Application of FEM

7/28/2019 Application of FEM

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Introduction into

Application

of

Finite Elemente Method

Institute for Internal Combustion Engines & Thermodynamics

Research Area Design

Dr. techn. Stephan Schmidt

[email protected]


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The Finite Element MethodThe Theory of the Finite Element

The major finite elements in structural mechanics

Procedure of the der FE-Analysis Pre-Processing

Solution

Post-Processing

Application examples

Content


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Content




Solution

Post-Processing



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Finite Element Method

Substitution of real structures which can not be solved in an analytic way by asimplified model.

The model consists of simple finite Elements, for which analytically solvableequations (element formulation) can be formulated.

Every FE calculation is an approximation of the reality.

The accuracy of the FE-calculation depends on the assumptions of boundaryconditions, the discretisation, the element formulation, the mesh quality andthe interpretation of the results.

The finite element method can be applied to structural mechanic, electrical,fluid dynamic and other problems.


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Discretisation Finite elements

Substitiut ion of the real structur by a simplified model


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Element formulation

lcF =

( )

( )2122

2111

uuclcF

uuclcF

+==

==

=

2

1

2

1

11

11

u

uc

F

F

u1 u2

1 2F1 F2

{ } [ ] { }uKF =


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Theory of the finite elements

Mathematical description of the element displacement

Composition of the single stiffness matrices to one global stiffness matrix [K]

Displacement of the nodes are unknown

Each degree of freedom at a node results in one equation

The equation {F} = [K] * {u} equilibrates the displacements with the forces

The solution of the equation for the whole system results in displacements andhence in stresses.


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Content




Solution

Post-Processing



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Discretisation by finite elements

Rigid: rigid connection of two nodes

Beam: elastic connection of two nodes

Shell: thin-wall surface element

Solid: volume element

Gap: gap element


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Finite elements: 1-dimensional

Rigid element: 2 nodes 6 degrees

of freedom per node

Linear beam element:

2 nodes & 6 degrees of freedom

per node


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Linear triangle shell element, 3nodes 3x6 degree of freedom

linear quad shell element4 nodes 4x6 degree of freedom

parabolic quad shell element, 8

nodes 8x6 degree of freedom


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linear tetraeder element

4 nodes 4x6 degree of freedom

linear wedge element


linear brick element (hexaeder)



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Content




Solution

Post-Processing



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Procedure of the FE Analysis

geometry

discretisatoin /mesh generation

problem definition =boundary condition

solution

evaluation

Preprocessing

Solution

Postprocessing


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Pre-Processing:

Generation or import of geometry data Simplification of the real structure

Transition of the simplified structure in a FE model (meshing)

Assignment of element properties

Assignment of material properties

Definition of boundary conditions

Solution: solution of the equation {F} = [K] * {d}

Post-Processing: evaluation and display of the results

displacements stresses

forces

etc.


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Pre-Processing:









forces

etc.


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Pre-Processing

Generation of the geometry in the

FE-program packages


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Pre-Processing

Import of the geometry from a

CAD-Program

Interfaces:

IGESVDA

Translator


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Pre-Processing:









forces

etc.


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Pre-Processing:









forces

etc.


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Pre-Processing

Manual meshing: Automated meshing:


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Pre-Processing

Element properties

Material properties


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Pre-Processing:









forces

etc.


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Pre-Processing

Lock of degree of freedom

Application of

- force- torque- pressure

- displacement


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Pre-Processing:









forces

etc.


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Solution

Equation solver Contakt Convergence


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Pre-Processing:









forces

etc.


