ANSYS Workbench Tutorial Release 14

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Placed Features, Assembly

2-1

Chapter 2 Placed Features, Assembly

2-1

OVERVIEW

In this chapter we illustrate DesignModeler creation of features whose shape predetermined. Among these are

IS

+ Holes + Rounds + Chamfers + Patterns In addition to these topics, at the end of the chapter we illustrate simple assembly modeling in ANSYS DesignModeler.

2-2

INTRODUCTION

Feature-based solid modeling involves the creation of part models by combining various features. The features illustrated in Chapter I are sometimes called sketched features because they were based upon sketched cross sections we created. Sketched features can have virtually any shape we desire. The basic parts of Chapter I can also be called base features since we started from scratch each time and created a new part. We can add features to base features to create more complex parts. If these added features have predetermined shapes they are often called placed features because all we need to do is specify the size and location or placement of the new feature on an existing base feature.

�"'-----------Placed Features, Assembly

2-2

rusion created earlier with a hole, a round and The figure below shows the L-shaped Ext . which features can be added to a a chamfer added to it. This demonstrates the m:nn~ 10 ful parts with the shapes desired base feature in order to create more complicate an use for specific tasks. . The tutorials that follow illustrate how to add these placed features to the basic parts created in Chapter 1.

Figure 2-1 Extrusion with placed features.

2-3

TUTORIAL

2A - ADDING A HOLE TO THE EXTRUSION

Follow the steps below to cut a hole in the top face of the short leg of the Chapter extrusion.

1

Start ANSYS Workbench and reload the L-section Extrusion 1.

ANSYS > Workbench> the fi Ie name you chose)

DesignModeler Geometry> Browse>

TutoriallA

(or

Now save this file under a new name for this tutorial. 2.

File> Save As > Tutorial2A (or another name you select)

We want to create the h~le on the top surface of the short leg of the extrusion. We will create a new plane on which to place the circle that generates the hole.

3.

Selection Filter: Model Faces (3D)

4.

Click on the top surface of the short leg.

~

Placed Features, Assembly

LFte

_.(re¥e

Coo::ep:

Tools

VIew

2-3

Help

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>;y~

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• 1"

Sketch!

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Treao.ilne

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"""' ....

'0PDirt

'Chvrter

~P/l'~

/

•,

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Figure 2-2 Surface selected. 5.

Create> New Plane (from the top menu)

A new plane is added to the tree structure (Plane4 in this illustration; your plane number may be different) and an axis system is provided. $A

Geometry

Desl~nModeler

.. ~

""'l1li""""" d f$l



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Figure 2-3 New plane is created.

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*"

" ..... ~_ ..

Placed Features,

2-4

Assembly

J ~~/ Generate

6.

Click Generate

7.

Select Plane4 > Then click on the Look at icon to view the Plane4

~7"rude &!eR''''''''

"Sweep ~ Skh/lolt

tf

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i

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............ +-----

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Figure 2-4 'Look at' new plane. We want to place a 10 mm diameter circular hole half way along the length of the 100 mm leg and 8 mm from the edge. 8.

Sketching>

Circle Draw a circle on the top face as shown in the figure below.

r-="""~T:::-='::. ..:.-

_..:,q.

Gr~s

"'ow ModIfy

~"""~~~~~~-~~'-' '", .... ep

ave your part u ing a new name. I.



~SOns\.oft

DTmJ"'f"'.

\l>BIend·

File> Save As > Tutorial2B

Set the selection filter.

[@

2.

election Filter: Edges

J.

elect the inside edge ofthe part.

Figure 2-8 Select the edge. 4.

Create>

Fixed Radius Blend

~

Placed Features, Assembly

1

File

Create

Concept

Tools

2-7

View Help

*- New Plane

~ tJ· lID

Tree

~

@

rm rm ,g.

:) Generate

Extrude Revolve

:r;

+

liaExtrude

@. $. @. ~ ~Revolve

Graphics

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B

~

SWn/Loft

I!II Thin/Surface ~ ..

FIxed Radius Blend Variable Radius Blend

::::: Vertex Blend

~

Chamfer

~

Pattern

Skate ~

I DetalS.



Body Operation

'" '"

Boolean Slice

~

Face Delete

!!Ii Edge Delete ~

Point

"

..

",

,

"

"

"

"

"

"

"

...."

New Plane Create a new plane for sketching on the top or bottom surface of the base disk

4.

Sketch an 8mm diameter circle on this plane. Dimension as shown in the next figure.

5.

Sketch an 18 mm line from the center of the base feature to the center of the small circle. Dimension as shown below. We'll use this line for angular reference.

6.

Locate the line with an angular dimension. Click first on the horizontal axis, then on the line. Drag to place the dimension as shown.

7.

Switch to Modeling. Select the sketch and then Extrude> Through All to create a hole.

Cut Material>

Placed Features, Assembly 2-10

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Figure 2-14 Placement of small hole.

8.

Add a 1 mm chamfer to the top edge of the 8 mm hole. See figure next page.

9.

Sketch a short line along the Z axis in the ZXPlane: Sketch3. We will use this for the pattern angular direction reference later. Tree Outline 8

GraphIcs

.tI~1 A: Geometry I±J ..

.

;:f.. XYPlane

8 ..;:f.. ZXPlane ..61 Sketch3 .. ;:f.. YZPlane Extrude!

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8 ..;:f.. PlaneS

..61 Sketch2 [+

.. ~

Extrude2

l

..

1 Part, ! Body

Sketching

Modeling

.................... ..-_-L-.....; __

I

Figure 2·15 Create a line along the Z axis.

Placed Features, Assembly

2-11

@

10.

Click Selection Filter: Model Faces (3D)

11.

Select the inside surface of the hole; then Ctrl > Select the surface of the chamfer so both items will be in the pattern.

Figure 2-16 Select the chamfer and hole.

12.

Create> Pattern

13.

Geometry> Apply (in details of Pattern I.)

14.

Pattern Type> Circular

15.

Selection Filter: Edges

16.

Axis> Click on Sketch3 and select the short Z axis line> Apply

17.

Angle> Evenly Spaced

18.

Number of Copies> 6 (Creates 7 instances total.)

Placed Features,

2-12

EI "y~

Assembly

Tutorial2E

rtJ·,,*," XYPlane B,,*," 2xPIane

Cl

L......

