Analysis and Design Response Surface Approach ................. ... ........................24
 Statistical Design of Experiments for Stochastic and Analysis Response Surfaces...25

4 DETERMINISTIC DESIGN OF COMPOSITE LAMINATES FOR CRYOGENIC
 ENVIRONMENT S ................ ...............28.................

 Introducti on ............... .... ............ .. ....... ..... ........................2
 Composite Laminates Analysis under Thermal and Mechanical Loading .................29
 Properties of IM600/133 Composite Materials ................. ................ ......... .30
 Deterministic Design of Angle-Ply Laminates ................. .............................34
 Optimization Formulation ................. ...............35...
 Optimizations without Matrix Cracking............... ...............36
 Optimizations Allowing Partial Matrix Cracking .............. ....................3
 Optimizations with Reduced Axial Load Ny .............. ...............39....

5 RELIABILITY-BASED DESIGN OF COMPOSITE LAMINATES FOR
 CRYOGENIC ENVIRONMENT S .............. ...............41....


 Reliability-Based Design Optimization ................. ...............41........... ....
 Problem Form ulation............... ....... ..... ... .................4
 Response Surface Approximation for Reliability-Based Optimization ........._....43
 Analysis Response Surfaces ................ ...............43........... ....
 Design Response Surfaces............... ...............45
 Refining the Reliability-Based Design ................. ............. ......... .......46
 Quantifying Errors in Reliability Analysis............... ...............47
 Effects of Quality Control on Laminate Design ................. ................. ..........48
 Effects of Quality Control on Probability of Failure ................. ............... .....49
 Effects of Quality Control on Optimal Laminate Thi ckne ss ............... .... ...........50O
 Effects of Other Improvements in Material Properties............... ...............51
 Summary .........___ ....... ...............54....

6 PROBABILISTIC SUFFICIENCY FACTOR APPROACH FOR RELIABILITY-
 BASED DESIGN OPTIMIZATION ................. ...............56........... ....

 Introducti on ................. .. ......... ...............56.......
 Probabilistic Sufficiency Factor .............. ........... ....... ...... .... .........6
 Using Probabilistic Sufficiency Factor to Estimate Additional Structural Weight
 to Satisfy the Reliability Constraint ................. ...............62...............
 Reliability Analysi s Using Monte Carlo Simulation ................. ....... .. ......... ........._.64
 Calculation of Probabilistic Sufficiency Factor by Monte Carlo Simulation......66
 Monte Carlo Simulation Using Response Surface Approximation. ................... .68
 Beam Design Example .............. ...............71..
 Design with Strength Constraint ............... .. ..... ...............7
 Design with Strength and Displacement Constraints .............. .....................7
 Sum m ary ................. ...............79.......... ......