Surrogate models for rotational stiffness of welded tubular Y-joints … · LOGO Surrogate models...

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Surrogate models for rotational stiffness of welded tubular Y-joints

International METNET Workshop09-10 February 2016, Tampere, Finland

M. Garifullin, M. Heinisuo, K. Mela, T. Tiainen, T. JokinenTampere University of Technology

LOGOScope of research

Main goalDevelop cost optimization methods for HSS structures

ProblemEvaluations in optimization often require time consuming computations(non-linear FEM).

Possible solutionSurrogate models (aka metamodels, response surface models)

Application of surrogate models• space mapping• aerospace industry• steel frame optimization

Our caseSurrogate models are used for the definition of

• Initial rotational stiffness• Moment resistance

of semi-rigid welded tubular joints.

Tampere University of Technology

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LOGO


Why?We want to use semi-rigid joints in the optimization of HSS structures.Previous researches have demonstrated the benefits of using semi-rigidjoints in optimization (Grierson, Simoes, etc.) No methods found in theliterature to define their moment resistance and rotational stiffness.Features of optimization

• require numerous (>1000) function evaluations• operations must be done extremely quickly

In this relation, surrogate modeling might be effective.

In this presentationSurrogate model development for initial rotational stiffness 3 / 33

Scope of research

LOGO


Task

Determine rotational stiffness C of welded tubular Y-joints with fillet welds

Algorithm

1. Surrogate model for rotational stiffness of a joint with butt welds

Sampling

Finite Element Modeling (FEM)

Surrogate modeling

2. Consider the effect of fillet welds4 / 33

Scope of research

LOGOSampling


Variables

b0 t0 b1 t1 fy0 fy1 φ

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LOGOSampling


Variables


• fy0 and fy1 have no effect for butt welds

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LOGOSampling


Variables


• fy0 and fy1 have no effect for butt welds• weak effect of t1

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LOGOSampling


Variables


• fy0 and fy1 have no effect for butt welds• weak effect of t1• replacing b1 by

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1

0

bβb

=

LOGOSampling


Variables


• fy0 and fy1 have no effect for butt welds• weak effect of t1• replacing b1 by

Variables Responseb0 t0 β φ C 9 / 33

1

0

bβb

=

LOGOSampling


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4

5

6

7

8

9

10

11

12

13

100 120 140 160 180 200 220 240 260 280 300

t 0[m

m]

b0 [mm]

SP

Ruukki

Ruukki

Eurocode

Sample points must:• cover the whole area of interest and be distributes evenly• meet the requirement of Eurocodes• contain at least 3 values for every variableEngineering justification for sampling

LOGOSampling


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40

60

80

100

120

140

160

180

200

220

100 120 140 160 180 200 220 240 260 280 300

b 1[m

m]

b0 [mm]

SPEurocode

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

100 120 140 160 180 200 220 240 260 280 300

β

b0 [mm]

SPEurocode

Totally: 285 points

LOGOFEM


Nonlinear Finite Element analysis in Abaqus

GoalCalculate rotational stiffness C for sample points

Mesh 2-layered, C3D8 hexahedral brick elementsWelds butt, TIE constraintMaterial elastic, E=210000 MPa, ν=0.3Verification see Budapest paperValidation tests of LUT

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LOGOSurrogate modeling


1. Construction

• Kriging method• ooDACE toolbox for Matlab

2. Validation

Validation points must:

• cover the whole area of interest• be distributes evenly• be random• be different from sample points

48 validation points were chosen

Criteria of acceptance:

• R2 ≥ 0.85• Error ≤ 10%

13 / 33 FEM

SURRFEM

CCC

Error−

=



Attempt I• average error 56%• maximum error 678%Graphical validation → model required improvements

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-400

-200

0

200

400

600

800

1000

1200

4,0 5,0 6,0 7,0 8,0 9,0 10,0

C[k

Nm

/rad]

t0 [mm]

Chord 100 mm, β=0.4

30 60 90 Sample points

-60

-40

-20

0

20

40

60

30 45 60 75 90

C[k

Nm

/rad]

φ [deg]

Chord 100x4, β=0.4

Surrogate model Sample points



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20

40

60

80

100

15 30 45 60 75 90 105

C[k

Nm

/rad]

φ [deg]

Chord 100x4, brace 40x4

Adding “pseudo” points3 “true” sample points



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y = 5E-06x4 - 0,0014x3 + 0,1661x2 - 8,7773x + 203,83

20

40

60

80

100

15 30 45 60 75 90 105

C[k

Nm

/rad]

φ [deg]


Adding “pseudo” points3 “true” sample points + 4th order polynomial regression



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y = 5E-06x4 - 0,0014x3 + 0,1661x2 - 8,7773x + 203,83

20

40

60

80

100

15 30 45 60 75 90 105

C[k

Nm

/rad]

φ [deg]


