When simulating a mechanical system, the time evolution of the generalized
coordinates used to represent the configuration of the model is computed as
the solution of a combined set of ordinary differential and algebraic
equations (DAEs). The second order differential equations can be regarded
as coming from Newton's second law. The algebraic equations come from the
geometric constraints that the generalized coordinates must satisfy for the
mechanism to be physically meaningful.
There are several ways in which the numerical solution of the resulting
index 3 DAE problem can be approached. The most well-known and
time-honored algorithms are the direct discretization approach, and the
state-space reduction approach, respectively. In the latter, the problem
is reduced to a minimal set of (potentially new) generalized coordinates in
which the problem assumes the form of a pure ODE. This approach is very
accurate, but computationally intensive, especially when dealing with large
mechanical systems that contain flexible parts, stiff components, and
contact/impact. The direct discretization approach is less accurate but
significantly faster, and it is the approach that is considered in this
talk.
In the context of direct discretization methods, the BDF formulas have been
the traditional choice for more than 20 years. This talk proposes a method
in which the BDF formulas are replaced by either the Newmark or the
Hilber-Hughes-Taylor (HHT) integration formulas. Successfully used in the
Structural Analysis world, this is a first attempt to employ these
integration formulas for industrial strength Dynamic Analysis applications.
The new method will be introduced, numerical results will be presented, and
a (rather long) list of open question will conclude the presentation.
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