Sketch3

,,*," Y2Plane $ "-f

1tI,,*,"

Extrude 1 PlaneS

~ .."{~

Extrude2

i·······.j

Chamfer 1

L.. ....Y"~

Pattern1

00.... Sketching

1 Part, ! Body Modeling

I

EI Details of Pattern! Pattern

Patternl

Pattern Type

Circular

Geometry

2 Faces Not selected

FD2, Angle

Evenly Spaced

FD3, Copies (>0) 1

Figure 2-17 Pattern parameters. J ') Generate

19. Click Generate.

The resulting hole pattern is shown next. The selected edge is used as the axis for determining the positive direction of incrementing the angular placement (taken according to the right-hand rule). !I-

Tree Out~ne B.t

*' .,61 *' .,61 .,*' .,lii!. .,61 *' .,61

A: Geometry

H .,

XYPlane Sketch!

-'1 .,

ZXPlane Sketch3

-:J

t-J ., -1.,

Y2P1ane Extrudel Sketch1 PlaneS Sketch2 Extrude2 Sketch2

.,61 .,' .,~ .t

Chamfer1 Pattern! 1 Part, 1 Body

.,

S"id

Sketching MOdeling

I

Figure 2-18 Circular pattern of chamfered h I o es.

--

----=.-- .

2-13

Placed Features, Assembly

Once again don't be surprised if the suffix numbers of the entities (Sketch, Extrude, etc) in your tree structures differ from those in the figures. Same with the lighting bolts indicating need for generation. Some experimentation with generation, views, etc. was conducted to obtain the figures presented here. If you have a problem, delete the problem object in the tree and start again. (The positive direction for incrementing the angular placement is along the selected edge according to the right-hand rule. Change Evenly Spaced to 35 degrees> 6 Copies and see what solid is produced.) Linear patterns are created using similar steps. The direction of the pattern can be along an existing edge or perpendicular to a surface.

2-7

TUTORIAL 2E - CLEVIS ASSEMBLY

The next figure shows an assembly model of the clevis device that is the subject of this final tutorial in this chapter.

Figure 2-19 Clevis assembly.

1.

Start DesignModeler, Select Inches Units, and start sketching on the XYPlane

The yoke is 4.5 inches in overall length, 2.5 inches at its widest point, and the opening is 2.0 inches in width. Use the sketching tools to create the figure shown next with dimensions as indicated. Arc by Tangent, Modify> Trim, and other tools will come in handy. If you make a mistake, just delete the item in question and redraw, or just start over.

Placed Features, Assembly

2-14

0.125

0.125 RO.500

RO.500

···:t ······························t 0.250

.11....,..~~~~4

---.-1 0.250

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n.soo

···················:.1····

_

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r

0.250

1----2.625 ----!'"t"--1.875

---:

Figure 2-20 Clevis sketch.

2.

Create the sketch shown above and extrude it symmetrically 0.5 inch. (Total

height will be 1.0 inch, 0.5 above the sketch plane, 0.5 inch below.) 3.

Create a new sketching plane on one of the yoke fingers and sketch the opening

shown. The two semicircles are separated by 0.25 inch. Tangent line and trim will be useful.

DO.SOO

c

r

0.500

1---0,500

-J

Figure 2-21 Slot sketch. 4.

Extrude this sketch through all, removing material.

We obtain the solid model shown next.

L.

2-15

Placed Features, Assembly

Figure 2-22 Complete clevis.

To this we want to add the stem and pin to complete the assembly. First hide the clevis. 5.

1 Parts, 1 Body> Solid> Right Click> Hide Body

6.

We'll create the stem first. View the XZ sketch plane and sketch the rectangle and circle below for creation of the brick-shaped stem extrusion. Use General for the linear dimension definitions.

t

06

,.

L7

L2

...................... ~- ...................................... \



..

I

vst----! ho------IIS---·

z

Figure 2-23 Stem sketch.

Refer to Figure 2-20 and give the L2 and V5 placements dimensions the values shown below.

Placed Features,

2-16

Assembly

8 Details of 5ketch3 Sketch

sketch3

show Constraints?

a Dimensions:

No

6

C06

0,5in

DL2

0,675 in

OL4

0,5in

OL7

0,5in

DV5

1.5 in

------; 4 in

Figure 2-24 Stem sketch dimensions.

7.

Switch to Modeling, Select the sketch of the Rectangle Extrude.

with Circle,

8.

Details of Extrude> Operation> and Depth> 1.0 (See below.)

Both _ Symmetric,

Add Frozen, Direction>

Click

The Add Frozen option adds the stem as a new, separate object and does not merge the new geometry into the existing clevis. The two parts remain separate.

J :)

9.

Generate

10.

2 Parts, 2 Bodies> Solid (Clevis) > Right Click> Show Body

Generale

Details ofEKtrudelO Extrude BaseObject

°

Extrude1 Sketch3

Operation

AddFrozen

DirectionVector

None(Normal)

Direction

Both· Symmetric

Type

Fixed

i

FDl, Depth(>0) 1 in

As ThlnfSurfece? MergeTopology?

No Ves----I

Figure 2-25 Stem extrusion and clevis.

Lastly we need to create the fastening pin that holds th bl plane to sketch on. e assem Ytogether. Create a new

2-17

Placed Features, Assembly 11.

Click XL Plane > Click the new plane icon Generate ] :)

*" on the third

line of icons >

Generate

~ A: Geometry - DesignModeler File Create

Concept

Tools

View

I

\ XVPlane Tree Outline

Figure 2-26 New plane icon. 12.

Right click on graphics screen> View> Bottom to get the view shown below.

z ......................

Figure 2-27 View for sketching pin. 13.

Sketch> Circle D2

Details View

EJ

Details of

-,

Sketch6

sketch

Sketch6

Show Constraints? No

EJ

Dimensions: 2

EJ

Edges: 1 Full Cirde

...............

Cr69

";...o---------'V3------!

Figure 2-28 Pin sketch.

Placed Features, Assembly 2-18 . is' Dimensionits diameter and location from the Z Put the center of the circle on t?e X Ax, h rizontal distance from the Z Axis to 1.5 Axis. Set the diameter to 0.5 Inches and the 0 inches. (See Figure 2-20.) Now create the pin extrusion using this sketch. 14.

Switch to Modeling, Select the sketch of the Circle, Click Extrude.

15.

