The objective of this work is to present techniques that can be used to study steady state solutions to systems generically described by the equation F(x; #21;) = dx dt = 0, where x 2 RN is the set of degrees of freedom (DOFs) of the system and #21; 2 R is a loading parameter. In particular, the implications of the presence of discrete and continuous symmetry to systems described by F(x; #21;) = 0 will be explored. Additionally, numerical techniques that can be used to “path-follow” the evolution of the DOFs as the loading parameter #21; is varied will be presented along with schemes to increase the computationally efficiency of the path following algorithms. These techniques can be used to obtain solutions to F(x; #21;) = 0 around regular and singular points. Additionally, methods to detect, and compute singular points of F will be presented. Finally, the benefits of these techniques will be illustrated through the computation of solutions to two typical problems.
University of Minnesota M.S. thesis. April 2010. Major: Aerospace Engineering & Mechanics. Advisor: Ryan Scott Elliott. 1 computer file (PDF); vi, 86 pages, appendices A-C.
Algorithms for branch-following and critical point identification in the presence of symmetry.
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