An explicit time integration technique for dynamic analyses


A simple explicit solution technique for problems in structural dynamics, based on a Modified Trapezoidal rule Method (MTM) approximation of the governing ordinary differential equations, is developed. The resulting conditionally stable explicit method (MTM) can be easily implemented and is extremely simple to use. Particular attention is focused herein on the concept of numerical stability of the proposed method for a free‐vibrational response of a linear undamped Single‐Degree‐Of‐Freedom system (SDOF). To examine the effectiveness, strengths, and limitations of MTM, error analyses for the natural period, the displacement, the velocity and the associated phase angle for a free undamped simple mass–spring system are derived and compared with Modified Euler Method (MEM) and the well‐known Newmark Beta Method (NBM). Numerical examples for a SDOF system and a Multi‐Degree‐Of‐Freedom (MDOF) system are presented to illustrate the strengths and the limitations of the proposed method. Copyright © 1995 John Wiley & Sons, Ltd

Publication Title

International Journal for Numerical Methods in Engineering