Details of Extrude> Operation> Add F rozen,. D"tree tion > Both - Symmetric; Depth> 1.25 Details View

8 Details ofE> Attach to Active CAD Geometry The model then appears as an object in the feature tree of your DesignModeler session. Alternate CAD system geometry interface support includes Autodesk Inventor,. Autodesk .Mechanical Desktop, CATIA, Pro/ENGINEER, Sohd Edge, SohdWorks, and Unigraphics. The IGES and STEP neutral file exchange formats for 2D 3D CAD product models, drawings, or graphics is also supp rted b DesignModeler. (See also Chapter 2) The bracket model hoe h y . ProIENGINEER, saved in the IGES f s own was created in t here orma,ten importe d'D'nMdl' In esig 0 e er using

S . rt Figure 3-14 IGE rmpo .

Modeling Techniques

3-9

File> Import External Geometry File> bracket.igs > Generate Models created in DesignModeler can also be exported in the IGES or STEP format for use with other CAD, graphics, or analysis software. Use the following sequence to export the file in the current DesignModeler session. File> Export>

3-5

IGES (*.igs, *.iges)

(or STEP)

SURFACE AND LINE MODELS

Surface models are necessary if one wishes to perform analysis using simplified planar or 3D surface models instead of solids. Line models are needed when line elements are being used in engineering truss or beam simulations. The important shell (plate) engineering bending models are supported in Workbench DesignModeler by providing for the DesignModeler creation of surface models subsequently analyzed using ANSYS plate element technology. Beam bending is supported by the creation of line models to which beam cross sections are attached. Planar surface models are used to support analysis of Plane Stress, Plane Strain and Axisymmetric problems.

3-6

TUTORIAL 3B - PLANAR SURF ACE MODELS

We will use the L section solid of Tutorial 3A to create a planar surface model in this tutorial. Later we will use this same solid to create a three-dimensional surface model. 1.

Start DesignModeler and Open the file for Tutorial 3A. The part is 15 x 25 x 2 x 10 mm long.

25.000

V1

L.~:::::1'Df-" 2.000

...

~5.000 :



HZ

Figure 3-15 L-shaped section.

2.

Select the sketch in the tree outline

y

Modeling Techniques

3-10 3.

Concept> Surfaces from Sketches ~ncePt A: Geometry

""

. ,,;faXYPlane

',,8 BIllD

Modeling

Lines From Points

Cllines From Sketches

fiJ Lines

1 ...,,;fa ZXPlane :. ,,;fa YZPlane ffi·,,~ Extrude! i±1.. ,,~ ! Part, ! Body

Sketching!

Tools View Help

3D Curve

"

Split Edges

()

Surfaces From Edges

~

Surf aces From Sketches

~

I

From Edges

\1\

Surfaces From Faces

,

Cross Section

Figure 3-16 Surfacesfrom sketches. 4.

Details of SurfaceSkl; Base Objects> Apply, Thickness> 1

Tutorial3A ." ;faXYPlane

....."*'"C!

Sketch! ZXPlane YZPlane

Cancel

,,*, I±i "I!l, Extrude!

Operation

Orient With Plane Normal? Yes Thickness (>=0)

",61

! mm

i±1 . ,,(il

-

! Part, ! Bd

X

Delete

I~Figure 3-17 Generatethe surface. 5.

Right Click SurfaceSkl > Generate

This creates the surface model. The solid we startedwith is no longer needed and may be deleted. 6.

Select Extrudel > Delete> OK

The surface model is shown in the figure to the right. Notice that no thickness is shown. However the I mm thickness we supplied will be carried as a numerical value into the selected analysismodule. 7.

'I

Save this model as T3C Figure 3-18 Surface model from Sk I.

Three-dimensional surface models can be developed from solids using the methods described next.

Modeling Techniques

3-7

3-11

TUTORIAL 3C - 3D SURFACE MODELS

Again use the L section solid of Tutorial 3A.

1.

Start DesignModeler and Open the file for Tutorial3A

once again.

We want to capture the middle surface of the bracket. 2.

Tools> Mid-Surface

([J Freeze ~

Uofreeze

~

Named Selection

~

Attribute

~

Jvlid-Surfece

...

Joint

@

Enclosure

...

Symmetry

iii Fill

ue

Surface Extension

Clll

Surface Patch

...

Surf ace Flip

Figure 3-19 Mid-Surface tool. 3.

Details of MidSurf2 > Face Pairs

4.

Use Ctrl Select to sequentially pick all the front and back face pairs on the bracket model> Apply.

Intersect Untrimm, ., No

Figure 3-20 Mid-Surface face pairs. 5.

Generate:)

Generate

To create the surface.

Modeling Techniques

3-12 Notice that this is a three-dimensional surface model.



Graphics

A: Geometry

,I @

B

*y'CI **-

XYPlane Sketch!

,I

',1

ZXPlane

,I

YZPlane Extrude 1

I±J B

,I

Ii!!,

,,0 MidSurf! ! Part, ! Body

,I

,I

Sketching

tll!lll!lill

Modeling

I

Details View

B Details or Body Body

Surface Body

Thickness (>=0)

2 mm

Thickness Mode

Refresh on Update

Surface Area

355 mm'

Vertices

6

fluid/solid

Solid

Figure 3-21 3D surface model of the L shaped section.

The thickness of the Surface Body is independent of the solid whose mid surface was used and is set by the user in Details of Body box as shown above. This thickness value (2 mm in our example) is carried into the analysis systems modules and is used for the calculations there. More detail on this is given in Chapter 8.

3-8 TUTORIAL 3D - LINE BODY MODELS In the final tutorial of this chapter we develop a line body model to which a cross section is assigned. This model is then used in the analysis module to compute response using beam element modeling.

structural

Modeling Techniques

3-13

1.

Start Workbench and DesignModeler. Set the units to inches.

2.

In DesignModeler sketch on the XY Plane.and use lines to Sketch a portal 120 inches high and 72 inches wide (two verticals and one horizontal line across the top). See the next figure.

120,000 VI

Figure 3-22 Portal. ...... -~-~-4·

3.

Modeling> Select the Sketch

4.

Concept> Lines from Sketches> Base Objects> Apply (The sketch is the base object.)

*''"eJEmllI *'

'" @ A: Geometry

l;J ""

XYPlane

: ',,*,

ZXPlane

L "

YZPlane 0 Parts) 0 Bodies

1...

