Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method

Pseudocode 3

Particle Swarm Optimization pseudocode.

Step (1) Set number of particles (𝑛_𝑃), number of parameters for each particle (𝑛_param), max

   number of generations (𝑛_𝐺), convergence tolerance (𝜀) and the number of

   consecutive no improvements loops (𝑛_𝜀), 𝛿 (ratio between position and speed)

Step (2) Set particles boundary values: max1∶𝑛_param, min1∶𝑛_param

Step (3) Randomly generate particles position 𝑃_𝑖⁽⁰⁾∣min(𝑖)<𝑃_𝑖⁽⁰⁾<max(𝑖) and velocity 𝑣_𝑖⁽⁰⁾

Step (4) Evaluate fitness function 𝐹_𝑖=𝑓𝑃_𝑖⁽⁰⁾,𝑖=1,…,𝑛_𝑃

Step (5) Set 𝑃_𝑏=𝑃⁽⁰⁾, 𝐹_best=𝐹, 𝐺_𝑏=min𝐹_𝑖, 𝑔_𝑏=indexofthemin𝐹_𝑖value

Step (6) for 𝑚=1 to 𝑛_𝐺

Step (7)   for 𝑖=1 to 𝑛_𝑃

Step (8)     Δ𝑣_𝑖=𝑐₁𝑎₁𝑃_𝑏𝑖−𝑃_𝑖^(𝑚−1)+𝑐₂𝑎₂(𝑃_𝑏𝐺𝑏−𝑃_𝑖^(𝑚−1))

Step (9)     𝑣_𝑖^(𝑚)=𝜙^(𝑚)𝑣^(𝑚−1)+Δ𝑣_𝑖

Step (10)   𝑃_𝑖^(𝑚)=𝑃_𝑖^(𝑚−1)+𝑣_𝑖^(𝑚)

Step (11)    Compute Volume fraction distribution (𝑉_𝐶) in the thickness for 𝑃_𝑖^(𝑚)

Step (12)     while 𝑃_𝑖^(𝑚)>max(𝑖)or𝑃_𝑖^(𝑚)<min(𝑖)or𝑉_𝐶<0or𝑉_𝐶>1

Step (13)      𝑣_𝑖^(𝑚)=𝑣^(𝑚−1)+𝛿⋅(max(𝑖)−min(𝑖))⋅random(0÷1)

Step (14)      𝑃_𝑖^(𝑚)=𝑃_𝑖^(𝑚−1)+𝑣_𝑖^(𝑚)

Step (15)      end while

Step (16)       Evaluate fitness 𝐹_𝑖=𝑓𝑃_𝑖^(𝑚),𝑖=1,…,𝑛_𝑃

Step (17)       for 𝑖=1,…,𝑛_𝑃

Step (18)      if 𝐹_𝑖<𝐹_𝑏𝑖 then 𝑃_𝑏𝑖=𝑃_𝑖^(𝑚) and 𝐹_𝑏𝑖=𝐹_𝑖

Step (19)      if 𝐹_𝑖<𝐺_𝑏 then 𝐺_𝑏=𝐹_𝑖 and 𝑔_𝑏=𝑖

Step (20)       end for

Step (21)  end for

Step (22) end for