Comparison of Several Step-by-step Integration Methods for Simutating the Trangent Response

A lot of integration methods are currently used for the integration of motion Mu+Cu+Ku=F. Some investigators have concluded that particular method is superior for a certain type of problems. However, a procedure which can be used to compare the merits of these methods in practical application for complex structural system is lacking. In the study of colliding of solids or blasting, the slope of the stress wave front is extremely steep. The simulation of the front slope by several steps makes the accuracy sometimes not good. In this study, three groups of integration method were compared for the step loading in order to know the accuracy of these methods for steep loading. These groups are 1. Central difference method in time, 2. Direct step by step integration method and 3. Finite element method in time. For the numerical example, the finite element bar model was employed.