A time integration scheme with energy–momentum conservation for a shell formulation with arbitrary geometric and material non-linearities

The paper is concerned with a time integration scheme which conserves energy, momentum and angular momentum for shells exhibiting arbitrary non-linearities in the strain–displacement relations together with a possible non-linear constitutive behaviour and displacement-dependent loading. The formulation is general and can apply to any shell formulation. However, we derive the equations for the specific case of the so-called seven-parametric shell theory which is characterized by a quadratic displacement field over the shell thickness. Numerical examples of large overall motion of shells are provided showing the main features of the algorithm.