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Multibody systems simulation software 77
The next step in building the model would typically be the definition of external
forces and internal force elements. External forces can be constant, time
histories or functionally dependent on any state variable. These forces can
also be defined to be translational or rotational. They can act in the global
system or can act in the local system of the body so that they effectively
‘follow’ the part during the simulation.
Users can also set up internal force elements acting between two parts
to represent springs, dampers, cables or rubber mounts. Internal force
elements will always act along the line of sight between the points the force
element connects on the two parts. These force elements are often referred
to as action–reaction forces as they always produce equal and opposite
forces on the two parts connected by the force element. The elements can
also be defined to act in only tension or compression and may be linear or
non-linear.
It is also useful if the multibody systems analysis program allows the definition
of elaborate mathematical equations within the data set. This enables
the user to formulate an expression involving user-defined constants, system
constants, system variables, arithmetic IFs, FORTRAN 90 or ANSI ‘C’
library functions, standard mathematical functions or ‘off-the-shelf’ functions
supplied with the main code to represent events such as impacts. The access
to system variables can be a powerful modelling tool. The user can effectively
access any displacement, velocity, acceleration or other force in the
system when defining the force equation. Forces can also be defined as a
function of time to vary or switch on and off as the simulation progresses.
Caution is needed to ensure formulations are continuous in the time
domain to avoid problems during the numerical solution of the resulting
equations. Recent versions of the software also include a general contact
force model between geometries associated with the rigid bodies.
Enforced displacement input can be defined at certain joints to be either
constant or time dependent. When a motion is defined at a joint it may be
translational or rotational. The motion effectively provides another constraint
so that the degree of freedom at that joint is lost to the motion. Motion
expressions can be defined using all the functions available as for force definitions
except that the only system variable that can be accessed is time.
A multibody systems analysis program will often provide a number of
elements with the capability to model flexibility of bodies and elastic connections
between parts. These may include features for modelling beam
elements, rubber bushings or mounts, plus a general stiffness and damping
field element. At various positions in a model rigid parts can be elastically
connected together in preference to using a rigid constraint element such as
a joint or joint primitive. Vehicle suspension bushes can be represented by
a set of six action–reaction forces, which will hold the two parts together.
The equations of force are linear and uncoupled. The user is only required
to provide the six diagonal coefficients of stiffness and damping. For more
complicated cases a general-purpose statement can be used to provide a
linear or non-linear representation of a flexible body or connection.
Using recent advances in software techniques to allow the combination of
component mode synthesis representations for the stiff, small amplitude,
linear dynamic behaviour of structural elements, one or more of the major