An Inverse Solution for Reconstruction of the Area Moment of Inertia of a Beam Using Deflection Data

S. Moaveni, K. C. Chou

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The main purpose of this study was to develop a mathematical model that could be used to determine the changes in the structural characteristics – such as changes that could occur due to corrosion in the cross-sectional area-moment-of-inertia of a bridge – from the knowledge of its loading and deflection. Reconstruction of the cross-sectional area-moment-of-inertia of a bridge from the knowledge of its loading and deflection is an inverse problem. In this investigation, the cross-sectional area-moment-of-inertias of a scaled model of simply supported steel bridge (with simulated corrosion) are reconstructed using the deflection and load data. The deflection data used in this inverse problem were numerically generated using the finite element method and the ANSYS software. The deflection data for each model were then used in the inverse problem to reconstruct the cross-sectional area-moment-of-inertias for the model. To solve the inverse problem, the solution domain was discretized into finite number of elements and nodes. The nodal deflections and slopes were represented by Hermite shape functions. For each element, the strain energy and the work done by the external forces were formulated. The minimum total potential energy principle was then used to create the stiffness matrices and reconstruct the area-moment-of-inertia for each element. The inverse model creates a set of linear equations that must be solved simultaneously. Moreover, since the formulation led to more equations than unknowns, the least squared method was used to minimize the errors associated with the solutions, and to match the number of equations with unknowns. Comparison of the inverse solutions with the direct solutions confirms that the variations in the area-moment-of-inertia for a bridge cross-section can be reconstructed, with good accuracy, from the knowledge of its loading and deflection.
Original languageEnglish
Pages (from-to)1155-1174
JournalInverse Problems in Science and Engineering
Volume19
DOIs
StatePublished - 2011

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