Micro/macro analysis of a composite Casa Day 22/11/06.
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Transcript of Micro/macro analysis of a composite Casa Day 22/11/06.
![Page 1: Micro/macro analysis of a composite Casa Day 22/11/06.](https://reader030.fdocuments.in/reader030/viewer/2022032804/56649edd5503460f94beddcf/html5/thumbnails/1.jpg)
Micro/macro analysis of a compositeCasa Day 22/11/06
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Aloha Airlines Flight 243
Motivation
Honolulu International Airport, Hawaii
At 24000 feet… loud clap
No visual exterior inspection (nor required)
Flight attendant swept out of the cabin
1 dead, 65 injured
$5 million damage
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Peel Test
45º
Force Displacement (constant speed)
Nickel layer
Substrate
Peel-Test Support
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Composites
Matrix
Inclusions
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Elasticity problem for a composite material
Matrix
InclusionsMatrix Inclusions
Material Interface
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Modelling
Matrix
InclusionsMatrix Inclusions
Material Interface
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Homogenisation
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Homogenisation
fu Α fu Α
0
uu
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Homogenisation
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Homogenised equations
Boundary Conditions
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Macro results
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Micro/Macro
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Domain decomposition
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Dirichlet – Neumann scheme
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Finite element approximation
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Finite element approximation
Schur complement system
• symmetric
• positive definite
• ill conditioned
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Algorithm
Dirichlet problem
Neumann Problem
Relaxation step
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Algorithm
is a preconditioner for
Theorem:
This process converges if
where is the maximum eigenvalue of .
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Heterogeneous domain decomposition
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Heterogeneous domain decomposition
Interface conditions
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Overview
homoge-
nisation
D-N
Interface conditions?
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Example
Reference solution
Macro domain
Meso domain
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Example
Macro domain
Meso domain
Absolute error for
the horizontal displacementu1-uref 0.6012
u2-uref 0.6701
u3-uref 0.1392
u4-uref 0.0305
u5-uref 0.0176
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Future Work
- Interface conditions discussion
- Crack propagation