0(

r Concept

Tools

View

,

lines From Points

~

lines From Sketches

ItJ

lines From Edges

\1\

3D Curve

Details View

Heip

Car

..... Split Edges

~

Surfaces From Sketches

~

Surfaces From Faces



Figure 3-23 Lines from sketches. A: Geometry

Generate This generates the line body without a cross section. Next we assign a cross section to this line.

",:f.

XYPlane Sketch! "",:f. ZXPlane ",:f. YZPlane 00 Linel

",c.2I

..,.c9

6.

Figure 3-24 Generate Line Body. Concept> Cross Section> Channel

..

H2

Cross Section

/

_ 72.000

__ Surf aces: From Edges:

5.

···

13 "'~

Sketching

1 Part, I Body

-I,D.

Modeling

I

Details View

We take the default size which is the 3 x 6 x 1 EI Details inch section shown below and assign it to the Body Line Body as shown in the second figure below: Faces Line Body> Details> Cross Sctn. Edges

Vertices

or line Body Line Body 0

3 4

Cross Section Not selected

w---------------r-

z

Modeling Techniques

3-14

I

6.000 concept

"

Tools

View

Help

W3

lines From Points

6J lines

From Sketches

ijJ

Lines From Edges

V\

3D Curve

IliI

Rectangular



Circular

3.000

o Circular Tube

W2

~ Channel Secbon

.... Split Edges

Co

Surfaces From Edges

C2I €J

:ii: 'i.

1.000

I Section Z Section

t3

Surfaces From Sketches

.. l Section

Surfaces From Faces

JL

T Section

A

Hat Section

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Cross Section

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I:iI Rectangular

Tube

III User Integrated ~

1.000

User Defined

tl

Figure 3-25 Choose Channel Section.

Tfee Outline B.,.

*' .. c:'iI .,...**"'

A: Geometry

8

S

..

XVPlane

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ZXPlane YZPlane line!

E1

"til

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v

r

Sketch!

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.,.e Channell 1 Part) 1 Body

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120000 Sketching

Modeling

I

V1

Details View

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Details: or Line Body

Body

line Body

Faces

o

Edges

3

Vertices

1 Not selected None

.:

72000 1---

H2

----"'i

Figure 3-26 Assign the channel to the line body.

7.

View> Show Cross Section Solids (Displays the orientation of the section.)

Modeling Techniques

f

[View

3-15

Help Shaded Exterior and Edge,

IF::::

, 1

Frozen Body Transparency

, ,

Edge Joint,

r

r.:.:- Cross Section Alignments Display Edge Direction

T::r:;-

I

Display Vertices

120000

Cross Section Solids

V1,

Ruler Triad Outline

Windows





/"--------. J2.D00 H2

....

r

-

~

....

Figure 3-27 Show cross section. The arrow normal to the portal plane (green on your screen) is aligned with the long edge of the channel cross section. Display the section orientation: Uncheck Cross Section Alignments, To adjust the orientation of the top beam select as follows. 8.

Turn on the Edge Selection Filter Reverse Orientation? > Yes

J~and

Pick the Top Line-Body Edge.

Figure 3-28 Close-up of section orientation.

3-16

Modeling Techniques

Detail, View

B line-Body Edges: 3 AlignmentMode

Selection

Cross Section Alignment Plane Normal AlignmentX

0

AlignmentY

0

AlignmentZ

1

Rotate

f-0-'-

__

-::1

..

Figure 3-29 Alignment options.

Figure 3-30 Reverse orientation of top cross section.

The adjustment options shown in Figure 3-29 can be used in a number of ways to obtain proper beam cross section orientation for the problem at hand. Some experimentation may be helpful.

9.

Save your work.

This Line-Body model can be expanded using the sketching methods described earlier to add more elements and dimensionality to the model. We add vertical and horizontal lines sketched in the YZ Plane and a Concept> 3D Curve diagonal line joining the two outer vertices. This modification is shown in the following figure.

Modeling Techniques

3-17

....

,

,

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Start ANSYS Workbench, begin a new Project.

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ANSYSClient Licensing EKM



Help Meshing Utilities

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Mechanical APDL (ANSYS) 14.0 Mechanical APDLProduct Launcher 14.0

U Uninstall14.0 • ~

Worl Component Systems to initiate the geometry object in the Project Schematic. See the next figure.

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orkbench

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Project

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8 Analysis Systems

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Design Assessment A

Electric

II Explk:it Dynamics IiJ Harmonic Response U Linear Buckling

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IJ Steady-State Thermal It Thermal-Electric Transient Structural

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Thermal Systems

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Microsoft Office Excel

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1!I Design Exploration

Figure 4-4 Project Schematic details. The question mark indicates that cell A-2 is incomplete. 2.

Select the small blue triangle for additional information. Click anywhere schematic to close the information box.

in the

Select a folder in a convenient location on your storage device and use Save As •.. to name the project T4A, Tbe project title, T4A, is displayed on the header as shown below and the Workbench project file T4A.wbpj and folder T4A files are created in the selected workspace. Take a minute to find and verify this, There are a number of ways to create and access geometry for your project. We discuss several, A., B., c., D., and E. in what follows,

4-5

ANSYS Mechanical I

A. » Create New Geometry in Design Modeler: Double click cell A2 to start Design Modeler. Select problem length units and proceed to create geometry as discussed in

Chapters 1 - 3. Save your DM work when you are finished. -

.

ANSYS Workbench

~

Select desired length untt:

r-

Meter

r

Fool

r:

Cenlimeter

r

Inch

r

Mlllimeler

r

Micrometer

r Always

use project unjt

r Always use selected untt r E.nable large model support OK Figure 4-5 A » Start new geometry in DesignModeler and set units.

B. » Access Previously Created Geometry in Design Modeler: Double click cell A2

to start Design Modeler. File> Load DesignModeler Database (See the next figure.) ]' A: Geometry - DesignModeler

r

File Create

@j

Concept

Tools

View

Help

Refresh Input

';!j Start

Over

0

DeSignModele, Database".

1 Load

(;I Save Project

IIExport. " Iji Attach Iji Import

to Active CAD Geometry External Geometry File ...

Figure 4-6 B » Loading existing DM file.

-------------------4-6

ANSYS Mechanical

C. » Access Geometry Previously Created and stored using another

solid modeler: SoIidWorks, etc) Double click cell A2 to start Design

(CATIA, ProIENGINEER, Modeler.

File> Import External Geometry File (Options include IGES and STEP formats) (See the next figure.)

i A: Geometry.

