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Static Structural Analysis
Chapter Four
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Training Manual
Linear Static Structural Analysis
Chapter Overview
In this chapter, performing linear static structural analysesin Simulation will be covered:
Geometry and Elements
Contact and ypes of Supported Assemblies
Environment, including !oads and Supports
Solving "odels
#esults and $ostprocessing
he capabilities described in this section are generally
applicable toANSYS DesignSpace Entralicenses and above% Some options discussed in this chapter may re&uire more
advanced licenses, but these are noted accordingly%
Free vibration, harmonic, and nonlinear structural analyses are
not discussed here but in their respective chapters%
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Basics of Linear Static Analysis
For a linear static structural analysis, the displacements '() are
solved for in the matri( e&uation below:
his results in certain assumptions related to the analysis:
*+ is essentially constant !inear elastic material behavior is assumed
Small deflection theory is used
Some nonlinear boundary conditions may be included
'F) is statically applied
-o time.varying forces are considered
-o inertial effects /mass, damping0 are included
It is important to remember these assumptions related to linear
staticanalysis% Nonlinear staticand dynamicanalyses are
covered in later chapters%
[ ]{ } { }FxK =
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A !eometry
In structural analyses, all types of bodies supported bySimulation may be used%
For surface "odies, thic1ness must be
supplied in the 23etails4 view of the2Geometry4 branch%
he cross.section and orientation of line "odiesare defined
within 3esign"odeler and are imported into Simulationautomatically%
For line bodies, only displacement results are available%
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# $oint %ass
A $oint "ass is available under the Geometry branch tomimic weight not e(plicitly modeled
A point mass is associated with surface/s0 only
he location can be defined by either:
/(, y, 60 coordinates in any user.defined Coordinate System
Selecting vertices5edges5surfaces to define location he weight5mass is supplied under 2"agnitude4
In a structural static analysis, the point mass is affected by
2Acceleration,4 2Standard Earth Gravity,4 and 2#otational
7elocity4% -o other loads affect a point mass%
he mass is 8connected9 to selected surfacesassuming no stiffnessbetween them% his is
nota rigid®ionassumption but similar to a
distri"uted massassumption%
-o rotational inertial terms are present%ANSYS License Availability
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# $oint %ass
A point mass will be displayed as a round, grey sphere As noted previously, only inertial loads affect the point mass%
his means that the only reason to use a point mass in a linear
static analysis is to account for additional weight of a
structure not modeled% Inertial loads must be present%
-o results are obtained for the $oint "ass itself%
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# %aterial $roperties
he re&uired structural material properties are Young's%odulusand $oisson's (atiofor linear static structural
analyses
"aterial input is under the 2Engineering 3ata4 branch, and
material assignment is per part under the 2Geometry4 branch
%ass densityis re&uired if any inertial loads are present )hermal e*pansion coefficientand thermal conductivityare
re&uired if any thermal loads are present
hermal loading not available with anANSYS Structurallicense
-egative thermal e(pansion coefficient may be input /shrin1age0
Stress Limitsare needed if a Stress ool result is present +atigue $ropertiesare needed if Fatigue ool result is present
#e&uires +atigue %oduleadd.on license
Specific loading and result tools will be discussed later
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B Assem"lies , Solid Body Contact
hen importing assemblies of solid parts, contact regionsare automatically created between the solid bodies%
Surface.to.surface contact allows non.matching meshes at
boundaries between solid parts
olerance controls under 2Contact4 branch allows the user to
specify distance of auto contact detection via slider bar
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# Assem"lies , Solid Body Contact
In Simulation, the concept of contact and targetsurfacesare used for each contact region%
;ne side of the contact region is comprised of 2contact4
face/s0, the other side of the region is made of 2target4 face/s0%
he integration points of the contact surfaces are restricted
from penetrating through the target surfaces /within a given
tolerance0% he opposite is not true, however%
hen one side is the contact and the other side is the target, this is
called asymmetric contact% ;n the other hand, if both sides are
made to be contact < target, this is called symmetric contactsince
neither side can penetrate the other%
=y default, Simulation uses symmetriccontactfor solid assemblies%
ForANSYS $rofessional licenses and
above, the user may change to
asymmetric contact, as desired%
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# Assem"lies , Solid Body Contact
Four contact types are available:
Bondedand No Separationcontact are basically
linear behavior and re&uire only > iteration
+rictionlessand (oughcontact are nonlinear
and re&uire multiple iterations% -owever. note
that small deflection theory is still assumed
hen using these options, an interface treatment
option is available, set either as 2Actual Geometry/and Specified ;ffset04 or 2Ad?usted to ouch%4
he latter allows the user to have A-S@S close the
gap to 8?ust touching9 position% his is available
forANSYS $rofessionaland above%
Contact Type Iterations Normal Behavior (Separation Tan!ential Behavior (Sli"in!
