A geometrically exact formulation of thin laminated composite shells

A geometrically exact approach is employed to formulate the equations of motion of thin multi-layered composite shells subject to excitations that cause large strains, displacements, and rotations. Ad hoc truncated kinematic approximations of the obtained semi-intrinsic theory delivers, as a by-product, the kinematics of the Koiter and the Naghdi theories of shells, respectively. Numerical simulations are carried out both for cylindrical and spherical shells: nonlinear equilibrium paths are constructed considering a quasi-static load increase. The comparisons between the results furnished by the geometrically exact theory and those obtained by Koiter and Naghdi theories show the high accuracy of the proposed nonlinear approach. Classical theories become increasingly inaccurate at deflection amplitudes of the order of the shell thickness, evidencing that significant misrepresentations of the system behavior are possible if reduced-order kinematics are taken into account.