TWO SIMPLE FAST INTEGRATION METHODS FOR LARGE-SCALE DYNAMIC PROBLEMS IN ENGINEERING

TLDR

The authors develop a new simple explicit two‑step method and a family of predictor–corrector integration algorithms for solving dynamic problems. These methods avoid solving simultaneous linear algebraic equations at each time step, are applicable to arbitrary damping matrices and diagonal mass matrices, and have been validated for accuracy, stability, and numerical dissipation through linear and nonlinear examples, including large‑scale railway engineering applications. The new algorithms achieve substantially higher computational speeds than popular alternatives and serve as fast, economical tools for large‑scale nonlinear dynamic analyses.

Abstract

A new simple explicit two-step method and a new family of predictor–corrector integration algorithms are developed for use in the solution of numerical responses of dynamic problems. The proposed integration methods avoid solving simultaneous linear algebraic equations in each time step, which is valid for arbitrary damping matrix and diagonal mass matrix frequently encountered in practical engineering dynamic systems. Accordingly, computational speeds of the new methods applied to large system analysis can be far higher than those of other popular methods. Accuracy, stability and numerical dissipation are investigated. Linear and nonlinear examples for verification and applications of the new methods to large-scale dynamic problems in railway engineering are given. The proposed methods can be used as fast and economical calculation tools for solving large-scale nonlinear dynamic problems in engineering.