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標題: A cubic Hermite finite element-continuation method for numerical solutions of the von Karman equations
作者: Chien, C.S.
Shih, Y.T.
關鍵字: von Karman equations;Bogner-Fox-Schmit elements;Totally clamped;boundary conditions;Bifurcation;Continuation methods;vonkarman equations;postbuckling behavior;boundary-conditions;bifurcation;approximation;plate
Project: Applied Mathematics and Computation
期刊/報告no:: Applied Mathematics and Computation, Volume 209, Issue 2, Page(s) 356-368.
We study a cubic Hermite finite element method for numerical solutions of the von Karman equations defined in a rectangular domain with totally clamped boundary conditions. A novel iterative method combined with a predictor-corrector continuation algorithm is exploited to trace solution curves of the von Karman equations. The fourth order finite element approximations compute accurate numerical solutions for the deformation and the Airy stress function as well as their first order partial derivatives and the mixed second order partial derivatives. In this regard, the classical predictor-corrector continuation method is interpreted in a different way. Our numerical results show that the bifurcation scenario of the von Karman equations with totally clamped boundary conditions is different from those with simply supported and partially clamped boundary conditions. (C) 2008 Elsevier Inc. All rights reserved.
ISSN: 0096-3003
DOI: 10.1016/j.amc.2008.12.054
Appears in Collections:應用數學系所

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