STRUCTURAL DESIGN OF ROTATIONAL AXIS COMPONENT OF THE TAIL STABILIZER VIA TOPOLOGY OPTIMIZATION

Bachelor in Aerospace Vehicle Engineering

Spring 2023-2024

Author:

Pau Cornudella Quer

Director/Co-director:

Alex Ferrer Ferre

Jose Antonio Torres Lerma

Miquel Guinart Garcia

Initial problem

TO introduction

Theorical background

Software

1

2

3

4

5

Difficulties and solutions

6

Final results

7

8

Conclusions

9

Questions round

OVERVIEW

V = 0.4 x V

f

i

1

Benchmark cases

10

Actual thesis problem

How can we design a cantilever to achieve 40% of its initial volume while maximizing its stiffness?”

2

In the context of aircraft design the weight savings are highly valuable. Improvement of fuel efficiency, flight range and payload capacity .

​

Topology optimization is a computational technique used to optimize a given material space, subject to certain constraints, in order to achieve the best performance for a structure.

NOTE:

Definition:

TOPOLOGY OPTIMIZATION

3

Lightness

Stiffness

TAIL STABILIZER ROTATIONAL AXIS DESIGN - SINGULAR AIRCRAFT

​

Designed for:

• Firefighting
• Logistics
• Search, rescue, and defense

Aerospace company specialized in the design and production of unmanned aerial systems (UAS).

FLYOX I

4

TAIL STABILIZER ROTATIONAL AXIS DESIGN

4

TOPOLOGY OPTIMIZATION STEPS

5

TOPOLOGY OPTIMIZATION STEPS

5

TOPOLOGY OPTIMIZATION STEPS

5

TOPOLOGY OPTIMIZATION STEPS

• Ease of fabrication
• Cost-effectiveness
• Compatibility with existing manufacturing processes

5

TOPOLOGY OPTIMIZATION STEPS

5

TOPOLOGY OPTIMIZATION STEPS

5

TOPOLOGY OPTIMIZATION STEPS

5

TOPOLOGY OPTIMIZATION STEPS

5

THEORICAL BACKGROUND

General formulation:

Box constriants

Initial domain

6

Minimum compliance problem:

Shape functionals

Compliance

Volume

Perimeter

Final volume

Cost function

Inequality constraint

Design variable

Maximize stiffness

THEORICAL BACKGROUND

6

Equilibrium equation

Equality constraint

DENSITY METHOD

LEVEL SET METHOD

THEORICAL BACKGROUND

TREATMENT OF THE DESIGN VARIABLE

7

DENSITY METHOD

1

8

LEVEL SET METHOD

2

Level set function

A Level set of a function is a set where the function takes on a given constant value

10

THEORICAL BACKGROUND

OPTIMIZERS

12

Responsible of doing all the calculations in each iteration and to solve the problem

2

NULLSPACE

Open-source data analysis and visualization application. It offers a simple user interface. Free of charge

Open-source code focused on machine learning and topology optimization, developed by the thesis director, Alex Ferrer, and collaborators. MATLAB language

SWANLAB GITHUB REPOSITORY CODE

SOFTWARE

13

PARAVIEW

Pre/Post processor for numerical simulations in science and engineering. It owns geometrical modelling, meshing data transformer to analysis software, as well as the analysis and visualization of numeric result.

GID SIMULATION

BENCHMARK CASES

14

2D CANTILEVER BEAM

2.075

2.08

2

LEVEL SET

15

BENCHMARK CASES

16

3D MBB BEAM

Density method - MMA optimizer

BENCHMARK CASES

16

3D MBB BEAM

Density method - NullSpace optimizer

BENCHMARK CASES

16

3D MBB BEAM

Density method - MMA optimizer

2.14

BENCHMARK CASES

16

3D MBB BEAM

Density method - NullSpace optimizer

2.14

2

NULLSPACE

17

TAIL STABILIZER ROTATIONAL AXIS DESIGN - SINGULAR AIRCRAFT

​

Designed for:

• Firefighting
• Logistics
• Search, rescue, and defense

Aerospace company specialized in the design and production of unmanned aerial systems (UAS).

