Calculation of Structural Response and Response Sensitivity with Improved Substructuring Method

Abstract

Structural responses and response sensitivities are frequently required in structural health monitoring, whereas the computation of structural responses and response sensitivities of a large-size model is time consuming. This paper proposes a substructuring method for the fast computation of structural responses and response sensitivities. Structural responses are projected onto the range space of a few master substructural eigenvectors to construct a simplified vibration equation. The contribution of slave eigenvectors is compensated by a residue space to achieve high accuracy. Due to this compensation of the residue, a few master eigenvectors are needed to ensure the fast computation of structural responses and response sensitivities with high accuracy, avoiding the inclusion of numerous substructural eigenvectors. In addition, response sensitivities with respect to a parameter are calculated from master eigenvector derivatives of one substructure only, whereas derivatives of other substructures are zeroes. As simplified vibration equations are quite small, the proposed substructuring method can very quickly calculate structural responses and response sensitivities. The proposed method is verified by a frame structure and a bridge structure.