Newmark is a subclass of TransientIntegrator which implements
the Newmark method. In the Newmark method, to determine the
velocities, accelerations and displacements at time t + \Delta t,
the equilibrium equation (expressed for the TransientIntegrator) is
typically solved at time t + \Delta t for \U_{t+\Delta t},
i.e. solve:
for \U_{t+\Delta t}. The following difference relations
are used to relate \Ud_{t + \Delta t} and \Udd_{t + \Delta t} to
\U_{t + \Delta t} and the response quantities at time t:
which results in the following
An alternative approach, which does not involve \Delta t
in the denumerator (useful for impulse problems), is to solve for the
accelerations at time t + \Delta t
where we use following functions to relate \U_{t + \Delta
t} and \Ud_{t + \Delta t} to \Udd_{t + \Delta t} and the response
quantities at time t:
which results in the following
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virtual int formTangent(void)