Abstract
We present a method for identifying the flexural rigidity and external loads acting on a beam using the finite-element method. We used mixed beam elements possessing transverse deflection and the bending moment as the primary degrees of freedom. The first step is to determine the bending moment from the transverse deflection and boundary conditions. The second step is to substitute the bending moment into the final equations with respect to the unknown parameters (flexural rigidity or external load). The final step solves the resulting system of equations. We apply this method to some inverse beam problems and provide an accurate estimation. Several numerical examples are performed and show that present method gives excellent results for identifying bending stiffness and distributed load of beam.
Highlights
In recent years, analyses of inverse problems have been actively promoted in a variety of science and engineering fields
We present a method for identifying the flexural rigidity and external loads acting on a beam using the finite-element method
We evaluated the efficacy of analysis techniques for identifying the flexural rigidity and distribution of loads acting on a beam
Summary
Analyses of inverse problems have been actively promoted in a variety of science and engineering fields. Arai et al [6] demonstrated a BEM for identifying out-of-plane dynamic pressure distributions applied to a thin elastic plate. Both Ronasi et al [7] and Rao & Ritti [8] demonstrated methods for estimating the load using a FEM. Jadamba et al [9] employed output least-squares functional to identify the Lamé parameters in the linear elasticity. We detail a methodology for identifying the distribution of flexural rigidity in a beam by using static deflection measurements.
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