Non-linear dynamics of flexible shell structures

The initial-boundary value problem in the weak form is formulated for the general six-field non-linear theory of branched shell structures. The extended time-stepping algorithm of the Newmark type is worked out for the non-linear dynamic analysis on the configuration space containing the rotation group SO(3). Within the finite element approximation, an accurate indirect C0 interpolation procedure on SO(3) with a transport of approximation domain is developed. Numerical simulations by the finite element method of 2D and 3D large overall motions of several flexible elastic shell structures are presented. It is shown that values of potential and kinetic energies may oscillate in time, but the total energy remains conserved during the free motion of the structures in space.