On the physical meaning of the dynamical equations governing geometrically-exact multilayer shells

Abstract

In this paper, the physical meaning of the equations governing geometrically-exact multilayer shells is provided through a totally new derivation by means of dynamic equilibrium consideration, starting from a 3-D continuum setting in curvilinear coordinates. The theory is valid for large deformation and large overall motion, as characteristic of geometrically exact formulations. The dynamic equilibrium derivation offers a clear physical insight into the meaning of the terms in the equations of motion; such insight was not afforded by previous derivations based on the principle of virtual power. In particular, we obtain directly the balance of angular momentum in true resultant couples, without the need to use the constitutive restriction as in our previous papers. Moreover, we also obtain here new expressions for the inertia operators that will greatly simplify the computational formulation, when compared to our previous work. In addition, an analytical justification of the inertial operators is also provided. The present formulation is independent of any kinematic assumption along the shell director, and is in particular valid for the case of shells with variable-length director (e.g., for modeling through-the-thickness deformation) and higher-order kinematic assumptions.