11.4 Stochastic Nonlinear Programming 655Figure 11.5 Column under compressive load.Mean diameter of the section=(d, σd)=(d, 0. 01 d)
Column length=(l, σl) =( 250 , 2. 5 )cmSOLUTION This problem, by neglecting standard deviations of the various quantities,
can be seen to be identical to the one considered in Example 1.1. We will take the
design variables as the mean tubular diameter (d)and the tube thickness (t):
X=
{
x 1
x 2}
=
{
d
t}
Notice that one of the design variables (d)is probabilistic in this case and we assume
thatdis unknown sinceσdis given in term of (d). By denoting the vector of random
variables as
Y=
y 1
y 2
y 3
y 4
y 5
y 6
=
P
E
ρ
fy
l
d