Remedy for Load Discontinuity in Time History Analysis

Discontinuity at the end of an impulse will lead to an amplitude distortion in a time history analysis. This amplitude distortion can be effectively reduced, if a very small time step is used to perform a complete step-by-step integration procedure. As a result, a lot of computational effort is involved. In this study, it will be shown that a significant amplitude distortion may also occur for a dynamic loading, which is not classified as an impulse. Furthermore, a remedy is proposed to overcome the difficulty caused by the load discontinuity. This remedy is very simple and it involves adjusting the input load at the time instant of discontinuity. In fact, the average of the two discontinuity values at the load discontinuity is taken to be the adjusting input load for the time instant of load discontinuity. The feasibility of this remedy is analytically verified and confirmed with numerical examples not only for impulses but also for dynamic loadings. Apparently, there is no extra computational effort needed for the remedy and it will not complicate the programming of dynamic analysis codes.