Implicit Higher-Order Accuracy Method for Numerical Integration in Dynamic Analysis

Abstract

New implicit higher-order accuracy (IHOA) time integration, which uses constant time step, is presented for dynamic analysis. By defining weighted factors, current displacement and velocity are assumed to be functions of the accelerations in the several previous time steps. Then, the optimum weighted factors are determined so that displacement and velocity errors in the Taylor series are minimized. The IHOA is conditionally stable and by using the Routh–Hurwitz criterion, permissible time step is obtained. For numerical verification of the proposed technique, some linear and nonlinear dynamic systems from finite element and finite difference will be analyzed and the results are compared with common implicit methods such as Newmark-β and Wilson-θ approach. Further, the dynamic relaxation method is applied to solve equivalent static systems, obtained in implicit algorithms. Results show that the proposed time integration is stable for common time steps and exhibits improved accuracy. The highly accurate, unique procedures for all dynamic problems and automatic operations are the main merits of the new method.