Donati Compatibility Conditions for Plates and Shells

The central problem of elasticity theory consists in finding the equilibrium position of an elastic body subjected to applied forces and boundary conditions. In the classical approach, the unknown is the displacement vector field inside the elastic body.By contrast, the unknown in an “intrinsic” approach is the strain tensor field, or equivalently the stress tensor field (by way of the constitutive equation), either of which conveys a more physical and geometrical meaning than the displacement field. But, while the mathematical foundations of the classical approach are by now well-established, those of the intrinsic approach are far from being so. The aim of this Proposal is to contribute to the intrinsic approach, by substantially extending its range of applications.