Explicit dynamic analysis using Dynamic Relaxation method

This paper deals with a new explicit framework for numerical dynamic analysis that could be applied to any explicit-implicit time integration, i.e. predictor-corrector time integrations. For this purpose, Dynamic Relaxation method is combined with the explicit-implicit time integrations so that the proposed algorithm is performed by full vector operations. This subject helps to obtain an explicit algorithm, which does not involve solving simultaneous system of equations in each time increment, even linear one. Moreover, the number of corrections, which is the main concern in the explicit-implicit algorithms, is selected automatically in the suggested procedure. Afterwards, some numerical examples are solved to illustrate the validity and the robustness of the proposed algorithm. Results show that applying the proposed framework to the higher order explicit-implicit integrations exhibits excellent accuracy in comparison with the well-known implicit Newmark-β and Wilson-θ schemes. Simplicity, more stable integration, automated procedure and vector operations are some of the salient features of the proposed algorithm.