Response Surface Approximation for Reliability-Based Optimization

 For the present work, response surface approximation of two types was created.

The first type is analysis response surface (ARS), which is fitted to the strains in the

laminate in terms of both design variables and random variables. Using the ARS, the

probability of failure at every design point can be calculated inexpensively by Monte

Carlo simulation based on the fitted polynomials. The second type of response surface is

design response surface (DRS) that is fitted to probability of failure as a function of

design variables. The DRS is created in order to filter out noise induced by the Monte

Carlo simulation and is used to calculate the reliability constraint in the design

optimization. The details of the ARS/DRS approach are given in chapter three.

Analysis Response Surfaces

 Besides the design and random variables described in the problem formulation, the

service temperature was treated as a variable ranging from 770F to -4230F in order to

avoid constructing analysis response surfaces at each selected temperature. Therefore, the

total number of variables was seventeen. However, the strains in the laminate do not

depend on the Hyve strain allowables, so the ARS were fitted to the strains in terms of

twelve variables, which included four design variables, four elastic properties, two

coefficients of thermal expansion, the stress-free temperature and the service temperature.

The range of the design variables (Table 5-3) for the ARS was chosen based on the

values of the optimal deterministic design. Ranges for random variables are automatically

handled and explained below. Using the ARS and five strain allowables, probabilities of

failure are calculated by Monte Carlo simulations, while the strain constraints were

evaluated at 21 uniformly distributed service temperatures between 770F and -4230F.