

A Two-Dimensional Model For Watershed Runoff And Pollutant Transport, Laura Jean Howard

Civil & Environmental Engineering Theses & Dissertations

A two-dimensional mathematical model is developed for the quantitative and qualitative analysis of watershed runoff for a given rainfall event. The runoff is routed through a receiving channel. The model is designed for use on a personal computer. Full documentation is included in the Appendix. The model is capable of accommodating downstream boundary conditions, temporally varied effective rainfall conditions, and spatially varied watershed conditions. Output takes the form of flow depths, discharges, and concentrations. The model was tested for quantity and quality using existing experimental data, and the results are presented herein.

A Variable Time-Step Midpoint Scheme For Hamiltonian Systems, Yosi Shibberu

Mathematical Sciences Technical Reports (MSTR)

A smooth time-step selection formula for the midpoint method is derived which minimize deviations in the Hamiltonian function along piecewise-linear phase space trajectories of autonomous Hamiltonian systems. The time-step formula is implemented in a second order pre­dictor/corrector scheme and applied to Kepler's problem. The formula significantly improves energy conservation as well as the accuracy of the configuration space trajectory. Peak errors in position and momentum coordinates are not significantly reduced, but the time behavior of the errors is markedly more regular.

Multipoint Quadratic Approximation For Numerical Optimization, Michael A. Blaylock

Theses and Dissertations

A quadratic approximation for nonlinear functions is developed in order to realize computational savings in solving numerical optimization problems. Function and gradient information accumulated from multiple design points during the iteration history is used in estimating the Hessian matrix. The approximate Hessian matrix is the available for a second order Taylor series approximation to the functions of interest. Several truss and frame models will be used to demonstrate the effectiveness of the new Multipoint Quadratic Approximation (MQA) in solving structural optimization problems.

Fixed Points Of Generalized Contractive Multi-Valued Mappings, Peter Z. Daffer, Hideaki Kaneko

Mathematics & Statistics Faculty Publications

In a recent paper N. Mizoguchi and W. Takahashi gave a positive answer to the conjecture of S. Reich concerning the existence of fixed points of multi-valued mappings that satisfy a certain contractive condition. In this paper, we provide an alternative and somewhat more straightforward proof for the theorem of Mizoguchi and Takahashi. Also the problems associated with fixed points of weakly contractive multi-valued mappings are studied. Finally, we make a few comments that improve other results from their paper (J. Math. Anal. Appl. 141 (1989), 177-188).

Msda A Machinery Selection Decision Aid For Stubble Management Practices, Linda Leonard, Andrew Green

Grain and other field crops published reports

MSDA is a user friendly program developed to help farmers predict stubble outcomes before acting on their management practice. This manual is an accompaniment to a computer program designed on Micorsoft Excel-macros. Its aim is to help farmers assess their current machinery and stubble handling ability and view options that may be adopted as best practice for their properties.

The program is designed with the complete season in mind. Information is gathered on the full complement of machinery used from harvest through to seeding, to allow farmers to see all choices available and enable them to choose the best system …

Multirate Time-Frequency Distributions, John R. O'Hair

Theses and Dissertations

Multirate systems, which find application in the design and analysis of filter banks, are demonstrated to also be useful as a computational paradigm. It is shown that any problem which can be expressed a set of vector-vector, matrix-vector or matrix-matrix operations can be recast using multirate. This means all of numerical linear algebra can be recast using multirate as the underlying computational paradigm. As a non-trivial example, the multirate computational paradigm is applied to the problem of Generalized Discrete Time- Frequency Distributions GDTFD to create a new family of fast algorithms. The first of this new class of distributions is …

Point And Interval Estimation Of Series System Reliability Using Small Data Sets, Craig J. Willits

Theses and Dissertations

This investigation explored the relative performance of several small-sample point and interval estimators for series system reliability. Among point estimators, the maximum likelihood estimator MLE was compared to the corresponding Bayes estimator. In addition, four interval estimators were compared Easterlings modified maximum likelihood integer estimator, the Lindstrom-Madden estimator, and Bayesian probability interval estimators constructed using approximate beta and Bayes Monte Carlo empirical posterior densities. The relative performance of the point estimators was assessed by comparing their mean square errors. For the four interval estimators, the interval coverage probability and the average interval lower bound were examined. The values of these …

Continuity Of Metric Projection, Pólya Algorithm, Strict Best Approximation, And Tubularity Of Convex Sets, Robert Huotari, Wu Li

