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PPrrooffeessssiioonnaallCCoouurrsseeSSeerriieessIINNTTRROODDUUCCTTIIOONNTTOOFFIINNIITTEEEELLEEMMEENNTTMMEETTHHOODD
Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
MODULE C1
MODELING STEPS IN FINITE ELEMENT METHOD
MODELINGSTEPSINFEM FEMSimulatingtheReality
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
Select the solution domain
Discretize the continuum
Choose inerpolation functions
Derive element characteristic
Draw the model geometry
Mesh the model geometry
Select element type
(The FEA software was written to do this)
FE procedures: FE software user steps:
MODELINGSTEPSINFEM FEMSimulatingtheReality
2
Assemble element
characteristic matrices and
vectors
Solve the system equations
Make additional
computations, if desired
(The computer will assemble it)
Input specified load and boundary conditions
(The compiler will solve it)
Request for output
Post-process the result file
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
EXAMPLE: Tension loading of a compact specimen
Objective
To determine internal states (displacements,
strains and stresses) in a C(T) specimensubjected to tension.
P
MODELINGSTEPSINFEM FEMSimulatingtheReality
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Select the solution domain
(Draw the specimen geometry)
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
MODELINGSTEPSINFEM FEMSimulatingtheReality
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
Input materials properties
(Sn-40Pb alloy)
E = 10,000 N/mm2
= 0.3
Elastic-plastic behavior
MODELINGSTEPSINFEM FEMSimulatingtheReality5
1E-3 1/s
1E-4 1/s
1E-5 1/s
0
10
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30
40
0.000 0.005 0.010 0.015 0.020 0.025
Strain
Stress(MPa)
30 oC
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
MODELINGSTEPSINFEM FEMSimulatingtheReality
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
MODELINGSTEPSINFEM FEMSimulatingtheReality
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
Specify load:
P Specify surface interaction:
-Tie center-line to surface of pin
- frictionless pin-hole surface contact
MODELINGSTEPSINFEM FEMSimulatingtheReality8
-
-specify load at mid of center-line:
CF2 = 7,000 N, ramp incrementally
Specify boundary conditions:
Fixed lower pin displacements: U1=U2=U3=0
Allow the upper pin to move in y-direction
(the specimen should be able to rotate at the pin hole)
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
MODELINGSTEPSINFEM FEMSimulatingtheReality
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
Select element type and discretize
(mesh) the model:
(mesh seedingandpartitioning are
used to control mesh size)
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MODELINGSTEPSINFEM FEMSimulatingtheReality12
Run the analysis
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
MODELINGSTEPSINFEM FEMSimulatingtheReality
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
MODELINGSTEPSINFEM FEMSimulatingtheReality
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
Post-process the results
upon successful complete run
MODELINGSTEPSINFEM FEMSimulatingtheReality17
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
Stress-Strain Response
EXAMPLE: Tension loading of a compact specimen
Stress Strain Curves Case One For 60Sn40Pb with Strain Rate 1E-3 1/s
30
40
Pa) ExperimentInput to Abaqus
MODELINGSTEPSINFEM FEMSimulatingtheReality20
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pprreeddiicctteeddrreessppoonnsseeooffmmooddeellssyysstteemm
-CChheecckkrreepprroodduucciibbiilliittyyooffssppeecciiffiieedd
bboouunnddaarryyccoonnddiittiioonnss
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10
20
0 0.005 0.01 0.015 0.02
Strain
Stress(
E = 10GPa
T = 30OC
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
MODELINGSTEPSINFEM FEMSimulatingtheReality
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
See inside the material
MODELINGSTEPSINFEM FEMSimulatingtheReality22
-Extract and interpret important
information / results
- Employ engineering judgment,intuition and lots of common senses
-Address accuracy and validity issue
Notch tip
Tensile
Compressive
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
Illustrative Example
Mesh, load, material propertiesand boundary conditions Elastic properties:
E = 210 GPa
= 0.3rigid pins
MESH REFINEMENT STUDY
MODELINGSTEPSINFEM FEMSimulatingtheReality23
Ux = uy = 0
Ux = 0
Plane stress case
Elastic analysis
Mesh refinement
t (sec.)
Toppin
disp.
(mm)
(200 s,10 mm)
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
Stress Distribution
y
MODELINGSTEPSINFEM FEMSimulatingtheReality24
A B
A B
Results (Observation)
Discussion (Explanation)
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Computational Solid Mechanics Laboratory (CSMLab)
Faculty of Mechanical Engineering
Effect of mesh size on calculated stress
MODELINGSTEPSINFEM FEMSimulatingtheReality25
