Nonlinear shell theory in convective description

Starting from the basic equations of the three-dimensional continuum a shel l theory will be derived, considering geometrically and physically nonlinea r effects, transverse shear strains and thickness stretching. Motion is des cribed using a material description with convected coordinates. This means the independent variables are the material coordinates Bi of the material p oints r and the time t. Due to the specifics of this description the shape of the coordinate lines, the base vector system and the metric are dependen t on space and time. In this case a rate formulation of the field equations proves to be useful, which leads to a nonlinear initial-boundary value pro blem. The nonlinearity is implied in the initial value problem whereas the boundary value problem is linear in terms of displacement rates.