A new family of explicit time integration methods

It is very promising for an integration method to possess unconditional stability and the explicitness of each time step simultaneously. For this purpose, a novel family of explicit methods, which can have unconditional stability, is developed and presented. For linear elastic systems, the numerical properties of the proposed family method are the same as the Newmark family method since they have the same characteristic equation. A subfamily of this family can have unconditional stability for linear elastic systems. However, the most important properties of this subfamily are unconditional stability for nonlinear systems, and comparable accuracy when compared to second-order accurate methods, such as the Newmark explicit method and constant average acceleration method. Hence, this subfamily might be very useful for general structural dynamic problems, where the response is dominated by low frequency modes only. This is because that the unconditional stability and comparable accuracy allow the use of a large time step, and the explicitness of each time step involves no iterative procedure. As a result, many computational efforts can be saved.