Horta Torus Structure

8/12/2019 Horta Torus Structure

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Langley Research Center

Static and Dynamic Model Update of anInflatable/Rigidizable Torus Structure

(Work In Progress)

Lucas G. Horta

and Mercedes C. Reaves

Structural Dynamics Branch

NASA Langley Research Center

FEMCI Workshop 2005

May 5, 2005


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Background The TSU* Hexapod is a generic test bed

that incorporates design features of

structures that can be packed for launchand deployed in space

Inflatable/rigidizable structures can be

inflated to more than 12 times their

packaged size enabling new space mission

scenarios

However, new fabrication techniques also

bring new modeling challenges

*TSU= Tennessee State University


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Objective and MotivationObjective-To develop a mathematical

and computational procedure to

reconcile differences between finite

element models and data from staticand dynamic tests

Motivation- All missions envisioned

for inflatable and rigidizable systemswill require state of the art controls

and accurate analytical models. In

the Hexapod case, the initial model

missed many important modes

10 20 30 40 50 60 70 80 90 100 11010

-5

10-4

10-3

10-2

10-1

Freq. (Hz)

Mag

Scale Factor = 0.11241 Sensor No. 12 Shaker 2

Test

NASTRAN

10 20 30 40 50 60 70 80 90 100 110-150

-100

-50

0

50

100

Freq. (Hz)

Phase(deg)

Initial ModelShaker No. 2


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ApproachFEM developed using commercial tools

Static test results used to update stiffness values

Dynamic test results used to update mass distribution

Probabilist ic assessment used to compute most likely set

of parameters

Update parameters computed via nonlinear optimization(genetic and gradient based)

Computational tools based on MATLAB

System ID using the Eigensystem Realization AlgorithmIncremental update of components starting with torus


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Model Update Procedure

Develop

baseline

fini te element

model Select

parametersfor update

Define parameter

bounds & probability

distribution

Compute output

probability &sensitivity valuesReduce parameter set

using sensitivity and

probability resultsSolve

optimization for

updated

parameters &probability


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Computational Framework

NASTRANStatic

Dynamic

Bulk DataFile

Output DataFile

MATLABOptimization

Probability

Sensitivity

System ID

External Inputs

1- Parameter selection

and prob. distribution

2- Experimental data


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Torus Description and Nomenclature

Urethane

Joint (typ.)

Tube (typ.)

O.D. 0.0181 m

1.858 m Joint flanget = 0.00508 m

Inner joint

t = 0.0063 m

Outer joint

t = 0.0032 m

Tube (typ.)

t = 0.00042 m


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Main Sources of Modeling

Uncertainties

Fabrication irregularities due to materials and

fabrication methods (irregular cross-section,irregular geometry, etc)

Unknown stiffness of adhesive bonded joints

Composite material property uncertainties,

effective single ply and rule of mixture

approximations


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STATIC TEST RESULTS


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Input Load and Sensor Location for Static

Tests

Support 1

Support 2Support 3

Loading

Point

1

23

4

5

6

7

8

9

10

11121314

1516

17

18

19

20

21

2223

24


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Static Test Parameters Selected

for Update1. Torus tube thickness

2. Urethane joint:

- Inner joint thickness

- Outer joint thickness- Joint flange thickness

3. Torus tube orthotropic material properties:

E1, E24. Urethane joint modulus of elasticity E


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Output Probability Statement

How probable is it to predict the measured

output?

