Stochastic Finite Element and Satellite Structure Design - Finite Element Analysis for Satellite Structures - page 246

Table 5.4 Sensitivity index of performance function with respect to design space parameters

Variable Sensitivity index

Load set 1 -0.000002

Load set 2 0.021617

Load set 3 -0.000379

Load set 4 -0.000078

Load set 5 0.003533

Ty of real constant set 1 -0.004883

Tz of real constant set 1 0.017350

Ty of real constant set 2 0.002037

Tz of real constant set 2 0.004685

Ty of real constant set 3 -0.001636

Tz of real constant set 3 -0.002339

Ty of real constant set 4 -0.002149

Tz of real constant set 4 -0.004768

Ty of real constant set 5 -0.005229

Tz of real constant set 5 -0.011481

Ty of real constant set 6 -0.003135

Tz of real constant set 6 -0.006266

E 0

Fy 0.000003

Table 5.5 Reliability analysis of the satellite structure

No. of
Iteration

Beta Performance

function

4.9003 (10 -1 )

1 7.7051e The probability of failure = 1-

normcdf(5.11367) = 1.5798 (10 -7 )

-1.4444 (10 -1 ) 2 7.2552e

-5.5430 (10 -1 ) 3 5.6596e

1.3402 (10 -1 )

4 5.1767e

-1.0334e (10 -2 ) 5 5.1368e

2.8054e (10 -5 ) 6 5.11367e

• Real_Constants(4,1:7) = [12 0.05 6 0.05 1 1 0]; Basis Wall
• Real_Constants(5,1:7) = [11 0.05 5 0.05 1 1 0]; Upper Frame
• Real_Constants(6,1:7) = [10 0.05 5 0.05 1 1 0]; Mounting Plate
• Material_Properties(1,1:12) = [72e6 0.06 150e3 0.11 2.63e-6 0 23e-6 0 1 1 1 1];
Reference Temperature used = 20 C o .
Simulations results are shown in Tables 5.4 and 5.5 . The critical value of prob-
ability of failure is 0.5, so the satellite structure has safe design. The ratio of the
calculated probability of failure to the its critical value proves that the factor of safety
used during the deterministic FE analysis can be reduced.