Application of Mathematical Programming Concepts to Structural System Reliability

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The research is to explore, adapt, and demonstrate the use of mathematical programming techniques for structural system reliability assessment - involving kinematic model search techniques, generalized multiparameter loading, extensions of basic approach, and characterization of polyhedral hypersurfaces. This project utilizes the analogy between structural analysis and mathematical programming in computing structural system reliability. Primary consideration is given to ductile frames with plastic collapse mechanisms, allowing extensive use of linear programming techniques. The kinematic approach to structural limit analysis has been shown previously to be expressible in a linear programming format, a feature that has been ueed for identifying the critical mode of failure. This research extends these concepts through the application of powerful mathematical programming techniques to the system reliabilities, and the combined system safety. The primal/dual linear programming analogy is applied to analyze structural systems by the static, or kinematic duality approach. Multiobjective programming is also investigated for generalized multiparameter loading. This research opens a new direction in the reliability analysis of seletively large structural systems. It can provide a practical tool for the probabilistic analysis of complex structures and the development of probability-based design criteria. Results of the work will be of importance in all branches of structural design includig buildings, bridges, offshore platforms, reactors and ships.