Response Sensitivity of Geometrically Nonlinear Force-Based Frame Elements

To expand the scope of accurate and efficient gradient-based applications in structural engineering, the direct differentiationmethod (DDM) is applied to compute the response sensitivity of force-based frame finite elements with combined material and geometric nonlinearity where the transverse displacement field is determined by curvature-based displacement interpolation. Sensitivity is developed for element-level parameters including constitutive properties, cross-section dimensions, and integration points and weights, as well as structural-level parameters corresponding to nodal coordinates. The response sensitivity is found to be significantly more complicated than for geometrically linear force-based elements because it requires the derivative of the transverse displacement field under the condition of fixed basic forces. Finitedifference calculations verify the DDM sensitivity equations for material and geometric nonlinear force-based element response while reliability analysis of a gravity-loaded steel frame demonstrates the efficiency of the DDM sensitivity in a gradient-based application. DOI: 10.1061/ (ASCE)ST.1943-541X.0000757. © 2013 American Society of Civil Engineers. CE Database subject headings: Sensitivity analysis; Frames; Optimization; Geometric nonlinearity. Author keywords: Sensitivity analysis; Frame elements; Geometric nonlinearity; Reliability; Optimization.