Optimized design of a wing box structure via automated FEM and

genetic algorithms

D. Fanteria, R. Zuddas

Università di Pisa - Dipartimento di Ingegneria Aerospaziale, via Girolamo Caruso, 8 - I56122, PISA, ITALY

Phone (+)39.050.2217211 e-mail: d.fanteria@ing.unipi.it

Objectives and approach

2

Long Term goalDevelopment of a complete process for the design and optimization of wing structures fortransport aircraft.

Objectives

Devise a design tool to be fast and easy to use with high flexibility to accommodatechanges in the structural architecture

Integrate PATRAN/NASTRAN Finite Element software within a commercial multi purposeoptimization environment (ModeFRONTIER)

Enhance the usability of multi-objective optimization with conflicting requirementswithin wing structural design

Assess development and computational costs for the whole design process

ApproachDevelop a reduced design exercise including all the potentially critical features of the real

project in order to ensure the significance of the tests

Introduce all the possible simplifications in order to reduce development resources

Definition of the design problem

3

Functions of the wing structure: • ensure an external shape under load with satisfactory aerodynamic performance

complex architecture and geometry

• withstand aerodynamic and mass loads within the aircraft operating envelope large number of Loading Cases

• guarantee an adequate aero-elastic behavior stiffness control

• comply with regulations (FAR/JAR) large number of design requirements

Design Objectives• Minimum weight

• Minimum costs

• Easy manufacturing

• Appropriate stiffness

COMPLEX DESIGN PROBLEM, DESCRIBED BY MANY DESIGN VARIABLES AND INVOLVING DIFFERENT, OFTEN CONFLICTING, REQUIREMENTS AND

OBJECTIVES

Structural design process: steps towards automation

DesignModifications

Design goalsachieved ?

Design concept

Structural models (FEM)

Structural response

Model Update

Yes

No

Analysis

Modeling

EvaluationCorrective Actions

Green: automatic actionRed: manual action

4

Final design

DesignModifications

Design goalsachieved ?

Design concept

Structural models (FEM)

Structural response

Model Update

YesNo

Analysis

Modeling

EvaluationCorrective Actions

Optimization environment

Final design

Finite element model definition • Conventional two spars multi

rib wing box architecture, with stiffened upper and lower panels.

5a

• The external geometry is defined either by key airfoil sections or through imported IGES surfaces.

Finite element model definition • Conventional two spars multi

rib wing box architecture, with stiffened upper and lower panels.

5b

• The external geometry is defined either by key airfoil sections or through imported IGES surfaces.

• The wing box is derived from wing master geometry by defining front and rear spar positions.

Finite element model definition • Conventional two spars multi

rib wing box architecture, with stiffened upper and lower panels.

5c

• The external geometry is defined either by key airfoil sections or through imported IGES surfaces.

• The wing box is derived from wing master geometry by defining front and rear spar positions.

• Internal layout is defined by stringer and rib pitch.

Finite element model definition • Conventional two spars multi

rib wing box architecture, with stiffened upper and lower panels.

5d

• The external geometry is defined either by key airfoil sections or through imported IGES surfaces.

• The wing box is derived from wing master geometry by defining front and rear spar positions.

• Internal layout is defined by stringer and rib pitch.

• A mesh is created taking into account the main structural items of the wing box architecture.

Finite element model definition • Conventional two spars multi

rib wing box architecture, with stiffened upper and lower panels.

5e

• The external geometry is defined either by key airfoil sections or through imported IGES surfaces.

• The wing box is derived from wing master geometry by defining front and rear spar positions.

• Internal layout is defined by stringer and rib pitch.

• A mesh is created taking into account the main structural items of the wing box architecture.

• The FE model is completed with element properties, loads and constraints.

Finite element model detailsGeneral Features Skins and webs are modeled with shell elements (CQUAD)

Stringers, uprights, posts, spar caps, failsafe angles and engine truss with rod (CROD) and beam (CBAR) elements.

6

• Ribs model includes web , posts, failsafe angles and uprights

• Webs are split into middle, upper and lower zones to account for reduced stiffness due to stringer mouse-holes (implicit modeling)

Stringers are permitted to run out at ribs

Finite element model loads• Loads are

introduced by means of MPC RBE3 in rib’s perimeter nodes

7a

• The aerodynamic pressure distribution is reduced at ribs

Finite element model loads• Loads are

introduced by means of MPC RBE3 in rib’s perimeter nodes

7b

• The aerodynamic pressure distribution is reduced at ribs

• The fuel masses are reduced at mid bay points

Finite element model loads• Loads are

introduced by means of MPC RBE3 in rib’s perimeter nodes

7c

• The aerodynamic pressure distribution is reduced at ribs

• The fuel masses are reduced at mid bay points

• The engine is modeled with a mass point

Evaluation of the structural response• Structural response is evaluated in terms of stress levels and deflections• Maximum stress components at mid-bay are used• Allowables considered to compute margins of safety are:

– Compressive critical stress in upper panel – Critical shear flow in spar webs – Yield stress – Ultimate shear strength in spar webs– Reference tensile stress in cruise flight (for durability) – Static residual strength of cracked stringer lower panel

• Stress levels and deflections are evaluated by means of a linear analysis with limit load cases (SOL 101).

