Non-linear ‘master-slave’ relationships for joints in 3-D beams with large rotations

A novel approach is presented for the analysis of spatial beam elements with end releases, in which, for each joint in the structure, an additional (slave) set of kinematic variables is introduced, which is directly related to the existing (master) set of variables at that node. This relationship is established according to the nature of the joint to be modelled and takes into account that the sliding/rotation takes place along/around the axis that is rigidly attached to the structural node and is thus not fixed in space. In this way, the most interesting releases such as revolute, spherical, prismatic and cylindrical joints can be analysed accurately and efficiently. The main concepts are applicable to any spatial beam finite element, provided that a displacement vector and a rotation matrix are defined at both end nodes. The numerical examples, in which a highly deformable space frame with different joints is analysed, demonstrates the accuracy of the proposed procedure and its advantages compared to the ‘penalty’ technique.