Abstract
The objective of this investigation is to develop a systematic procedure that can be effectively used for modeling joint constraints for the absolute nodal coordinate formulation. To this end, the non-generalized intermediate coordinates are introduced to derive a mapping between the generalized slope coordinates and the non-generalized rotational coordinates used for defining the orientation constraints with rigid bodies. With this mapping, a wide variety of joint constraints can be defined for a flexible body modeled using the absolute nodal coordinate formulation in terms of the non-generalized intermediate coordinates, and existing constraint libraries formulated for the rotational coordinates can be employed for the absolute nodal coordinate formulation without modifications. Furthermore, in order to define a rigid cross-section at the joint definition point, orthonormality condition are imposed on the generalized slope coordinates and, as a result, the generalized slope vectors at this point can be defined as an orthonormal triad. This leads to a simpler form of constraint equations defined between the generalized slopes and the non-generalized rotational coordinates. It is also demonstrated in the paper that this set of constraint equations can be used to eliminate the non-generalized coordinates as well as the dependent Lagrange multipliers from the equations of motion. Several numerical examples are presented in order to demonstrate the use of the systematic joint constraint formulation developed in this investigation.
