Transcript Snímek 1

Static Analysis of Beam
by Finite Element Method
In Ansys Workbench version 13
HORYL Petr
Ostrava 2012
Contents
• Open Static Structural
• Design Modeler (DM) – Geometry
• Model – input Geometry from DM,
Connections, Mesh
• Static Structural - Boundary Conditions
(Force, Moment, Line
Pressure, Joints)
• Solution – Results (Displacement, Internal
Forces, Stress…)
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Simply Beam Structure
q= 2.5 kN/m
A
F = 3kN
a = 46o
M = 4 kNm
Part1
3m
B
Part2
6m
C
D
Part3
5m
a) Maximum deflection
b) Course of internal forces - axial force, shearing force and bending moment
c) Maximum of normal stress
Cross-section of beam: D = 152 mm, d1 = 60 mm
D
d1
Material properties: Steel Young's modulus of elasticity E = 2.1E5 MPa,
Poisson's ratio ν = 0.3
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New Project
After starting the Workbench 13 select the type of analysis – „Static
Structural“(arrow No 1) and type new name of project (2)
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Material Properties
In window „Engineering Data“ we choose „Click here to add a new material“ . Potom napíšeme
jméno nového materiálu „Beam Material “ (Arrow no 1) a výběrem „Isotropic Elasticity“ (2) jsme
vyzváni k zadání příslušných materiálových dat v nově se otevírající tabulce hodnot ve spodní
části okna (3.). Zpět se vrátíme příkazem „Return to Project“ (4.)
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Units „mm“
Now we can select „Units“ (1). For example „Metric“ with „mm“ (2)
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Open Geometry => Window „Design Modeler“
For creation beam geometry you must click on row „Geometry“ (1). Name of
opening window will be „Design Modeler“
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Geometry - Points
In the next window „Geometry“ we start creation of the four point from A till D, see picture of beam.
Click on „Point“ (1), in the card below left choose „Manual Input“ (2), type “Coordinates X, Y, Z” of
the point (3) and click on “Generate”(4). You can “Rename”(5) Point1 to PointA. In the middle of
window you can see “PointA”(6). Repeat it for PointB to PointD.
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Geometry – 4 Points
All 4 Points were created.
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Geometry – Lines
Now we continue creation geometry namely lines. Click on „Concept“(1), in the menu top left
and choose „Lines From Points“(1). Hold “Ctrl“ keyboard button and select by left mouse
button “PointA”(2) and “PointC”(3). Confirm by mouse “Apply”(4) and click on “Generate”(5).
We have created Part1 of our beam. Repeat it for Part1 and Part2
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Geometry – 3 Lines => Part1 to Part3
All 3 Lines were created.
PointA
Part1
PointC
Part2
PointD
Part3
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PointB
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Cross section
Now we select cross section of our beam. Click on „Concept“(1), in the menu top left and
choose „Cross Section“(2) and “Circular Tube”(3). In the card below left, type outer “Ro“ and
internal “Ri” radius(4). In main window you see cross section(5).
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Cross section for our beam
Click on „Line Body“(1), in the menu top left and choose „Cross Section“ and “Circular
Tube”(2). Confirm it by “Generation“(3). Save Project and Exit Design Modeler.
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Transition between Geometry and Model
For the correct transition between windows „Geometry“ and „Model“must be checked „Geometry
Import“. In our project window click on „Tools (1) – Options - Geometry Import (2)“ and check
tick box „Line Bodies“(3). Now open window „Model“ (4).
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Creation Path in Construction Geometry
To plot internal forces in the beam-shaped „Shear Force - Bending Diagramm“, we must
choose on beam „Path“. In Modeler window click on „Model“(1), „Construction Geometry“(2)
and „Path“(3). Then change the „Details of Path“(4) for „Path Type“(5) on „Edge“(6).
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Creation Path in Construction Geometry - continue
Click on „Path“(1). Choose „Line“(2) in Selection boxes. Hold “Ctrl“ keyboard button
and select by left mouse button all three lines from left to right. Click on „Apply“(3).
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Creation Path in Construction Geometry - continue
We get right „Path“(1) for whole beam from starting „Edge“(2) to ending „Edge“(3)
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Mesh Generation
Left mouse button click on „Mesh“(1), open „Element Size“(2) in Details of „Mesh“
and type 50mm (2). Click right mouse button again on Mesh and „Generate
Mesh“(3). Zoom right end of our beam and look at Circular Tube Cross Sections(4) .
