Discrete Variables

8/17/2019 Discrete Variables

1/15

Genetic Structural Optimization applied with

Tension, Flexibility and Buckling Constraints

MSc. Rafael Sommer - TMSAMSc. Rodrigo de Souza - TMSA

PhD. Jun Sérgio Ono Fonseca - UFRGS

TMSA – Bulk Handling Technology S.A.

Porto Alegre – RS, Brazil


2/15

COMPANY OVERVIEW

Company Foundation – 1966

Head Quarters Location – City of

Porto Alegre

Manufacturing Plant – Located in

a 70,000 m2 property with more

than 30,000 m2 of industrial

buildings and offices

ISO 9001 Certified

Around 450 Employees

More than 45 graduated Engineers


3/15

COMPANY OVERVIEW

MARKETS

• Agro-industry

• Fertilizers• Port Facilities

• Cement Plants

• Mining Industry

• Steel Plants

• Coal Power Plants• Cellulose

• Petrochemical

MAIN PRODUCTS

• Belt Conveyors

• Ship Loaders• Stackers

• Chain Conveyors

• Bucket Elevators

• Grain Cleaners

• Dust Control Systems• Electrical and Control Systems


4/15

COMPANY OVERVIEW

Mission: Supply electromechanical solutions with low environmental impact

and higher perceived value for conveying and processing solid bulk materials

AGP’s and Louis Dreyfus’ Ship Loaders supplied for Port Facilities


5/15

OPTIMIZATION FORMULATION

FEM Model, considered support and loads Structure while loading a Vessel


6/15


1) Minimize W = ρ

2) Minimize

nel

i

ii L A1

i axial flection

Optimization Objectives: Optimization Constrains:

bkl i

maxµµ

i

nel i ,...1

nel i ,...1

Optimization Variables:

),..,,( 21 nel A A A A

Where:

W = Structure Mass

A = Cross Sectional Areas of ElementsL = Length of Elements

= Combined Stress

= Linear Buckling Stress

= Displacement of Elements

blk

iµ


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List of available profiles for the optimization process

PROFILES DIMENSIONS

CROSS SECTIONAL

AREAS [cm2]

INERCIALMOM.

AXIS 1-1; 2-2 [cm4]

1 Angle bar 2" x 2" x 1/4" 6,0 14,6

2 Angle bar 2 1/2" x 2 1/2" x 1/4" 7,6 29,2

3 Angle bar 3" x 3" x 1/4" 9,3 50,04 Angle bar 3" x 3" x 5/16" 11,4 62,8

5 Angle bar 3" x 3" x 3/8" 13,6 73,2

6 Angle bar 3" x 3" x 1/2" 17,7 92,2

7 Angle bar 4" x 4" x 1/4" 12,5 126

8 Angle bar 4" x 4" x 5/16" 15,5 154

9 Angle bar 4" x 4" x 3/8" 18,4 181

10 Angle bar 5" x 5" x 3/8" 23,3 36311 Square tube 100 x 100 x 1/4" 23,8 350

12 Square tube 120 x 120 x 1/4" 28,2 603

13 Square tube 143 x 143 x 5/16" 42,8 1308


8/15


Flow Chart created at modeFRONTIER for the optimization study


9/15

OPTIMIZATION RESULTS

Mass (W) x Tension ( ) Graphic


10/15


3 ” x3/8 ” 3 ” x5/16 ”

”

5 ” x3 /8 ”

Tubo143x5/16

4 ” x5 /16 ”

”

2 ” x1/4 ”

2 ½ ”x1/4 ”

3 ” x1/4 ”

”

3 ” x1/ 4 ”

4 ” x5/16 ”

4 ” x5/16 ” 5 ” x3/ 8 ”

2 ½ ”x1/4 ”

Tubo143x5 /16 ”

”

FEM Results: Structure Profiles,Combined Stress and Displacements

levels in Original Structure

Total Weight: 2430 Kg

Max. Comb. Stress: 153,5 Mpa

Max. Deformation:29,3 mm


11/15


Stress levels in

original model.

Total Weight:

2430 Kg

Stress levels in

optimized model

(point A).

Total Weight:

1810 Kg


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3 ” x1/2 ” 4 ” x3/8 ” 3 ” x3/8 ”

”

2 ” x1 /4 ”

2 ” x1/4 ”

”

2 ½ ”x1/4 ”

”

Tubo100x1/ 4 ”

2 ” x1/ 4 ”

2 ½ ”x1/4 ”

4 ” x3/8 ”

2 ” x1/4 ”

”

3 ” x1/4 ”

2 ½ ”x1/4 ”

3 ” x1/2 ”

4 ” x3/8 ”

”

3 ” x3/8 ”

”

2 ” x1/4 ”

2 ½ ”x1/4 ”

2 ” x1/ 4 ”

2 ½ ”x1/4 ”

4 ” x1/ 4 ”

”

3 ” x1/4 ”

”

FEM Results: Structure Profiles,

Combined Stress and Displacements

levels in Optimized Structure (point A)

Total Weight: 1810 Kg

Max. Comb. Stress: 148,5 Mpa

Max. Deformation:39,5 mm


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CONCLUSIONS

• An integration between structural analyses (ANSYS Workbench v.11)

and multi-objective optimization (modeFRONTIER v 4.1) has shown to

be an efficiency tool for a parametric optimization with discrete

variables.

• The ship loader structure has been successful optimized by means of

genetic algorithm.

• The presented work achieved an structure with 25% less mass and

stress levels, as the same as the original structure (3% less). Theoriginal structure stress condition was already considered a good

condition (~150MPa).


14/15

NEXT STEPS

• Generate an structure model as real as possible, to avoid any bias over the

results, due to a FEM model simplified.

• Include dynamic analyses to the FEM solution to constrain any kind of

vibration resonance solution.

• Add a fatigue tool to the FEM solution for test the model against repetitive

load cases.

• Test the same optimization with Monte Carlo algorithm with variance controlto find for another solutions and compare with the results presented today.

• Generate optimizations where the main objective is costs minimization.


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COMPANY OVERVIEW

[email protected]

www.tmsa.ind.br

Any question or doubt, do not hesitate to get in contact.

Visit our website:
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Discrete Variables