Efficient Computation of Response Sensitivities for Inelastic Structures

Response sensitivities with respect to the parameters of a finite element model are useful in many applications. The direct differentiation method (DDM) is commonly utilized to obtain such results. In recent years, the DDM has been extended to include sensitivities of inelastic response with respect to material, load, and geometry parameters. While the DDM is more efficient and accurate than finite difference methods, considerable cost is still associated with the computation of response sensitivities for inelastic problems. In this paper it is demonstrated that the computational cost can be significantly reduced for certain types of problems that are common in structural engineering. A novel event-based computation strategy is suggested, whereby sensitivities of the final response are obtained more efficiently than in the ordinary DDM. It is also demonstrated that sensitivity contributions from all inelastic material points are not needed for statically determinate structures. Numerical examples involving a truss structure, a steel frame structure, and a reinforced concrete frame structure are presented to demonstrate the efficiency of the presented developments.