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