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