Robust and Reliability-Based Design Optimization of a Composite Floor Beam

This thesis investigates the advantages and disadvantages of using probabilistic optimization methods in aircraft structural design. The necessity to achieve a design insensitive to system’s variations (robust) and less likely to fail (reliable) is addressed, in order to reduce costs and risk of accidents. Mathematical formulations of Robust Design Optimization (RDO), Reliability-Based Design Optimization (RBDO) and the hybrid Robust and Reliability-Based Design Optimization (RRBDO) are presented, highlighting the differences between the concepts of robustness and reliability. In these probabilistic formulations, uncertainties due to manufacturing tolerances and material defects are considered. Fundamentals of optimization are introduced, presenting different search methods and emphasizing the concept of multi-objective optimization. A brief review of statistics and probability basics are presented as well, in order to better understand the stochastic optimization processes. Because of the complex nature of composite structures, the need of surrogate models to predict structural responses arose. In order to build meta-models, Design of Experiments (DOE) methods are used to determine the location of sampling points in the design space. Monte Carlo Simulations (MCS), creating random samples, are used to propagate uncertainties from the surrogate model inputs to variations in model outputs. MCS embedded in optimization processes, are used to determine the statistical parameters of the responses and the probability of failure. Different flowcharts for the three probabilistic methods are developed, in order to better understand, through graphical representations, the design and optimization frameworks. To validate these frameworks and to show the different results of the various approaches, an application to a composite floor beam is considered. Different optimization algorithms and surrogate models were compared, in order to speed up the optimization process and reduce modelling errors. The deterministic design resulted in a not robust and not reliable design. Whereas, stochastic approaches accounting for uncertainties, resulted in enhanced robustness (Robust Design), enhanced reliability (Reliable Design) or a combination of both (Robust and Reliable Design). Robust Design Optimization resulted globally better in terms of robustness. As for reliability based methods, either RBDO and RRBDO led to reliable designs, but the latter minimizes variability of the responses, hence resulting in a more robust design.