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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: [email protected]
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