Table 5-3. Range of design variables for analysis response surfaces
Design
variables
Range 200 to 300 200 to 300 0.0125 to 0.03 inch 0.0125 to 0.03 inch
The accuracy of the ARS is evaluated by statistical measures provided by the JMP
software (Anon. 2000), which include the adjusted coefficient of multiple determination
(R2agi.) and the root mean square error (RMSE) predictor. To improve the accuracy of
response surface approximation, polynomial coefficients that were not well characterized
were eliminated from the response surface model by using a mixed stepwise regression
(Myers and Montgomery 1995).
The statistical design of experiment of ARS was Latin Hypercube sampling or
Latin Hypercube design (LHS, e.g., Wyss and Jorgensen 1998), where design variables
were treated as uniformly distributed variables in order to generate design points
(presented in Chapter 3).
Since the laminate has two ply angles and each ply has three strains, six ARS were
needed in the optimization. A quadratic polynomial of twelve variables has 91
coefficients. The number of sampling points generated by LHS was selected to be twice
the number of coefficients. Tables 4 shows that the quadratic response surfaces
constructed from LHS with 182 points offer good accuracy.
Table 5-4. Quadratic analysis response surfaces of strains (millistrain)
Analysis response surfaces based on 182 LHS points
Error Statistics
E1 in Bi ez in Bi Yl in Bi E in 82 ez in 82 Y1 in 82
R2agj 0.9977 0.9956 0.9991 0.9978 0.9961 0.9990
RMSE Predictor 0.017 0.06 0.055 0.017 0.055 0.06
Mean of
1.114 8.322 -3.13 1.108 8.328 -3.14
Response