=onded # Close" Close"
-o Separation # Close" $pen
Frictionless %<iple $pen $pen
#ough %<iple $pen Close"
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# Assem"lies , Solid Body Contact
For the advanced user, some of thecontact options can be modified
Formulation can be changed from 2$ure
$enalty4 to 2Augmented !agrange,4 2"$C,4 or
2-ormal !agrange%4
2"$C4 is applicable to bonded contact only
2Augmented !agrange4 is used in regular A-S@S
he pure $enalty method can be thought of as
adding very high stiffnessbetween interface of
parts, resulting in negligible relative movement
between parts at the contact interface%
"$C formulation writes constraint e/uations
relating movement of parts at interface, so norelative movement occurs% )his can "e an
attractive alternative to penalty method for
"onded contact
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# Assem"lies , Solid Body Contact
Advanced options /continued0: As e(plained in Chapter , the pinball
region can be input and visuali6ed
he pinball region defines location of near&
field open contact% ;utside of the pinball
region is far&field open contact%
;riginally, the pinball region was meant tomore efficiently process contact searching,
but this is also used for other purposes,
such as bonded contact
+or "onded or no separation contact. if gap
or penetration is smaller than pin"all region.
the gap0penetration is automaticallye*cluded
;ther advanced contact options will be
discussed in Chapter >>%In this case, the gap between
the two parts is bigger than the
pinball region, so no automatic
gap closure will be performed%
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# Assem"lies , Surface Body Contact
ForANSYS $rofessionallicenses and above, mi(edassemblies of shells and solids are supported
Allows for more comple( modeling of assemblies, ta1ing
advantage of the benefits of shells, when applicable
"ore contact options are e(posed to the user
Contact postprocessing is also available /discussed later0
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# Assem"lies , Surface Body Contact
Edge contact is a subset of general contact For contact including shell faces or solid
edges, only bonded or no separation
behavior is allowed%
For contact involving shell edges, only
bonded behavior using "$C formulation is
allowed%
For "$C.based bonded contact, user can set
the search direction /the way in which the multi.
point constraints are written0 as either
the target normalorpin"all region%
If a gap e(ists /as is often the case with
shell assemblies0, thepin"all regioncan be
used for the search direction to detect
contact beyond a gap%
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# Assem"lies , Contact Summary
A summary of contact types and options available inSimulation is presented in the table below:
his table is also in the Simulation online help% $lease refer to
this table to determine what options are available%
-ote that surface body faces can only participate in bonded or no
separation contact% Surface body edges allow "$C.based bonded
contact only%
Contact 'eometry Solid =ody Face Solid =ody Edge Surface =ody Face Surface =ody Edge
All ty pes Bon"e" No Separation Bon"e" No Separation Bon"e" only
All )orm&lations All )orm&lations All )orm&lations %*C )orm&lation
Symmetry res pecte" Asymmetric only Symmetry respec te" Asymmetric only
Bon"e" No Separation Bon"e" No Separation Bon"e" only
All )orm&lations All )orm&lations %*C )orm&lation
Asymmetric only Asymmetric only Asymmetric onlyBon"e" No Separation Bon"e" only
All )orm&lations %*C )orm&lation
Symmetry respecte" Asymmetric only
Bon"e" only
%*C )orm&lation
Asymmetric only
Solid =ody Face
Solid =ody Edge
Surface =ody Face
Surface =ody Edge
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# Assem"lies , Spot 1eld
Spot welds provide a means of connecting shell
assemblies at discrete points
ForANSYS DesignSpacelicenses, shell contact is not
supported, so spotwelds are the only way to define a shell
assembly%
Spotweld definition is done in the CA3 software% Currently,
only 3esign"odeler and Bnigraphics define spotwelds in a
manner that Simulation supports%
Spotwelds can also be created in
Simulation manually, but only at
discrete vertices%
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Solid:or1s
Inventor
Solid Edge
"echanical 3es1top
CAIA 7
CAIA 7D
ACIS /SA0$arasolid
IGES
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C Loads and Supports
here are four types of structural loads available:
Inertial loads
hese loads act on the entire system
3ensity is re&uired for mass calculations
hese are only loads which act on defined $oint "asses
Structural !oads hese are forces or moments acting on parts of the system
Structural Supports
hese are constraints that prevent movement on certain regions
hermal !oads
Structurally spea1ing, the thermal loads result in a temperaturefield, which causes thermal e(pansion on the model%
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)ime )ype
A time type option is available at certain license levels%
