Conjugate gradient type methods for numerical solutions of the von K'arm'an equations
| Autor: | Tsou, Wei Sheng, 曹惟勝 |
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| Rok vydání: | 1998 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 86 We investigate bifurcation scenario of the von K'arm'an equations defined inrectangular domains. Both simply supported and partially clamped boundary conditionsare considered. First, we study how various conjugate gradient (CG) type methodscan be incorporated in the context of continuation methods to trace solution curves of the discrete von K'arm'an equaitons. Next, we discuss linear stabilitiesof the von K'arm'an equations with partially clammped boundary conditions. Inparticular, the first five eigenvalues and associated eigenfunctions of the linearized von K'arm'an equations are obtained via computer algebra. These CGtype methods are exploited to slove linear systems as well as to detectsingularity along solution paths of the discrete problem. Sample numericalresults are reported. Our results show that for different boundary conditionsthe bifurcation scenario of the von K'arm'an equations depends on the lengthof the domain. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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