Response Sensitivity Formulations for Geometrically Nonlinear Finite Element Analysis

Graduation data: 2017Access restricted to the OSU Community, at author's request, from 2017-06-12 to 2018-06-12Significant amounts of uncertainty owing to both modeling decisions and inher-\ud ent randomness are present in simulating the material and geometric nonlinear\ud response of structural systems to extreme loading. Computing the sensitivity of\ud structural response with respect to model parameters indicates which parameters\ud have the largest affect on the response, which can in some cases be more important\ud to an engineer than only the deterministic response. Considering the large num-\ud ber of parameters in a structural model, accurate and efficient response sensitivity\ud computations, or gradients of the structural response, are required for nonlinear\ud structural reliability, optimization, and system identification analyses. Response\ud sensitivity for geometric nonlinear finite element analysis are presented including a\ud geometrically-nonlinear displacement based-beam column element formulation, the\ud displacement control nonlinear static solution method, and the corotational trans-formation of space frame finite elements. The direct differentiation method (DDM)\ud is used to derive the response sensitivity equations for the aforementioned formu-\ud lations. The response sensitivity equations for geometric nonlinear displacement-\ud based beam-column element are formulated in the deformed configuration using\ud Lagrangian strain. The derivation of the sensitivity equations for the displace-\ud ment control solution method is performed according to an incremental-iterative\ud solution strategy. The sensitivity equations of space frame formulations require\ud the derivative of the system triads in the deformed configuration according to the\ud corotational theory and the numerical algorithms for its implementation in a finite\ud element setting.\ud The derived equations are implemented in the OpenSees software framework.\ud To verify the accuracy of the derived equations, standalone sensitivity analysis\ud is performed by comparing the response sensitivity results obtained by the DDM\ud with those obtained by the finite difference method (FDM). The standalone sen-\ud sitivity analysis is performed for different element, material, and section models.\ud Furthermore, the response sensitivity equations are utilized to perform reliabil-\ud ity and ranking of importance measures for complex steel and reinforced concrete\ud structures