Starting from the basic equations of the three-dimensional continuum a shell theory will be derived, considering geometrically and physically nonlinear effects, transverse shear strains and thickness stretching. Motion is described using a material description with convected coordinates. This means the independent variables are the material coordinates θ{sup}i of the material points P 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 dependent 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 problem. The nonlinearity is implied in the initial value problem whereas the boundary value problem is linear in terms of displacement rates.
展开▼
