Response sensitivity for geometrically nonlinear displacement-based beam-column elements

Abstract

Accurate and efficient response gradients are required in structural reliability, optimization, and system identification applications where the structural system is expected to yield under significant deformations. The direct differentiation method (DDM) is applied to the response sensitivity of displacement-based beam-column finite elements with geometric nonlinearity due to moderate rotations in the basic system. The derived sensitivity equations are implemented in the OpenSees software framework. Stand-alone sensitivity analyses using the DDM and finite difference method (FDM) validate the sensitivity equations for example structures with nonlinear static and dynamic response. Finite element reliability analysis of a steel frame shows that, relative to a geometrically linear formulation, using geometrically nonlinear displacement-based elements increases the probability of failure and affects the importance ranking of the random variables. In addition, for a performance function based on residual capacity at a target lateral displacement, the frame strength at the design point is higher than that obtained when using geometrically linear elements. The developed sensitivity equations increase the number of nonlinear finite element formulations available for gradient-based applications in structural engineering.