8-1 Isogrid-stiffened cylindrical shell with internal isogrid and external rings with
 isogrid pattern oriented along circumferential direction for increased bending
 stiffness in hoop direction .............. ...............93....

8-2 Isogrid-stiffened cylindrical shell with internal isogrid and isogrid pattern oriented
 along circumferential direction for increased bending stiffness in hoop direction;
 the zero degree direction for the composite laminates in isogrid and skin panel are
 show n .............. ...............99....

8-3 1st iteration of DIRECT windowing for 2 dimensional example, Goldstein-Price
 (GP) function (Finkel, 2003), and (b) further iterations on GP function with
 potentially optimal boxes shaded and subsequently divided along longest
 dim ension(s). ............. ...............107....

A-1 Quadratic fit to al (1.0E-6/oF) .............. ...............110............ ...

A-2 Sixth-order fit to a2 (1.0E-4/oF) ................. ......... ...............110 ..

A-3 Quadratic fit to El (Mpsi) ................. ...............111..............

A-4 Quartic fit to E2 (Mpsi) ................. ...............111..............

A-5 Cubic fit to G12 (Mpsi) ................. ...............112..............

A -6 Q uartic fit to Cl2............... ...............112 

B-1 Contour plot of probabilistic safety factor design response surface approximation
 and test points along the curve of target reliability ................. .......................1 13

B-2 Contour plot of probability of failure design response surface approximation and
 test points along the curve of target reliability. The negative values of probability of
 failure are due to the interpolation errors of the design response surface
 approxim ation............... .............11

B-3 Contour plot of safety index design response surface approximation and test points
 along the curve of target reliability ....._.. ................ ............... 114 ...