DesignModeler

File Creete Concept Tools View Help

/1;)

RefreshInput

':d Start Over E3 load DesignModelerDatabese... Q SaveProject ~

Export...

~

Attach to Active CADGeometry

.i1

lmport Extetndl Geornettv Fife .. ,

Figure 4-7

Be »

Importing from an alternate format.

This process starts the alternate solid modeler, loads that modeler's geometry to DeslgnModeler, and closes the alternate solid modeler.

file, transfers

the

D. » Access Geometry in Active CAD t . Modeler. sys em. Double click ceU A2 to start Design File> Attach to Active CAD Geometry

Tools View Help

~'

i1Impor~nal Figure 4-8 D»

-----

G~metry File...

Attach to A . ctlve CAD Geometry.

I

4-7

ANSYS Mechanical I

E. » Start Workbench from your alternate Solid Modeler. An example of this using ProlENGINEER is shown below. Note the ProlE icon is shown in cell A2 in the Workbench Project Schematic.

, Double click cell A2 to start DesignModeler, then use Generate :) ProlE geometry.

tj) Named

Selection Manager

Generate

to attach the

PIoiect Schematic

@Workbench Help

o About Workbench Geometry Interface A

ANSConConfig ANSYSGeom

2 Geometry

Figure 4-9 E»

3.

Starting Workbench from ProIENGlNEER.

Getting back to Tutorial4A, with the geometry attached, Double Click Toolbox> Analysis Systems > Static Structural to add the analysis to the Project Schematic. (Or drag it from the Analysis Systems column to the Schematic.) •

o @

Figure 4-10 Adding Static Structural Analysis from the Toolbox.

o m!l

x

q.

Fluid Flow (CFX) Fluid Flow (FLUENT) A

Harmonic Response linear BucldinQ

2

Magnetoslatic Modal

II Random

IIResponse

~ry lIibratlon Spectrum

Rigid Dynamics

S Sh~e

Optimizatton

III Static Structural

o

Steady-State

Thermal

m Thermal~Electric

I Statk Structural

Transient Structural

4.

To share the geometry, Left click on DM Geometry in cell A2 and drag it to Static Structural cell B3.

4-8

ANSYS Mechanical

A

2

I

B

,,--=

L: __

2 •

Geometry

3

(ill)

Engineering Data Geometry

4

Model

5

Setup

6

Solution Results Static Structural

Figure 4-11 Sharing geometry. 5.

Double Click on Model in cell B4.

The Workbench display now shows the Static Structural Analysis that is associated with this Project, and the tree Structure on the left contains project items that include Model, Geometry, and Mesh. See the figure below.

'"

Ed< "'"

~.

Q

HoI>

llit> Took

"I' I 'I' roo·

@ @

"'1",,,,_ $...

""Show"'""

Mesh:)~

~Mesh

Oulh

..

tJ

;;_.

roo roo e-

ibt ~

~ ,;:

HEdgoC_ • MeshCortrli ... .,-

@\

e.

@. ~

Q.

:;:,

e

A· A· A· A· A· " H I-Ir""",_

lb,

_ y

. ProJee:t

'" iii M....

l..)

static """ ....e

Systems

Structural (85)

....C3 Analysis Settings

}il11 FrictJonless Support

fl..Force Fi ~

SotuUon (86)

Figure 4-12 Plate quadrant in Static Structural Mechanical module. Since the geometry was. created using mm, the length units for the simulation should be mm also. Check the units usmg the Units pull-down menu Unit M . N s, mY, rnA) . m s> etnc (mm, kg, ,

6.

Highlight Material in the Details of "T4A" wind

ow.

-----------------1'4 4-9

ANSYS Mechanical I

7Units

Tools

I

Help

Metric (m, kg) NJ

S,

I :)~olve

(J



t$lI

Outline

'iIb

Project

8

VJ A)

f!1!I

Model (B')

8

.t~

Metric (em, gJ dyne, 5, VI A)

Frl'letnc (rom, kg, N 5, mV rnA) Metric (mm, t, N,

5J

Eb

j

J

B

j

u.s, Customary (in} Ibm, lbf

F

OF) 5,

Static Structural (OS) Analysis Settings B .,~ Solution (86) ~ Solution Information

,,(:4

V, A)

OF) 5) V,

Details of "HA"

A)

r±l Graphics 8 Definition

Degrees

~

Properties

Suppressed

Radians

Frad/s RPM

r;-

'18 .

Metric (urn, kg! IJN, SI V rnA) (ft) Ibm, Ibf,

-I'*'

.---

HA Coordinate Systems

~Mesh

mV, rnA)

Metric (rom, det, N, s, mV, rnA)

u.s, Customary

Geometry

)fil

No

Stiffness Behavior

Aexible

CoordinateSystem

Default CoordinateSystem

Reference Temperature

By Environment

8 Material Structur

Celsius (For Metric Systems)

at steel

Yes Ves

Kelvin (For Metric Systems)

Figure 4-13 Check Units and Material assignment. To return to the Project Schematic, Select T4A - Workbench running shown in the taskbar at the bottom of the screen.

from the programs

Figure 4-14 Workbench elements shown in the Taskbar. 7.

Double click Engineering Data, cell B2 to view the Material Properties Data for Structural Steel, the default material that has been assigned to this part.

B

A

Geometry

• 5 6

Solution

f •

7

9 Result,

I •

static structUfa! (ANSYS)

Figure 4-15 Project Schematic. Be sure View> Properties and Outline are checked. Properties for the default material Structural

Steel are shown.

·~--------------~ ANSYS Mechanical I

4-10 j Up d ate

. t Projec

A \07 Return to Project

:.fT1 I· I

V. Conp.."'Kt dOG 'U'

'::,. "

I~Ju~line of Schematic 82: Englneenng Data B

A

IEngineering Data Sources

q. X

y

"

D

C

Description

2 Fatigue Data at zero mean stress comes from 1998 ASME BPVCode, SectionB, Div 2, Table 5·110,1

3 Click here to add a new material



v

'" tlme Row -c_',. '-tru·tur:s15teel Pt operties or- vu .:1.

y

I.

1

'iB

2 3

I±I

6

EI

~

A

B

Property

Value

Density

I

C

ID

7850

kg m -3

.:.1 EJ

Isotropic Secant Coefficient of Thermal Expansion

r

Y!:l

Isotropic

X E

.~!N

Unit A

q.

