Sensitivity analysis of weakened beams on elastic foundation with Green's functions

Christmann & Pfeifer, C + P Engineering GmbH & Co. KG, In der Werr 11, D-35719 Angelburg, GermanyThe approach of Sensitivity Analysis with Green’s Functions (SAGF) [1,2] was developed to predict changes in deformations,stresses or eigenfrequencies of structures resulting from stiffness modifications or cracking by considering only the weakenedor damaged parts of the structures. This approach results in a local analysis instead of a global analysis by recalculating thewhole structure. Consequently, it is computationally less time-consuming than the conventional methods based on a globalanalysis. The key idea of the SAGF approach is based on the comparison between the elastic strain energies of the originaland the weakened structures and the substitution of the virtual displacements by the corresponding Green’s functions [1,2].Furthermore, an approximate approach for the sensitivity analysis was suggested which is described in [1,3] in details. Thisapproach enables us to predict the changes in the structural responses due to the stiffness weakening in the beam or in theelastic Winkler foundation by considering only the internal forces or the deflections of the original unweakened system. Inaddition, an iterative method was developed to enhance the accuracy of the SAGF approach.In this paper, the local SAGF method for sensitivity analysis of elastic beams on Winker foundation with stiffness weakeningis presented. The accuracy and the efficiency of the proposed method are verified by using a numerical example.