Mathematics & Statistics Faculty Publications

The notion of tubularity of a convex subset, K, of l∞ (n) was originally introduced to study the convergence of the Pólya algorithm. It is shown in the present paper that this geometric condition provides a characterization of thosed closed convex sets onto which the set-valued metric projection is continuous. In the development of this result, Rice′s strict best approximation is characterized in three new ways, and is shown, assuming tubularity of K, to be a continuous selection. The class of sets on which the Pólya algorithm is known to converge is enlarged to include …

Time-Discretization Of Hamiltonian Dynamical Systems, Yosi Shibberu

Mathematical Sciences Technical Reports (MSTR)

Difference equations for Hamiltonian systems are derived from a discrete variational principle. The difference equations completely determine piecewise-linear, continuous trajectories which exactly conserve the Hamiltonian function at the midpoints of each linear segment. A generating function exists for transformations between the vertices of the trajectories. Existence and uniqueness results are present as well as simulation results for a simple pendulum and an inverse square law system.

Electrostatic Positioning Of Droplets In Turbulent Flows (Lstm 375/Te/93), Nihad E. Daidzic, Adrian Melling

Aviation Department Publications

Report LSTM 375/TE/93, Lehrstuhl fuer Stroemungsmechanik Universitaet Erlangen-Nuernberg Cauerstr. 4, 8520 Erlangen Germany.

Optimal Control And Differential Games With Measures, E. N. Barron, R. Jensen, J. L. Menaldi

Mathematics Faculty Research Publications

We consider control problems with trajectories which involve ordinary measureable control functions and controls which are measures. The payoff involves a running cost in time and a running cost against the control measures. In the optimal control problem we are trying to minimize this payoff with both controls. In the differential game problem we are trying to minimize the cost with the ordinary controls assuming that the measure controls are chosen to maximize the cost. We will characterize the value functions in both cases using viscosity solution theory by deriving the Bellman and Isaacs equations.

Construction Of Process Control Charts Using Asymmetric Data, Bruce Sivwright

Theses : Honours

As part of my undergraduate degree I studied various areas in quality control. Included in these areas of study was the concept of control charts, which are becoming increasingly more important in industry for effective manufacturing processes. The general form for constructing a control chart assumes that the outcomes of the process conform to a normal distribution. Data gathered at an industrial site in Western Australia illustrates that this is not always the case. The distribution of the data collected for a specific manufacturing process was found to be significantly different from the normal distribution, in that it was right …

Some Stability Problems In Droplet Formation And Breakup (Report Lstm 351/T/92)., Nihad E. Daidzic

Aviation Department Publications

In this study the instability of droplets and cylindrical jets is investigated. The understanding of these processes has both academic and practical value. Instability of cylindrical jets is theoretically investigated for infinitesimal and finite, but small initial amplitudes (linear and nonlinear stability). For droplets, only linear theory is presented. It is assumed that the capillary force play a dominant role. It is determined that the viscosity exerts a damping effect. In the first section we give an introduction, after which the linear stability theory of cylindrical liquid jets is presented. In the third section the nonlinear jet stability theory is …

Hierarchical Flux-Based Thermal-Structural Finite Element Analysis Method, Sandra P. Polesky

Mechanical & Aerospace Engineering Theses & Dissertations

A hierarchical flux-based finite element method is developed for both one- and two-dimensional thermal-structural analyses. Derivation of the finite element equations is presented. The resulting finite element matrices associated with the flux-based formulation are evaluated in closed-form. The hierarchical finite elements include additional degrees of freedom in the approximation of the element variable distributions by the use of nodeless variables. The nodeless variables offer increased solution accuracy without the need for defining actual nodes and rediscretizing the finite element model. Thermal and structural responses obtained using the hierarchical flux-based method are compared with results obtained from a conventional linear finite …

Singular Ergodic Control For Multidimensional Gaussian Processes, J. L. Menaldi, M. Robin, M. I. Taksar

Mathematics Faculty Research Publications

A multidimensional Wiener process is controlled by an additive process of bounded variation. A convex nonnegative function measures the cost associated with the position of the state process, and the cost of controlling is proportional to the displacement induced. We minimize a limiting time-average expected (ergodic) criterion. Under reasonable assumptions, we prove that the optimal discounted cost converges to the optimal ergodic cost. Moreover, under some additional conditions there exists a convex Lipschitz continuous function solution to the corresponding Hamilton-Jacobi-Bellman equation which provides an optimal stationary feedback control.