Sample points

Ext sample points

Adding “pseudo” points3 “true” sample points + 4th order polynomial regression4 extrapolated “pseudo” sample points



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y = 5E-06x4 - 0,0014x3 + 0,1661x2 - 8,7773x + 203,83

20

40

60

80

100

15 30 45 60 75 90 105

C[k

Nm

/rad]

φ [deg]


Sample points

Ext sample points

Int sample points

Adding “pseudo” points3 “true” sample points + 4th order polynomial regression4 extrapolated + 2 interpolated “pseudo” sample points



Improved C-φ curve

Same approach for all variablesTotal: 285 sample points + 1869 pseudo points = 2154 points

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20

40

60

80

100

15 30 45 60 75 90 105

C[k

Nm

/rad]

φ [deg]


Surrogate modelSample pointsPseudo points



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0

200

400

600

800

1000

1200

4,0 4,5 5,0 5,5 6,0 6,5 7,0 7,5 8,0 8,5 9,0 9,5 10,0

C[k

Nm

/rad]

t0 [mm]

Chord 100 mm, β=0.4

306090Sample points

Improved C-t0 curve



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Improved C-β curve

0

500

1000

1500

2000

2500

3000

0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80

C[k

Nm

/rad]

β

Chord 100x6

306090Sample points



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3D plot C-(φ+β)



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Attempt II• average error 8%• maximum error 28%• inaccurate points 16



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Analysis of validation pointsAll inaccurate points were connected to prediction in β

Pseudo points were corrected

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

0,25 0,35 0,45 0,55 0,65 0,75 0,85

C[k

Nm

/rad]

β

Chord 300x12.5, φ=30°

Area of large mistakes



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Attempt III• average error 8% → 6%• maximum error 28%• inaccurate points 16 → 11



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Next improvements• Improved C-φ curves• Local improvements

Final surrogate model• average error 6% → 4%• maximum error 28% → 16%• inaccurate points 11 → 4

Created surrogate model allowed to calculate rotational stiffness Cfor a joint with butt welds and any combination of its parameters

Surrogate model:• Does not require computationally consuming FEM• Gives the results very quickly (less than 1 sec)• Might be used for any number of evaluations

LOGOEffect of fillet welds


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For surrogate modeling only butt welds were used. In practice filletwelds are used for joints.Fillet welds increase the stiffness of joints and this effect should be takeninto account.Moreover, full strength weld size depends on the steel grade. So, for filletwelds material properties should be taken into account.

Bracematerial S355 S460 S500 S550 S700

Weld size 1.15t1 1.50t1 1.60t1 1.62t1 1.64t1

To implement the effect of welding we proposed the following idea:1. Use constructed surrogate model with butt welds.2. Replace the brace width b1 by the equivalent brace width beq > b1

Main question: How to calculate beq?



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New formula for beq:

where kfw is a correlation coefficientHow determine kfw?

1 1 2 2eqb b b a< < +

fweq kabb ⋅+= 221



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Algorithm for determining kfw (FEM)

Calculate C for a joint with real b1 and fillet welds

Find a joint with but welds and beq which has the same C

Determine beq

Calculate kfw



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40 cases were analyzed by FEM.In most cases kfw lies in the interval 0.5…0.8.

For simplicity we suggest using discrete values of kfw :• 0.6 for S355• 0.7 for S700The error does not exceed 10%



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0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5

C100x4-B70x4-90C100x4-B70x4-30

C200x7.1-B140x7.1-90C200x7.1-B140x7.1-60C200x7.1-B140x7.1-30

C300x12.5-B200x7.1-90C100x4-B40x4-90

C100x7.1-B40x4-90C300x12.5-B80x5-90C200x7.1-B50x4-90C200x7.1-B50x4-60C200x7.1-B50x4-30

C200x12.5-B50x4-90C200x12.5-B50x4-60C200x12.5-B50x4-30

C / Cbutt

Fillet, S355

Fillet, S700

1. Fillet welds increase rotational stiffness, in mean 1.5 times for S355steel grade and 2.0 times for S700.

2. The effect is stronger for joints with high β.

Fillet welds vs. butt welds

LOGOConclusions


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1. There exists no method to calculate the initial rotational stiffness forwelded tubular Y-joints for different angles φ. Surrogate modelingseems to be a reasonable solution for this task.

2. ooDACE toolbox represents the best tool for surrogate modelconstruction.

3. Pseudo points, both extrapolated and interpolated, are necessary toget the physically reasonable surrogate model.

4. The effect of the full strength fillet weld is considerable for therotational stiffness. The mean factor in our cases was 1.5 for S355steel grade and 2.0 for S700 steel grade.

5. The simple rule can be used for the correlation factors to predict theeffect of the weld size:

• kfw = 0.6 for S355• kfw = 0.7 for S700• Linear interpolation between.

LOGOThe end


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