Lagrangian Formulation of Sandwich Shell Theory

Using both direct and index notation, the finite deformation of convected coordinate systems is briefly reviewed. Eulerian stress and moment resultant tensors for an idealized sandwich shell are defined by integration across a director surface. Introduction of Lagrangian stresses into these integrals leads to the definition of the first and secong Piola-Kirchhoff resultants. Based on previously established virtual work principles, equations of equilibrium and dynamic boundary conditions referred to the undeformed state are derived in terms of both sets of Lagrangian stress resultants. Constitutive relations for the second Piola-Kirchhoff resultants are indicated.