Sensitivity Analysis for Displacement-Controlled Finite-Element Analyses

Abstract

Displacement-controlled finite-element analyses are typically employed to simulate the nonlinear static response of structural systems where a loss of load carrying capacity due to localized material failure and/or geometric nonlinearity is expected. To utilize applications such as reliability, optimization, and system identification for structural systems where the peak load capacity is a random variable or where the performance function is defined in terms of the applied load, accurate and efficient gradients of the displacement-controlled response are required. The direct differentiation method (DDM) is applied to the displacement control method in order to compute response sensitivity with respect to the applied load, which is treated as a variable within each pseudotime step. The resulting sensitivity gives the change in structural load carrying capacity with respect to changes in uncertain parameters. To verify the derived sensitivity equations, comparisons between the DDM and the finite-difference method (FDM) are performed through standalone sensitivity analyses of structural systems with material and geometric nonlinearity. Reliability analyses of a steel frame show the importance measures obtained when the performance function is defined in terms of the structural resistance to applied loads in a displacement-controlled analysis are similar to those obtained in a load-controlled analysis where the performance function is defined in terms of the structural displacements.