Composite laminates are in widespread use in the aerospace industry. As well as sa tisfying strength and stiffness criteria, the final laminate design has to be manufacturable in terms of compatibility between adjacent panels, thus introducing conflicting constraints on the allowed laminate stacking sequences. An attempt to automate the laminate design process is described. The method uses a mixture of a genetic algorithm and heuristics to satisfy the various design and manufacturing constraints. Multiple zones are allowed, where each zone defines a panel together with a set of applied loads. Guide laminates and a blending methodology allow each zone to share common plies. This creates ply continuity across the structure and avoids the scenario seen in other laminate optimisation tools where each optimised zone contains unrelated laminates which are not practical from a manufacturing perspective

Coates, T.

Emanuel, M.

Peterson, B.

Smith, A.

University of Queensland eSpace

5th Australasian Congress on Applied Mechanics, ACAM 2007  
10-12 December 2007, Brisbane, Australia 
Automation of optimal laminate design. 
 
T. Coates1 A. Smith2 M. Emanuel1 B. Peterson1 
 
1GKN Aerospace Engineering Services, Australia  
2451° CONSULTING, Australia 
 
Abstract: Composite laminates are in widespread use in the aerospace industry. As well as satisfying 
strength and stiffness criteria, the final laminate design has to be manufacturable in terms of 
compatibility between adjacent panels, thus introducing conflicting constraints on the allowed laminate 
stacking sequences. An attempt to automate the laminate design process is described. The method 
uses a mixture of a genetic algorithm and heuristics to satisfy the various design and manufacturing 
constraints. Multiple zones are allowed, where each zone defines a panel together with a set of 
applied loads. Guide laminates and a blending methodology allow each zone to share common plies. 
This creates ply continuity across the structure and avoids the scenario seen in other laminate 
optimisation tools where each optimised zone contains unrelated laminates which are not practical 
from a manufacturing perspective. 
Keywords: blending, composite, design, engineering automation, genetic algorithm, heuristics, 
manufacturing constraints, optimisation, laminate. 
1 Introduction 
The design of minimum weight structures using composite materials requires the laminates to satisfy 
structural requirements such as strength and stability. In addition, where a laminate is tailored to have 
differing numbers of plies and ply orientations for zones of a monolithic panel with different loading, 
the resulting design must have good manufacturability. This places a restriction on the valid laminate 
stacking sequences for adjacent zones. 
This paper describes an automated method for the design of multiple zone laminates. Heuristics, such 
as limits on ply orientation percentages and balancing of laminates which are typically found in the 
aerospace industry are also i ncluded. 
Optimisation of the laminates uses a genetic algorithm which provides a non-deterministic search of 
the solution space for the global optimum. It is based on the concept of natural selection and includes 
elements for population initialisation, parent selection, cross-over, mutation and selection of 
successive generations. Holland [1] is attributed with the original work on genetic algorithms which has 
been refined since. A guide based design approach [2] is used in conjunction with the genetic 
algorithm to cater for the presence of multiple related zones, and builds on the work of Salamonsen 
[3]. 
The genetic algorithm considers a population of guide laminates that satisfy the global constraints and 
requirements. The individual zones are blended by removing as many plies as possible from the guide 
laminate while still satisfying the local strength and stiffness requirements. This approach results in a 
design that is completely blended in terms of ply continuity across zones but with an associated weight 
penalty when compared to a solution where each zone is optimised independently. The guide based 
design may not be truly  optimal, but tests show that the additional weight for a blended design 
compared to an unblended optimal design is small. 
2 Method 
The process has two main parts (Figure 1), guide generation or global optimisation and local or zone 
optimisation. The global optimisation begins by generating an initial set of laminates which are random 
with regard to number of plies and ply orientation. Heuristics are considered by applying constraints to 
the set of laminates and their stacking sequences are adjusted to sati sfy the following. 
1. Minimum and maximum total number of plies in the laminate. 
2. Whether there are fixed plies at the middle, top and bottom surfaces or core in the laminate. 
Core can be specified as a fixed middle ply. 
  
3. Minimum and maximum percentage of a particular ply orientation in the laminate. Orientations 
currently allowed are 0°, 90°, +45° and -45° for a unidirectional tape material, and 0°/90°and 
±45° for a fabric material. 
4. The maximum number of plies of the same orientation that can be adjacent. 
5. Whether the laminate is symmetric or not about the mid plane. 
6. Whether the laminate is balanced or not. A laminate is balanced if, for every unidirectional ply 
at an angle +q there is an identical ply at -q. 
  
