Method for Structural Model Update Using Dynamically Measured Static Flexibility Matrices

Abstract

A new method is presented for parametric correction of full-order analytical stiffness matrices from reduced-order dynamically measured static flexibility matrices. The measured static flexibility matrix is formed using modal data in conjunction with a residual flexibility estimate. The algorithm corrects model parameters by minimizing a static flexibility matrix error residual constructed for measurement degrees of freedom only. By utilizing a flexibility matrix residual instead of one derived using stiffness matrices, numerical problems associated with inverting a rank-deficient measured flexibility matrix are avoided. Posing the problem in terms of flexibility matrices also avoids the problems of modal correspondence, mode selection, and modal truncation. In addition, incorporating static reduction relationships into the error residual makes prior eigenvector expansion or model reduction unnecessary. Two formulations for the error residual are presented: an explicit inverse formulation and one derived from a pseudoinverse relationship. The second leads to an exact linear update problem when all of the model degrees of freedom are measured. Numerical simulation results demonstrate that both formulations are capable of localizing and quantifying local stiffness errors in a full-order finite element model from reduced-order measurements. Experimental results for a cantilever beam structure are also presented.