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Straight and curved finite elements of class \(C^ 1\) and some applications to thin shell problems. (English) Zbl 0809.73062

Křižek, M. (ed.) et al., Finite element methods. 50 years of the Courant element. Conference held at the Univ. of Jyväskylä, Finland, 1993. New York, NY: Marcel Dekker, Inc. Lect. Notes Pure Appl. Math. 164, 63-77 (1994).
Summary: General thin shell problems are generally formulated on plane reference domains \(\Omega\) with curved boundary. Then, the definition of very accurate conforming approximation methods requires the use of curved \(C^ 1\)-elements which are entirely compatible with the classical rectilinear \(C^ 1\)-elements. In this contribution, we analyze such methods in the context of curved \(C^ 1\)-element compatible with the Argyris element (\(P_ s\)-triangle) for the approximations of general thin shell problems and of junctions between thin shells.
For the entire collection see [Zbl 0802.00026].

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K15 Membranes
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