Figure 1. Process Flow 
 
These heuristics vary to some extent between different aerospace companies  and vary more widely in 
other industries where composites are used, but the algorithm is such that they can easily be changed 
or added to. The inclusion of heuristics in the algorithm negates the need for a subsequent step of 
adjusting the laminate to increase manufacturability. This additional step is often responsible for not 
achieving the most optimum design. 
The resulting guide laminates are then analysed for static strength and buckling. Static strength is 
calculated using classical laminate theory [4, 5] and buckling analysis is performed with an internal 
GKN library of closed form solutions. These can easily be replaced with customer specific methods. 
No 
Global Optimisation Local Optimisation 
Local 
Optimisation  
Initial Guides 
Calculate Margins of 
Safety 
Control based on Ply & 
Laminates Constraints 
Calculate Penalties 
Calculate Fitness & 
Ranking Guides 
Calculating Fitness & 
Ranking Guides 
Converged or 
Limit Reached  
No 
New Guide Generation 
based on Genetic Algorithm 
Guide-Based Local Optimisation 
 
 
 
 
 
 
 
Local optimisation on each Zone: 
Ranking following each iteration 
of 
Ply removal à Failure Criteria à 
Penalties process 
Zone 1 Zone 2 Zone n  
Each Guide 
Yes Converged or 
Limit Reached  
No 
New Guide Generation 
based on Genetic Algorithm 
Yes 
Yes 
Exit 
Exit Start 
  
The analysis results are then used to calculate a fitness value, F, for each laminate. The fitness value 
is used to determine which laminates will be used in future generations. The lower the value of F is, 
the more likely it is that the laminate will survive to succeeding generations of the genetic algorithm. 
F = 1+ FI + BR + N + P; for FI < 1 and BR < 1 
F = 1,000,000; for FI  1 or BI  1        (1) 
where FI is the ratio of applied to allowable strain, BR is the ratio of applied load to the critical buckling 
load, N is the total number of plies in the laminate and P is an overall penalty value which is a 
summation of individual penalty values multiplied by the quantity of plies which violate the design 
constraints of balance, contiguity and maximum and minimum percentages of particular ply 
orientations. P can be thought of as additional plies in the laminate which necessarily reduce the 
fitness of the laminate. Laminates with values of FI or BR which are greater than 1, thus indicating 
failure, have a very high value of F assigned to them, ensuring their elimination from future 
generations. 
The fittest 25% of the laminate population is then used as the basis for the next generation by applying 
random mutations by ply swapping within a laminate and between laminates (cross breeding). In 
addition the top 25% remains unchanged and an additional 25% of the population is generated in the 
same random way as the initial guide laminates. 
The process then continues iterating until convergence which is defined as a set number of 
generations without improvement in the fittest design. The resulting set of guide laminates then satisfy 
the design, strength and stiffness constraints across all zones uniformly. These are then used as the 
starting set of guide laminates for the local optimisation block. This block is the same as the global 
optimisation block with the addition of a blending step which removes plies from the guide laminate for 
each zone until the removal of more plies would result in not meeting the strength and stiffness 
requirements. This removal can be done from the outer plies inwards, or in the case of a symmetric 
laminate from the middle plies outwards. One of the zones will remain with no plies removed. This is 
the critical zone for that guide laminate. The other zones will have fewer plies but will always have 
common plies with the guide laminate thus ensuring ply continuity across all zones. No concept of 
zone connectivity is present. Each zone effectively has ply continuity with every other zone. The 
fitness value, F, for each guide laminate is calculated as 
å
=
´=
n
1Z
ZZ AFF           (2) 
where FZ is the fitness value for each zone calculated using equation 1 and AZ is the area of the zone. 
The iteration then continues in the same way as the global optimisation block by generating a new set 
of guide laminates. Convergence is defined in the same way as the global optimisation block. 
3 Example 
Consider a structural panel consisting of nine zones with differing dimensions (Table 1). Each zone or 
sub panel can have single curvature for which the radius is specified. Material properties and 
allowables are shown for the carbon fibre fabric in Table 2.  
Table 1. Zone Data. 
Zone Size X (in) Size Y (in) Radius (in) 
1 10.000 15.000 100.000 
2 12.000 12.000 90.000 
3 12.000 10.300  
4 9.500 11.000 68.750 
5 10.200 20.100 88.000 
6 9.780 19.100 91.345 
7 8.100 15.542  
8 5.450 4.880  
9 18.130 12.448  
Table 2. Material Properties 
    E11 (psi)   9.0E+6 
    E22 (psi)    9.0E+6 
    G12 (psi)    1.0E+6 
t (in) 0.008 
  12   0.05 
   (lb/in3)   0.06 
T1    0.005 
C1    0.004 
T2    0.005 
C2    0.004 
12    0.008 
13,23 (psi)  10.0E+3 
  
