Post on 06-Apr-2018
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Finite Element Analysis II
Todays Lecturer: Johan ClausenDepartment of Civil Engineering
Email: jc@civil.aau.dk
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Finite Element Analysis II 2
Finite Element Analysis II
Lectures: Jesper Winther Strdahl and Johan Clausen
The finite element method for structural and solid mechanics
Derivation for stiffness matrices for different elements
Programming of beam and membrane elements (skiveelementer in Danish)
(Re-?) introduction to Abaqus: Meshing and modelling techniques
As usual course information can be found on
\\files.civil.aau.dk\i5jcc\public_html\7sem_finite_element\Finite_element_v2.htm. The
webpage is currently under revision. An e-mail will be sent to you in the event of a
change to the webpage that affects the downloadable items (slides, programs) or the
information regarding the material you have to read before each lecture.
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Finite Element Analysis II 3
Todays lecture: Abaqus, meshing and other things
Modelling of a simple structure in Abaqus
Meshing
Element types
The meshs significance on the stress field
How to model plasticity and other non-linear phenomena
3D meshing
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Finite Element Analysis II 4
Abaqus
A general purpose commercial finite element code
Can model many types of problems linear and non-linear
Structural, heat, flow, conduction, magnetism, dynamic....
The users own materials, elements, etc. can be programmed into Abaqus
Conclusion: VERY versatile and market leader in advanced FE-analysis (mostly in academia)
Drawback 1: Somewhat harder to learn to use compared to other commercial FE-programs
Drawback 2: Commercial licenses are very expensive (Cowi has one license in Denmark)
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Finite Element Analysis II 5
Plane element types
Rods and beams (Danish: stnger og bjlker)
Triangular and quadrilateral membrane elements (Danish: skiveelementer)
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Finite Element Analysis II 6
Three-dimensional element types
Three-dimensional rods and beams
Plate elements
Combined plate and membrane element
Three-dimensional solid (tetrahedral, hexahedral, wedge)
And many more...
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Finite Element Analysis II 7
Modelling a simple plane structure with membrane elements
The material is steel with E= 0.21 106 MPa and = 0.3
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Finite Element Analysis II 8
Modelling a simple plane structure with membrane elements Step 1
Start Abaqus and click Create Model Database
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Modelling a simple plane structure with membrane elements Step 2
Double click Part and fill out the dialogue box Click continue when the box is filled out
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Finite Element Analysis II 10
Modelling a simple plane structure with membrane elements Step 3
Click the Create lines connected button The lines can be drawn by mouse clicks or
by typing in the coordinates as shown
Sketch the part by typing the coordinates
given in slide 7
The window can be adapted to the object
any time by clicking Auto Fit View.
When finished click the Create lines
connected button again and click done-
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Modelling a simple plane structure with membrane elements Step 4
The part SteelThing can be seen in the modeltree by clicking the expansion +
The options under SteelThing can be seen by
expanding the model tree
Go into the mesh-mode by double-clicking
mesh (Empty)
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Modelling a simple plane structure with membrane elements Step 5
The Mesh menu buttons (only some are explained)
Mesh seeds: Specification of
mesh nodes on the boundaries. Is
used to control mesh density.
Mesh controls. Controls the
mathematical algorithm used
to divide the structure into
triangles and quadrilaterals
Create an element mesh
Specify the element type. For example:
Structural or heat conduction.
Linear or 2nd degree shape functions.
Integration point rule (Gauss order)
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Finite Element Analysis II 13
Modelling a simple plane structure with membrane elements Step 6
Open the menu in the seed button by pressing the lower right corner of the button
The different buttons are:
1. Seed part: Used for seeding the entire part
2. Seed Edge by Number: Give the number of elements
on a specific edge
3. Seed Edge by Size: Set the element size on an edge
4. Seed Edge biased: The distance between the nodes
change over the edge
5. The last two buttons are for deleting seeds
1 2 3 4 5
Click Seed Edge by Number (2)
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Finite Element Analysis II 14
Modelling a simple plane structure with membrane elements Step 7
Select the edges and set the appropriate number as shown 2 elements
2 elements
1 element
Type the number here
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Finite Element Analysis II 15
Modelling a simple plane structure with membrane elements Step 8
Press assign mesh controls Select the options as shown in the dialogue box
Click ok
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Modelling a simple plane structure with membrane elements Step 9
Press Assign element type Select the options as shown in the
dialogue box. Remenber to untick the
Reduced integration check box
Press OK
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Modelling a simple plane structure with membrane elements Step 10
Press Mesh Part Press yes under the drawing area
You should now see the depicted
mesh
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Finite Element Analysis II 18
Modelling a simple plane structure with membrane elements Step 11
Double click on the Materials flag in themodel tree
Enter the name Steel in the Name field
Under Mechanical, select Elasticity and
Elastic
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Finite Element Analysis II 19
Modelling a simple plane structure with membrane elements Step 12
Fill in the properties fields and press ok
Important: Abaqus does not check units
in any way! As the dimensions of our model
was entered in mm the all stress terms (e.g.
Eand loads) must be entered in MPa to be
dimensionally consistent.
If we had entered the dimensions in m
the stress terms should have been in Pa.
