System reliability and optimization of composite structures

Traditional deterministic methods of engineering design generally use experience-based safety factors to account for uncertain structural behavior. In order to quantify these uncertainties in mechanical properties and loads, probabilistic analysis methods have to play an important role in the composite structural analysis and design. Currently available methods in probabilistic analysis application to composite structures use only the first ply failure assumption and do not probabilistically assess composite structural ultimate failure. Therefore, the central idea of this dissertation is to develop a practical method that is able to predict the structural ultimate failure probability of composite structures.; In this research, a probabilistic progressive failure analysis method is proposed by combining deterministic progressive failure analysis and system reliability theory. The application of this method ranges from simple laminates to practical composite structures. The proposed methodology may be briefly described as: A composite structure is treated as a system and ply-level failure modes, such as matrix cracking, delamination and fiber breakage, are treated as components. System failure is caused by a number of component failures, which form complete failure sequences starting from the initial failure to structural system collapse. The branch and bound method is used to identify the important failure sequences, and the system failure probability is computed through the union of the important failure sequences. Trade-offs between accuracy and efficiency for the proposed approach are investigated and several efficient approximations for practical implementation are developed. The proposed methods are combined with a commercial finite element software, and demonstrated for practical application to a composite aircraft wing.; The proposed system reliability method is extended to the optimum design of composite structures. The optimization is formulated so that structural weight minimization is used as the objective function and the reliability requirements (component-level and system-level) are used as constraints. A scaling factor is introduced to calibrate the system failure probability to the first ply failure probability of an equivalent degraded structure. This technique drastically reduces the computational effort and maintains the feasibility of including system reliability in composite structure optimization.