Discontinuous time-integration method for dynamic contact impact problems

A new time-integration method is proposed using the generalized derivative concept to simulate the dynamic phenomena with sudden constraint occurring in dynamic contact/impact problems. By the adoption of the generalized derivative concept and the jump assumption, discontinuity can be incorporated in time integration, and as a result, the algorithm does not need any other special consideration of jumps in dynamic field variables due to sudden constraint, such as dynamic contact-release conditions. To observe the characteristics of the proposed time-integration method, stability and convergence analyses are carried out. The analyses prove that the proposed method with linear approximation in the time domain yields unconditional stability and third-order accuracy In numerical tests, several dynamic contact/impact problems are analyzed by straightforward application of the proposed time-integration method with the exterior penalty method. From the tests, it is shown that the proposed time-integration method can be used successfully with the penalty method in numerical simulations of dynamic contact/impact problems.