Reliability-based structural optimization using response surface approximations and probabilistic sufficiency factor

Uncertainties exist practically everywhere from structural design to manufacturing, product lifetime service, and maintenance. Uncertainties can be introduced by errors in modeling and simulation; by manufacturing imperfections (such as variability in material properties and structural geometric dimensions); and by variability in loading. Structural design by safety factors using nominal values without considering uncertainties may lead to designs that are either unsafe, or too conservative and thus not efficient.; The focus of this dissertation is reliability-based design optimization (RBDO) of composite structures. Uncertainties are modeled by the probabilistic distributions of random variables. Structural reliability is evaluated in term of the probability of failure. RBDO minimizes cost such as structural weight subject to reliability constraints.; Since engineering structures usually have multiple failure modes, Monte Carlo simulation (MCS) was used employed to calculate the system probability of failure. Response surface (RS) approximation techniques were used to solve the difficulties associated with MCS. The high computational cost of a large number of MCS samples was alleviated by analysis RS, and numerical noise in the results of MCS was filtered out by design RS.; RBDO of composite laminates is investigated for use in hydrogen tanks in cryogenic environments. The major challenge is to reduce the large residual strains developed due to thermal mismatch between matrix and fibers while maintaining the load carrying capacity. RBDO is performed to provide laminate designs, quantify the effects of uncertainties on the optimum weight, and identify those parameters that have the largest influence on optimum design. Studies of weight and reliability tradeoffs indicate that the most cost-effective measure for reducing weight and increasing reliability is quality control.; A probabilistic sufficiency factor (PSF) approach was developed to improve the computational efficiency of RBDO, to design for low probability of failure, and to estimate the additional resources required to satisfy the reliability requirement. The PSF is a safety factor needed to meet the reliability target. The methodology is applied to the RBDO of composite stiffened panels for the fuel tank design of reusable launch vehicles. Examples are used to demonstrate the advantages of the PSF over other RBDO techniques.