Intrinsic P (2, 1) Thin Shell Model and Naghdi’s Models without A Priori Assumption on the Stress Tensor

In earlier papers (cf. [6, 7, 8, 9, 5]) a completely intrinsic differential calculus on C1,1 submanifolds of codimension one in RN 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 C1,1 submanifold of RN. 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.