Connection forces in deformable multibody dynamics

In the dynamic formulation of holonomic and nonholonomic systems based on D'Alembert-Lagrange equation, the forces of constraints are maintained in the dynamic equations by introducing auxiliary variables, called Lagrange multipliers. This approach introduces a set of generalized reaction forces associated with the system generalized coordinates. Different sets of variables can be used as generalized coordinates and accordingly, the generalized reactions associated with these generalized coordinates may not be the actual reaction forces at the joints. In rigid body dynamics, the generalized reaction forces and the actual reaction forces at the joints represent equipollent systems of forces since they produce the same total forces and moments at and about any point on the rigid body. This is not, however, the case in deformable body analyses wherein the generalized reaction forces depend on the system generalized reference and elastic coordinates. In this paper, a method for determining the actual reaction forces at the joints from the generalized reaction forces in deformable multibody systems is presented.