Load discontinuity in step-by-step integration

In this article, both analytical and numerical studies show that a load discontinuity will lead to an amplitude distortion in performing the step-by-step integration. It is also found that the relative amplitude error caused by load discontinuity is closely related to, but not proportional to, the value of the load discontinuity. In general, this amplitude distortion can be reduced if a very small time step is used for a whole step-by-step integration procedure. Hence, a lot of computational efforts will be involved. In order to reduce these computational efforts a remedy is proposed herein. The remedy is proposed to perform a very small single time step immediately after the load discontinuity to reduce amplitude distortion. Since only a very small time step is performed in the step-by-step integration, many computational efforts can be saved. The feasibility of this remedy is analytically proved and numerically confirmed.