Finite deformation higher-order shell models and rigid-body motions

This paper focuses on the developments of higher-order shell models by employing the new concept of interpolation surfaces (I-surfaces) inside the shell body. We introduce N (NP 3) I-surfaces and choose the values of displacements with correspondence to these surfaces as fundamental shell unknowns. Such choice allows, first, to develop various higher-order shell models in a very compact form and, second, to derive non-linear strain–displacement relationships, which are completely free for arbitrarily large rigid-body motions. The general 3N-parameter shell model is proposed in the framework of the Lagrangian description. The special 9, 12 and 15 parameters cases (corresponding to N = 3, 4 and 5) have been dealt in detail. The proposed shell models account for thickness stretching and the complete 3D constitutive equations are utilized. The displacement vectors of equally located I-surfaces for each model are represented in a convected curvilinear coordinate system allowing one to develop directly finite deformation geometrically exact shell finite elements which could be discussed in future works.