Finite element response sensitivity analysis using three-field mixed formulation: general theory and application to frame structures

This paper presents a method to compute response sensitivities of finite element models of structures based on a three-field mixed formulation. The methodology is based on the direct differentiation method (DDM), and produces the response sensitivities consistent with the numerical finite element response. The general formulation is specialized to frame finite elements and details related to a newly developed steel–concrete composite frame element are provided. DDM sensitivity results are validated through the forward finite difference method (FDM) using a finite element model of a realistic steel–concrete composite frame subjected to quasi-static and dynamic loading. The finite element model of the structure considered is constructed using both monolithic frame elements and composite frame elements with deformable shear connection based on the three-field mixed formulation. The addition of the analytical sensitivity computation algorithm presented in this paper extends the use of finite elements based on a three-field mixed formulation to applications that require finite element response sensitivities. Such applications include structural reliability analysis, structural optimization, structural identification, and finite element model updating.