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Boundary Conditions -> JointA in PointA
Click on „Static Structural“ insert „Supports“(1) and „Remote Displacement“(2).
Because joint in PointA has free only rotation around axis Z, we must change these
degree of freedom in row “Rotation Z“ to „Free”(3). Click on selecting box for “Point”
and select “PointA”(4) and click on “Apply”(5). Rename „Remote Displacement“ in
the tree to „JointA“(6)
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Boundary Conditions -> JointA in PointA continue
Picture shows only one free degree of freedom for JointA namely “Rotation: 0,, 0,,
Free”(1). Rename this row in tree to “JointA”(2).
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Boundary Conditions -> JointB in PointB
On the same way we create “JointB”(1), but here we have two Free degree of freedom :
“X Component - Free”(2) and “Rotation Z - Free”(3). We renamed joint to “PointB”(4)
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Boundary Conditions -> Force, Moment and Line Pressure
Click right mouse button on “Static Structural – Insert”(1). In the next step, we will
need “Force”(2), “Moment”(3) and “Line Pressure”(4).
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Boundary Conditions -> Force
Click right mouse button on “Static Structural“(1) „Insert“(2) and „Force”(3).
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Boundary Conditions -> Force continue
In the left below table „Details of „Force“(1) change in row „Define by“ to „Components“(2).
Type -2084 into row „X Component“(3) e.g. FX=F*cos(alfa)= 3000*cos(46). Type -2158 into row „Y
Component“(4) e.g. FX=F*sin(alfa)=3000*sin(46). Click on selecting box for “Point”(6) and select
“PointD”(7) and click on “Apply”. In the middle of window you can notice red force vektor(8)
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Boundary Conditions -> Moment
Similarly as Force, specify moment to „PointC“(1) as „Z Component“(2) -4E6 N.mm. In
the middle of window you can notice sense of bending moment M, drawn in red (1)
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Boundary Conditions -> Line Pressure
Similarly as previous boundary conditions specify „Line Pressure“ on „Part2“(1). You
must select box „Line“(2) from selection boxes. Into table „Details of „Line Pressure“(3)
type -2,5 N/mm in row „Y Component“(4) and click on „Apply“(5).
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Boundary Conditions -> Line Pressure continue
In the middle of window you can notice red „Line Pressure“(1) with Y Component
-2,5 N/mm(2).
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All Boundary Conditions in one picture
If you click on „Static Structural“ you can see all Boundary Conditions with their
values(1).
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Solution
Now befor Solution we must prepare results which we need for our example
analysis. It could be „Deformation“(1), „Beam Results“(2) for getting internal forces
or „Beam Tool“(3) for stress results.
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Solution
As you can see, we select: „Total Deformation“, „Axial Force“, „Total Shear
Force“, „Total Bending Moment“(1) and „Directional Shear-Moment Diagram
(VY-MZ-UY)“(2). Befor selecting row „Directional Shear-Moment Diagram (VYMZ-UY)“(2) in table „Details of …“, we must select in row „Path“ the same name
for our beam also „Path“(3).
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Solution – Beam Tool and Force Reaction
We can add also: „Beam Tool“(1) with three possibility of resulting stress. „Direct
Stress“, „Minimum Combined Stress“ and „ Maximum Combined Stress“(2).
Important are also reaction forces. Click on „Probe“(3) and „Force Reaction“(4).
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Solution – Force Reaction continue
After clicking on „Probe“ and „Force Reaction“ select in table „Details of „Force
Reaction“(1) row „Boundary Condition - JointA“(2). After that you can see
small green table in the place of JointA „Force Reaction“(3). Do the same proces
for JointB.
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Solution - Solve
Start computing proces with clicking on „Solve“(1)
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Results – Total Deformation
Details on exercises
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Results – Total Deformation
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Results – Axial Force
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Results – Shear Force
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Results – Bending Moment
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Results – Axial Sress
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Results – Maximum Combined Sress
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Results – Shear-Moment-Diagram
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Results – Force Reaction in JointA
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Results – Force Reaction in JointB
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