Static condensation method for the reduced dynamic modeling of mechanisms and structures

In this paper, a novel static condensation method is extended to mechanisms and structures with internal joints. The formulation is framed inside the static reduction techniques in a similar way to the classic Guyan–Iron reduction. A new class of joint nodes is added to the existing classes of inner and boundary nodes to consider joint constraints inside the compatibility conditions. Within the set of joint nodes, a reduced subset of independent nodes can be individuated to perform the static reduction. A simple connection rule is provided to determine the independent nodes of a mechanical system composed of rigid bodies, flexible components and joints. The inner and boundary nodes are then expressed in terms of the independent joint nodes to form a new transformation matrix able to reduce the stiffness and mass matrices of the original system without connections. Joint stiffness and external forces are also included in the final reduction process. Finally, two examples prove the efficiency and demonstrate the equivalence and compatibility of the proposed method with other static reduction techniques in order to create a unique substructuring framework.