Implementation of Complex Position Constraints in the Kinetic Dynamic Relaxation Method

The traditional Kinetic Dynamic Relaxation (KDR) method can only deal with simple constraints such as the fixed joints, which restricts its practical applications. This study has proposed a new algorithm to implement the complex position constraints in KDR. The proposed algorithm is developed by transforming the position constraints to the acceleration form through combining time differentiation and Taylor expansion with dimensional analysis, and then solving the governing equation of the constraint forces with the Newton’s 2nd law. For the nonlinear constraints, projection technique is applied to avoid the drift-off phenomenon. Several tests have been performed to verify the proposed algorithm. The numerical results show the algorithm is adaptive in both linear and nonlinear problems and works efficiently.