Deterministic interval uncertainty methods of structural analysis

Science and engineering attempt to model uncertainties embedded in physical systems. Methods, like statistics, typically model uncertain quantities as nondeterministic. Techniques concerned with deterministic uncertainty offer alternatives to more traditional approaches. To model deterministic uncertainty in Structural Engineering models, this dissertation applies a form of mathematics called Interval Analysis (IA) to the displacement method of matrix structural analysis.; Interval Analysis adapts traditional numerical operations by replacing traditional numbers with intervals of numbers that model uncertain values. Principles of independence and extremes help define rules of interval arithmetic and operations. For interval-valued systems of linear equations, linear programming finds extreme values. When compared to results of crisp, or non-interval analysis, IA will generate overestimated results that contain infeasible solutions.; Building interval-valued models for the displacement method uses analytical equations whenever possible. Interval values substitute for crisp entries using interval arithmetic for operations. To analyze an uncertain interval-valued structural model, three primary steps must occur: checking for interval width, finding unknown orthants, and pruning overestimation that results from interval arithmetic.; The three steps work in succession. An algorithm for checking interval width, the Interval Reduction Algorithm (IRA), first detects when interval width exceeds critical percent uncertainties. Models tested in this dissertation demonstrate that IA-based analysis limits uncertainty to relatively low values. After checking interval width, the Orthant Selection Algorithm (OSA) finds unknown orthants to build a more complete displacement solution space. After IRA determines displacements contained in each orthant, the analysis computes element force values and continues to the pipeline algorithm. The pipeline algorithm trims values of element force according to a proposed form of equilibrium for interval forces. Besides balancing with external forces, the algorithm prunes overestimation from elements using relative stiffness.; The proposed technique in this dissertation offers a new and complete approach to solving problems of structural mechanics that adapts intervals to model uncertainty. However, given the limitations in interval width and complexities in trimming overestimation, current methods that employ IA lack robustness. Proposed future work might eliminate many of these problems to eventually create a viable technique.