Table 45. Optimal laminates for temperature dependent material properties with Ezu Of
0.0110 (optimized for 21 temperatures)
6, 6,t; tha (inch) Probability of failure
(degree) (degree) (inch) (inch)
0.00 28.16 0.005 0.020 0.100 (0.103) 0.019338 (0.014541)
27.04 27.04 0.010 0.015 0.100 (0.095) 0.000479 (0.001683)
25.16 27.31 0.005 0.020 0.100 (0.094) 0.000592 (0.001879)
a Numbers in parentheses indicate unrounded thickness
b The probabilities were calculated by the methodology described in the chapter 5

SEpsilon1 Epsilon2 +Gammal 2
 4 M~2
0.012
0.010
0.008
0.006
0.004
0.002
0.000
0.002!
0.004
0.006
Temperature (oF)
Figure 45. Strains in optimal laminate for temperature dependent material properties
with EZu Of 0.01 10 (second design in Table 43)
These optimal laminates have similar thickness but different ply angles. The failure
probabilities of the continuous designs are shown in parentheses. The high failure
probabilities of the first design (continuous and discrete) clearly show a smaller safety
margin than the other two. The second and third designs show that a slight rounding can
change the failure probability significantly. Designs with two similar ply angles have
much lower failure probabilities than designs with two substantially different ply angles.
The failure probabilities of these laminates are too high (compared with 104 to 106), and
this provides incentives to conduct reliabilitybased design.