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Post-Processing

Display of results

point 8 velocity x

-2.E+00

-2.E+00

-1.E+00

-5.E-01

0.E+00

5.E-01

1.E+00

2.E+00

2.E+00

10.00000 10.01000 10.02000 10.03000 10.04000 10.05000 10.06000 10.07000 10.08000 10.09000 10.10000

time [s]

velocity[mm/s]

Gehusepunkt 8 Orig vx

Gehusepunkt 8 New A

Gehusepunkt 8 New B


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Simple beam

Cylinder Normal modes for accustic analysis

Cover Normal modes for accustic analysis

Piston Cylinder deformation by operating conditions

Transient analysis of a compressor housing

Vibration analysis of a Scooter powertrain


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3D CAD structure


li i l


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FE model based on linear beam elements


A li i l


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FE model based on linear shell elements


A li ti l


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FE model based on linear hexaeder


A li ti l


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Deformation


A li ti l


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Stress (von Misses)


A li ti l


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Stress in axial direction


A li ti l


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Distortion energy




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Cylinder CATIA-Model




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Cylinder Normal modes




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Cover CATIA-Model




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Cover Normal modes




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Piston-Cylinder

FE-Model

mechanical load:

ignition pressure 27 bar

Thermal load:

piston: 200C - 335Ccylinder: 155C - 225C

Temperatur distribution

at piston pin




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Piston - Cylinder




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Cooling compressor 3D- CATIA Model

Cooling compressor FE- Volume model




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Cooling compressor view bottom up locations of force

introduction




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Cooling compressor MBS-Model




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Loadfunction Point 1 x-Direction

-2.00E+02

-1.50E+02

-1.00E+02

-5.00E+01

0.00E+00

5.00E+01

10.00000 10.01000 10.02000 10.03000 10.04000 10.05000 10.06000 10.07000 10.08000 10.09000 10.10000

Time[sec]

Force[mN]

Result of MBS-Analysis = Input to FE-Analysis




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Cooling compressor

deformation




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Cooling compressor points of evaluation




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point 6 displacement y

-2.E-03

-1.E-03

0.E+00

1.E-03

2.E-03

3.E-03

4.E-03

10.00000 10.01000 10.02000 10.03000 10.04000 10.05000 10.06000 10.07000 10.08000 10.09000 10.10000

time [sec]

displacementy[mm]

Gehusepunkt 6 Orig

Gehusepunkt 6 New A

Gehusepunkt 6 New B ypoint 6 velocity y

-3.E+00

-2.E+00

-2.E+00

-1.E+00

-5.E-01

0.E+00

5.E-01

1.E+00

2.E+00

2.E+00

3.E+00

10.00000 10.01000 10.02000 10.03000 10.04000 10.05000 10.06000 10.07000 10.08000 10.09000 10.10000

time [s]

velocity[mm/s]

Gehusepunkt 6 Orig vy

Gehusepunkt 6 New A

Gehusepunkt 6 New B

Cooling compressor

evaluation:

displacement / time



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Procedure FEM-Analysis usingI-DEAS

Ablauf FEM mit I-DEAS


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Ablauf FEM mit I DEAS

Geometry

Discretisation Mesh

Material

Element

Boundary

Condition

s

L.CR.S.

B.C.S.

extrusion

So

lver S.S

Solve

Post-

Process.

Results

Show

drawing



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Ablauf FEM mit I DEAS

physical property table

materials

meshing

extrudieren

zeichnenGeometry

Discretisation Mesh

Material

Element

Boundary

Condition

s

L.CR.S.

B.C.S.

So

lver S.S

Solve

Post-

Process.

Results

Show



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b au S


materials

load case

restraint set

boundary condition set

meshing

extrudieren

zeichnenGeometry

Discretisation Mesh

Material

Element

Boundary

Condition

s

L.CR.S.

B.C.S.

So

lver S.S

Solve

Post-

Process.

Results

Show



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materials

load case

restraint set


solution set

manage solve

meshing

extrudieren

zeichnenGeometry

Discretisation Mesh

Material

Element

Boundary

Condition

s L.C

R.S.

B.C.S.

So

lver S.S

Solve

Post-

Process.

Results

Show



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materials

load case

restraint set


solution set

manage solve

results

display

meshing

extrudieren

zeichnenGeometry

Discretisation Mesh

Material

Element

Boundary

Condition

s L.C

R.S.

B.C.S.

So

lver S.S

Solve

Post-

Process.

Results

Show

Documents

Application of FEM