ABAQUS中定义弹簧单元

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.