The work in this report is motivated by the performance-based engineering approach advocated by PEER. A comprehensive, object-oriented software framework for finite element sensitivity and reliability analysis is developed. The work builds on the existing software OpenSees.
An essential ingredient in finite element reliability analysis is accurate, consistent and efficient computation of 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. Shape sensitivity results allow inclusion of uncertainty in nodal coordinates in reliability analysis.
The developed software framework is used to investigate and address challenges particular to nonlinear finite element reliability analysis. As a result, smoothed material models, modifications in existing search algorithms, and a search algorithm hitherto not used in reliability analysis are developed. 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.
A User’s and Developer’s Guide for the sensitivity and reliability modules in OpenSees is de- veloped. Several numerical examples, including a highway bridge used as a test-bed by PEER, are presented to demonstrate the new capabilities of the software.
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