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STUDY OF MINIMUM LENGTH SCALES CONSTRAINT IN LIGHTWEIGHT MATERIALS

BACHELOR FINAL THESIS

AUTHOR

​

ARTURO BALTANÁS MEZQUITA

DIRECTOR

​

ÀLEX FERRER FERRÉ

CODIRECTOR

​

JOSE ANTONIO TORRES LEMA

Degree in Aerospace Technology Engineering

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INDEX

MOTIVATION

TOPOLOGY OPTIMIZATION

MANUFACTURING & SCALE RESTRICTIONS

​

FEASIBILITY STUDY

CONCLUSION

METHOD EXPLANATION

BACKGROUND

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TOPOLOGY OPTIMIZATION

MANUFACTURING & SCALE RESTRICTIONS

​

FEASIBILITY STUDY

CONCLUSION

METHOD EXPLANATION

BACKGROUND

MOTIVATION

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MOTIVATION

MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

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USE CASE EXAMPLE

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

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MOTIVATION

USE CASE EXAMPLE

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

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MOTIVATION

USE CASE EXAMPLE

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MOTIVATION

TOPOLOGY OPTIMIZATION

MANUFACTURING & SCALE RESTRICTIONS

​

FEASIBILITY STUDY

CONCLUSION

METHOD EXPLANATION

BACKGROUND

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TOPOLOGY OPTIMIZATION

MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

OVERVIEW

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MASS DISTRIBUTION VARIABLES

MINIMUN COMPLIANCE

PROBLEM

COMPLIANCE IS A

MESURE OF FLEXIBILITY

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TOPOLOGY OPTIMIZATION

MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

DESIGN VARIABLE

LEVEL SET APPROACH

SOLVE INCOMPATIBILITIES

DENSITY APPROACH

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χ

ρ

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MOTIVATION

TOPOLOGY OPTIMIZATION

MANUFACTURING & SCALE RESTRICTIONS

​

FEASIBILITY STUDY

CONCLUSION

METHOD EXPLANATION

BACKGROUND

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MANUFACTURING CONSTRAINTS

MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

MANUFACTURING

ADDITIVE MANUFACTURING

IT IS THE TECHNOLOGY THAT BEST MANUFACTURES TOPOLOGICALLY OPTIMIZED DESIGNS.

THE MOST RESTRICTIVE PARAMETER IS THE MINIMUM MANUFACTURING SCALE

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MANUFACTURING CONSTRAINTS

MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

MINIMUN LENGTH SCALE

THE MINIMUM SCALE MUST BE COMPLIED IN THE EMPTY ZONE AND IN THE MATERIAL ZONE

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MANUFACTURING CONSTRAINTS

MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

POSTPROCESS

APPLY THE RESTRICTION IN A POSTPROCESS

VS

APPLY THE RESTRICTION OVER THE ALGORITHM

THE OBJECTIVE IS TO MAKE A POST PROCESSING AS LESS AGGRESSIVE AS POSSIBLE

AVOID LOSS OF PERFORMANCE ON THE PIECE

AS THEY ARE DESIGNS

HIGHLY OPTIMIZED EVERY, PORTION OF MATERIAL IS CRITICAL

A POST PROCESS WILL ALWAYS BE NECESSARY

THE SIMPLEST WAY TO AVOID THE PROBLEM WOULD BE SOLVING IT IN THE POST PROCESSING

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MOTIVATION

TOPOLOGY OPTIMIZATION

MANUFACTURING & SCALE RESTRICTIONS

​

FEASIBILITY STUDY

CONCLUSION

METHOD EXPLANATION

BACKGROUND

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METHOD EXPLANATION

MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

THRESHOLD PROBLEM

FILTER

BLENDS THE DISTRIBUTION OF MATERIAL ACCORDING TO A RADIUS OF INFLUENCE

PROJECTOR

PROJECTS THE GRAY ZONES TOWARDS DENSITIES 0/1

 

η

β

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

THRESHOLD PROBLEM

IMPOSING SCALE ON ONE PHASE

 