he default time type for loading is 2static4
2Se&uence4 and 2harmonic4 time types are available as
options /harmonic analysis is covered in the Advanced =
training0
Se&uence loading allows a series of static time steps to be
set up in advance and solved at once
Se&uenced results can be reviewed step by step
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)ime )ype
Specify the desired number of se&uence
steps in the details of the Environment%
Enter the value of the load for each step by
first highlighting the desired step in the
graphics window%
he chart in the graphics window displays thevariation of the load%
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)ime )ype
he wor1sheet view provides a
graphical representation of each
load9s se&uence%
#esults of a se&uenced simulation
can be reviewed by highlighting the
&uantity of interest and pic1ing the
desired se&uence from the graphics
window%
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# Acceleration 2 !ravity
An acceleration can be defined on the system
Acceleration acts on entire model in length5timeEunits%
Bsers sometimes have confusion over notation of direction% If
acceleration is applied to system suddenly, the inertia resists
the change in acceleration, so the inertial forces are in the
oppositedirection to applied acceleration
Acceleration can be defined by Components or 7ector
Standard Earth Gravity can also be applied as a load
7alue applied is %HD m5sE/in SI units0
Standard Earth Gravity direction can only be defined along
one of three orld Coordinate System a(es%
Since 2Standard Earth Gravity4 is defined as an acceleration,
define the direction as opposite to gravitational force, as noted
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# (otational 3elocity
#otational velocity is another inertial load available
Entire model spins about an a(is at a given rate
Can be defined as a vector, using geometry for a(is and
magnitude of rotational velocity
Can be defined by components, supplying origin and
components in orld Coordinate System -ote that location of a(is is very important since model spins
around that a(is%
3efault is to input rotational velocity in radians per second%
Can be changed in 2ools J Control $anel J "iscellaneous J
Angular 7elocity4 to revolutions per minute /#$"0 instead%
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# +orces and $ressures
$ressure loading:
$ressures can only be applied to surfaces and always act
normal to the surface
$ositive value acts into surface /i%e%, compressive0
negative value acts outward from surface /i%e%, suction0
Bnits of pressure are in force per area
Force loading:
Forces can be applied on vertices, edges, or surfaces%
he force will be distri"uted on all entities% his
means that if a force is applied to two identical
surfaces, each surface will have half of the forceapplied% Bnits are massKlength5timeE
A force is defined via vector and magnitude or by
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# Bearing Load
=earing !oad /was called 2=olt !oad4 in prior releases0:
=earing !oads are for cylindrical surfaces only% #adial
component will be distributed on compressive side using
pro?ected area% E(ample of radial distribution shown below%
A(ial component is distributed evenly on cylinder%
Bse only one bearing load per cylindrical surface% If the
cylindrical surface is split in two, however, be sure to selectboth halves of cylindrical surface when applying this load%
!oad is in units of force
=earing load can be defined
via vector and magnitude or
by components /in anyuser Coordinate System0%
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# %oment Load
"oment !oad:
For solid bodies, a moment can be applied on any
surface
If multiple surfaces are selected, the moment load
gets apportioned about those selected surfaces
A vector and magnitude or components /in user.definedCoordinate System0 can define the moment% he moment acts
about the vector using the right.hand rule
For surface bodies, a moment can also be applied to a verte(
or edge with similar definition via vector or components as
with a surface.based moment
Bnits of moment are in ForceKlength%
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# (emote Load
#emote !oad:
Allows the user to apply an offset force on a surface or edge
of a surface body
he user supplies the origin of the force /using vertices, a
cylinder, or typing in /(, y, 60 coordinates0% A user.defined
Coordinate System may be used to reference the location%
he force can then be defined by vector and magnitude or by
components /components for direction is in Global CS0
his results in an e&uivalent force on
the surface plus a moment caused by
the moment arm of the offset force
he force is distributed on the surface
but includes the effect of the moment
arm due to the offset of the force
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# Supports 4!eneral5
Fi(ed Support:
Constraints all degrees of freedom on verte(, edge, or surface
For solid bodies, prevents translations in (, y, and 6
