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structural_mechanics_softening.py
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Mon, Oct 28, 23:50
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text/x-python
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rAKA akantu
structural_mechanics_softening.py
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#!/usr/bin/env python
# coding: utf-8
# # Test of Structural Mechanics
# In this test there is a beam consisting of three parts, all have the same materials.
# The left most node is fixed.
# On the right most node a force is applied in x direction.
#
# After a certain time, the material of the middle _element_ is waekened, lower Young's modulus.
# In each step the modulus is lowered by a coinstant factor.
import
akantu
as
aka
import
numpy
import
numpy
as
np
try
:
import
matplotlib.pyplot
as
plt
has_matplotlib
=
True
except
ImportError
:
has_matplotlib
=
False
# ### Creating the Mesh
# Create a mesh for the two dimensional case
beam
=
aka
.
Mesh
(
2
)
# We now create the connectivity array for the beam.
beam
.
addConnectivityType
(
aka
.
_bernoulli_beam_2
)
# We need a `MeshAccessor` in order to change the size of the mesh entities.
beamAcc
=
aka
.
MeshAccessor
(
beam
)
# Now we create the array to store the nodes and the connectivities and give them their size.
beamAcc
.
resizeConnectivity
(
3
,
aka
.
_bernoulli_beam_2
)
beamAcc
.
resizeNodes
(
4
)
# #### Setting the Nodes
Nodes
=
beam
.
getNodes
()
Nodes
[
0
,
:]
=
[
0.
,
0.
]
Nodes
[
1
,
:]
=
[
1.
,
0.
]
Nodes
[
2
,
:]
=
[
2.
,
0.
]
Nodes
[
3
,
:]
=
[
3.
,
0.
]
# #### Setting the Connections
Conn
=
beam
.
getConnectivity
(
aka
.
_bernoulli_beam_2
)
Conn
[
0
,
:]
=
[
0
,
1
]
Conn
[
1
,
:]
=
[
1
,
2
]
Conn
[
2
,
:]
=
[
2
,
3
]
#### Ready
# We have to make the mesh ready.
beamAcc
.
makeReady
()
# ### Creating the Model
model
=
aka
.
StructuralMechanicsModel
(
beam
)
# #### Setting up the Modell
# ##### Creating and Inserting the Materials
mat1
=
aka
.
StructuralMaterial
()
mat1
.
E
=
1e9
mat1
.
rho
=
1.
mat1
.
I
=
1.
mat1
.
Iz
=
1.
mat1
.
Iy
=
1.
mat1
.
A
=
1.
mat1
.
GJ
=
1.
mat1ID
=
model
.
addMaterial
(
mat1
,
'mat1'
)
mat2
=
aka
.
StructuralMaterial
()
mat2
.
E
=
1e9
mat2
.
rho
=
1.
mat2
.
I
=
1.
mat2
.
Iz
=
1.
mat2
.
Iy
=
1.
mat2
.
A
=
1.
mat2
.
GJ
=
1.
mat2ID
=
model
.
addMaterial
(
mat2
,
'mat2'
)
mat3
=
aka
.
StructuralMaterial
()
mat3
.
E
=
mat2
.
E
/
100000
mat3
.
rho
=
1.
mat3
.
I
=
1.
mat3
.
Iz
=
1.
mat3
.
Iy
=
1.
mat3
.
A
=
mat2
.
A
/
100
mat3
.
GJ
=
1.
mat3ID
=
model
.
addMaterial
(
mat3
,
'mat3'
)
# ##### Initializing the Model
model
.
initFull
(
aka
.
AnalysisMethod
.
_implicit_dynamic
)
# ##### Assigning the Materials
materials
=
model
.
getElementMaterial
(
aka
.
_bernoulli_beam_2
)
materials
[
0
][
0
]
=
mat1ID
materials
[
1
][
0
]
=
mat2ID
materials
[
2
][
0
]
=
mat1ID
# ##### Setting Boundaries
# Neumann
# Apply a force of `10` at the last (right most) node.
forces
=
model
.
getExternalForce
()
forces
[:]
=
0
forces
[
2
,
0
]
=
100.
