The nonlinear finite element(FE) analysis has been widely used in the design and analysis of structural or geotechnical systems.The response sensitivities(or gradients) to the model parameters are of significant importance in these realistic engineering problems.However the sensitivity calculation has lagged behind,leaving a gap between advanced FE response analysis and other research hotspots using the response gradient.The response sensitivity analysis is crucial for any gradient-based algorithms,such as reliability analysis,system identification and structural optimization.Among various sensitivity analysis methods,the direct differential method(DDM) has advantages of computing efficiency and accuracy,providing an ideal tool for the response gradient calculation.This paper extended the DDM framework to realistic complicated soil-foundation-structure interaction(SFSI) models by developing the response gradients for various constraints,element and materials involved.The enhanced framework is applied to three-dimensional SFSI system prototypes for a pilesupported bridge pier and a pile-supported reinforced concrete building frame structure,subjected to earthquake loading conditions.The DDM results are verified by forward finite difference method(FFD).The relative importance(RI) of the various material parameters on the responses of SFSI system are investigated based on the DDM response sensitivity results.The FFD converges asymptotically toward the DDM results,demonstrating the advantages of DDM(e.g.,accurate,efficient,insensitive to numerical noise).Furthermore,the RI and effects of the model parameters of structure,foundation and soil materials on the responses of SFSI systems are investigated by taking advantage of the sensitivity analysis results.The extension of DDM to SFSI systems greatly broaden the application areas of the d gradient-based algorithms,e.g.FE model updating and nonlinear system identification of complicated SFSI systems.
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