An explicit discontinuous time integration method for dynamic-contact/impact problems

In this work, an explicit solution procedure for the recently developed discontinuous time integration method is proposed in order to reduce the computational cost while maintaining the desirable numerical characteristics of the discontinuous time integration method. In the present explicit solution procedure, a two-stage correction algorithm is devised to obtain the solution at the next time step without any matrix factorization. To observe the numerical characteristics of the proposed explicit solution procedure, stability and convergence analyses are performed. From the stability analysis, it is observed that the proposed algorithm gives a larger critical time step than the central difference method. From the convergence analysis, it is found that the present method with linear approximation in time gives the third order convergence that is higher than that of the central difference method. To check the performance of the proposed method in simulating impact problems, several numerical tests are carried out, and some of the results are compared with those obtained from the central difference method. Numerical tests show that the proposed explicit algorithm gives a much more robust numerical solution compared to the central difference method.