ICJ

EI

Elasticity

f[]

.:.1

7

Derive from

B

Young's Modulus

2E+11

9

Poisson's Ratio

0,3

10

Bulk Modulus

1.6667E+11

Pa

11

Shear Modulus

EJ

7,6923E+10

Pa

0

12

I±I

16

I±I

24 25 26 27

'iB Alternating Stress Mean Stress E Strain-Life Parameters 'iB Tensile Yield Strength 'iB Compressive Yield Strength 'iB Tensile Ultimate Strength 'iB Compressive Ultimate Strength

Young's .. ,

IillI

Pa

n

.:.1

EI Tabular

[[J

EI 2,5E+08

Pa

2,5E+08

Pa

4,6E+OB

Pa

0

Pa

.:.1 EI ro .:.1 lE:l ro .:.1 [J ID .:.1 D []

Figure 4-16 Material properties for structural steel. Note that structural steel has Tensile and Compressive Yield Strengths of 250 MPa. and that because it's unknown, zero has been assigned to the Compressive Ultimate Strength. 8.

Select Return to Project (Topof sereen)

~RelurntO"'oject

The Mesh item in the project tree has a lighting bolt symbol next to it indicating that the finite element mesh for this simulation has not yet been created. Workbench simulation will automatically develop a finite element mesh appropriate to the problem. 9.

MESH: Right click Mesh and select Generate Mesh

4-11

ANSYS Mechanical I

The default mesh that is created consists of a little over one hundred three-dimensional 8 or 20 node brick elements as shown.

8-""

.

~--

,-._-

Project Model (84)

fil

*. - A'flmr"

$"".,)iSt

Geometry

[£- .....

Coordinate



Systems ~---j

.,.s ~~:-_I"_,e_rt -\ ,;

_

Update

Preview Show :) Create ________

Pinch Controls



Loads> Force.

Environment ~ ....Inertial ... @"toads ... @" Supports ... ll-

Outline

la Project 8 ~ Model (04) [fJ

l±}-

.;fjI 0/*

I

@... Pressure

Geometry Coordinate

Systems

~Mesh

8

£:1 Static Structural (05) -

,,{;j,

EJ

@"Loads • @. Supports.

./

@" Hydrostatic Pressure

¥'

!d

Force

Analysis Settings

@.. Remote Force

?fi1 Solution (06) '. 'AIl Solution Information

'tI,

Bearing Load

Figure 4-18 Structural loads menu. ~

Be sure that the Face selection filter is highlighted @ and click on the area on the right end of the solid model.

·-------------------~ ANSYS Mechanical

I

4-12

12.

Geometry>

Apply (Note: It's easy to forget this step.)

13.

Define (the force) by (X Y Z) Components, X Component ~

.

_._,-,

'-~=:iellt-'~~ [email protected] ~~7lSi~s:-:-~·ii~.c~Olid~·it~~-;~:.::$Il,:.~"''''~FE~ ..:..-~~;.:·-=--= j

""""

Project

ril"'_

8"" Ij] I"1ofkI(B4)

;t... Coorchte

~'1 ......

B: static St:rudlWal

__

E

(ANSYS)

Systems ..

Stalk structural (85)

.2:i ArWtsis PQf~s~ .ft. """'

S- ~

.--.:

F.~ Tine: 1. s

.... 0 Mesh

B

= 50 kN

Force: 50000 N

Components: 50000, 0., 0, N

5ettnos

Solution (86)

-.AD SOlution

Information

."

Figure 4-19 Tensile loading. Next apply the displacement constraints; rotate the plate so that you can see the bottom, and small end. These are surfaces on planes of symmetry and no point on these surfaces can move across the plane of symmetry. Symmetry requires that we constrain the displacements perpendicular to these surfaces. We can use the Frictionless Support condition to do that. We also restrain the back surface also so as to prevent rigid body motion in a direction perpendicular to the plane of the plate. See the figure below.

~

Fixed Support

~

Displacement

til

K

Remote Displacement

(jK velootv

~

Impeder»

~

Ft ictionless Support

~

Compression Only Support

~

Cylindrical Support

e Boundar- '

I

Figure 4-20 Displacement constraints. 14.

Environment>

Supports> Frictionless Support

15.

Ctrl > Left Click to select the three surfaces> Apply.

4-13

ANSYS Mechanical I

B Scope Scoping Method

Geometry Selection

Geometry

3 Faces

B Definition Type

Frictionless Support

Suppressed

No

Figure 4-21 Frictionless Support constraints. Check your work by clicking on each of the items under Environment in the model tree to be sure the loadings and constraints are applied as desired. Or click Static Structural to see all of the constraints you have applied. If you find something wrong, just highlight the item in the model tree and edit it in the 'Details' box to correct the error, or Right Click, delete the item from the outline tree and apply the condition again. (Note that the back face is not really a plane of symmetry. To be absolutely correct we should have sliced down through the 10 mm thickness and analyzed an octant instead of a quadrant. However since the 10 mm dimension is so small in comparison with the other dimensions, there is little error in the approach we used. Try it both ways to see.) B: Static Structural

(ANSYS)

Static Structur ai Time: 1. s

II Frictionless •

Support

Force: 50000 N

v

Figure 4-22 Structural Static 'Environment' settings. To complete the model building process we need to specify what result quantity or quantities we would like to have calculated and displayed. In this problem we are most interested in the stress and deformation in the X Axis direction.

ANSYS Mechanical 4-14

Project

EJ

~

Model (84)

,,*

!tl"m.,A'il r.tJ... "'~

B

Geometry Coordinate Systems Mesh

"f8 S~~tic Structural

(85) Analysis Settings

!"",,,,fJ

L.."p~Force

Frictionless suppor~

>O~.Q

El'~' Y,

• ,.

""'r'

Solution Information

Figure 4-23 Solution result options menu, 16.

Solution>

Stress> Normal> Orientation>

Also select Deformation

X Axis

and insert the Directional Deformation in the X Axis. Solution l\lId Deformation • l\lIe Strain • l\lIa Stress

q.