For surface and line bodies, prevents translations and
rotations in (, y, and 6
Given 3isplacement:
Applies 1nown displacement on verte(, edge, or surface
Allows for imposed translational displacement in (, y, and 6 /in
user.defined Coordinate System0
Entering 2H4 means that the direction is constrained
!eaving the direction blan1 means that the entity is free to
move in that direction
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# Supports 4Solid Bodies5
Frictionless Support:
Applies constraint in normal direction on surfaces
For solid bodies, this support can be used to apply a
8symmetry9 plane boundary condition since 8symmetry9 plane
is same as normal constraint
Cylindrical Constraint: Applied on cylindrical surfaces
Bser can specify whether a(ial, radial, or tangential
components are constrained
Suitable for small.deflection /linear0 analysis only
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# Supports 4Solid Bodies5
Compression ;nly Support:
Applies a compression.only constraint normal to any given
surface% )his prevents the surface to move in the positive
normal direction only%
A way to thin1 of this support is to imagine a 8rigid9 structure
which has the same shape of the selected surface% Note that
the contacting 4compressive5 areas are not 6nown "eforehand
Can be used on a cylindrical surface to model a
/referred to as 2$inned Cylinder4 L%>0
-otice the e(ample on the right,
where the outline of the undeformed cylinder
is shown% he compressive side retains the shapeof the original cylinder, but the tensile side is free to deform%
)his re/uires an iterative 4nonlinear5 solution
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# Supports 4Line0Surface Bodies5
Simply Supported:
Can be applied on edge or verte( of surface or line bodies
$revents all translations but all rotations are free
Fi(ed #otation:
Can be applied on surface, edge, or verte( of surface or line
bodies
Constrains rotations but translations are free
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# Summary of Supports
Supportsand Contact(egionsmay both be thought of as being
"oundary conditions%
Contact (egionsprovides a 8fle(ible9 boundary condition between
two e(isting parts e(plicitly modeled
Supportsprovide a 8rigid9 boundary condition between the modeled
part an a rigid, immovable part not e(plicitly modeled
If $art A, which is of interest, is connected to $art =, consider
whether both parts need to be analy6ed /with contact0 or
whether supports will suffice in providing the effect $art = hason $art A%
In other words, is $art = 8rigid9 compared to $art AM If so, a support
can be used and only $art A modeled% If not, one may need to
model both $arts A and = with contact%
Type o) S&pport +0&ivalent Contact Con"ition at S&r)aces o) *art
Fi(ed Support Bonded contact1ith a ri!i"( immovable part
Frictionless Support No Separation contact1ith a ri!i"( immovable part
Compression ;nly Support Frictionless contact1ith a ri!i"( immovable part
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# )hermal Loading
emperature causes thermal e(pansion in the model
hermal strains are calculated as follows:
where is the thermal e(pansion coefficient /CE0, )refis the
reference temperature at which thermal strains are 6ero, )is
the applied temperature, and this the thermal strain% hermal strains do not cause stress by themselves% It is the
constraint, temperature gradient, or CE mismatch that
produce stress%
CE is defined in 2Engineering 3ata4
and has units of strain per temperature he reference temperature is defined in the
2Environment4 branch
( )refz
th
y
th
x
th TT===
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# )hermal Loading
hermal loads can be applied on the model
Any temperature loading can be applied /see Chapter on
hermal Analysis for details0
Simulation will always perform a thermal solution first, then
use the calculated temperature field as input when solving the
structural solution%
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or1shop %> N !inear Structural Analysis
Goal:
A D part assembly representing an impeller type pump is
analy6ed with a >HH- preload on the belt%
D 1or6shop 78
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E Solution Options
Solution options can be set under the 2Solution4 branch
he A-S@S database can be saved if 2Save
A-S@S db4 is set
Bseful if you want to open a database in A-S@S
wo solvers are available in Simulation
he solver is automatically chosen, although some
informative messages may appear after solution
letting the user 1now what solver was used% Set
default behavior under 2ools J ;ptions O J
Simulation: Solution J Solver ype4
he 23irect4 solver is useful for models containing
thin surface and line bodies% It is a robust solver
and handles any situation%
he 2Iterative4 solver is most efficient when solving
large, bul1y solid bodies% It can handle large models
well, although it is less efficient for beam5shells%
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# Solution Options
ea1 springs can be added to stabili6e model
