Consistent Finite-Element Response Sensitivity Analysis

This paper examines the important issue of response sensitivities of dynamic models of structural systems to both material and (discrete) loading parameters. Plasticity-based finite-element models of structural systems subjected to base excitation such as earthquake loading are considered. The two methods for computing the response sensitivities, namely, (1) discretizing in time the time continuous-spatially discrete response equations and differentiating the resulting time discrete-spatially discrete response equations with respect to sensitivity parameters, and (2) differentiating the time continuous-spatially discrete response equations with respect to sensitivity parameters and discretizing in time the resulting time continuous-spatially discrete response sensitivity equations, are clearly distinguished. The discontinuities in time of the response sensitivities arising due to material state transitions in the plasticity models, and their propagation from the quadrature point level to the global structural response level are discussed using a specific one-dimensional plasticity model. The procedure to obtain the exact sensitivities of the numerical nonlinear finite-element response, including proper capture of their discontinuities, is formalized. Application examples illustrating the concepts are presented at the end.