Evaluation of a direct time integration scheme for dynamic analysis

Abstract

Direct integration schemes are important tools used in the dynamic analysis of many structures. It is critical that the solutions obtained from these schemes produce accurate results. Currently, one of the most widely used direct integration schemes is the trapezoidal rule. It is favored because it is a method that requires single steps and its results are second-order accurate. However, in cases where there are large deformations and longer integration times, the trapezoidal rule fails. A new composite method scheme shows promise in maintaining stability where the trapezoidal rule fails. It is a two step method that makes use of the trapezoidal rule and the three-point Euler backward method. The purpose of this study is to compare the trapezoidal rule and the new composite method using two nonlinear problems in order to determine if the composite method generates more accurate results than the trapezoidal rule.