Static Damage Identification of 3D and 2D Frames

Abstract

A new algorithm for static damage detection of three- and two-dimensional frames is presented in this paper. This approach is based on the minimization of difference between the measured and analytical static displacements of frames. The damage detection problem is solved as a nonlinear constrained structural optimization. In this strategy, the global structural stiffness matrix is parameterized. To achieve the goal, a new technique based on the eigen decomposition of the local elemental stiffness matrix is suggested. Structural damage is modeled as a reduction in cross-sectional properties of the elements. It is assumed that the stiffness matrix of the structure is perturbed due to damage. Hence, the damaged structural stiffness matrix is presumed to be the sum of the stiffness matrix of the undamaged structure and the perturbation matrix. Consequently, the sum of these matrices should be inverted in each iteration. Instead of the common ways of inversion, Sherman–Morrison–Woodbury formula is employed. Prior to the outset of the optimization procedure, the number of design variables, the amount of reductions in cross-sectional properties, is decreased by introducing a new suggested technique. This scheme is based on the nodal equilibrium equations. To illustrate the robustness and efficiency of the authors’ algorithm, several numerical problems are solved.

Keywords:

• Damage assessment
• Frame structure
• Matrix inversion
• Optimization
• Static problem
• Sherman–Morrison–Woodbury formula
• Updated matrix

Notes

^#Communicated by I. Elishakoff.