Studies of Newmark method for solving nonlinear systems: (I) basic analysis

The performance of the Newmark method in the solution of linear elastic systems can be reliably predicted by the currently available evaluation techniques. However, its performance for solving nonlinear systems is still not clear. Therefore, its numerical characteristics in the solution of nonlinear systems are explored in this study by using a newly developed technique. Only a specific implementation of the Newmark method is studied in this paper although there are several possible implementations for this integration method. It seems numerical properties of the Newmark method in the solution of linear elastic and nonlinear systems can be entirely captured by the newly developed technique. Although this technique is only aimed at a specific time step, it is still indicative for the whole step-by-step integration procedure since this procedure consists of each time step.