A One-Parameter Controlled Dissipative Unconditionally Stable Explicit Algorithm for Time History Analysis

A new family of one-step integration methods is presented herein. A free parameter is used to control the numerical properties and it can be considered as an indicator of numerical dissipation for the high frequency modes. This family method can have unconditional stability, explicit formulation and desired numerical damping, which implies that the low frequency modes can be accurately integrated while the spurious growth of high frequency modes can be suppressed or even eliminated. In addition, a zero damping ratio can be achieved. Since the unconditional stability and explicit formulation are integrated together for the proposed family method, it can drastically reduce the computational efforts when compared to the traditional integration methods.