Seismic Response Sensitivity Analysis of Large Complex Nonlinear Systems Using a Direct Differentiation Method With Perturbed Stress Sensitivity

ABSTRACT Response sensitivity analysis plays an important role in optimization algorithms that require gradients or sensitivities of structural responses, including finite element reliability analysis, structural optimization, system identification and finite element model updating. The direct differentiation method (DDM) is an accurate and efficient method for response sensitivity calculations. However, it may require significant efforts to differentiate analytically and software implement the finite element response sensitivities at various hierarchies, that is, structure, element and material levels. Among these calculations, the stress sensitivity calculation is often one of the most challenging, particularly for complicated three‐dimensional or nonsmooth material constitutive models. To overcome this challenge, this paper presents a DDM formulation that bypasses the analytical stress differentiation step, typically the most complicated part of the DDM, by introducing a perturbed stress sensitivity (PSS) approach within the DDM framework (referred to as DDM‐PSS). Both conditional and unconditional stress sensitivities are calculated with different perturbation strategies, resulting in negligible computational effort. The method is applicable to any material model and retains accuracy comparable to that of the traditional DDM, while eliminating the need for model‐specific analytical stress sensitivity derivations. Three examples are presented to validate the proposed method, including a large complex nonlinear dam‐reservoir‐foundation coupling system. A detailed study of accuracy and efficiency is provided. The results demonstrate that DDM‐PSS offers an accurate solution for response sensitivity analysis with minimal effort and almost identical computation time to that of traditional DDM.