β

η

THE INFLUENCE RADIUS DEFINES THE MINIMUM SCALE

THE APROXIMATION PARAMETER DEFINES THE PROJECTION POWER

THE THRESHOLD DEFINES THE DIRECTION OF PROJECTION

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METHOD EXPLANATION

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

FILTER

DISCRETE FILTER

PDE FILTER

 

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METHOD EXPLANATION

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

PROJECTOR

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METHOD EXPLANATION

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

PROJECTOR

APPROXIMATE STEP FUNCTION

AS HIGHER THE β PARAMETER IS, THE BEHAVIOUR IS MORE APPROXIMATED TO ORIGINAL STEP FUNCTION CURVE

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METHOD EXPLANATION

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

PROJECTOR

E

I

D

η > 0.5

η = 0.5

η < 0.5

E

R

O

D

E

D

I

N

T

E

R

D

I

L

A

T

E

D

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METHOD EXPLANATION

E

I

D

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

ROBUST FORMULATION

SINCE THEY ARE NON-DIFERENTIABLE VARIABLES,

THE BOUND FORMULATION IS USED.

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METHOD EXPLANATION

MEETS THE MINIMUM SCALE IN BOTH PHASES

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MOTIVATION

TOPOLOGY OPTIMIZATION

MANUFACTURING & SCALE RESTRICTIONS

​

FEASIBILITY STUDY

CONCLUSION

METHOD EXPLANATION

BACKGROUND

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METHOD EXPLANATION

MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

STUDY CASES

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INCLINED SIMPLE BEAM WITH ASYMMETRIC LOAD

CANTILEVER BEAM

MECHANICAL ARCH

GRIPPER

 

 

β vs η*

 

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METHOD EXPLANATION

MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

0.1

0.1

0.3

β

η*

 

1.5

APROXIMATION PARAMETER (β)

PROVIDES POWER TO THE PROJECTOR

PROVIDES SENSITIVITY TO THE THRESHOLD (η)

β =1.5 OFFERS THE BEST RESULTS

COMPUTATIONALLY EXPENSIVE

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ROBUST FORMULATION STUDY

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

ROBUST FORMULATION STUDY

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METHOD EXPLANATION

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

ROBUST FORMULATION STUDY

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METHOD EXPLANATION

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

ROBUST FORMULATION STUDY

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METHOD EXPLANATION

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MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

AS THE THRESHOLD APPROACHES ZERO

THE DIFFERENCE BETWEEN FIELDS REGARDING THE INTERMEDIATE IS ACCENTUATED

ERODED VS INTERMEDIATE COMPLIANCE

DILATED VS INTERMEDIATE COMPLIANCE

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METHOD EXPLANATION

ROBUST FORMULATION STUDY

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MOTIVATION

TOPOLOGY OPTIMIZATION

MANUFACTURING & SCALE RESTRICTIONS

​

FEASIBILITY STUDY

CONCLUSION

METHOD EXPLANATION

BACKGROUND

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CONCLUSIONS

MANUFACTURING

INPOSE MANUFACTURING RESTRICTION

FEASIBILITY STUDY

CONCLUSION

THE PROPOSED METHODOLOGY IS ABLE TO GUARANTEE THE MINIMUM SCALE ON THE STRUCTURE

β

η

 

RELEVANT FOR A CORRECT PROJECTION

HAS SENSITIVITY TO THE FINAL SCALE OF THE FIGURE

IT IS THE FACTOR THAT IMPOSES THE MINIMUM SCALE TO BE IMPOSED

COMPUTATIONALLY EXPENSIVE

THE MINIMUM SCALE IS NOT GUARANTEED FOR ITS ENTIRE RANGE OF POSSIBLE VALUES

THE PARAMETERS CONFIGURATION RECOMMENDATION

β = 1.5

η* = 0.05

 

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3D PRINTER WHOSE MINIMUM LENGTH SCALE IS ESTABLISHED AT R5h

NOT MANUFACTURABLE

MANUFACTURABLE

EXAMPLE CASE