Abstract
In earlier papers (cf. [6, 7, 8, 9, 5]) a completely intrinsic differential calculus on C 1,1 submanifolds of codimension one in R N has been developed. Its potential has been illustrated by investigating some linear models of thin shells based on truncated series expansions with respect to the variable normal to the midsurface. In this paper we characterize the solution space of the P(2, 1) model for an arbitrary constitutive law and a midsurface with Lips-chitzian boundary in a C 1,1 submanifold of R N. We further obtain Naghdi’s thin shell models by elimination of variables in the P(2, 1) model without using the a priori assumption σ33 = 0 on the stress tensor σ.
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Delfour, M.C. (1999). Intrinsic P (2, 1) Thin Shell Model and Naghdi’s Models without A Priori Assumption on the Stress Tensor. In: Hoffmann, KH., Leugering, G., Tröltzsch, F., Caesar, S. (eds) Optimal Control of Partial Differential Equations. ISNM International Series of Numerical Mathematics, vol 133. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8691-8_9
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DOI: https://doi.org/10.1007/978-3-0348-8691-8_9
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