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ABAQUS
中定义弹簧单元
2011-12-16 17:57
Abaqus
Analysis User's Manual
29.1.1
Springs
Products: Abaqus/Standard
Abaqus/Explicit
Abaqus/CAE
References
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Overview
Spring elements:
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can couple a force with a relative
displacement;
in
Abaqus/Standard
can
couple
a
moment
with
a
relative
rotation;
can be linear or
nonlinear;
if linear, can be dependent
on frequency in direct-solution
steady-
state dynamic analysis;
can be
dependent on temperature and field variables; and
can be used to assign a structural
damping factor to form the
imaginary
part of spring stiffness.
The terms
“force” and “displacement” are used throughout the
description of spring elements. When
the spring is associated with
displacement degrees of freedom, these
variables are the force and
relative
displacement
in
the spring.
If the springs
are
associated with
rotational degrees of
freedom, they are torsional springs; these
variables will then be the moment
transmitted by the spring and the
relative rotation across the spring.
Viscoelastic spring behavior can be
modeled in Abaqus/Standard
by
combining
frequency-
dependent
springs
and
frequency-dependent
dashpots.
Typical
applications
Spring elements are used
to model actual physical springs as well as
idealizations of axial or torsional
components. They can also model
restraints to prevent rigid body
motion.
They are also used to represent
structural dampers by specifying
structural damping factors to form the
imaginary part of the spring
stiffness.
Choosing an appropriate element
SPRING1 and SPRING2 elements are
available only in Abaqus/Standard.
SPRING1
is
between
a
node
and
ground,
acting
in
a
fixed
direction.
SPRING2
is between two
nodes, acting in a fixed direction.
The
SPRINGA element is available in both
Abaqus/Standard and
Abaqus/Explicit.
SPRINGA
acts
between
two
nodes,
with
its
line
of
action
being the line joining the two nodes,
so that this line of action can
rotate
in large-displacement analysis.
The
spring behavior can be linear or nonlinear in any
of the spring
elements in Abaqus.
Element types SPRING1 and SPRING2 can
be associated with displacement
or
rotational degrees of freedom (in the latter case,
as torsional
springs). However, the use
of torsional springs in large-displacement
analysis requires careful consideration
of the definition of total
rotation
at
a
node;
therefore,
connector
elements
()
are
usually
a
better
approach to providing torsional springs
for large-displacement cases.
Input
File
Usage:
U
se the
following option to
specify
a
spring
element
between
a node and ground,
acting in a
fixed direction:
, TYPE=SPRING1
Use the
following option to
specify
a
spring
element
between
two nodes, acting in
a fixed
direction:
,
TYPE=SPRING2
Use the
following option to
specify
a
spring
element
between
two
nodes
with
its
line
of
action
being
the line joining the two
nodes:
, TYPE=SPRINGA
Abaqus/CAE
Usage:
P
roperty or Interaction module:
< br>SpecialSprings/DashpotsCreate
,
then
select
one
of the following:
Connect
points
to
ground
:
select
points:
toggle
on
Spring stiffness
(
equivalent to
SPRING1
)
Connect two
points
: select points:
Axis
:
Specify
fixed direction
: toggle on
Spring
stiffness
(
equivalent to
SPRING2
)
Connect
two
points
:
select
points:
Axis
:
Follow
line of action
: toggle on
Spring stiffness
(
equivalent to
SPRINGA
)
Stability considerations in
Abaqus/Explicit
A SPRINGA element
introduces a
stiffness
between two degrees of freedom
without
introducing
an
associated
mass.
In
an
explicit
dynamic
procedure
this
represents an
unconditionally
unstable
element.
The nodes
to
which
the spring is attached
must have some mass contribution from adjacent
elements;
if
this
condition
is
not
satisfied,
Abaqus/Explicit
will
issue
an
error
message.
If
the
spring
is
not
too
stiff
(relative
to
the
stiffness
of the adjacent
elements), the stable time increment determined by
the
explicit dynamics procedure () will
suffice to ensure stability of the
calculations.
Abaqus/Explicit does not use the
springs in the determination of the
stable time increment. During the data
check phase of the analysis,
Abaqus/Explicit computes the minimum of
the stable time increment for
all
the
elements
in
the
mesh
except
the
spring
elements.
The
program
then
uses
this
minimum
stable
time
increment
and
the
stiffness
of
each
of
the
springs to
determine the mass required for each spring to
give the same
stable time increment. If
this mass is too large compared to the mass
of
the
model,
Abaqus/Explicit
will
issue
an
error
message
that
the
spring
is too stiff compared
to the model definition.
Relative
displacement definition
The relative
displacement definition depends on the element
type.
SPRING1 elements
The
relative displacement across a
SPRING1
element is the
i
th component
of displacement of the spring's node:
where
i
is
defined as described below and can be in a local
direction
(see ”).
SPRING2 elements
The
relative displacement across a SPRING2 element is
the difference
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:
where
i
and
j
are
defined
as
described
below
and
can
be
in
local
directions
(see ”).
It is important to
understand how the SPRING2 element will behave
according
to the
above
relative displacement
equation since
the
element
can
produce
counterintuitive
results.
For
example,
a
SPRING2
element
set
up in the following way
will be a “compressive” spring:
If the nodes displace so that and , the
spring appears to be in
compression,
while
the
force
in
the
SPRING2
element
is
positive.
To
obtain
a “tensile” spring,
the SPRING2 el
ement should be set up in
the
following way:
SPRINGA
elements
For
geometrically
linear
analysis
the
relative
displacement
is
measured
along the direction
of the SPRINGA element in the reference
configuration:
where is the
reference position of the first node of the spring
and is
the reference position of its
second node.