tsinghua university·beijing 2012-05-18 real-time dynamic hybrid testing coupled finite element and...
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Tsinghua University·Beijing
2012-05-18
Real-time dynamic hybrid testing coupled finite element and shaking table
Jin-Ting Wang, Men-Xia Zhou & Feng Jin
Outlines
Introduction to testing system1
Finite element numerical substructure2
Single-table testing for soil-structure interaction analysis3
Dual-table testing for travelling wave effect analysis4
Summaries5
1. Introduction to testing system
System framework of Tsinghua real-time dynamic Hybrid testing System (THS)
MTS Controller
MTS ControllerHost PC
Ethernet
Ethernet
SimulinkHost PC
SimulinkTarget PC
Ethernet
Fiber
Scramnet
Scramnet
Control Room
Data Acquisition
Ethernet
Table 1
Table 2
Ethernet
1.1. The shaking table loading system
Two identical uni-axial shaking tables
Working area: 1.5 X1.5 m2 for each table
Bearing capacity: 2 tone.
The frequency range: 0–50 Hz.
The maximum acceleration: 3.6 g for bare table, 1.2 g for full loaded.
Host PC Controller
Feedback
Reference
Ethernet
Target PC
Fiber
Scramnet card
FE numerical substructure
Ethernet
Sensor
Shaking table
Data acquisition system
Test specimen
1.2. The distributed real-time calculation system
Real-time calculation system was constructed on a standard PC with the help of xPC TARGET software
Host PC: Develop procedure and debug code
Target PC: Execute real-time calculation
Host PC Controller
Feedback
Reference
Ethernet
Target PC
Fiber
Scramnet card
FE numerical substructure
Ethernet
Sensor
Shaking table
Data acquisition system
Test specimen
1.3. The shared common RAM network
SCRAMNet cards
The data transfer speed reaches up to 16.7 MB/s
The latency is not more than 250 ns.
Host PC Controller
Feedback
Reference
Ethernet
Target PC
Fiber
Scramnet card
FE numerical substructure
Ethernet
Sensor
Shaking table
Data acquisition system
Test specimen
1.4. The real-time data acquisition systemHost PC Controller
Feedback
Reference
Ethernet
Target PC
Fiber
Scramnet card
FE numerical substructure
Ethernet
Sensor
Shaking table
Data acquisition system
Test specimen
Hardware: PXI hardware system
Software: LabVIEW Real-Time Module
The sample rate of single channel can reach 4.4 kHz.
Outlines
Introduction to testing system1
Finite element numerical substructure2
Single-table testing for soil-structure interaction analysis3
Dual-table testing for travelling wave effect analysis4
Conclusions5
2.1. About FE substructure of RTDHT
Chen and Ricles (2012) developed an independently compiled program named “HybridFEM”.
The program was compiled in Matlab, and can perform FE analysis.
An RTDHT was carried out with the numerical substructure simulated as an FE model with 71 beam elements.
Chen C, Ricles JM. Large scale real-time hybrid simulation involving multiple experimental substructures and adaptive actuator delay compensation. Earthquake Engineering and Structure Dynamics 2012; 41(3): 549-569.
2.1. About FE substructure of RTDHT
Saouma et al. (2012) developed an independently compiled
program named “Mercury”.
The program is a set of two identical programs: MATLAB
version for instruction, prototyping, and pre-test evaluation; C+
+ version designed for embedding into real-time system.
Data was interacted by hybrid elements in the program.
An RTDHT was implemented with the numerical substructure
simulated as an FE model with 140 flexibility-based elements.
Saouma V, Kang DH, Haussmann G. A computational finite-element program for hybrid simulation. Earthquake Engineering and Structure Dynamics 2012; 41(3): 375-389.
2.2. Our solution to FE substructure
An independently-developed FE analysis block was compiled in S-function.
The new developed block is fully compatible with built-in Simulink blocks.
Don’t need the hybrid elements for data interaction.
Solid elements are used in our FE model.
Target PC
Finite element analysis program
2.3. Generation of the user-compiled block
The FE analysis program is compiled in C++.
The C++ program is then transplanted into S-function
following the special calling syntax.
Finally, the user-compiled block is incorporated into the
Simulink procedure to develop the FE numerical
substructure.
A C++ FE analysis program
User-complied block
FEM_solver
S-function
transplant into S-function
incorporate into Simulink
procedure
FE numerical substructure
2.4. Execution of the user-compiled block
Simulation Start
mdlInitializeSizes
mdlInitializeSampleTimes
mdlStart
mdlOutputs
mdlTerminate
Simulation End
initializationphase
simulation loop
termination phase
read FE model dataform matrices
input external loadsolve FE equation
release memory
allocate memorydetermine parameters
determine sample time
2.5. Task Execution Time
The dynamic response of a linear FE model with 66 nodes (132 DOFs) is solved to check the calculation speed of the numerical substructure with FE function.
2.5. Task Execution Time
0
1
2
0 1000 2000 3000 4000
Step
TET(
ms)
The task execution time
The frequency of the shaking table controller in THS
is 1/2048 s.
The task execution time of
most simulation steps is about
0.47 ms, but it may
significantly increases at a
certain step. This leads to the
real-time calculation interrupt.
2.5 Task Execution Time
The system management
interrupt occasionally occurs
in the CPU chip.
A “disableSMI” block is added
to the Simulink procedure. 0
0. 2
0. 4
0. 6
0 1000 2000 3000 4000 5000
Step
TET(
ms)
The real-time calculation
completed successfully.
