Response Sensitivity of Geometrically Nonlinear Force-Based Frame Elements

Abstract

To expand the scope of accurate and efficient gradient-based applications in structural engineering, the direct differentiation method (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. Finite-difference 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.