On unique kinematics for the branching shells

We construct the unique two-dimensional (2D) kinematics which is work-conjugate to the exact, resultant local equilibrium conditions of the non-linear theory of branching shells. It is shown that the compatible shell displacements consist of the translation vector and rotation tensor fields defined on the regular parts of the shell base surface as well as independently on the singular surface curve modelling the shell branching. Discussing relations between limits of the translation vector and rotation tensor fields when approaching the singular curve, and analogous fields given only along the singular curve itself, several types of the junctions are described. Among them are the stiff, entirely simply connected and partly simply supported junction as well as the elastically and dissipatively deformable junction, and the non-local elastic junction. For each type of junction the explicit form of the principle of virtual work is derived.