If 2$rogram Controlled4 is set, Simulation tries to
anticipate under.constrained models% If no
2Fi(ed Support4 is present, it may add wea1 springs
and provide an informative message letting the user
1now that it has done so
his can be set to 2;n4 or 2;ff4% o set the default
behavior, go to 2ools J ;ptions O J Simulation:Solution J Bse ea1 Springs4%
In some cases, the user e(pects the model to be in
e&uilibrium and does not want to constrain all
possible rigid.body modes% ea1 springs will help
by preventing matri( singularity%
It is good practice to constrain all possible rigid.body
motion, however%
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# Solution Options
Informative messages are also present:
he type of analysis is shown, such as 2Static
Structural4 for the cases described in this section%
If a nonlinear solution is re&uired, it will be indicated
as such% #ecall that for some contact behavior and
compression.only support, the solution becomes
nonlinear% hese type of solutions re&uire multiple
iterations and ta1e longer than linear solutions%
he solver wor1ing directory is where scratch files are
saved during the solution of the matri( e&uation% =y
default, the E"$ directory of your indows system
environment variable is used, although this can be
changed in 2ools J ;ptions O J Simulation: Solution
J Solver or1ing 3irectory4% Sufficient free spacemust be on that partition%
Any solver messages which appear after solution can
be chec1ed afterwards under 2Solver "essages4
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+ (esults and $ostprocessing
7arious results are available for postprocessing:
3irectional and total deformation
Components, principal, or invariants of stresses and strains
Contact output
#e&uires A-S@S $rofessional and above
#eaction forces
In Simulation, results are usually re&uested "eforesolving,
but they can be re&uested afterwards, too%
If you solve a model then re&uest results afterwards, clic1 onthe 2Solve4 button , and the results will be retrieved% A
new solution is not re&uired if that type of result has "een
re/uested previously/i%e%, total deformation was re&uested
previously but now direction deformation is added0%
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# $lotting (esults
All of the contour and vector plots are usually shown on
the deformed geometry% Bse the Conte(t oolbar to change
the scaling or display of results to desired settings%
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# Deformation
he deformation of the model can be plotted:
otal deformation is a scalar &uantity:
he (, y, and 6 components of deformation can be
re&uested under 23irectional%4 =ecause there is
direction associated with the components, if a
2Coordinate System4 branch is present, users can
re&uest deformation in a given coordinate system%
For e(ample, it may be easier to interpret displacement for a
cylindrical geometry in a 8radial9 direction by using a cylindrical
coordinate system to display the result% 7ector plots of deformation are available%
#ecall that wireframe mode is the easiest
to view vector plots%
222
zyxtotal UUUU ++=
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# Deformation
3eformation results are available for line, surface, and solid
bodies
-ote that 2deformation results4 are associated with
translational 3;F only% #otations associated with the 3;F of
line and surface bodies are not directly viewable
=ecause deformation /displacements0 are 3;F which
Simulation solves for, the convergence behavior is well.behaved when using the Convergence tool
7ector deformation plots cannot use2Alert4 or 2Convergence4
tools because they are vector &uantities /(, y, 60 rather than a
uni&ue &uantity /( or y or 60% Bse Alert or Convergence tools
on 2otal4 or 23irectional4 &uantities instead% 2otal4 deformation is an invariant, so 2Coordinate Systems4
cannot be used on this result &uantity% Also, 27ector4
deformation is always shown in the world coordinate system%
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# Stresses and Strains
Stresses and strains can be viewed:
2Strains4 are actually elasticstrains
Stresses and /elastic0 strains are
tensors and have si( components
/(, y, 6, (y, y6, (60 while thermal
strains can be considered a vector
with three components /(, y, 60
For stresses and strains, components can be
re&uested under 2-ormal4 /(, y, 60 and 2Shear4
/(y, y6, (60% For thermal strains, /(, y, 60 components are under
2hermal%4
Can re&uest in different results coordinate systems hermal strains not available with an A-S@S Structural license
;nly available for shell and solid bodies% !ine bodies currently do
not report any results e(cept for deformation%
2E&uivalent $lastic4 strain output is covered in Chapter >>ANSYS License Availability
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# Stress )ools
Safety Factors can be calculated
based on any of failure theories:
3uctile heories:
"a(imum E&uivalent Stress
"a(imum Shear Stress
=rittle heories: "ohr.Coulomb Stress
"a(imum ensile Stress
