Structural sensitivity analysis in nonlinear and transient problems using the local response function technique

The main aim of this work is the mathematical formulation, computational implementation and the application of the local version of the Response Function Method (RFM) to analyze structural design sensitivity in nonlinear structures and problems. This method is based on the Finite Element Method-based determination of the polynomial response function between design parameter and the structural state function like displacements or temperatures. One may use this numerical technique in its global version, where a single polynomial is determined for the entire computational domain or, in the case of nonlinear, transient analyses or the heterogeneous domains, in the local approach-where nodal response function are to be determined. The application of this methodology is illustrated with three examples--transient heat transfer in the homogeneous rod, the elastoplastic analysis of 2D truss as well as the eigenvibrations for a large scale 3D structure, where time, increment and eigenvalue dependent variations of the first and the second order sensitivities with respect to the physical and material parameters are computed. The first order gradients computed with the use of the RFM approach are contrasted with the finite difference computations.