Alternative integration methods for problems in structural dynamics Original Research Article

Runge-Kutta methods for the time integration of the equations of motion in structural dynamics are presented. The methods belong to a class called SDIRK (singly-diagonally-implicit Runge-Kutta) methods. The computational cost needed per step is comparable to Newmark methods with α damping. The methods proposed are L-stable which means that they instantly damp out the higher modes in the solution. The numerical dissipation can be controlled by a parameter. Both second and third order methods are presented. Some characteristics of the methods are compared with the Newmark method with α damping.