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between the
i
th component of displacement of the spring's first node and the
j
th component of displacement of the spring's second node, with
i
and
j
defined as shown in
Figure 5.9
. For a SPRINGA element, the relative dis-
placement in a geometrically linear analysis is measured along the direction
of the SPRINGA element. While in geometrically nonlinear analysis, the
relative displacement across a SPRINGA element is the change in length
in the spring between the initial and the current configuration.
The spring behavior can be linear or nonlinear. In either case, modelers
must associate the spring behavior with a region of their model. Modelers
can define linear spring behavior by specifying a constant spring stiffness
(force per relative displacement). The spring stiffness can depend on temper-
ature and field variables. For direct-solution steady-state dynamic analysis,
the spring stiffness can depend on frequency, as well as on temperature
and field variables. On the other hand, modelers can define nonlinear spring
behavior by giving pairs of force-relative displacement values. These values
should be given in ascending order of relative displacement and should be
provided over a sufficiently wide range of relative displacement values so
that the behavior is defined correctly. ABAQUS [1.29] assumes that the
force remains constant (which results in zero stiffness) outside the range
given; see
Figure 5.10
. Initial forces in nonlinear springs should be defined
by giving a nonzero force at zero relative displacement. The spring stiffness
can depend on temperature and field variables. Modelers can define the
direction of action for SPRING1 and SPRING2 elements by giving the
Force,
F
Continuation assumed
if
u
>
u
4
F
4
F
3
F
2
F
(0)
u
1
u
2
u
3
u
4
Displacement,
u
F
1
Continuation assumed
if
u
<
u
1
Figure 5.10 Nonlinear spring force-relative displacement relationship according to
ABAQUS [1.29].
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