LIST OF FIGURES
Figure pg
2-1 Double loop approach: reliability analysis coupled inside design optimization...... 12
2-2 Design potential approach: reliability constraints approximated at design potential
point dpk; reliability analyses still coupled inside design optimization...................15
2-3 Partial safety factor approach: decouple reliability analysis and design
optimization ................. ...............17................
3-1 Analysis response surface and design response surface approach: decouple
reliability analysis and design optimization ................ ..............................25
3-2 Latin Hypercube sampling to generate 5 samples from two random variables........27
4-1 Polynomials fit to elastic properties: El, E2, Gl2, and C112 .............. ..................31
4-2 Polynomials fit to coefficients of thermal expansion: a1 and u2 ................... .........32
4-3 Geometry and loads for laminates ................ ...............35...............
4-4 The change of optimal thickness (inch) with temperature for variable and constant
material properties (EZu Of 0.0110) ................. ...............37..............
4-5 Strains in optimal laminate for temperature dependent material properties with Ezu
of 0.01 10 (second design in Table 4-3) ................. ...............38...........
5-1 Tradeoff plot of probability of failure, cost, and weight (laminate thickness) for
[+25]s................ ...............53
6-1 Probability density of safety factor. The area under the curve left to s=1 measures
the actual probability of failure, while the shaded area is equal to the target
probability of failure indicating that probabilistic sufficiency factor = 0.8 .............61
6-2 Cantilever beam subj ect to vertical and lateral beading............_.__ ........._._ .....62
6-3 Monte Carlo simulation of problem with two random variables................_._..........66
7-1 Cantilever beam subj ect to vertical and lateral beading.............__ ..........__ .....84