Assessments of Structure-Dependent Integration Methods with Explicit Displacement and Velocity Difference Equations

A family of structure-dependent integration methods has been proposed by Gui et al. for time integration. Although it has desirable numerical properties, such as unconditional stability, explicit formulation and second-order accuracy, it has some adverse properties, such as a poor capability to capture structural nonlinearity, an overshoot in a high frequency steady- state response and a weak instability in the high frequency response of nonzero initial conditions. The causes of these adverse properties are explored. A poor capability to capture structural nonlinearity may originate from the convergence rate of 1 in velocity error. This family method has an overshoot in a high frequency steady-state response and this overshoot can be eliminated by adding a load-dependent term into the displacement difference equation. It is also analytically verified that the family method generally has no weak instability. However, the special member with λ = 4, i.e., CR explicit method, is shown to have a weak instability. Thus, it must be prohibited from practical applications although many applications of this method were found in the literature.