An objective minimal constraint formulation for the analysis of elastic articulated structures

An implicit formulation for cylindrical joints (pivots) connecting slender rods in large deformations is presented exploiting the G¹ map at the beam's end. The rotation at the end of the rod is decomposed in the rotation of the pivot axis and a rotation around this axis. A mixed variational formulation that uses the spherical linear interpolation for the rotations is implemented. It allows to effectively model both rigid and elastic mechanisms. The proposed formulation is applied to several examples ranging from spherical scissor mechanism to elastic deployable structures that exploit the onset of instability for achieving the target shape.