Measuring, using, and reducing experimental and computational uncertainty in reliability analysis of composite laminates

The failure of the composite hydrogen tanks on the X-33 Reusable Launch Vehicle (RLV) from combined thermal and mechanical failure modes created a situation where the design weight was highly sensitive to uncertainties. Through previous research of sensitivity and reliability analysis on this problem, three areas of potential uncertainty reduction were recognized and became the focal points for this dissertation.The transverse elastic modulus and coefficient of thermal expansion were cited as being particularly sensitive input parameters with respect to weight. Measurement uncertainty analysis was performed on transverse modulus experiments, where the intermediate thickness measurements proved to be the greatest contributor to uncertainty.Data regarding correlations in the material properties of composite laminates is not always available, however the significance of correlated properties on probability of failure was detected. Therefore, a model was developed for correlations in composite properties based on micromechanics, specifically fiber volume fraction. The correlations from fiber volume fraction were combined with experimental data to give an estimate of the complete uncertainty, including material variability and measurement error. The probability of failure was compared for correlated material properties and independent random variables in an example pressure vessel problem. Including the correlations had a significant effect on the failure probability, however being unsafe or inefficient can depend on the material system.Reliability-based design simulations often use the traditional, crude Monte Carlo method as a sampling procedure for predicting failure. The combination of designing for very small failure probabilities and (&sim10-8 - 10-6) and using computational expensive finite element models, makes traditional Monte Carlo very costly. The separable Monte Carlo method, which is an extension of conditional expectation, takes advantage of statistical independence of the limit state random variables of the response and capacity for improved accuracy in reliability calculations. The separation of response and capacity sampling enables flexible sample sizes, permitting low samples of the more expensive component (usually the response). In turn, this motivates the beneficial reallocation of uncertainty by reformulating the limit state. The variance estimator was derived for separable Monte Carlo and three example problems were used to compare the Monte Carlo methods. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html)...