Direct integration methods in nonlinear structural dynamics

Abstract

This paper reviews some recent developments in direct time integration methods for nonlinear structural dynamics. The developments pertain to the use of linear multistep difference operators in conjunction with the pseudo-force approach. The paper is organized into three main sections. An introductory section provides an overview of the transient response analysis problem. A section on computational aspects deals with the organization of the numerical calculations; this material is largely based on a recent detailed study of linear dynamic calculations [1–2]. A section on integration methods highlights algorithmic aspects that impact the selection of integrator for nonlinear problems and discusses adaptive analysis features such as stepsize control and implicit matrix scaling techniques. An appendix section outlines the functional organization of modular “integration driving” software.