8.masat 20112-13 smearedcrackmodel mindlinshell
TRANSCRIPT
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SMEARED CRACK MODEL FOR MATERIAL
NONLINEAR ANALYSIS OF MINDLIN SHELLS
U n i v e r s i t y o f M i n h o
Department of Civil Engineering
Guimares, Portugal
[email protected] www.civil.uminho.pt
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8/11/2019 8.MASAT 20112-13 SmearedCrackModel MindlinShell
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Lighter parts of the panel
Developed Lightweight SFRSCC panel
30 mm thick
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
Acess punching resistance
PasteTotal volume
(%)
CementCEM I 42.5R
(kg)
Limestonefiller
(kg)
Water
(dm3)
Super-plasticizer
*
(dm3)
Finesand
(kg)
Coarsesand
(kg)
Crushedaggregates
(kg)
0.34 364.28 312.24 93.67 6.94 108.59 723.96 669.28
T50 = 4.6 seconds; fcm= 52 MPa; Ecm= 31GPa
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RESEARCH AIMS
Propose a model for simulating the behavior
of cement based laminar structures failing inbending and in shear
Use Reissner-Mindlin theory in the context of
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
layered shell
Propose a strain-stress softening diagram forthe out-of-plane shear
Compare the proposed model withexperimental punching tests in SFRSCC panels
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Numerical Model
Reissner-Mindlin theory was selected
damage due to crack formation andpropagation was simulated by discretizing the
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
0
0
crco
mf mf mf
crco
s ss
D
D
=
For the case of cracked concrete theconstitutive law is:
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Numerical Model
In-plane components
z
xy
x
x
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
y
x x
y
y
yxxy
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z
yz
xz
Numerical Model
Out-of-plane components
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
y
xdistribuio real
distribuio aproximada
yz
xz
real distribution
approximatedistribution
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Numerical Model
In-plane cracked concrete constitutive matrix
( ), ,1
, ,
ccrco co co co
mf e mf e mf e mf
T Tcrco cr cr r r
mf
c
eT T T T DD D D DD
= +
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
x1
x2
t
Crack
n
cr
n
cr
t
cr
tcr
n w
s
0
0
crcr I
cr
II
DD
D
=
, 2
1 01 0
11
0 02
co cmf e
ED
=
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Numerical Model
Crackconstitutive matrix
n1Dcr
ncr
n,1cr
n,2cr I
fG crcr =
,
cr
n p
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
0
0
cr
I
cr
I
cr
IDD
D =
n,ucr
cr
D
Dcr
n2
n3
crnn,3crn,2
cr
n,3cr
nsecDcr
bl
1
cr
II cD G
=
1
,
1
pcr
n
cr
n u
=
,,
,2 2 ,
cr cr
n n p =
,1 1 ,
cr cr
n n u = ,2 2 ,cr cr
n n u = ,
cr
n u
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Numerical Model
Out-of-plane
constitutive matrix
23
,sec
31
,sec
0
0
crco IIIs
III
DD
D
=
linear behaviorOP
OP
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
p
Gc DIII,sec
GIII
f
lb
OP
max OP
OP
uOP
maxOP
p
max-OP
-OPu
-OPmax
-OPp
p-OPShear stress-strain
diagram
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Inverse Analysis
Fracture mode I
8 node serendipityplane stress elements2 2 inte ration oints
8 node serendipityplane stress elements1 2 inte ration oints
(a)5
10
15
20
25
scatter of experimental results
experimental average results
numerical simulation
(b)
Load[kN]
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
x
y
elastic behaviour
elastic-cracked behaviour
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
Deflection[mm]
i i fG
Fracture parameters
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Panels failing in bending
Model appraisal
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
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30
40
50
60
oad
[kN]
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
0.0 0.5 1.0 1.5 2.0
0
10
20
Average Displacement [mm]
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Panels failing in shear
150 150
150
150
300
300
Steel Plate
(100x100x10)
Q Q'
Panel Prototype
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
SFRSCC
Steel Plate (100x100x10)
Actuator
150 150300(x300)
80
30
Q-Q'
Polystyrene
500
Test setup
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Numerical Simulation
FEM Mesh
+
Point load
m
x2
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
65
0mm
+
6 50 mm
T
hickness-111
0
x1
Line springs
T
hickness-310
m
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Numerical SimulationRelationship between the force and the
deflection at the center of the test panel
50
60
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
0
10
20
30
40
0 2 4 6 8 10
Displacement (mm)
Force(kN
)
SFRSCC - experimental
SFRSCC - linear out-of-plane shear
SFRSCC - softening out-of-plane shear
Plain concrete
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Numerical Simulation
Vertical displacement field
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
Punching critical contour
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Conclusions
A softening diagram was proposed to model,
after crack initiation, both out-of-plane shearstress-strain constitutive laws
Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering
The developed model is based on FEM and wasimplemented in the FEMIXcomputer program.
A very good agreement between theexperimental results and the proposed modelis observed.
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Joaquim Barros
Modeling and Advanced Structural Analysis Techniques
University of Minho Department of Civil Engineering