A Surface Viewed as a Function of
Its Two Fundamental Forms
Professor Philippe G. Ciarlet
City University of Hong Kong
In most two-dimensional nonlinear shell theories, such as that proposed by W.T Koiter, the stored energy function is a simple expression of the first and second fundamental forms of the unknown deformed middle surface of the shell. This observation suggests an alternate approach to nonlinear shell theory, where the fundamental forms would be regarded as the primary unknowns, instead of the customary displacement field of the middle surface. Such an approach yields a constrained minimization problem, where the unknowns must naturally satisfy, possibly in a weak sense, the classical Gauss and Codazzi-Mainardi equations. This approach, which often bears the name of "intrinsic theories for shells" in the Engineering and Computational Mechanics circles, presents the advantage of directly providing the stresses inside a shell. The aim of this talk is to review some recent progress that constitute significant steps toward a mathematical justifications of this approach, such as:
- proofs of the continuity of a surface as a function of its fundamental forms for various natural topologies;
- a proof of a nonlinear Korn inequality "on a surface".
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Date: |
April 21, 2006 (Friday) |
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Time: |
4:00 – 5:00pm |
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Place: |
Room 517, Meng Wah Complex |
Tea will be held in
Room 516, Meng Wah Complex
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All are welcome |
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