A New Family of Explicit Model-Based Integration Algorithms for Structural Dynamic Analysis

Abstract

A new family of explicit model-based integration algorithms for solving the equations of motion for linear and nonlinear systems is developed. These algorithms are also known as structure-dependent algorithms because the integration parameters are functions of the complete model of the structural system. A variety of numerical properties of the proposed algorithms, including consistency and local truncation error, stability, numerical dispersion and energy dissipation, overshooting, and frequency response under arbitrary excitation, are investigated using the discrete control theory and amplification matrix for linear elastic systems. In addition, the discrete control theory is applied for assessing the stability of the proposed algorithms for nonlinear structural systems. It is observed that the proposed algorithms exhibit the same numerical characteristics as the well-known Newmark family of integration algorithms. Compared with three existing model-based integration algorithms, i.e. the Chen–Ricles, modified Chen–Ricles, and Gui’s algorithms, the proposed algorithms possess more general and versatile numerical features. As a result, the new family of explicit model-based integration algorithms can be potentially used to solve complicated linear and nonlinear structural dynamics problems.