Linear Torus Solution

Probability

Bands

w range

w

v

v range

Output No. 1

Output No. 2

Updated parameters

Sample Space 300 points


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Displacement Results: Test, Baseline, and

Updated Model

Measurement locations

Target 1

Z = -4.54 mm

Load =42.1 N

Support 1

Support 2

Support 3

Torus structure displacement under load

-6

-5

-4

-3

-2

-1

0

1

2

3

1 2 3 4 6 7 8 9 10 11 12 14 15 16 17 18 19 20 22 23 24

Measurement location

Baseline

Update

Update Gen

Average Test

VerticalDisplacement(mm)

Torus static test results

=1.1 =0.01

Support 1

Support 2Support 3

Loading

Point

12 3

45

6

7

8

910

11121314

1516

17

18

19

20

21

2223

24


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Static Update Summary

14.1-13.90.008730.011570.011680.00860.01016

Flange

thickness

16.920.00.005270.005070.007610.005070.00634Inner jointthickness

-11.019.60.003520.003790.00380.002530.00317

Outer joint

thickness

9.4130.00039120.0003760.0004960.00030240.000432

Tube

thickness

-6.103.21E+093.03E+093.33E+092.73E+093.03E+09Joint E

5.405.83E+106.16E+106.77E+105.5E+106.16E+10Tube E1,E2

%

Change

Genetic

%

Change

FMIN

Optimum

Genetic

Optimum

FMIN

Upper

Bound

Lower

BoundBaselineParameters


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Dynamic Test Configuration

Force gageSpring/cable

suspension

Suspension 1

Suspension 2

Laser

Vibrometer

Shaker

Suspension 3

Retro-

reflective

Target (typ.)


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Shaker and Sensor Locations for Dynamic

Tests

Suspension 1

Shaker 1Z

Suspension 2Shaker 2ZC

CC

C

C

C

C

C

C

C

C

C

14

16

17

1

5

4

2

7

8

11

10

1315

18

3

6

9

12

Shaker4 XY

Suspension 3


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Sample Set of Identification Results

(Drive Point 1 & 2)

0 20 40 60 80 100 12010

-5

100

105 Predicted (- -) and Real FRFs for input No. 1 and output No. 11

Frequency (Hz)

Amp

litud

e

0 20 40 60 80 100 120-200

-100

0

100

200

Frequency (Hz)

Phase

(deg

)

0 20 40 60 80 100 12010

-4

10-2

10

0

102 Predicted (- -) and Real FRFs for input No. 2 and output No. 17

Frequency (Hz)

Amp

litude

0 20 40 60 80 100 120-200

-100

0

100

200

Frequency (Hz)

Phase

(deg

)

Shaker No. 1

Shaker No. 2


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1279.81433.81194.8955.8Joint 7 density

990.761433.81194.8955.8Joint 8 density

1063.51433.81194.8955.8Joint 10 density

1150.51433.81194.8955.8Joint 11 density

1239.21433.81194.8955.8Joint 13 density

1433.81433.81194.8955.8Joint 14 density

1080.21433.81194.8955.8Joint 16 density

1231.41433.81194.8955.8Joint 17 density

10931433.81194.8955.8Joint 1 density980.591433.81194.8955.8Joint 2 density

996.081433.81194.8955.5Joint 4 density

1204.61433.81194.8955.5Joint 5 density

1770.42200.81834.01467.2Torus tube density

2400.43502.22918.52334.8Spring 3

3169.83502.22918.52334.8Spring 2

2752.93502.22918.52334.8Spring 1

Optimum ValueUpper BoundNominal ValueLower BoundParameter^

Dynamic Update Summary*

* list of parameters not based on statistical analysis


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Work To Be Done Establish repeatability of test data

Complete probabilistic assessment of dynamic FRF to verifyparameter selection

Compute updated parameters for dynamic case using non-gradient based optimizer

Verify computational accuracy with refined FEM

Implement error localization algorithm to examine potential FEM

problem areas Compute Modal Assurance Criterion using reduced mass matrix

Re-test with increased sensor count to improve spatialresolution for test and analysis modes

Refine system ID results to improve areas near FRF zeros


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Concluding Remarks

Computational procedure using MATLAB in place

Initial updates completed using static and dynamic tests

results

Updated solution for static case is in good agreement with test

Selected parameters for static analysis showed low output

probability values when used to predict observed solution

Two step approach using output probabilit ies fol lowed by

optimization provides good physical insight into the problem

Dynamic test and analysis results need to be re-visited

Procedure computationally intensive but well suited for multi-

processor systems

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Horta Torus Structure