Jason Magoon

Abstract

Engineers are researching solutions to resolve many of today's technical challenges. Numerical techniques are used to solve the mathematical models that arise in engineering problems. A numerical technique that is increasingly being used to solve mathematical models in engineering research is called the B-spline Collocation Method. The B-spline Collocation Method has a few distinct advantages over the Finite Element and Finite Difference Methods. The main advantage is that the B-spline Collocation Method efficiently provides a piecewise-continuous, closed form solution. Another advantage is that the B-spline Collocation Method procedure is very simple and easy to apply to many problems involving partial differential equations. The current research involves developing, and extensively documenting, a comprehensive, step-by-step procedure for applying the B-spline Collocation Method to the solution of Boundary Value problems. In addition, the current research involves applying the B-spline Collocation Method to solve the mathematical model that arises in the deflection of a geometrically nonlinear, cantilevered beam. The solution is then compared to a known solution found in the literature.

Library of Congress Subject Headings

Spline theory; Computer-aided design; Engineering design--Mathematical models

Publication Date

2-1-2010

Document Type

Thesis

Department, Program, or Center

Mechanical Engineering (KGCOE)

Advisor

Ghoneim, Hany

Comments

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: QA224 .M34 2010

Campus

RIT – Main Campus

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