1. A novel approach towards optimizing lightweight structures
B. Goller, R. Winkler, M. Gratt
3rd Workshop on Structural Analysis of Lightweight Structures Natters, May 15, 2014

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Contents
Introduction
Methods of analysis
Implementation in FE-software
Examples
Conclusions
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Introduction
Main aspect in the competiveness is the identification of weight saving opportunities.
Material, fuel consumptions and hence costs drive the design of lightweight structures. €
competiveness
weight
time
Development of novel approaches for optimization are a an approach to meet these challenging requirements.
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Introduction
RF (composite, metallic, sandwich) > 1.0
Requirements:
Displacement constraints
Limitations of manufacturing
Huge number of design variables
Large set of constraints
Computational feasibility
RFbolt,axial > 1.0
RFbearing,bypass > 1.0
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Introduction
Constraint optimization problem:
f (x)
min
gi(x) ≤ ci, for i=1…m
subject to
x … design variables (number of plies, fiber angle, thickness of metals, etc.)
f (x) … objective function (e.g. total mass)
gi (x) … constraint function (strength criteria, design constraints, etc.)
Classical optimization algorithms might soon reach their feasible limits due to the dimensionality of the problem.
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6. Methods of analysis Proposed novel approach:
Iterative adaptation strategy
Start configuration
Structural analysis with load increment
i+1
Local change of thickness, angle
Source:
W. Liebermeister, University of Berlin
Adapted structure for load increment
i+1
Final configuration for targeted load level
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Methods of analysis
Criterion for monolithic composite parts:
Strain criterion: max e < 0.35%
Strategy:
Determine number of plies, stacking sequence and draping angle such that criterion is fulfilled
Yamada-Sun:
Details will be presented by Egon Verginer
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Methods of analysis
Criterion for metallic parts:
Yielding criterion: t
σ11
σ12
RF … reserve factor
fy … yield stress
σMISES … VON MISES stress
σ12
σ22
Strategy:
Increase thickness t such that RF>1.0
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Methods of analysis
Criterion for fasteners:
sn … normal stress of bolt
ss … shear stress of bolt
Increase bolt diameter
Bolt failure:
Increase bolt diameter & thickness of connected elements
Pull through:
nut
Increase bolt diameter & thickness of connected elements
Bearing failure:
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10. Implementation in FE-software
Beginning of Analysis
Adaptive change of element properties requires access to element routines (→ re-programming or implementation of improved element routines as a first step.
Adaption strategy is integrated in the element routines.
Current properties of each iteration of the single elements are to be stored and accessed (→external database)
UEXTERNALDB
Start of Step
Creation of element stiffness matrix
UEL
Creation of load vector
Back to start of step
Solution of governing equation
UEL
Evaluation of elemental output
UEXTERNALDB
Write output
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End of step

11. Implementation in FE-software
SQLITE database is a suitable means for storing and accessing efficiently large amount of data
For each iteration a new database is created, where the current value of the optimization process are written.
For the creation of the element stiffness matrix, the database of the previous step is accessed.
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Examples
Plate with hole under tension
Uniform loading at right edge
Fully clamped at left edge
Ply type: Fabric
Initial stacking: (45/0/0/45) s 3s
Analytical solution:
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Examples
Number of plies
The highest number of plies is located in the areas of the stress peaks
Maximum number of 50 plies (user defined value) is reached in this area
Draping angles
The load path can be recognized by the identified draping angles
Due to the presence of plies with a0°, the curvature of the solution is not as pronounced as expected from the analytical solution
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Examples
Illustration of fastener optimization routine:
Three shell structures connected by 3 single- and 3 double-lap shear fasteners
Two straps are clamped on the left edges, all three are loaded uniformly on the right edges.
Fasteners and connected elements are dimensioned against bolt failure, pull through and bypass.
Single-lap shear fasteners
Double-lap shear fasteners
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Examples
Diameter of bolts
The highest increase of the diameter is performed for those two fasteners, where the initial analysis shows the largest forces.
Number of plies
The number of plies is updated according to bearing and bypass criterion.
The highest number of plies is required for the highest loaded fastener .
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Outlook
Current example:
Optimization of a part of the winglet structure (~ 1 Mio. DOFs)
Results after 10 iterations for 3 loadcases each (1.5 h of analysis time):
Next step:
Smoothing of the results in order to obtain a producible layup
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Conclusions
A novel approach for the optimization of lightweight structures has been presented.
The advantage of this approach is its applicability to FE-models involving a high number of design variables.
The results shown in this presentation have been obtained after 10 iterations, which suggests its usability in case of large numerical models.
Acknowledgements
This project is financially supported by the Austrian Space Applications Programme (ASAP) of the Austrian Ministry for Transport, Innovation and Technology (BMVIT), which is deeply appreciated.
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