Cantilever beam optimization

(file: beam\beam-script.qsl)

 

Cantilever beam

 

Variables:

              Height - HEIGHT [5 50]

              Bredth - BREDTH [20 250]

 

Objective 1: Minimum cross section area:

              AREA = HEIGHT * BREDTH;

Objective 2: Minimum bending stress:

              SIGMA-B = 6.0*FORCE*LENGTH/(BRDTH*HEIGHT*HEIGHT);

 

Constraints

%bending stress: SIGMA-B <= 200

CONS(1)=6.0*FORCE*LENGTH/(BRDTH*HEIGHT*HEIGHT);

%cross section stress: TAU <= 100

CONS(2)=1.5*FORCE/(BRDTH*HEIGHT);

%deflection: DEFLN <=5

CONS(3)=4.0*FORCE*LENGTH^3/(EE*BRDTH*HEIGHT^3);

%Height over bredth ratio: H-ON-B <= 10

CONS(4)=HEIGHT/BRDTH;

%Critical force: F-CRIT >=5000

CONS(5)=(4.0*sqrt(GG*(BRDTH^3*HEIGHT+HEIGHT^3 *BRDTH)*EE*(BRDTH^3*HEIGHT)/(144.0*(1.0-NU*NU)))/(LENGTH*LENGTH));

 

Constants

    LENGTH = 1500;     FORCE = 5000;    FACTOR = 2;    EE = 216620;

    GG = 86650;         NU = 0.27;       SIGMAY = 200

 

Open file beam\beam-script.qsl. This example can be repeated using beam\beam-exe.qsl and beam\beam-spreadsheet.qsl, that contain alternative definitions for the beam model.

Plot contours  for the AREA and show the constraint lines.

You will find out that only the Deflection (blue) and the HonB (red) constraints are active. Click Optimization (in the ‘Variables’ section) to initiate the optimization module:

Choose an optimization method to find the minimum of the AREA. We have used a sequence of Genetic algorithm and a gradient search, specified in the Sequence field (GaGrad.optseq).

Click ‘Return’ to come back to contours.

Show results on the plot.

Multiobjective optimization. Use again optimization module  :

Click ‘Optimize’ and after the procedure has finished, go to the ‘Visualization’ section to see the pareto front. You can place markers to interrogate the front further.

*** Optimal solution : 

OBJ1 --> AREA

OBJ2 --> SIGMAB

CON1 --> SIGMAB

CON2 --> DEFLN

CON3 --> TAU

CON4 --> FCRIT

CON5 --> HONB

   No       VAR1       VAR2       CON1       CON2       CON3       CON4       CON5  OK?       OBJ1       OBJ2

 2552    16.2701   156.7641   112.5456     4.9714     2.9405137869.3632     9.6351  Yes  2550.5707   112.5456       2551

   No       VAR1       VAR2       CON1       CON2       CON3       CON4       CON5  OK?       OBJ1       OBJ2

 1703    13.3367   180.1206   104.0010     3.9982     3.1221121976.7466    13.5056    0  2402.2138   104.0010  <-- Marker     1

 2494    50.0000   250.0000    14.4000     0.3989     0.60003358947.3117     5.0000    1 12500.0000    14.4000  <-- Marker     2