Outline ~

EJ

Project @J Model (84)

!tl'>~

IB',,,, B-

*-

,f8

fl)a Equivalent (von-Mises)

EJ

Principal

.fi'Q. Frictionless Support

,~

Solution (86) ",.

lila Middle Principal

eO'

Coordinate Systems

"'Mesh Static Structural (85) ,",t;l AnaiysisSettings Force

;.-"Pot

fl)a Stress •

"0" Maximum

Geometry

y1]]

" ~

Minimum Principal

Solution Information NormalStress

~

Directional Deformation

lila Maximum Shear lila Intensity

~

Notmal

Details of "Normal Stress

B Scope ScopingMethod

$a Shear

Geometry

lflIa

Vector Principal

lflIa Error

q.

n

El

IGeometry Selection IAll Bodies

Definition

Type

INormal Stress

Orientation

IX

Axis

~

Figure 4-24 Select X-direction normal st ress output.

-

---- I

I

4-15

ANSYS Mechanical I

Notice that Solution, Normal Stress, and Directional Displacement items have lightning bolt indicators meaning that we need to highlight one or the other and select complete the simulation solution. ANSYSWorkbench

17•

to

Solve

(g)

Solution Status

Overall Progress ..

:;

S0Ive

:)

Solve

4

Solving the: rnethemencel model •• ,

The solution progress is shown in the ANSYS Workbench Solution Status window.

Stop Solution

Interrupt Solutlon

Figure 4-25 Solution status.

ITIDProbe

When the solution is found, click on the normal stress to view the computed stress results. 18.

Solution > Stress > Normal Stress (In the graphics window - Right click> View> Front; use the pull-down menu to Show Elements.)

6: Static Structural Normal Stress Type:

Show Undeformed

WireFr ame

@

Show Undeformed

Model

[fi

Show Elements

(ANSYS)

Normal Stress(X Axis)

Unit::MPa

Global Coordinate Time: 1

System

101 ..59 Mall

95.184 62.782 70.36 57.978 45.576

I

33.174

zO.nz 8.3702 -4.0317 Min B: Static Structural (ANSYS) Normal Stress d)( ) Type: Normal stress (tmveraoe X Axis.,....... unit:: MPa "'" Global Co«dinate System Time: 1

101.59

"l!l~IlI••

"l""""I'....

"-;.1!lResults

r"""'..,1 '

MirlirrMn

~'i"i·""~DI •• ~'"

Aver~d Nodal Difference NoM! Fraction EIement:a1 Difference Element~ fr",Uon

MaM

95.05 82.515 69.979 51.444 44.908 32.373 19.838 7.3022 -5.2332 Min

Figure 4-26 X direction normal stress; Averaged Display, Unaveraged Display.



Pi 4-16

ANSYS Mechanical

I

The solution for the X direction normal stress shows a maximum value of 107 MPa. This value is well below the material yield stress of 250 MPa, so the elastic solution that we have performed is valid. To check this result, find the theoretical stress concentration factor for this problem in a text or reference book or from a web site. For the geometry of this example we find K, = 2.17. We can compute the maximum stress using (Kt)(load)/(net cross sectional area). Using the net section of the whole bar and total loading of 100 kN we obtain:

ax MAX

= 2. I 7 * F * /[(0.4 -

0.2) * 0.01] = 108.5MPa

The computed maximum value is 107.6 MPa which is less than one percent (assuming that the published value of K, is correct, that is).

error

If we list the solution information we find that I I 3 SOLID186 elements were used in the model. A search of the ANSYS Mechanical Help system shows these to a ..~ Solution (86) 113 SOLID186 be 20 node brick elements. ,..... jJJ Solution Information The maximum B: Static Directional

Structural

deformation

in the X direction is about 0.083 mm.

(ANSY5)

Deformation

Type: Directional

DeFormation(X

Axis)

Unit: mm Global Coordinate System Time: 1

0.083109

Max

0,073875 0,064641 0.055406 Q,lM6172

0.036937 0.027703 0.018469 0,0092344 OMin

Figure 4-27 X direction deformation. Before we move on, let's compute and display the str Insert a stress error in the solution item in the project ~::error 19.

Solution>

Stress>

Error>

Solve

,

-; Solve

Computed results are shown in the next figure.

hs.._iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

_

estimate for this problem.

4-17

ANSYS Mechanical I 8: Statk: structural (AMSYS) Structural Error Type: structlJ'o!Il Error Unit: mJ Time: 1

0.042548 Max 0.03762 0.033093 0,026365

0.023638 0.01891 O,OtiIS3 0,0094555 O,OO~7281

5.8971e-1 Min

Figure 4-28 Computed structural error estimates. The error estimates shown above can be used to help identify regions of potentially high error in the solution and thus show where the model might benefit from a more refined mesh. These error estimates are used in Workbench automatic adaptive meshing and convergence procedures we discuss later. For now we note that the Structural Errors shown are error estimates based upon the difference between the computed smoothed (averaged) stress distribution for the object and the stresses calculated by the finite element method for each element in the mesh (unaveraged). The data are expressed in an energy format (energy is nonnegative) so that the sign of the difference between the estimated stress and the computed stress does not influence the results. The estimated error is displayed for each element. For accurate solutions the difference between the smoothed stress and the element stress is small or zero, so small values of Structural Error are good. We know the above solution is accurate because we compared our result with tabulated results. The small error estimates shown above reflect this, as do the Averaged and Unaveraged results plotted above. If you want the computed results in a different system of units, just change the units in Mechanical after you've computed the results. In the current problem, for example: Max stress Sx = 107.5 MPa = 16,504 psi Max deflection = 0.083 mm = 0.0033 inches

Units

To improve the accuracy we'll generate a model with more elements. There are many ways to control the mesh in Workbench. In what follows we use one of the sizing options. 20.

Mesh> Details of Mesh > Relevance Center> Medium (Coarse is the default.) Solve again.

• ANSYS Mechanical

4-18

,Outline

(i Project

EJ

--

~ Model (84) 1$J".,jiD Geometry ItI·· '",,* Coordinate ,,~

Systems

Mesh

EJ ..",8 Static Structural (8S)

'"",fa

AnalysisSettings

,..,,fill' FrictionlessSupport ··fl...Force 8"[email protected] Solution

(86)

,

;.".,.AIl Solution Information :,.,,~ ,.....~

NormalStress Structural Error

Details of "Mesh" EJ Defaults Physics Preference

Mechanical

Relevance

o

EJ Sizing Use Advanced SizeFunction ~O:-ff-;:__

':l

Medium IEE~le~m~e~nt~S;iz~e~ rrnitial SizeSeed

....