FLYOX I

18

TAIL STABILIZER ROTATIONAL AXIS DESIGN

18

DESIGN REQUIREMENTS - BOUNDARY CONDITIONS

19

• Red blocks attached by 4 screws each
• Ball bearings allow the rotation of the arm

• The rotational movement is restricted by an hydraulic piston
• Attached thought the purple circles hole

DESIGN REQUIREMENTS - LOAD CONDITIONS

Load conditions coordinate axes

20

Load conditions at the Center of Pressures, (STANAG 4671 regulations)

Load conditions at the Center of Pressures, (STANAG 4671 regulations)

Load conditions coordinate axes

20

DESIGN REQUIREMENTS - LOAD CONDITIONS

DESIGN REQUIREMENTS - LOAD CONDITIONS

21

Final load conditions to apply

DIFFICULTIES AND ALTERNATIVE SOLUTIONS - MESHING PROCESS

22

1 : MESH REFINEMENT

Aspect:

• First meshes with 1-2 M elements
• High mesh quality

​

Problem:

• MATLAB has a maximum array size limit

2 : SMALL CHANGES IN THE MATERIAL DOMAIN

​

Solution:

• Imposed overall number of elements

Aspect:

• Wide range of element sizes

​

Problem:

• Time consumption on small elements areas
• Differential changes over time

Solution:

• Similar elements size

DIFFICULTIES AND ALTERNATIVE SOLUTIONS

23

3 : TIME CONSUMPTION

Aspect:

• Meshes of 300.000-500.000 elements

​

Problem:

• Time consumption significally increased

4 : LOW-QUALITY MESHES AND CARTESIAN MESHES

Solution:

• Create low-quality meshes

Aspect:

• Not allowing GiD to correct element sizes

​

Problem:

• Crash of GiD meshing process

Solution:

• Redesign of the piece vertex

DIFFICULTIES AND ALTERNATIVE SOLUTIONS

23

3 : TIME CONSUMPTION

Aspect:

• Meshes of 300.000-500.000 elements

​

Problem:

• Time consumption significally increased

4 : LOW-QUALITY MESHES AND CARTESIAN MESHES

Solution:

• Create low-quality meshes

1 SUCCESSFUL MESH OF 155.854 ELEMENTS

DIFFICULTIES AND ALTERNATIVE SOLUTIONS

24

4 : LOW-QUALITY MESHES AND CARTESIAN MESHES

Aspect:

• Cartesian meshing process

​

Problem:

• Non compatible mesh output document with Swan Lab

Solution:

• Avoid this meshing type and talk with GiD

5 : SUDDEN CONVERGENCE DUE TO LINE SEARCH PARAMETER

​

Aspect:

• SwanLab code can struggle to find a value that still minimizes the cost

​

Problem:

• Line search parameter crash

Solution:

• Limit the Line Search value

DIFFICULTIES AND ALTERNATIVE SOLUTIONS

25

6 : UNWANTED MATERIAL REMOVAL

Aspect:

• First ball bearing prevents the area between the two ball bearings to work

​

​

Problem:

• Material removal from regions where no work is performed, but are needed

Solution:

• Implement isFixed function

RESULTS

V = 0.9 x V

f

i

• Not real load conditions
• Y-axis force applied on its farthest face
• Volume constraint set at 0.9

26

RESULTS

V = 0.9 x V

f

i

26

RESULTS

• Real load conditions (Condition 7)
• Volume constraint set at 0.7

V = 0.7 x V

f

i

27

RESULTS

V = 0.7 x V

f

i

27

RESULTS

27

DENSITY METHOD

6

Overall, this thesis has offered an opportunity to explore how SwanLab code performs with large domains and highly constrained problems, particularly in the aerospace industry.

General code overview: Time optimization is high, mesh inputs are limited and material removal options are small.

Introduction to object-oriented coding has been sucessful, with its upcoming benchmark cases, which have demonstrated the principal differences between Density and Level Set methods.

Deep literature review has been conducted to explore the fields of topology optimization and aerospace structural design.