The task execution time
Outlines
Introduction to testing system1
Finite element numerical substructure2
Single-table testing for soil-structure interaction analysis3
Dual-table testing for travelling wave effect analysis4
Conclusions5
3.1. Finite soil foundation
A shear frame mounted on the finite soil foundation was
tested.
, sc
Finite soilfoundation
Exten
d
Finite soilfoundation model
U
Superstructurephysical model
Shaking table
Interactionforce
Displacement
m
k c
(1) Physical substructure
The upper steel plate mass is 5.28 kg.
White noise excitation shows that the natural frequency of the frame is 4.57 Hz.
The stiffness and damping are calculated as 4350 N/m and 13.07 N∙s/m, respectively.
It can be considered as a single DOF system in the in-plane movement.
Physical substructure
(2) Numerical substructure
50 four-node solid elements, 66 nodes.
A total of 132 DOFs.
The material properties: mass density 2000 kg/m3;
elastic modulus 200 MPa; poisson’s ratio 0.2.
FE numerical substructure
0 1 2 3 4 5-0.6
0.0
0.6
acce
lera
tion
(g)
time (s)
Abaqus RTDHT
(3) Acceleration at frame top
The peak of the acceleration at frame top is 0.56 g by
RTDHT while 0.49 g by pure FEM, the error is 10.9%.
0 1 2 3 4 5-0.3
0.0
0.3
acce
lera
tion
(g)
time (s)
Abaqus RTDHT
(3) Acceleration at frame bottom
The peak of the acceleration, at frame bottom is 0.22 g
by RTDHT while 0.19 g by pure FEM, the error is 12.1.
0 1 2 3 4 5-4
0
4
disp
lace
men
t (m
m)
time (s)
Abaqus RTDHT
(4) Displacement at frame bottom
The peak of the displacement at frame bottom is 4.06
mm by RTDHT while 3.84 mm by pure FEM, the error
is 5.4%
3.2. Infinite soil foundation
The foundation is regarded as infinite
The radiation damping is simulated by the viscous-
spring artificial boundary.
, sc
Semi-infinitesoil foundation
Exten
d
Semi-infinte soil artificial
boundary model
U
Superstructurephysical model
Shaking table
Interactionforce
Displacement
m
k c
(1) Effect of the radiation damping
0 1 2 3 4 5-0.6
0.0
0.6ac
cele
rati
on (
g)
time (s)
with AB without AB
The dynamic response remarkably decreases due to
the radiation damping effect of the infinite foundation.
The peak of the acceleration decreases by 43% at
frame top and 39% at frame bottom.
Acceleration at frame top
(2) Effect of foundation stiffness
0 1 2 3 4 5-0.8
0.0
0.8
acce
lera
tion
(g)
time (s)
Cs=204.1m/s Cs=816.5m/s
The dynamic response under soft soil is considerably
smaller than that under hard soil.
The peak of acceleration decreases by 53% at frame
top and 60% at frame bottom.
The SSI of different soil conditions differs remarkably.
Acceleration at frame top
Outlines
Introduction to testing system1
Finite element numerical substructure2
Single-table testing for soil-structure interaction analysis3
Dual-table testing for travelling wave effect analysis4
Conclusions5
4.1. Design of the testing
Two shear frames are tested as the physical substructure by two
shaking tables.
The foundation is simulated by the FE numerical substructure.
, scSemi-infinite soil foundation
Exten
d
Exten
d
Distance
Shear frame No.1
Shear frame No.2
Semi-infinite soil artificial boundary model
1k
1c
1m
2k
2c
2mSuperstructure physical model
Shaking Table 1
Interaction force 1
Displacement 1
Shaking Table 2
Shear frame No.1
Shear frame No.2 Interaction
force 2
Displacement 2A B
4.2. Physical substructure
The shear frame No.1 used in the experimental
substructure is the same as before.
The shear frame No.2 is very similar with No.1.
Mass / kg Stiffness / N/m
Damping / N∙s/m
Natural frequency / Hz
Damping ratio
shear frame No.1
5.28 4353.4 13.0688 4.57 4.31
shear frame No.2
5.20 4387.1 14.9438 4.62 4.95
4.3. Numerical substructure
k1
c1
m1 m2
c2
k2
A BC
Shear frame No.1
Shear frame No.2
viscous-spring artificial boundary
There are 48 four-node solid elements and 65 nodes.
The viscous-spring artificial boundary is set at the
truncated boundary.
4.4. Acceleration at the frame top
0 1 2 3 4 5-0.4
0.0
0.4
acce
lera
tion
(g)
time (s)
Shear frame No.1 Shear frame No.2
Local amplification
The dynamic responses of two shear frames have
significant phase difference.
The phase difference is about 0.046 s.
The travelling wave effect has been simulated.
2.0 2.2 2.4 2.6 2.8 3.0-0.4
0.0
0.4
acce
lera
tion
(g)
time (s)
Shear frame No.1 Shear frame No.2
t
Outlines
Introduction to testing system1
Finite element numerical substructure2
Single-table testing for soil-structure interaction analysis3
Dual-table testing for travelling wave effect analysis4
Conclusions5
Summaries
An FE analysis block is compiled in S-function.
Thus an RTDHT system coupled finite element
calculation and shaking table testing is achieved.
The dynamic soil-structure interaction and the
travelling wave effect are simulated in RTDHT by
using the FE numerical substructure.
The capacity of the real-time hybrid testing is
improved due to the FE numerical substructure.
Acknowledgement
This research was supported by the
National Natural Science Foundation of China
(Nos.51179093). The support is gratefully
acknowledged.
Thank you for your attention!