In this chapter we presented the results of applying the dynamic cohesive node insertion and the multi-time step nodal subcycling method to 1-D systems. Analysis in 1-D allowed us to use simple problems with verifiable solutions. Based on the analysis of several different problems, we gained a better understanding of the best and worst methods and ways to tackle future problems in 2-D.
The results have shown that multi-time step nodal subcycling is a good approximating method which allows for different time steps in different regions or a problem. As a result, we are able to distribute the lower time steps to more critical regions while larger time steps can be used in less critical ones. Implementing this algorithm in a standard finite element formulation generates significant computational savings for problems having significantly more non-subcycled nodes. When the ratio of non-subcycled to subcycled nodes is small, the cost due to the implementation of the algorithm offsets any savings achieved through its use. In addition, subcycling is inherently and approximation method and so some information is lost which, in turn, decreases the accuracy of the solution.
We have also shown that dynamic insertion requires some form of pre-stretching of cohesive nodes to minimize the nodal oscillations associated with blind insertion. The timing results for this method have generated significant computational savings while the solution was still quite accurate.