CONCLUSIONS

THANK YOU

1. DUYSINX, Pierre; LORIA, Alessandro T. Rotta. Topology optimization in aircraft and aerospace structures design. Archives of Computational Methods in Engineering. 2015, vol. 22, no. 4, pp. 595–629. Available from doi: 10.1007/s11831-015-9151-2.

​

2. ZHU, Jihong; ZHOU, Han; WANG, Chuang; ZHOU, Lu; YUAN, Shangqin; ZHANG, Weihong. A

review of topology optimization for additive manufacturing: Status and challenges. Chinese Journal of Aeronautics. 2021, vol. 34, no. 1, pp. 91–110. Available from doi: https://doi.org/10.1016/j.cja.

2020.09.020.

​

3. MICHELL, A. G. M. LVIII. The limits of economy of material in frame-structures. The London,

Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1904, vol. 8, no. 47, pp. 589–597.

Available from doi: 10.1080/14786440409463229.

​

4. MAXWELL, J. C. I.—On Reciprocal Figures, Frames, and Diagrams of Forces. Transactions of the Royal Society of Edinburgh. 1870, vol. 26, no. 1, pp. 1–40. Available from doi: 10.1017/S0080456800026351.

BIBLIOGRAPHY

5. LOGÓ, Janos; ISMAIL, Hussein. Milestones in the 150-Year History of Topology Optimization: A Review. Computer Assisted Methods in Engineering and Science. 2020, vol. 27, no. 2-3, pp. 97–132. issn2956-5839. Available from doi: 10.24423/cames.296.

​

6. BENARD, Andre; BENDSØE, Martin P. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering. 1988, vol. 71, no. 2, pp. 197–224. Available also from: https://www.sciencedirect.com/science/article/abs/pii/

0045782588900862.

​

7. SVANBERG, Krister; SVARD, Henrik. Density Filters for Topology Optimization Based on the Pythagorean Means. Structural and Multidisciplinary Optimization. 2013, vol. 48, no. 5, pp. 859–875. issn 1615-1488. Available from doi: 10.1007/s00158-013-0938-1.

​

8. EVANGELOS, Tyflopoulos; DAVID, Flem, et al. State of the art of generative design and topology optimization and potential research needs. 2019. Available also from: https : / / www . researchgate . net / publication / 334974685 _ State_of_the_art_of_generative_design_and_topology_optimization_and_potential_research_needs.

BIBLIOGRAPHY

9. BENDSØE, M. P.; SIGMUND, O. Material Interpolation Schemes in Topology Optimization. Archive of Applied Mechanics. 1999, vol. 69, no. 9, pp. 635–654. issn 1432-0681. Available from doi: 10.1007/ s004190050248.

​

11. SVANBERG, Krister. The Method of Moving Asymptotes—A New Method for Structural Optimization. International Journal for Numerical Methods in Engineering. 1987, vol. 24, no. 2, pp. 359–373. Available from doi: 10.1002/nme.1620240207.

​

12. SWANLAB. SwanLab: A Repository of Projects Related to Machine Learning and Optimization [Online]. 2021. Available also from: https://github.com/SwanLab.

​

13. GID Simulation [https://www.gidsimulation.com/]. [N.d.].

​

14. NATO STANDARDIZATION OFFICE. STANAG 4671: Unmanned Aircraft Systems (UAS) Control Segment (UCS) Architecture. [https://nso.nato.int/nso/nsdd/main/list-promulg]. [N.d.].

​

BIBLIOGRAPHY

15. Singular Aircraft [https://singularaircraft.com/]. [N.d.].

​

16. Topology Optimization in a World of Fields and Implicit Geometry. nTop. Available from: https://www.ntop.com/resources/blog/topology-optimization-in-a-world-of-fields-and-implicit-geometry/

17. Topology Optimization. Lightbau. Available from: https://lightbau.de/en/topology-optimization/

​

BIBLIOGRAPHY

BACK SLIDES

DENSITY METHOD - INTERPOLATION SCHEMES

1

SIMP TECHNIQUE:

SIMP : Solid Isotropic Material with Penalization

C(ρ = 1)

Elasticity tensor of the material

Density function

Penalty factor

p≥3

9

p=3

LEVEL SET METHOD

2

11

SHAPE DERIVATIVE TECHNIQUE:

TOPOLOGICAL DERIVATIVE TECHNIQUE:

How the cost function changes with respect to small perturbations in the boundaries of the domain.

