RamSeries manual
The direct integration methods seek the history of the dynamic response in time. The response is not obtained in continuous form but rather for a predetermined series of points in time ti.
One of the most popular direct integration methods is the Newmark method. Starting-point is the governing equation of a structure with various degrees of freedom:
For time t=ti , this equation takes on the following form:
The velocity and the acceleration are expressed as follows:
Substituting these expressions into the equation of motion, we obtain
where,
Usually the initial conditions are that the structure posesses neither displacement nor velocity.