# Dirichlets
# Block all dofs of the first node, since it is fixed.
# All other nodes have no restrictions
boundary
=
model
.
getBlockedDOFs
()
boundary
[
0
,
:]
=
True
boundary
[
1
,
:]
=
False
boundary
[
2
,
:]
=
False
boundary
[
3
,
:]
=
False
# ### Solving the System
# Set up the system
deltaT
=
1e-9
model
.
setTimeStep
(
deltaT
)
solver
=
model
.
getNonLinearSolver
()
solver
.
set
(
"max_iterations"
,
100
)
solver
.
set
(
"threshold"
,
1e-8
)
solver
.
set
(
"convergence_type"
,
aka
.
SolveConvergenceCriteria
.
solution
)
# Perform N time steps.
# At each step records the displacement of all three nodes in x direction.
N
=
10000
*
60
disp0
=
np
.
zeros
(
N
)
disp1
=
np
.
zeros
(
N
)
disp2
=
np
.
zeros
(
N
)
disp3
=
np
.
zeros
(
N
)
times
=
np
.
zeros
(
N
)
switchT
=
None
switchEnd
=
None
softDuration
=
1000
SoftStart
=
(
N
//
2
)
-
softDuration
//
2
SoftEnd
=
SoftStart
+
softDuration
if
(
softDuration
>
0
):
softFactor
=
(
model
.
getMaterial
(
'mat3'
)
.
E
/
model
.
getMaterial
(
'mat2'
)
.
E
)
**
(
1.0
/
softDuration
)
mat2
=
model
.
getMaterial
(
'mat2'
)
for
i
in
range
(
N
):
times
[
i
]
=
deltaT
*
i
if
((
SoftStart
<=
i
<=
SoftEnd
)
and
(
softDuration
>
0
)):
if
switchT
is
None
:
switchT
=
times
[
i
]
elif
(
i
==
SoftEnd
):
switchEnd
=
times
[
i
]
#
mat2
.
E
*=
softFactor
#
model
.
solveStep
()
disp
=
model
.
getDisplacement
()
disp0
[
i
]
=
disp
[
0
,
0
]
disp1
[
i
]
=
disp
[
1
,
0
]
disp2
[
i
]
=
disp
[
2
,
0
]
disp3
[
i
]
=
disp
[
3
,
0
]
disps
=
[
disp0
,
disp1
,
disp2
,
disp3
]
maxMin
=
[
-
1.0
,
1.0
]
for
d
in
disps
:
maxMin
[
0
]
=
max
(
np
.
max
(
d
),
maxMin
[
0
])
maxMin
[
1
]
=
min
(
np
.
min
(
d
),
maxMin
[
1
])
if
has_matplotlib
:
#plt.plot(disp0, times, color='k', label = "left node (fix)")
plt
.
plot
(
disp1
,
times
,
color
=
'g'
,
label
=
"middle, left node"
)
plt
.
plot
(
disp2
,
times
,
color
=
'g'
,
linestyle
=
'--'
,
label
=
"middle, right node"
)
plt
.
plot
(
disp3
,
times
,
color
=
'b'
,
label
=
"right node"
)
if
(
softDuration
>
0
):
plt
.
plot
((
maxMin
[
1
],
maxMin
[
0
]),
(
switchT
,
switchT
),)
plt
.
plot
((
maxMin
[
1
],
maxMin
[
0
]),
(
switchEnd
,
switchEnd
),
)
plt
.
title
(
"Displacement in $x$ of the nodes"
)
plt
.
ylabel
(
"Time [S]"
)
plt
.
xlabel
(
"displacement [m]"
)
plt
.
xlim
((
maxMin
[
1
]
*
1.3
,
maxMin
[
0
]
*
1.1
))
plt
.
legend
()
plt
.
show
()
# If the softening is disabled, then the displacement looks wierd.
# Because the displacement first increases and then decreases.
# In this case `softDuration > 0` holds.
#
# However if the softening is enabled, it looks rather good. The left middle
# node will start to vibrate, because it is not pulled in the other direction.
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