Convergence Studies in Nonlinear Finite Element Response Sensitivity Analysis

A method to compute the “exact” or consistent sensitivities to material and loading parameters of the numerical nonlinear finite element response was developed by other researchers and the second author. This general method is referred to in the literature as the Direct Differentiation Method (DDM). This paper focuses on the behavior of stand-alone sensitivity results. It presents the results of convergence studies of the DDM performed in the context of materially-nonlinear-only finite element models of frame structures and for two types of analysis commonly used in earthquake engineering, namely nonlinear static push-over analysis and nonlinear response history analysis. Convergence of nonlinear finite element response sensitivities obtained using forward finite difference analysis towards those obtained using the DDM is examined. Convergence of response sensitivities with progressive refinement of both the spatial and temporal discretizations is also investigated based on some application examples. Convergence of response sensitivities is compared with convergence of the corresponding response parameters. Both global (e.g., floor displacement) and local (i.e., plastic curvature, accumulated plastic curvature) response parameters are considered.