real-time dynamic hybrid testing coupled finite element and shaking table

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


Ethernet

Sensor

Shaking table


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


Ethernet

Sensor

Shaking table


Test specimen

1.4. The real-time data acquisition systemHost PC Controller

Feedback

Reference

Ethernet

Target PC

Fiber

Scramnet card


Ethernet

Sensor

Shaking table


Test specimen

Hardware: PXI hardware system

Software: LabVIEW Real-Time Module

The sample rate of single channel can reach 4.4 kHz.

Outlines





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


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





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.


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





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





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!

real-time dynamic hybrid testing coupled finite element and shaking table

Documents

compiled program

fe analysis program

fe numerical substructure

fe model

c program

fe analysis block

realtime system

hybrid elements