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Special Matrices and Shape Factors for Linear Empirical Similitude Method

[+] Author Affiliations
Srikanth Tadepalli, Kristin L. Wood

University of Texas - Austin, Austin, TX

Paper No. IMECE2008-67973, pp. 133-143; 11 pages
doi:10.1115/IMECE2008-67973
From:
  • ASME 2008 International Mechanical Engineering Congress and Exposition
  • Volume 14: New Developments in Simulation Methods and Software for Engineering Applications
  • Boston, Massachusetts, USA, October 31–November 6, 2008
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4875-3 | eISBN: 978-0-7918-3840-2
  • Copyright © 2008 by ASME

abstract

Empirical Similitude Method (ESM) is a technique developed to enhance the applicability of similarity methods to incorporate more realistic experimental data and scaling effects. Much of the development has been motivated by the premise of forging a relationship between experiential information and physical systems that have inherent non–linear variables and factors affecting their response. We augment this procedure by incorporating the Toeplitz and Hankel matrices, and solve the modified linear ESM problem using the conjugate gradient method, highlighting the potential benefits in the process. A simple deflection example is illustrated for lucidity and a comparison is made between all the available methods for contrast. A final extension into the use of shape factors is made using a numerical example.

Copyright © 2008 by ASME
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