Novel frictional algorithm implementing angular increment for two-dimensional frictional systems

This study proposes a new frictional algorithm that implements angular increment. The proposed algorithm is used to solve the numerical solutions of dynamic problems in two-dimensional frictional systems. It can accurately obtain the motion responses of a lumped mass under time-varying external forces, and it can compensate for the shortcomings of the numerical frictional algorithm that implements a time step. Specifically, the proposed algorithm 1) overcomes the difficulties encountered when the angles between resultant tangential forces and slip motion are infinitely close, 2) provides accurate solutions for two-dimensional systems under fierce planar motions, and 3) calculates the responses of the mass within a reasonable period. We compare the computation accuracy, efficiency, and robustness of the proposed frictional algorithm and the previous frictional algorithm through several representative scenarios. We reveal that the proposed algorithm has superior computation accuracy, efficiency, and robustness for two-dimensional frictional problems involving slip/stick transitions and sharp bending.