It is shown that the utilization of the Filonenko-Borodich set of functions, as the comparison functions in the Boobnov-Galerkin method leads to the result that coincides with the closed-form solution for the clamped-clamped uniform beam under uniformly distributed load. It is hoped that this remarkable, direct coincidence could be used in graduate courses and books on mechanics of solids.
Coincidence of Boobnov-Galerkin and Closed-Form Solutions in an Applied Mechanics Problem
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Oct. 30, 2001; final revision, Nov. 8, 2002. Associate Editor: D. A. Siginer.
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Elishakoff , I., and Zingales , M. (October 10, 2003). "Coincidence of Boobnov-Galerkin and Closed-Form Solutions in an Applied Mechanics Problem ." ASME. J. Appl. Mech. September 2003; 70(5): 777–779. https://doi.org/10.1115/1.1598474
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