Load cases for each zone and those that apply to all zones together with the analysis type required 
are shown in Table 3. Multiple load cases can be applied to a single zone or all zones. In this 
example, zones 5, 6 and 9 are only loaded by the common cases A.1 to A.5 which apply to all zones. 
No loads which are specific to these zones are applied. 
The resulting design is constrained to be a symmetric laminate. There is a limit of 3 adjacent plies 
which can have the same orientation, and minimum and maximum values of 0% and 100% on the 
allowed quantities of 0°/90°and ±45° orientations. There are no fixed plies. There are 50 guide 
laminates in each population. Runs were done with blending from the outer plies inwards and from the 
middle plies outwards.  
Results for both blending options are shown in Table 4. One advantage of the algorithm is that even 
with one blending method it produces a number of equally optimum designs which generally have 
different layups but the same number of plies, allowing the designer a choice for the final design. In 
addition the two blending options can produce quite different layups but with the same number of plies 
for each zone. 
For nine zones with the load cases and analysis types shown in Table 3 there are 84 analyses 
required for each iteration of the global optimisation loop. The same number is required for the guide 
laminates in the local optimisation loop. Additionally, analyses are required for each step of the zone 
blending when plies are being removed. The number of these cannot be estimated a priori. In the case 
of blending from the surface inwards in this example there were 71 generations in the global 
optimisation block and 43 generations in the local optimisation block. This gives a minimum of 9576 
analyses of strength or buckling to be performed. It can be seen that the time consuming part of 
producing a composite panel design is taken in the structural analysis routines. This is a disadvantage 
of genetic  algorithms in general. It is well known that genetic algorithms are less computationally 
efficient than other methods due to their scatter gun approach to the design space. However, there is 
a smaller probability that this approach will converge to a non optimal local minimum as can happen 
with other optimisation methods. Obviously, the analysis routines that are used in the application 
should be as efficient as possible with a preference for simple closed form solutions over other 
methods for the buckling analysis. Due to the randomness inherent in the algorithm, different runs with 
Table 3. Loading Data. 
Zone Load ID Static Buckling Nx (lb/in) Ny (lb/in) Nxy (lb/in) My (lbin/in) 
All A.1 P P 290.45  23.44  
All A.2 P P 323.70    
All A.3 P     -1165.40  
All A.4   P -38.70  194.50  
All A.5 P   551.66 1176.20 1103.20  
1 1.1 P   201.30    
1 1.2 P   -323.60 103.20 78.93  
1 1.3 P    548.90   
2 2.1 P    5307.80   
2 2.2 P   2398.70    
2 2.3 P   55.30 2208.70 1134.50  
3 3.1 P   3583.80 135.70 2237.00  
3 3.2 P P -449.00  278.00  
3 3.3 P    4657.30 4192.80  
3 3.4 P   3669.00 2235.90 2354.10  
3 3.5 P   2559.40 3972.40 1567.90  
4 4.1 P P 248.90  145.87  
4 4.2 P P 254.80  256.70  
7 7.1 P P -268.90  -134.55  
8 8.1 P P -65.88  130.78  
8 8.2 P   2268.00  2215.10 112.76 
  
the same data take different times. In this case run times were typically 4 to 6 minutes on an Intel® 
Xeon 3.4GHz desktop PC. 
The randomness of the genetic algorithm also results in different solutions for different runs with the 
same data. It has been noted that at times a slightly heavier solution is the result with typically one or 
two extra plies in one zone. This is also a function of the input parameters such as the value of the 
number of generations without improvement which defines convergence. Results show different 
laminates for the two different blending directions but with equal numbers of plies and the same weight 
of 8.45 lb. By contrast, an 
unblended solution has 10, 18, 22, 
8, 10, 10, 16, 20 and 12 plies 
respectively for the 9 zones with a 
weight of 8.07 lb. The global 
blending process has thus added 
extra plies to zones 2 and 3 with a 
weight penalty of 4.7%. This 
indicates that if the blended design 
is not truly optimal, it is close to 
being so for all practical purposes. 
4 Comparison with a 
manual approach. 
A traditional approach was applied 
to the above problem. The process 
involved using available laminate 
analysis tools but optimisation was 
done manually by mimicking to 
some extent the automated 
method. The most critical zone for 
strength and buckling was 
determined and then the laminate 
for that zone was manually 
adjusted and reanalysed a number 
of times until it was judged that the 
Table 4. Final Design Solution (half laminate). 
Zone Zone Global 
Ply 1 2 3 4 5 6 7 8 9 
  