• Ultimate conditions are derived by dividing ultimate allowables by the relevant factor of safety

8

Geometry and mesh

(PATRAN)

Analysis(NASTRAN)

Parametric model creation(MATLAB & PCL)

Creation of report files

(PATRAN)

Margins of safety

(MATLAB)

Cycle Start

.ses

.xdb

.bdf

weightstressesdeflections

.ses

Automation of the design cycle

9

Cycle End

Design Variables Design evaluation

Design variablesGeometry and mesh parameters Internal properties data

Wing box dimensions:

chord, span, front and rear spar position

Structural layout:

Rib spacing and stringers pitch

Mesh control:

Number of elements along edges of main components (panels, spars and ribs)

Materials

Thicknesses and area distributions

10

• Use of distributions, fully defined by a limited number of variables, which are converted into single thickness values at each bay in the FE model

• Skin thickness along span are assumed to be linear and not increasing towards wing tip to be compliant with typical metal construction practice

• Only four variables are needed to define the thickness in the example shown

Managing of model complexity: the thickness distribution example

An example of design objectives and constraints for the current problem

Objectives and constraints for optimization

Objective Minimum weight structure

Objective Control reserve factors distribution

Constraint Reserve factors >0

• The design cycle is managed within an environment (ModeFRONTIER) which can handle different optimization strategies: in particular Genetic Algorithms (GA) are suited for the present problem

• GA allow multi objective optimization based on the definition of a fitnessfunction derived from both design objectives and constraints

• Configurations with higher fitness functions are allowed to “breed” to give birth to successive design generations.

11

Automated modeling process at work (1)

12

13a

Automated modeling process at work (2)

13b

Automated modeling process at work (2)

Example: stringers pitch optimizationOptimization processOpt. Strategy MOGA II

Initial population creation method

Reduced Factorial

No. of designs per generation

32

No. of generations 169

No. of configurations 5429

Total run time 125 h 41 m

Average run time 1 m 23 s

Geometrical data

Spars Webs Thickness [mm] 4-8

Cap cross section 2 As

Ribs Inboard Spacing [mm] 350

Outboard Spacing [mm] 450

Thickness [mm] 4

Skins Thickness [mm] 5-10

Upper stringers

(Zee)

Pitch [mm] 80-160

h/b 0.6-1.2

ts/t 0.9-2.25

Lower stringers

(Zee)

Pitch [mm] 100-180

h/b 0.6

ts/t 0.9-1.1St

tb

h

14

Weight trend

15

Weight vs. tip deflection

16a

Weight vs. tip deflection

16b

Weight vs. tip deflection

16c

Stiffer vs. lighter configuration

Stiffer Configuration(No. 1370)

Lighter Configuration(No. 3951)

Weight (Kg) 1634 1271

Tip deflection (%)

7.7 10.3

Upper stringers pitch (mm)

84 92

Lower stringers pitch (mm)

132 120

17

Internal stresses

Stiffer configuration

Lighter configuration

18

Safety margins envelopes

Stiffer configuration Lighter configuration

19

ALL

SMσσ

−=1

Thickness distributions

α βUpper 0.75 0.55

Lower 0.7 0

Front 0.35 0.05

Rear 0.55 0.5

α βUpper 0.6 0.25

Lower 0.25 0

Front 0.7 0.1

Rear 0.6 0.3

Stiffer configuration Lighter configuration

20

Equivalent skin thickness distributions

21

Stiffer configuration Lighter configuration

tb

SA bAtt S

eq +=

Conclusions

22

A specific design tool to automatically manage the structuraldesign process has been presented which is based on theintegration of PATRAN and NASTRAN within an optimizationenvironment.

Main capabilities of such a tool have been shown thorough areduced design exercise dealing with the optimization of a wingbox structure that includes the majority of potentially criticalfeatures of a real project

Multi-objective optimizations carried out using genetic algorithms haveproduced a class of refined designs satisfying conflicting requirements

The completion of the design exercise required a limited developmenttime and reasonable computational resources