Generative Structural Design and Optimization of Modern ... · Stiffener [mm] 20 30 10 Bonded Section, Web, Crown Stiffener Spacing [mm] 100 300 100 Panel Buckling Uniaxial, Biaxial,

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Generative Structural Design and Optimization of Modern Electric Aircraft

Darmstadt 2019 Bertram Stier


Outline

2

• Motivation

• Challenge Problem

• Practical Generative Design

• Summary


Outline

3

• Motivation• Trends

• Industry Reaction



• Summary


Trends

4

Source: Urban Mobility Scoreboard, Texas A&M Transportation Institute

Carbon Dioxide Infromation Analysis Center, Global Carbon Project

• Demand for transportation increases quicker than infrastructure expansion

• CO2 emission regulations become more strict

• Lots of time and money ‘wasted’ in traffic

• Congestion and pollution in cities increases

Expanding rail and road is expensive

and might still not meet demands


Industry Reaction

5

Opportunity: electric urban air traffic

• (Operational) Emission free

• Fast enough

• Indiviual, on demand

• Comfortable, convenient

Challenges

• Regulations (noise, safety, piloting, ...)

• Infrastructure (vertiports, apps, ...)

• Public acceptance

• Viability (economic, range, ...)

Task: Minimize energy consumption per traveled mile. For given system, less total mass translates to less req. enery.

For given energy density (of batteries), decreasing structural mass translates to range or payload increase

Lillium

Audi/Airbus


Outline

6

• Motivation

• Challenge Problem• Chosen Structure: Wing Section

• A Common Situation


• Summary


Selecting Example Structure

7

Lillium

Audi/AirbusBell Nexus

Joby Aviation


Challenge Problem: Wing Section

8

Conceptual Design Phase

Big part of cost decided

Open design space

Often air foil shape given

Answer fundamental questions

Structural layout (How many ribs)?

Concept (Monolithic/ Sandwich/ Stiffened)?

Material (is it worth paying the extra money)?

Needs to ...

... be light

... be manufacturable

... meet criteria

• Strength

• Stiffness

• Stability

Situation

Lack of information

Not a lot of time

Well founded decisions requires detailed analysis

....is expensive and time consuming

Non-Exhaustive Search

results in

Untapped Potential

worst case: not viable

180 mm


Design Space, Restrictions and Criteria

9

Property Standard Tape

High End

Tape Fabric

E1t [GPa] 140.0 185.0 56.0

E1c [GPa] 120.0 160.0 52.0

E2t [GPa] 9.0 10.0 56.0

E2c [GPa] 9.0 10.0 52.0

G12 [GPa] 3.4 3.7 2.7

ν12 0.32 0.32 0.10

X1t [MPa] 1820.0 3460.0 735.0

X1c [MPa] 1470.0 1870.0 520.0

Y2t [MPa] 75.0 80.0 820.0

Y2c [MPa] 230.0 280.0 480.0

S12 [MPa] 95.0 160.0 110.0

t [mm] 0.21 0.2 0.3

ρ [kg/m³] 1550.0 1500.0 1550.0

Dimensions Failure CriteriaLayup Rules

(Tape/Fabric)

Monolithic LaminateMin Max Incr Laminate

T [# Plies] 3 50 1 Ply Max Stress1, Stress2, Stress12 Min Max Incr

Ply Tsai-Hahn Interaction %0° 10/0 80/30 20/10

Panel Buckling Uniaxial, Biaxial, Shear %45° 10/0 60/30 20/10

%90° 10/0 50/0 20/0

Sandwich CompositeMin Max Incr Face Sheets

T Top Face [# Plies] 2 8 1 Ply Max Stress1, Stress2, Stress12 Min Max Incr

T Core [mm] 5 20 5 Ply Tsai-Hahn Interaction %0° 10/0 80/10 20/10

T Bot. Face [# Plies] 2 8 1 Core Shear Strength %45° 10/10 50/30 20/10

Panel Buckling Uniaxial, Biaxial, Shear %90° 10/0 50/0 20/0

Composite Hat StiffenedMin Max Incr Skin

T Skin [# Plies] 4 10 2 Ply Max Stress1, Stress2, Stress12 Min Max Incr

T Web [# Plies] 2 4 2 Ply Tsai-Hahn Interaction %0° 10/10 80/30 20/10

T Foot [# Plies] 2 4 2 Section Crippling %45° 10/0 60/0 20/0

T Crown [# Plies] 2 6 2 Local Buckling of Open Span, Closed Span, %90° 10/0 50/0 20/0

H Stiffener [mm] 20 30 10 Bonded Section, Web, Crown Stiffener

Spacing [mm] 100 300 100 Panel Buckling Uniaxial, Biaxial, Shear Min Max Incr

W Foot [mm] 25 - - %0° 0/20 50/80 10/20

W Crown [mm] 30 40 10 %45° 0/20 0/80 0/20

Angle 70 - -

Typical design criteria and layup rules

Typical material parameters

Load Case Tip Deflection

Hovering > 25 mm

Stiffness criterionConcepts

From FAA/EASA, aeroelastics, handling, tooling, maufacturing, analysis, ...

Time consuming to create detailed model for each combination


FE Model

10

9000 S4R Elements

Limit Load Factor: 1.2

Ultimate Load Factor: 1.5

Up Gust

Landing

Hovering

Battery pack

Root

Plane Remains Plane

Fixed Reference Point

Tip

Plane Remains Plane

‘Rotor’ Forces

What situation is critical?