1 2 3 4 5 6 7 8 9 
1 
(surface)                 45                                                 45 45 45 45 45 45 45 45 45 
2                 45                                                  0 0 0 0 0 0 0 0 0 
3                 45                                                  0 0 0 0 0 0 0 0 0 
4         0 0                                 0          45 45 45 45 45 45 45 45 45 
5         0 0                                 0          0 0 0         0 0 0 0 0 
6         45 45                         45 45                  45 45                         45 45 45 
7         0 0                         0 0                  0 0                         0 0        
8         0 0                         0 0 0           45 45                         45 45        
9 45 45 45         45 45 45 45 45           45 45                                 45        
10 45 45 45 45 45 45 45 45 45           0 0                                 0        
11 45 45 45 45 45 45 45 45 45                   45                                                
12 0 0 0 0 0 0 0 0 0                   45                                                
13 (mid) 45 45 45 45 45 45 45 45 45                   0                                                
No. 
Plies 10 20 26 8 10 10 16 20 12   10 20 26 8 10 10 16 20 12 
  Blend Inwards. Weight=8.45 lb   Blend Outwards. Weight=8.45 lb 
Table 5. Manual Design Solution (half laminate). 
Zone Global 
Ply 1 2 3 4 5 6 7 8 9 
1 (surface)     0             
2    0        
3    45        
4    0        
5    0     0   
6    45     45   
7   0 0     0   
8   0 0     0   
9   45 45    45 45   
10   0 0    0 0   
11   45 45    45 45 45 
12 0 0 0 0 0 0 0 0 0 
13 0 0 0 0 0 0 0 0 0 
14 45 45 45 45 45 45 45 45 45 
15 0 0 0 0 0 0 0 0 0 
16 (mid) 45 45 45 45 45 45 45 45 45 
No. Plies 10 20 32 10 10 10 16 24 12 
Manually Blended. Weight=8.96 lb 
  
best solution had been found. The laminates for the other 8 zones were then determined by removing 
plies from the critical zone laminate. 
The final design would be different depending on the engineer designing the laminates. A more 
experienced engineer might be able to produce a solution that took less time and was lighter due to 
the application of knowledge about how composites behave under different loading conditions and the 
effect of different stacking sequences on the structural response. In this case the design was 
completed by an experienced engineer without knowledge of the automated solution. 
Results (Table 5) show that the final design weight is 0.51 lb greater than the automated design, 
equating to a weight penalty of 6.0% compared to the automated solution and 11.0% over an 
automated unblended solution. Including data preparation and input, the time taken to produce the 
design was 10 hours which compares with 1 hour for the automated method. Additionally the manual 
approach produced one design whereas the automated method produced many. 
5 Conclusions and recommendations 
Design of minimum weight composite material structures which satisfy structural and manufacturing 
requirements, whether in aerospace or other industry applications, can be successfully achieved using 
guide laminate based blending and a genetic optimisation algorithm. A test case shows that the 
method generates a low weight design which for practical purposes is optimal. The ability of the 
genetic algorithm to generate multiple designs of equal weight along with the ability to control the 
design through options such as blend direction and heuristics provides a strong justification for using 
the method. The blending methodology ensures that the resulting designs are easily manufactured 
due to ply continuity across multiple zones. The automation of what is a time consuming design 
process gives a practical final design in a fraction of the time required by traditional manual design 
optimisation methods. 
Future work includes refining and increasing the efficiency of the supporting analysis methods, 
introducing the concept of zone connectivity and allowing the design of sandwich structures where the 
core is allowed to be placed at any position in the laminate. 
6 Acknowledgements 
The authors wish to thank the Cooperative Research Centre for Advanced Composite Structures for 
their collaboration with GKNAES in developing the optimisation algorithm and a prototype version of 
the software. 
7 References 
[1] Holland, J. H., Adaptation in Natural and Artificial Systems, Ann Arbor, MI, The University of Michigan 
Press, 1975. 
[2]  Adams, D. B., Watson, L. T., Gürdal, Z. and Anderson-Cook, C. M., Genetic algorithm optimization and 
blending of composite laminates by locally reducing laminate thickness, Advances in Engineering Software, 
Vol. 35, Issue 1, pp. 35-43, 2004.   
[3]  Salamonsen, M., Application of a Genetic Algorithm to the Design of Composite Laminates, 
Undergraduate thesis, University of New South Wales, 2005. 
[4] Jones, R. M., Mechanics of Composite Materials, Tokyo, McGraw-Hill, Kogakusha, 1975. 
[5] Baker, A., Dutton, S., Kelly, D., Composite Materials for Aircraft Structures, 2nd Edition, AIAA Education 
Series, Reston VA, 2004. 
 


Automation of optimal laminate design

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