Evaluating Structural Engineering Finite Element Analysis Data ...

Matija Radovic and

Dr. Jennifer McConnell

Evaluating Structural

Engineering Finite Element Analysis Data

Using Multiway Analysis Results

Background

Introduction

Methodology

Conclusion

Finite Element Analysis (FEA) • Common tool in structural engineering • Predicts structural behavior • Based on a discretization of structural parts

into geometric shapes (elements) • The number of elements in a typical model

could vary anywhere from hundreds to millions

Results

Background

Introduction

Methodology

Conclusion

FEA in Current Practice • Only a small fraction of this available data

(such as min. and max. stresses) are quantitatively analyzed

• Big data techniques provide opportunity for more holistic analysis

• Likely to be advantageous for comparing differences in competing design options

Load increments

Stre

sses

(p

si)

Results

Background

Introduction

Methodology

Conclusion

Goal: • To explore the use of multiway data

analysis techniques in analyzing structural engineering FEA output

Scope: • Propose a new procedure for interpreting

FEA data in structural engineering • Propose using multiway method (Tucker3

tensor decomposition) in evaluation of FEA data

• Make recommendations for future use of multiway tools in structural engineering FEA

Results

Background

Introduction

Methodology

Conclusion

Tucker3 Tensor Decomposition • Type of higher order singular value

decomposition • Decomposes 3D array into sets of scores

that describe the data in a more condensed form

Results

Background

Introduction

Methodology

Conclusion

FEA Subject Bridge

Results

Background

Introduction

Methodology

Conclusion

0 LPF5 LPF

10 LPF17

0

6000

12000

18000

24000

30000

36000

0

0.05

0.1

0.15

0.2

0.25

0.3

Results

Background

Introduction

Methodology

Conclusion

Data Preprocessing for Tensor Decomposition, cont.

0 LPF5 LPF

10 LPF17

0

6000

12000

18000

24000

30000

36000

0

0.05

0.1

0.15

0.2

0.25

0.3

psi

0 LPF5 LPF

10 LPF17 L

0

6000

12000

18000

24000

30000

36000

0

0.2

0.4

0.6

0.8

0 LPF5 LPF

10 LPF17

0

6000

12000

18000

24000

30000

36000

0

0.2

0.4

0.6

0.8

G1 BF G4 BF

XG1 XG2

Results

Background

Introduction

Methodology

Conclusion

Data Preprocessing for Tensor Decomposition • To carry out Tucker3 decomposition, the data

must be organized in a 3-way (3-mode) format

• 1st mode- 7 element groups (4 girder groups and 3 cross-frame groups)

• 2nd mode - 51 stress ranges (51 stress histogram bins)

• 3rd mode -17 loading increments (LPFs).

Results

Background

Introduction

Methodology

Conclusion

Determining Appropriate Tucker3 Model Fitting procedure based on: • Percent variance explained

• Optimal model complexity

Results

Background

Introduction

Methodology

Conclusion • High negative scores in Component 1 -narrowest spread in stress distribution

• High positive scores in Component 2 -

widest spread in stress distribution

Results: Element Group Loading Scores

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

G1G2

G3 G4

XG1

XG2

XG3

Component 1

Com

pone

nt 2

15 16 14 13 12 17 11 10 9 8 7 6 5 1 2 3 40.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

LPFsResults

Background

Introduction

Methodology

Conclusion

• High positive scores in Component 1 and high negative scores in Component 2 low LPFs

• High positive score in Component 2 high LPFs.

Results: LPF Loading Scores

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

1

23

4

5

6

78

910

11121314151617

Component 1

Com

pone

nt 2

Results

Background

Introduction

Methodology

Conclusion

Comparing Tucker3 Results to Experimental Results

15 16 14 13 12 17 11 10 9 8 7 6 5 1 2 3 40.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

LPFs

Results

Background

Introduction

Methodology

Conclusion

• Innovative method of FEA data interpretation

• Possible ability to highlight latent behavior

of bridge components subjected to increasing load

• Ability to quantify and differentiate the

stress profiles of different bridge components

Conclusions