A Mathematical Model And Simulation Of Natural Circulation Loop Thermalhydraulics, Nihad E. Daidzic

Aviation Department Publications

In this work, a simple, nonlinear, seventh-order mathematical model with lumped parameter analysis of the thermalhydraulic processes in a natural circulation steam boiler loop is presented. Digital simulation has been performed in order to predict open loop transients in severe accidental situations. Parts of the circulation loop such as the steam drum, downcomer, and riser were modelled separately on the basis of the integral balance equations. The two-phase flow in the steam drum and in the riser was modelled with the aid of a homogeneous-equilibrium, two-phase flow model. Special care was taken to ensure the stability of the numerical scheme, …

Computation Of Planar Store Trajectories Using An Adaptive Grid Procedure, William D. Hack

Theses and Dissertations

The objective of this research was to compare a quasi-analytical, potential flow/three-degree-of-freedom model to an implicit-Euler algorithm for the calculation of store trajectories. The implicity algorithm uses a cell- centered, finite-volume, spatial discretization applied to the Euler equations, written in time-dependent, curvilinear-coordinates. A flux-differencing Roe scheme is employed to find the split-fluxes and the Steger/Warming flux-vector method is used to calculate the flux-Jacobians. The potential flow and implicit- Euler algorithm are combined with a three-degree-of-freedom algorithm to evaluate the planar, freefall trajectories of a simple store shape. The research uses two different grid-modification techniques in the implicit algorithm evaluation. Data …

Miscellaneous Publication 17/91 - Mudas - Model Of An Uncertain Dryland Agricultural System: A Description, R. S. Kingwell, A. D. Bathgate

Farm Systems and Economics research reports

In the early 1980s, the Department of Agriculture developed a mixed integer whole-farm mathematical programming model of the dryland farming system in the eastern wheatbelt of Western Australia (Morrison et al. 1986). The model named MIDAS (Model of an Integrated Dryland Agricultural System) was constructed, tested and scrutinised by a multi-disciplinary team of researchers, advisers, farm management consultants and farmers (Kingwell 1987a). The model described in some detail the biology and finances of the dryland farming system in an average season and calculated profit-maximising farm plans.

MIDAS remains an often used tool in research and extension, being applied to many …

Mapping Efficient Numerical Methods To The Solution Of Multiple Objective Linear Programs, Michael A. Shields

Theses and Dissertations

This investigation was initiated to increase the speed, accuracy and capacity of m-simplex algorithms for solving multiple objective linear programming problems. Specifically, improvements were sought through the application of general numerical techniques. It soon became apparent that the m- simplex algorithm, like the simplex algorithm, is heavily dependent upon the technology of solving related systems of linear equations. The numerical arguments for the application of LU triangular matrix factorization techniques to simplex computations are well known. OF special significance to m-simplex performance is the case of rank-k updates to basis factorizations. A stable and efficient LU approach to the rank-k …

A Duality Approach To Best Uniform Convex Approximation, S. E. Weinstein, Yuesheng Xu

Mathematics & Statistics Faculty Publications

Let C[a, b] be the space of continuous functions on [a, b] endowed with the uniform norm llƒll _∞ = sup{ Iƒ(x)1 :x∈ [a, b]}. Let K be the set of convex functions defined on [a, b]. A function g* ∈ K is said to be a best uniform convex approximation to ƒ ∈ C[a, b] if ∥ƒ - g*∥ _∞ = inf { ∥ƒ - g∥_∞ : g ∈ K}.

Grid Generation And Flow Computation About A Martian Entry Vehicle, John Edward Stewart

Mechanical & Aerospace Engineering Theses & Dissertations

A number of vehicles are currently being proposed for a manned mission to Mars. One of these vehicles has a modified blunt-nosed cone configuration. Experimental results have been obtained for this vehicle in 1968. These results show lift-over-drag ratios comparable to those needed for Mars entry. Computations are performed here to verify the earlier results and to further describe the flight characteristics of this vehicle.

An analytical method is used to define the surface of this vehicle. A single-block volume grid is generated around the vehicle using an algebraic Two-Boundary Grid Generation algorithm (TBGG) and transfinite interpolation. Euler solutions are …

Numerical Investigation Of A Non-Newtonian Material Through A Sudden Pipe Expansion, V. G. Masanja

Tanzania Journal of Engineering and Technology (TJET)

A numerical method for solving two dimensional elliptic boundary-value problems of fourth order is used for finding stationary solutions of the equations of motion for a laminar flow through a sudden pipe expansion of an incompressible non-Newtonian fluid with a constitutive equation of the Reiner-Rivlin (R-R) type. Results for the Newtonian fluid, which is a special case, are in excellent agreement with those by previous investigators and they demonstrate the reliability, superiority and accuracy of the method. Results for the non-Newtonian cases could be of value for fixing ideas about visco-elastic behaviour although the R-R fluid allows only inelasticity: this …