ithin each stress tool safety factor,
safety margin and stress ratio can be
plotted
-ote: see appendi( and the
Simulation documentation for more
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# Contact (esults
Contact #esults:
Contact results can be re&uested for selected
bodies or surfaces which have contact elements%
Contact elements in A-S@S use the concept of
contact and target surfaces% Only contact surfaces
report contact results "$C.based contact, the
target surfaces of any contact, and edge.based contact do notreport results% !ine bodies do not support contact%
If asymmetric or auto.asymmetric contact is used, then contact
results will be reported on the 8contact9 surfaces only% he 8target9
surfaces will report 6ero values, if re&uested%
If symmetric contact is used, then contact results will be reported
on both surfaces% For values such as contact pressure, the actual
contact pressure will be an average of both surfaces in contact%
Contact results are first re&uested via a 2Contact ool4 under
the Solution branch%ANSYS License Availability
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# Contact (esults
he user can specify contact output under 2Contact ool4
he or1sheet view easily allows users to select which
contact regions will be associated with the 2Contact ool4
#esults on 8contact9 or 8target9 sides /or both0 can be selected
from the spreadsheet /symmetric vs% asymmetric contact0
Specific contact results chosen from Conte(t oolbar
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Select contact regions you want to
review /add more 2Contact ool4
branches to loo1 at contact region
output separately0%
#ight.clic1 on the wor1sheet to seeother available options%
For the 2Contact ool4, then
re&uest contact output results, and
those results will correspond to
selected contact regions%
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# Contact (esults
ypes of Contact #esults available:
Contact $ressureshows distribution of normal contact
pressure
Contact $enetrationshows the resulting amount of
penetration whereas contact !apshows any gap
/within pinball radius0%
Sliding Distanceis the amount one surface has slid with
respect to the other% +rictional Stressis tangential contact
traction due to frictional effects%
Contact Statusprovides information on
whether the contact is established /closed
state0 or not touching /open state0% For the open state, near.field means that it is
within pinball region, far.field means that it is
outside of pinball region%
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Contour results are plotted with the
rest of the model being translucent
for easier viewing%
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# Contact +orces
If 2#eactions4 are re&uested for 2Contact ool4, forces and
moments are reported for the re&uested contact regions
Bnder the 2or1sheet4 tab, contact forces for all re&uested
contact regions will be tabulated
Bnder the 2Geometry4 tab, symbols will show direction of
contact forces and moments%
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# (eaction +orces at Supports
#eaction forces and moments are output for each support
For each support, loo1 under the 23etails4 view
after solution% #eaction forces and moments are
printed% P, y, and 6 components are with respect
to the world coordinate system% "oments are
reported at the centroid of the support%
he reaction force for wea1 springs, if used, isunder the 2Environment4 branch 3etails view
after solution% he wea1 spring reaction forces
should be small to ensure that the effect of wea1
springs is negligible%
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# (eaction +orces at Supports
he 2or1sheet4 tab for 2Environment4 branch has a
summary of reaction forces and moments
If a support shares a verte(, edge, or surface with another
support, contact pair, or load, the reported reaction forces may
be incorrect% his is due to the fact that the underlying mesh
will have multiple supports and5or loads applied to the same
nodes% he solution will still be valid, but the reported valuesmay not be accurate because of this%
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# +atigue
If the Fatigue "odule add.on license is available, additional
post.processing involving fatigue calculations is possible
he 2Fatigue ool4 provides stress.based fatigue calculations
to aid the design engineer with evaluating the life of
components in the system
Constant or variable amplitude loading, proportional or non.
proportional loading is possible
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3amage "atri( at Critical !ocation Contour of Safety Factor
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! 1or6shop 79 , 9D vs :D Analysis
or1shop % N Comparing 3 and 3 Structural Analysis
Comparing 3 and 3 structural analyses%
Shown here are the 3 sector model and the 3 a(isymmetric model%
$ressure Cap
#etaining #ing
http://workshops/AWS90_Workshop_04-2.ppthttp://workshops/AWS90_Workshop_04-2.ppt
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