Stiffness Separation Method for Reducing Calculation Time of Truss Structure Damage Identification

Abstract

The inversion of a high-dimensional stiffness matrix with unknown parameters is time-consuming. In this study, a stiffness separation method is used to solve the large-scale matrix inversion problem. Substructures are isolated from the overall structure by mapping the substructure-related matrix, and the solvable equilibrium equations for the substructures can be established. This method divides the entire stiffness matrix into the sub-stiffness matrices, and the size of the matrix is reduced, thus greatly reducing the stiffness matrix inversion workload. Meanwhile, this paper refines the formulation of the stiffness separation method and presents the compatibility of forces and displacements with the stiffness matrix. A space-truss structure with different damage cases is studied to validate the effectiveness of the proposed method. The division of the structure into single and multi-region scenarios is considered, and the effect of the size and number of substructures on the damage identification is analyzed. These results demonstrate that the stiffness separation method can reduce the computational effort required for analyzing large-scale truss structures.