A Novel Composite Time Integration Algorithm with Unconditional Stability and Minor Period Elongation

Strong stability and highly accurate responses are well known features of composite time marching algorithms which are a recent type of numerical time integration methods In these methods each time step is marched with multiple sub-steps and a different method is applied on each sub-step. This paper concerns with a new composite time integration in which a two sub-steps are assumed to be present in each time increment; the well-known Newmark method is applied on the first sub-step and the second sub-step is solved using a Newton-Cotes formula of integration. An unconditional stability region is determined for the constant parameters to be chosen from. Additionally, precision assessment is performed on the proposed method and proved that minor period elongation as well as a reasonable amount of numerical dissipation is produced in the responses obtained by the proposed method. Finally, as a practical assessment of the proposed method, several benchmark problems are solved using the proposed method

Keywords:

composite time integration , unconditional stability , numerical dissipation , period elongation