If in doubt, always use the basic SI-units,
then you never go wrong. (i.e. length in m,
force in N, stress in Pa, and so on)
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Modelling a simple plane structure with membrane elements Step 13
Double click the Sections flag in the model tree Type in the name in the dialogue box
Select settings as shown and press continue
In the Edit Section dialogue select steel as the
material and press OK
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Modelling a simple plane structure with membrane elements Step 14
Double click the Sections Assignment flag in the model tree (in the SteelThing expanded menu) Select the part in the drawing window and click Done
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Modelling a simple plane structure with membrane elements Step 15
Assign the SteelSection and click ok
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Finite Element Analysis II 23
Modelling a simple plane structure with membrane elements Step 16
Expand the Assembly flag in the model tree and double click in Instances
Select the SteelThing part and click ok
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Finite Element Analysis II 24
Modelling a simple plane structure with membrane elements Step 17
Expand the Steps flag in the model tree. You can now see that there is only one step defined, Initial
Double click on Steps
Fill in the dialogue box as shown
Click continue
You have now created the step in which the load is
applied. The initial step is always present and is always the
first step.
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Modelling a simple plane structure with membrane elements Step 18
Fill in the dialogue box as shown and press OK
If, later on, you are going to
include large displacements in youcalculations, this is where you do
it, by setting Nlgeom to on
Also, if you are to perform non-
linear analyses you should enter
the Incrementation flag and
change the settings found here
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Finite Element Analysis II 26
Modelling a simple plane structure with membrane elements Step 19
Double click on the Loads flag in the model tree
Fill in the dialogue box as shown and press Continue.
Note that we select a Pressure load and not a
line load. The line load is used for beam
elements
Note that the load is applied in the LoadStep
step and not in the Inititial step.
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Finite Element Analysis II 27
Modelling a simple plane structure with membrane elements Step 20
Select the top edge of the structure and
press Done
Fill in the dialogue box as shown and
press OK
Note that pressure is given as a
negative number. This is due to the fact
that a positive pressure always acts
towardsthe surface on which it is applied.
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Finite Element Analysis II 28
Modelling a simple plane structure with membrane elements Step 21
An array of arrows representing the pressure
load can now be seen
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Finite Element Analysis II 29
Modelling a simple plane structure with membrane elements Step 22
Double click on the BC flag on the model tree
(BC is an abreviation of Boundary Conditions)
Select Displacement/Rotation and fill in the
dialogue box as shown.
Click Continue.
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Modelling a simple plane structure with membrane elements Step 23
Select the lower edge and press Done
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Finite Element Analysis II 31
Modelling a simple plane structure with membrane elements Step 24
As the edge is free to move in the horizontal (x)
direction but supported in the vertical (y) directon
only tick the box U2
Press OK
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Finite Element Analysis II 32
Modelling a simple plane structure with membrane elements Step 25
Expand the BCs flag. the Vertical support condition should now be visible
Double click on the BCs flag once more to
create the horizontal support
Fill in the dialogue box as shown and press
Continue.
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Finite Element Analysis II 33
Modelling a simple plane structure with membrane elements Step 26
Select the lower left corner of the structure and press Done
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Finite Element Analysis II 34
Modelling a simple plane structure with membrane elements Step 27
Constrain the corner in the horizontal direction and press OK
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Finite Element Analysis II 35
Modelling a simple plane structure with membrane elements Step 28
Double click on the Jobs flag to create a calculation job Fill in the dialogue box as shown
Click Continue
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Finite Element Analysis II 36
Modelling a simple plane structure with membrane elements Step 29
If you like you can fill in a description Then click OK
By expanding the Job flag you
should now see your job
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Finite Element Analysis II 37
Modelling a simple plane structure with membrane elements Step 30
To submit a job for calculation right click on the job name Choose Submit
If a dialogue box appears, click OK
Your job is now being calculated
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Finite Element Analysis II 38
Modelling a simple plane structure with membrane elements Step 31
You can now see that your job is running To monitor you job while running right click on the job name and select Monitor
A dialogue box appears where you can monitor your job.
You can close the box by pressing Dismiss
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Finite Element Analysis II 39
Modelling a simple plane structure with membrane elements Step 32
To go to the post-processing unit to see the results right click on the job name Select Results
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Finite Element Analysis II 40
Modelling a simple plane structure with membrane elements Step 33
Press the Plot contours on deformed shape button
This will show the von Mises Stress contours on
the deformed structure.
To view other stresses select the field Output
option in the main tool bar. Here you can select the
result that you want to plot.
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Finite Element Analysis II 41
Modelling a simple plane structure with membrane elements Step 34
To find out the node number and itsdisplacement click the Tool- drop down
menu
Select Query
In the Query dialogue box select
Node
Click on the node on the inside corner(denoted A on slide 7)
You can now see the node number and
the nodal displacement
Note the node number
Repeat with node B on slide 7 and
note the displacement. You will need it for
comparison later.
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Finite Element Analysis II 42
Modelling a simple plane structure with membrane elements Step 35
To find out the exact stress value of a point select Query in menu Tools
Select Probe values in the dialogue box
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Finite Element Analysis II 43
Modelling a simple plane structure with membrane elements Step 35
Tick the boxes as shown and move the cursor to where you want to see the von Mises stress
Note the values of the
stress at point A from slide
no. 7 (the indside corner).
You will need this value later
in the lecture.
Here you need the node
number that you noted
earlier, in order to know
which of the displayed
stress values belongs to the
corner node.
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Finite Element Analysis II 44
Different meshing techniques
Demonstrated by lecturer
Exercise: Try to mesh the structure with different mesh techniques and different elements
(triangular, quadrilateral, linear shape functions, 2nd degree shape functions). For each mesh note
the von Mises stress of point A and the displacement of point B. Do they differ in each case?
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Finite Element Analysis II 45
Non-linear analyses
von Mises plasticity
Large displacements
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Finite Element Analysis II 46
Analysis of a shell structure
The load is a uniform pressure load The holes are centrally placed circles with a radius of 10 mm
The shell thickness is 2 mm
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Finite Element Analysis II 47
Use of symmetry
We make use of symmetry to reduce the number of elements
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Thank you for your attention