Stiffened Composite Panel Design

• Based on “Improved genetic algorithm for the design of stiffened composite panels,” by Nagendra, Jestin, Gurdal, Haftka, and Watson, Computers and Structures, pp. 543-555, 1996.

• Standard genetic algorithm did not work well enough even with simplified structural model (finite strip).

• Algorithm was improved based on simplified version of the panel design problem (e.g. fixed blade height, single laminate).

Geometry and loading

20,000 /

5,000 /x

xy

N lb in

N lb in

Modeling in PASCO• Finite strip model assume that in one direction we

can use sine solution, while in the other the displacement can have general shape.

• Panel Analysis and sizing code (Stroud and Anderson) based on analysis code by Wittrick and Williams.

Optimization problem

• Minimize the weight of the panel

• Design variables ply angles of skin (), ply angles of blade ()and flange (same), blade height.

• Outer plies limited tofor damage tolerance.• Constraints: Buckling load multiplier, strain-failure

load multiplier, balanced laminates, no more than four contiguous plies of same orientation.

2 2

4 2

960 , 30 , 72

s s b b b f

s b b f

W t n A n A n A

A in A H A in

Optimization formulation

• Constrained version• Plies in stacks of two.• Unconstrained version

• Contiguity violation: Number of contiguous zero or ninety stacks in excess of 2 (for example 2 for

,( , , )

1

1

0

i bb b s

H

b

s

Minimize W H n n

Suchthat

g

2

2

1

1

min ,

cont failfail

fail cont fail

fail b s

WP

F

W P

1

10sk bl

cont

nv nvP

Material properties

• Today’s graphite-epoxys can do much better.

Genetic code

Selection and Crossover

• Rank based fitness and roulette wheel selection.

• Original crossover is a 2-point crossover applied to entire genome.

• Two children produced.• Improved crossover applied individually to each

of the three substrings.• Crossover applied with 95% probability. If not,

first parent copied into next generation.

Mutations

• Mutation applied to one child with each gene mutated with 3% probability to random new gene.

• Improved mutation separates orientation mutations from deletion and addition mutations.

• Stack deletion: First select randomly skin or blade. Then stack closest to mid-plane deleted with Probability of 2-3%.

• Stack addition: Skin or blade selected randomly, then random stack added at mid-plane.

• New: Permutation, intra-laminar swap, inter-laminar swap.

Results with original GA

• What is the main difference between rounded continuous optimum and GA design?

Tuning the algorithm

• Probabilities associated with the different operators tuned on a simplified problem.

• For simplified problem, the blade laminate and blade height was fixed based on previous results.

• This reduced number of designs from to

Improved GA designs• What is different?

Comparison