Finite element reliability and sensitivity methods for performance-based engineering

The work in this dissertation is motivated by the performance-based engineering approach advocated by the Pacific Earthquake Engineering Research (PEER) Center. This approach requires a consistent analysis of uncertainty propagation through a model, and an accurate assessment of probabilities associated with prescribed performance events for structures. Towards this end, a comprehensive software framework for finite element sensitivity and reliability analysis is developed. The work builds on the existing finite element software OpenSees developed by PEER researchers. An object-oriented approach is employed, rendering a transparent software that is easy to maintain and extend.; An essential ingredient in finite element reliability analysis is accurate, consistent and efficiently computed response sensitivities. Using the direct differentiation method, a unified formulation of finite element response sensitivities with respect to material, load and shape parameters is developed and implemented. The formulation is general and accounts for material and geometric nonlinearities, as well as dynamic effects. The results are consistent with but more general than those found in the literature. Shape sensitivity results allow inclusion of uncertainty in nodal coordinates in reliability analysis. This source of uncertainty is found to be significant for frame-type structures and should be accounted for in reliability analysis, if present. It is shown that the top-level response sensitivity equations may become nonlinear under certain conditions. Important computer implementation issues for inelastic problems are highlighted.; The developed software framework is used to investigate and address challenges particular to nonlinear finite element reliability analysis. The first-order reliability method and the importance sampling method are used for computing probabilities and mean out-crossing rates, the latter for dynamic problems. Convergence in the search for the design point, which is a necessary ingredient in both methods, may be impeded by response gradient discontinuities, numerical noise, strong nonlinearities, or non-convergence of the finite element analysis for certain outcomes of the random model parameters. Models and methods are developed to address these problems. These include smoothed material models, modifications in existing search algorithms, and the introduction of a search algorithm hitherto not used in reliability analysis. It is also shown that, contrary to previous belief, elastic unloading in inelastic structures does not lead to discontinuity in the sensitivity of the displacement response.; A User's and Developer's Guide for the sensitivity and reliability modules in OpenSees is developed. Several numerical examples are presented to demonstrate the new capabilities of the software. These include a comprehensive study of a highway bridge, which is used as a test-bed by PEER.