S.Nagendra, D.Jestin, Z.Gurdal, R.T.Haftka and L.T.Watson Computers & Structures, Vol. 58, No. 3, pp , 1996.

Transcription

1 S.Nagendra, D.Jestin, Z.Gurdal, R.T.Haftka and L.T.Watson Computers & Structures, Vol. 58, No. 3, pp , Presented by Vignesh Solai Rameshbabu

2 Introduction Simple programming technique which mimics natural genetics is known as genetic algorithm. It consists of reproduction, crossover, mutation, permutation, ply addition and deletion Strengths: Laminate stacking sequence design Close to global minimum Weakness: High computational costs Improved GA: Reduced computational costs Improve the reliability Lighter design weight reduced by 4%

3 High Performance composites High tensile strength Impact resistant Thickness is less Buckling critical Tuning of Flexural properties Stacking sequence tailoring Stacking sequence optimization GA Improved GA - tailoring the genetic operators and thereby improve the reliability and reduce the computational cost. Composite Panels Layered composite laminate(skin) supported by stiffeners which is also made up of composite laminates(blade).

4 Problem Description Length 30 in ; Breadth 32 in N x = 20,000 lb/in; N xy = 5000 lb/in Balanced and Symmetric 0 0, ±45 0, 90 0 Blade and Flange Identical Laminates Number of Identical Plies Adjacent 4 to prevent matrix cracking No zero ply in skin laminate Outer Plies - ±45 0 To avoid damage due to compressive loading Program used to run the genetic algorithm - PASCO

5 Optimization Formulation Fitness Function: Where, W Panel Weight Critical failure load factor. - Critical Buckling load factor = / 1 - Strength Failure load factor= / 1

6 Optimization Formulation (contd..) q Penalty parameter Ɛ Bonus parameter P cont - Ply contiguity parameter => where and are defined as the number of 0 0 or 90 0 stacks in excess to the constraint value in skin and blade laminates resp. The objective function is penalized for designs that do not satisfy the failure constraints using penalty parameter. A small fraction of the critical failure load factor is subtracted from the weight of the design when it satisfies the failure constraints using bonus parameter.

7 Genetic Code Design variables Blade height, No. of plies, orientation Angle Genetic Length of the string is fixed code Empty 0 Upper bound for skin 15; Upper bound for blade 25; 0 1 Empty stacks - * ; Eg: 12-ply laminate- [*/*/*/90 2 /±45 4 /0 2 ] ±45 2 All zeros move towards outside when packed L h based on the desired precision of approximation Genetic code for Blade height includes 0s, 1s and 2s and the string is a nine digit ternary number. Blade height is calculated from the design string as follows

8 Genetic Code (contd..) For [Y lh,....., Y 2, Y 1 ] ; where, X u Upper bound = in X l - Lower bound = 1.5 in Substrings Blade height(9), Skin laminates(15) and Blade laminates(25) Design string concatenation of the substrings Design string Length = 49 No zero ply in skin laminate Outermost stack always has ±45 stack. Complete set of possible designs = 3 9 x (4-1) 15-1 x = 3 9 x 3 14 x 4 24 = 2.65 x 10 25

9 Implementation Generation of random initial population Translation of genetic string into PASCO input Evaluation of mass, buckling loads, strains and loads. Posting the results Evaluation of fitness, ranking Separation of elitist and creation of new population using various genetic operators.

10 Genetic Operators Processing of evaluated population to Basic Genetic Improved Genetic create a new one. It combines most desirable characteristics of the older population It guarantees for the best design in the final population Selection of two identical parents was not allowed in improved GA. Algorithm Crossover Mutation Permutation Algorithm Substring Crossover Stack deletion, Stack Addition, Orientation mutation Intralaminate and Interlaminate swap.

11 Crossover Trade the characteristics of their designs by exchanging parts of strings. Probability P c is higher. (i.e) P c Substring crossover: Applied to each substring representing skin, blade and stiffener height ht separately. Six point crossover instead of two point crossover.

12 Mutation ti Small changes in children produced by crossover. Mutation Probability P m is very low. (i.e) P m Before mutation - L m After mutation - L m New Mutation: Stack deletion: (P del ) Stack closest to the mid plane is deleted and packed. Before stack deletion - L m After stack deletion - L m After string packing - L m Stack addition:(p add ) Added d at the mid-plane and all other stacks are shifted without t changing the order. Before stack deletion - L m After stack deletion - L m Orientation Mutation:(P om ) Mutation occurs at random for orientation change.

13 Permutation Inversion of the order of genes between two randomly assigned points. Before permutation L m After permutation L m Intralaminate swap: (P ils ) Swapping within the laminate, either in skin or in blade(never in both) Before intralaminar swap L m After intralaminar swap L m Interlaminate swap: (P ilsw ) Exchanges stack between skin and blade laminates. Before interlaminate swap After interlaminate swap SKIN L m SKIN L m BLADE L m BLADE L m

14 Population Diversity Diverse population adapts quickly to the changes and allows to search for the productive niches. Avoid premature convergence by increasing the design space. Heterogeneity measure where, S ij No. of genes that are different between designs i and j n d - population size L string length Tendency to become homogeneous increases with the increase in the number of trials.

15 Algorithm Performance and Tuning Probabilities of the gene operators (P c, P m, P p )were tuned to reduce the computational costs. Using basic GA, by fixing H b = in and blade laminate set to [±45/(±45 2 /0 4 ) 2 /(±45 2 /0 4 ) 2 /±45/0 2 ] s and varying only the skin laminate, the design space reduced from 2.65 x to approximately 4.78 x 10 6 and the mass got reduced from lb to lb, but the result was not reliable. Hence the probabilities of the new genetic operators( P del, P add, P ils, P ilsw ) were tuned to obtain the optimal performance of the algorithm.

16 Tuning of improved GA Step 1: Tuning P ils, P ilsw,p del Increasing P del causes decrease in reliability because of deletion of large number of plies which causes premature convergence. Step2: Tuning H b. The best design had a mass of lb for H b = 3.25 in. (1.18% increase) Full problem tests: (based on 150 generations and population of 20) Method 1% Reliability 2% Reliability Basic GA crossover Improved GA-crossover Basic GA Mutation Improved GA Mutation 35 63

17 Conclusion Weight was reduced from 25.5 lb to lb. It has given the near optimal design Reliability of the improved GA is higher.

18 References Design and Optimization of Laminated Composite Materials. Gurdal, Zafer, Raphael T. Haftka and Prabhat Hajela, New York: John Wiley & Sons, Inc., An Introduction to Genetic Algorithms Melanie Michelle, A Bradford book. The MIT press. S.Nagendra, R.T.Haftka, Z.Gurdal and J,H,Starnes Jr, Design of a blade stiffened composite panels with a hole. Composite Structures. t 18, (1991)

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