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Construction of an Optimal Beam Using Newton's Method
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Construction of an optimal beam is a typical inverse problem. Similar problems arise in many fields of science when we cannot solve the problem from its cause. They are important since they give information about parameters that cannot be observed directly.

The problem for this project was to find the width of a beam with constant height that minimizes the stored bending energy of a deected beam. With the Lagrange multiplier method, mathematical models of the Euler-Bernoulli beam were set up for the constrained optimization problem. It was solved with two numerical methods, steepest descent method and Newton's method which were implemented in Matlab.

The results of our calculations with a uniform load show that the optimal beam with rectangular cross section is symmetric, at its widest in the middle and thinnest at the ends.

Place, publisher, year, edition, pages
2015.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-168136OAI: oai:DiVA.org:kth-168136DiVA: diva2:814465
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Available from: 2015-05-27 Created: 2015-05-27 Last updated: 2015-05-27Bibliographically approved

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