Outline

11

• Motivation


• Practical Generative Design• Practical / Generative

• Structural Optimization Approach

• Procedure

• Traditional Results

• Beyond

• Summary


Practical / Generative

12

Practical: utilize strengths

Engineer Computer

Creative Does not get bored

Intuition Unbiased

Experience Good memory

Imagination Fast math

Responsibilities/Work shareGuides Provides data

Evaluates Analyses

Generative: Collaborative/interactive

Decisions augmented by insight generated by optimization

Optimization restricted by demands/requirements


Structural Optimization Approach

13

Equivalent stiffness

Concept Definition Force

Localization

Finite Element Analysis

FEM Update

Mesh

Section Forces

Displacements

Stiffness

Homogenization

Strength Analysis

Local Stability

Panel / Section

Stability Analysis

HyperSizer Smeared Stiffness

Approach

Hyper FEA

CLT

𝐾𝑒𝑙 =𝐴 𝐵𝐵 𝐷

Analytical

Plate

Forces per

ObjectStresses

per Ply


Procedure Overview

14

Restrict stiffness

modification to Spar Caps

Use Adjoint Variable Design Sensitivity

Analysis to generate stiffness targets per

Element

Optimize Zone Shape

(same design domains)

Use Adjoint Variable Design Sensitivity

Analysis to generate stiffness targets per

Zone

FEA FEA

Splitup wing

skin structure

to components

Define concepts and materials and assign to components

Vary buckling length for

components and size to local

criteria

Choose best rib layout,

concept and material

VBA

FEA

Global Stiffness Target

Final Optimization

Structural Layout, Concept and Material Trade Study


Stiffness Target Generation

15

during ‚Hovering‘

(Min/Max constraints)

Tip deflection restricted to 20mm in z-direction

Restrict optimization domain Adjoint Variable Design Sensitivity Method

Variable for each FE element

Improve Manufacturability

Zone Optimization (Penalty based target similarity aggregation)

Define Spar Cap zone min- stiffness target Adjoint Variable Design Sensitivity Method

Variable for each Zone

Spar Caps


Concept, Structural Layout and Material

16

0 Ribs5 Ribs

Finite Element Analysis

Concept Definition Rib Spacing Material Combination

Hyper FEA

Assignment

via script

Load path convergence

Sizing Optimization

to all requirementsAbaqus


Results – Weight Trends

17

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

0 Ribs 1 Rib 2 Ribs 3 Ribs 4 Ribs 5 Ribs

Wei

ght

[kg]

Standard Material

Top Wing Skins Bottom Wing Skins Leading Edge Trailing Edge

Ribs Monolithic Sandwich Hat Stiffened

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

Mo

no

lith

ic

San

dw

ich

Hat

Sti

ffe

ned

0 Ribs 1 Rib 2 Ribs 3 Ribs 4 Ribs 5 Ribs

Wei

ght

[kg]

High End Material

Top Wing Skins Bottom Wing Skins Leading Edge Trailing Edge

Ribs Monolithic Sandwich Hat Stiffened

Total weight distribution for different design concepts over number of ribs


Results - Reasoning

18

Sandwich 0 Ribs Composite Hat 5 Ribs

• Local stability driven

• ‚bad choice‘ of producibility

and tooling constraints


Best Candidate Evaluation

19

Monolithic – HE – 0 Rigs: 7.16 kg (best: 4.85 kg)

Hat Stiffened – HE –3 Ribs: 4.86 (best: 4.82 kg)

Sandwich – HE –3 Rib: 3.63 kg (best: 3.63 kg)

Mixed Concepts

1 Rib : 3.4 kg

Critical CriterionCritical Load Case

Margin of SafetyBest Concept


Beyond Traditional

20

Y

XZ

Ny

MxyMx

90s

45s

0s

Ny

MxyMx

Zone Based Ply Based

Required

Plies

Ply Generation

Stacking

From User defined design zones

To Optimized design zone shape

From Zones, Laminate, stacking

To Organic Ply shapes


Composite Design Setup

21

Ply extension constraintsDesign and Tooling Restrictions

Stength and Stiffness Criteria

Layup and

Stacking Preferences


Design Optimization Process

22

CAD Init FEA HyperSizer

FEA Run

Update loads

Import and Size

Strength

Stiffness

Stability

Automatic

loop

Tight Coupling with FEA

HyperSizer

Setup Ply

Optimization

Review

Export

Complex Section ShapesPly Shapes


Free Form Ply Shapes

23

Native Catia Geometry

- Points

- Splines

- Smooting


Review and Report and Archive

24

Margin of Safety

Critical Criterion

Final Weight 2.7 kgBest Uniform Design per Panel: 3.4 kg


Outline

25

• Motivation



• Summary


Summary

26

• Demand from trends / observations

• Actively generated ideas to meet demands

• Definition of requirements and design space

• Practical, generative design exploration

• Structural analysis approach

• Interactive design exploration

• Effective informed decisions

• Best design analysis

• Beyond traditional

?

!

Questions

Requirements

Answers

Design

Documents

Generative Structural Design and Optimization of Modern ... · Stiffener [mm] 20 30 10 Bonded Section, Web, Crown Stiffener Spacing [mm] 100 300 100 Panel Buckling Uniaxial, Biaxial,