Integration Step Size and Its Adequate Selection in Analysis of Structural Systems Against Earthquakes

Abstract

True behaviour of an arbitrary structural system is dynamic and nonlinear. To analyze this behaviour in many real cases, e.g. structures in regions under high seismic risk, a versatile approach is to discretize the mathematical model in space, and use direct time integration to solve the resulting initial value problem. Besides versatility in application, simplicity of implementation is an advantage of direct time integration, while, inexactness of the response and the high computational cost are the weak points. Considering the sizes of the integration steps as the main parameters of time integration, and concentrating on transient analysis against ground acceleration, this chapter presents discussions on: (1) the role of integration step size in time integration analysis, specifically, from the points of view of accuracy and computational cost, (2) conventionally accepted comments, codes/standards’ regulations, and some modern methods for assigning adequate values to the integration step sizes in constant or adaptive time integration, and concludes with some challenges on time integration analysis and integration step size selection in structural dynamics and earthquake engineering.