4569846498

104 Mutibody Systems Approach to Vehicle Dynamics
I
I
I
DM (I, J)
L
DM (I, J)
J
J
J
Fig. 3.26
COMPRESSION
Positive force
AT FREE LENGTH
Zero force
Spring in compression, at free length and in tension
TENSION
Negative force
F S
DM (I, J)
L
F S k(L DM (I, J))
Compression
Tension
Fig. 3.27
Formulation of a linear spring force
This should not be confused with the components of any reaction force recovered
at the I or the J marker. The sign of these will be dependent not only on
the state of the spring but also on the orientation of the spring force line of
action and the reference frame in which the components are being resolved.
The formulation of the spring force F S is shown graphically in Figure 3.27.
Note that the formulation used here produces a force that is positive in compression
and negative in tension. This is opposite to the convention used for
stresses in stress analysis and finite element programs. An example of the syntax
that could be used to formulate this using a SFORCE statement, would be
SFORCE/0509,I0205,J0409,TRANS,FUNCTION
40*(250-DM(0205,0409))
where using the units that are consistent throughout this text we would have:
FUNCTION the spring force F S (N)
The spring stiffness k 40 N/mm
The free length L 250 mm
DM(0205,0409) the magnitude of the displacement between I and J
(mm)