~c~olarls.e •• Fine

Smoothing

Me ium

Transition

Fast

SpanAngle Center

Coarse

MinimumEdge Length

10,0 mm

~

/

Figure 4-29 Relevance Center mesh settings.

l08.69MaM

0.00064178

96,196

0,00057047

83,702

0,00049916

71.208

0.00042785

58,714

Max

0,00035654

46,219

0,00028523

33,725

0,00021393

21.231

0,00014262

8.7371

7.130ge-5

-3.757 Min

1.0396.-9

Min

Figure 4-30 Stress and error estimates based on a medium mesh. 21.

,

Repeat this process using the Fine Mesh setting.

I

4-19

ANSYS Mechanical I

E1 Sizing Use Advanced Size Function

off ----~ Coarse Coarse Medium

Figure 4-31 Relevance Center Fine mesh settings.

108.82 MaM

1.3248e-S Max

96.303

1.1776e-5

83.79

1,0304e-5

71.277

8.8323e-6

58.764

7. 3603e-6

46.251

5.8882e-6

33.738

4.4162e-6

21.225

2.9441e-6

8.7124

1.4721e-6

-3.80D6 Min

5.9703e-12 Min

Figure 4-32 Stress and error estimates based on the fine mesh. 22.

Let's compute another solution for a mesh that is coarser than the first one. Set the Element Size = 50 mm and remesh. We get the results shown below.

102.69 Max

1.6264 MaM

90,89

1.4457

79.086

1.265

67.282

1.0843

55.477

0.9036

43.673

0.72269

31.869

0.54217

20.064

0.36146

8.2599

0.18075

-3.5444 Min

4.321ge-S Min

Figure 4-33 Stress and error estimates based a very coarse mesh.

These results are summarized in the table below. Note that with the finer meshes we obtain a maximum stress of about 109 MPa. With the very coarse mesh we get about 103 MPa., about 6 percent in error.

----------------- ... 4-20

ANSYS Mechanical

I

Table 4A.l - Results Summary Number of Elements

36 137 511 3182

Maximum Deformation in X direction mm 0.0831 0.0831 0.0831 0.0831

Maximum Stress in X direction MPa 102.7 107.8 108.8 108.8

It is important to note the approximate nature of the Finite Element Method and the convergence of the stress results with mesh refinement as illustrated in the above table. Note that with a coarse mesh you can get results that are in error, only about 6 percent in this case, but don't accept results from an initial mesh without question. (Set the element size to 75 mm, and see what you get.) Also note that the tabulated displacement results show no change to three significant figures indicating that the displacements converge more rapidly than the stresses. This is usually the case. The strains (hence stresses) are the spatial directives of the displacement distributions within the object, i.e., E, == etc.

au/ ax,

We will do two more experiments before moving on. Return to the 50 mm mesh and change the stress plotting option. 23.

Select Normal Stress> Display Option> Unaveraged. Recalculate ~ ~

Norm.1 St re ss Directional Deformation

~

Structural Error

Details of ''NormI- N••

Enter 15 mm > Generate OJ

Blend

~""'Ildt

__

sm,tLoft

~.Tl"in/Surface

I--~---·_-

!.~i.i"!'

14 VaMbie

I < Vertex

I

Radius Blend

Blend

~Ch.>mf".

_

J:::~''''' Sketc •

Boolean

""..,j .. "',

J %i.

III~face Delete

'do< """.

,-'-----

Figure 4-49 Part in DesignModeler.

1';J IIExtrlXle

'i'''T.i~c.:::::;::---.:!.'

Q,pl;"

r,;. Details or fBlend3

Rxed-:RcdIusEi;;d 'F6Ieo:!3 : rol, RdJs(>0) "Is,;;;Geomet:rL _.

1 Edge

Figure 4-50 Updated DesignM d I

o e er geometry.

".

~

I

...

4-29

ANSYS Mechanical I Now update the Static Structural Analysis model to the new geometry. 16.

Return to the Project Schematic view. Left click on the small blue triangle in cell B4, Model.

...

... 2

Eli)

Geometry Geometry

../

.. -........"

2

"'-

3 4

I. ij)})

B

Enginee~ingData

../

..

Geometry

../

..

ri)··~~d~i·····"····"·····_·······~··~~ ....................................................... ,

5

Setup

6

@

Solutio

7

@

Results

Upstream data has been added or updated. Right-click and choose Refresh or Update to read the updated data. You can also select Edit to perform a Refresh and open the model in the 1\'1echanicalapplication.

Static S

Systems and Cells ANSYS Workbench Figure 4-51 Model information screen. 17.

Right Click in cell B4, Model and select Update.

(M)

Edit ...

I~ Duplicate

-~

Transfer Data To New

-

II

Update

Ii!

Refresh

14

Clear Generated Data Reset

~

Rename Properties

-

-

-

Quick Help

Figure 4-52 Update the model. After the update is complete, return to the Static Structural

Mechanical screen.

ANSYS Mechanical

4-30

18.

I

Reset the mesh Relevance to Coarse and en t er 0 for Element Size to reset it to Default. 5izing Use Advanced Size Function

Off

Relevance Center

Coarse

Element Size

Default

Initial Size Seed

Active Assembly

Smoothing

Medium

Transition

Fast

Span Angle Center

Coarse

Minimum Edge length

10,0 mm

-

Figure 4-53 Reset element size. The project now IS " . . updated;, the material load and frictionless supports remain the same; the analysis proceeds as bel" ore.

Structural (ANSYS)

B; statk

NoonaI

-) Solve

Stress

Type: Normal Stress ( X Axis ) Unit: MPa Global Coordinate

System

Time: 1

100.73 Max 89,127 77,528 65,929 54,33 42,731 31.131 19,532 7,9333 -3.6658 Min

Figure 4-54 Default mesh for modified geometry. The computed maximum stress associated with the 15 mm comer radius is about 101 MPa. We can control the accuracy of the solution manually as we did in previous examples or we can request an automatic iterative solution process to be employed that will use models with successively smaller element sizes while monitoring the change in the requested solution quantity. This is essentially an automation of what we did manually earlier.

4-31

ANSYS Mechanical I Select maximum Normal Stress as the quantity to monitor during iterative solution. 19.

Right click Normal Stress> Insert> Left click Convergence ~

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Stress

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Energy

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Data

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Coordinate Systems

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Convergence

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Result

Ii: commands Figure 4-55 Insert convergence criterion. Define the allowable change in the maximum Normal Stress between solutions. 20.

Details of "Convergence" > Allowable Change> 1 percent El ~

Solution (06)

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