How the cost function changes with respect to the introduction of small voids in some areas of the domain

BACK SLIDES - LOAD CALCUALTIONS

BACK SLIDES - LOAD CALCUALTIONS

BACK SLIDES - ISFIXED FUNCTION

BACK SLIDES - BUDGET

• 20€/hour Junior engineering hours.
• 40€/hour Thesis director, co-director, and company meetings.

BACK SLIDES - ENVIRONMENTAL AND SOCIAL IMPACT

• Material savings up to 60%.

​

• Simulating these designs and validating them before manufacturing avoids the need to create a high number of prototypes before arriving at an optimal one. This not only reduces material usage but also the manufacturing time and associated costs.

​

• Can potentially reduce the CO2 emissions in the future reducing the weight of aircraft components

• Provision of new knowledge and technological advancements to all contributors, including engineers and companies.

SOCIAL IMPACT

ENVIRONMENTAL IMPACT

BACK SLIDES - SCHEDULE

BACK SLIDES - SCHEDULE

BACK SLIDES -FUTURE LINES OF DEVELOPMENT

6

A

Adaptation of the code for different mesh types: As mentioned on Section 5.4.4, many mesh configurations generated by GiD mesh documents contained duplicated nodes, discontinuities between nodes, and other issues. Manually fixing these irregularities would be highly time-consuming, so, adapting the code to accommodate these irregularities would enable the analysis of differences between various mesh types (Cartesian, Tetrahedral, Hexahedral, etc.)

Adaptation of the code for quicker optimizers: As has also been seen, the time consumption is another critical aspect of SwanLab code, particularly in 3D large domain and constrained problems. Adapting the code to reduce the time consumption when calculating the mathematical problem could be a possible future line of development

Comparison between optimizers: Similar to benchmark problems, an evaluation between available optimizers would provide insights of the code’s versatility and its ability to handle varying mesh configurations effectively.

​

6

A

Material Selection: Investigating and simulating different materials (varying Young’s modulus and Poisson’s ratio) could result in different final material distributions, which could also align with the requirements. Also the consideration of factors such as weight, strength, durability, and manufacturing feasibility should also be analysed for comparison purposes.

Code development for preventing areas from material removal: During this thesis, an isFixed function was developed to prevent material removal within a specific distance from mesh points x1 to x2. This feature could be improved by introducing restrictions to only specific nodes or even face areas.

Simulation with smaller final Volume targets: As discussed in Section 5.5, different Volume targets have been analyzed. Despite that, expanding simulations to include smaller Volume targets could provide ideas of extremely weight-reduced optimized configurations.

​

BACK SLIDES -FUTURE LINES OF DEVELOPMENT

6

Additive manufactured design and physical validation: Finally, to ensure the reliability and real-world applicability of the proposed structural design, a 3D printed optimized model could be created and validated through physical tests.

BACK SLIDES -FUTURE LINES OF DEVELOPMENT

BACK SLIDES -BENCHMARK CASES

12

2D MBB BEAM

BACK SLIDES - MESHING PROCCESS

BACK SLIDES - ROTATIONAL AXIS

BACK SLIDES - SCOPE

2

THE PROJECT INCLUDES:

• Review of aerospace structural design, tail stabilizers, and TO techniques.
• Introduction and familiarization with object-oriented code and SwanLab repository code.
• Definition and resolution of 2D and 3D benchmark problems.
• Development of a conceptual design of the rotational axis component.
• Implementation of advanced TO algorithms to redefine and optimize the geometry of the component.
• Adjustments using FEM for improved optimization results.

​

THE PROJECT NOT INCLUDES:

• In-depth study of TO theory.
• Development of code for TO

BACK SLIDES - DISPLACEMENTS

2

Non realistic displacements

​

• E1 (ρ = 1)=1
• E0 (ρ = 0)=1e-3

​

• nu1 (ρ = 1)= = 1/3;
• nu0(ρ = 0) = 1/3;

​

• Non dimensional forces

​

​

​

​