Elementary, Static Beam Theory is as Accurate as You Please

[+] Author and Article Information
J. M. Duva, J. G. Simmonds

Department of Applied Mathematics, University of Virginia, Charlottesville, VA 22903

J. Appl. Mech 57(1), 134-137 (Mar 01, 1990) (4 pages) doi:10.1115/1.2888294 History: Accepted March 20, 1989; Received March 20, 1989; Online March 31, 2008


Starting with a solution of elementary beam theory and integrating polynomials in the thickness coordinate, we generate kinematically-admissible strain fields and statically-admissible strain fields whose average approximates the actual two-dimensional strain field in an orthotropic beam to within a relative mean square error of the order of magnitude of an arbitrary power of the ratio of the thickness of the beam to a characteristic wavelength of the elementary beam solution.

Copyright © 1990 by The American Society of Mechanical Engineers
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